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Aspects of Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling: Bibliography

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Acknowledgment PART I Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook PART II Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX B APPENDIX C Bibliography CHAPTER 7 - ENTANGLEMENT ENTROPY AND PAGE CURVE FROM THE M-THEORY DUAL OF THERMAL QCD ABOVE T AT INTERMEDIATE COUPLING c 7.1 Introduction and Motivation In doubly holographic approaches, as described in 5.3.2 of chapter 5, a gravitational dual black hole is connected with an external CFT bath [202]. As an illustration, gravity in d-dimensions is connected with the external bath in d-dimensions, wherein d-dimensional exterior bath possesses a corresponding holographic dual in (d + 1)-dimensions. In such models, we take into consideration two variants of the previously mentioned configuration. We look at two distinct types of extremal surfaces in these models. The very first one corresponds to the Hartman-Maldacena-like surface [144], that begins from the position at which gravity interacts with with an external bath, i.e., at the defect, and traverses the black hole horizon to get to the defect of the thermofield double associated with doubly holographic setups, and the entanglement entropy involvement via the aforementioned surface possesses linear time dependency, leading to information paradox at later times. The other type of surface includes the island surface, that begins at the exterior bath and ends on the KarchRandall brane [142, 143]. The contribution of entanglement entropy coming from the island surface becomes time independent and takes over beyond the Page time. The Page curve is obtained through the combination of the entanglement entropy contributions obtained from both the extremal surfaces. As we discussed in 5.3.2, in some cases, the gravity becomes massive on the Karch-Randall branes, and one was unable to get the Page curve with massless gravity localized on the KarchRandall branes. In this chapter, we have looked at this major issue of doubly holographic setup from M-theory perspective in the presence of O(R4 ) terms in the supergravity action. We have a different situation from the literature that we have a non-conformal bath (QCD bath), and the doubly holographic setup is being constructed from a top-down approach[1] with the inclusion of higher derivative terms in the supergravity action. Interestingly, the issue of the massive graviton is absent in our setup, and one can get the Page curve with massless gravity on the end-of-the-world(ETW) brane. We cannot utilize the island approach for non-conformal backgrounds because currently there is no recognized Cardy-like formula for the non-conformal theories. As a result, we used the previously mentioned doubly holographic frameworks technique to arrive at the Page curve. In the context of our scenario, on the gravity dual side, there is a M-theory dual consisting of higher derivative terms, whereas on the gauge theory side, we find nonconformal thermal QCD-like theories at the intermediate coupling, the model is discussed in 1.4 of chapter 1. In the present chapter, we created a doubly holographic setup analogous to [7,203], where the researchers utilize a conformal theory on their gauge theory side. There are two types of potential surfaces to think about: Hartman-Maldacena-like and island surfaces. The Hartman-Maldacena-like surface has been accountable for the gradual linear temporal growth of Hawking radiation’s entanglement entropy. Above the Page time, the entanglement entropy component via the island surface takes over and this is not dependent upon time, so we extract the Page curve using the M-theory dual, which includes O(R4 ) corrections. As a remark, we used the formula of [127] to compute the entanglement entropy with the inclusion of higher derivative terms and when higher derivative terms are absent then we used the Ryu-Takayanagi formula to compute the entanglement entropy [107]. 7.2 Doubly Holographic Setup in M Theory From the work of [127], we could compute the entanglement entropy associated with holographic dual theories with the inclusion of higher derivative terms. We could express the analogue of the generalised entropy functional described in equation (5.17) using [127] for M-theory dual in the presence of O(R4) terms as follows: and inserting it into (7.20) yields: 7.3.1 At O(β) and we assume the constant is zero. 7.3.2 No Boundary Terms Generated at O(R4) The eleven-dimensional supergravity action, which includes O(R4 ) terms, is presented by the following: where, As a result, we are able to identify that a usual boundary term including covariant derivatives of metric fluctuations that would have to be cancelled out by a suitable boundary term (using Stokes theorem) is: The (dual to the) unit normal vector to provided by: W Hence, Utilizing, 7.4 Page Curve without Higher Derivative Terms Here, we obtained the Page curve using the doubly holographic setup constructed in 7.2. In this part, we do not consider the ( ) terms in the supergravity action. Therefore, we used the Ryu-Takayanagi formula to compute the entanglement entropies of Hartman-Maldacena-like and Island surfaces in 7.4.1 and 7.4.2. The Page curve has been obtained in 7.4.3. In the absence of ( ) terms, the = 1, = 11 supergravity action has been provided as follows: O R4 O R4 N D 7.4.1 Entanglement Entropy Contribution from Hartman-Maldacena-like Surface To calculate the time-dependent entanglement entropy associated with a Hartman-Maldacena-like surface, we first look at the induced metric on a constant x 1 slice, which was calculated utilizing (7.20) as follows: The area density functional for a Hartman-Maldacena-like surface could be calculated using (7.23) as follows: implying Using (7.27) and (7.30), we obtained: Now we identify time via the integral: As a result, the Hartman-Maldacena-like surface’s entanglement entropy is: 7.4.1.1 Hartman-Maldacena-like Surface Analytics/Numerics After integrating all of the angular coordinates and consequently including a (2π) 4 emerging from integration w.r.t. ϕ1,2, ψ, x10, the area corresponding to the Hartman-Maldacena-like surface is obtained as: As a result, the entanglement entropy related with a Hartman-Maldacena-like surface grows linearly with time. 7.4.2 Entanglement Entropy Contribution from Island Surface We take a constant t slice to calculate the entanglement entropy for an island surface. As a result, utilizing equation (7.20), we expressed the induced metric associated with the island surface as follows: where C is the constant. We simplified the expression (7.43) utilizing equation (7.41) as given below: When we solved the preceding equation for x˙(r), we were provided with: Constant could be calculated using the equations (7.45) and (7.46), as shown below: C Taking the previously stated expression of C, the equation (7.44) reduces to the following structure: Now, the area density functional associated with the island surface has been simplified using the equations (7.41) and (7.48). Hence, the entanglement entropy associated with the island surface is obtained as follows: Since, there is no time dependence in (7.50), and hence entanglement entropy of the Hawking radiation for the island surface is constant. 7.4.2.1 Island Surface Analytics When (7.49) is evaluated, the entanglement entropy is as follows: implying 7.4.3 Page curve at LO from Areas of Hartman-Maldacena-like and Island Surfaces 7.5 Page Curve with Higher Derivative Terms We obtained the Page curve corresponding to a neutral black hole in with the inclusion of higher derivative terms that are quartic in the Riemann curvature tensor in this section. This section has been broken into four subsections. We calculated the entanglement entropy associated with the HM-like surface in subsection 7.5.1, discussed the “Swiss-Cheese” structure of the identical surface in subsection 7.5.2, computed the entanglement entropy of island surface in 7.5.3, and at last obtained the Page curve corresponding to an eternal black hole in subsection 7.5.4 utilizing the outcomes that were obtained from previous subsections. We conducted the same analysis as in 7.4. [127] was used to compute the entanglement entropy associated with Hartman-Maldacena-like surface and island surface in with the inclusion of higher derivative terms. In generic higher derivative gravity theories, we are able to calculate the holographic entanglement entropy (5.8) as follows: • When the holographic dual consists of a ( + 1) dimensional gravitational background, then with the help of the embedding function, compute the induced metric associated with the co-dimension two surface. d • Using the above-mentioned induced metric, compute (5.8). This yields the holographic entanglement entropy as an expression of the embedding function and its derivatives. • Find the solution to the embedding function’s equation of motion. • In higher derivative gravity theories, putting the solution found in the previous step inside the action yields the holographic entanglement entropy. To determine the second part in the formula (5.8), we must first compute the four types of derivatives for the Hartman-Maldacena-like and island surfaces, which are listed below: The numerator and denominator coefficients in the preceding equation are x = xR for the Hartman-Maldacena-like surface and x = x(r) for the island surface. All four types of variations occurring in equation (7.54) for the Hartman-Maldacena-like surface in appendix C.5.1 and island surface in appendix C.5.2 have been computed and listed. 7.5.1 Entanglement Entropy Contribution from Hartman-Maldacena-like Surface Hartman-Maldacena-like surface in M-theory dual corresponds to a co-dimension two surface situated at x 1 = xR. Utilizing equation (5.8), we are able to write the mathematical expression that describes the entanglement entropy associated with a Hartman-Maldacena-like surface as follows: where g denotes determinant of the induced metric defined in (7.23) for the co-dimension two surface. For the metric (7.23), the entanglement entropy associated with the Hartman-Maldacena-like surface using (7.55) and appendix C.5.1 after the angular integrations is obtained as: where The equation (7.58) has the following solution: substitution of (7.59) in (C.20) yields: Keeping the term up to the leading order in N, we could write the embedding function t(r) as follows: The entanglement entropy of the Hawking radiation corresponding to the Hartman-Maldacenalike surface is computed as given below: utilizing (C.13) and (7.59), (7.66) is expressed as: Similarly, 7.5.3 Entanglement Entropy Contribution from Island Surface The island surface is a co-dimension two surface that exists at a continuous time slice, much like the Hartman-Maldacena-like surface. Therefore, we can formulate the formula for the holographic entanglement entropy as follows: Hence, we found that: and, Thus, the island surface’s equation of motion associated with embedding x1(r) is as follows: (7.89)’s solution is provided as: implying, The above equation has the following solution: The black hole entropy for the metric (7.19) is obtained as: Therefore, the entanglement entropy for the island surface after substitution of β simplified as: From Fig. 7.5 and utilizing (7.101), it is obvious that (7.97) ∼ (7.98) means that a lower constraint will be placed on rh, the non-extremality parameter in the M-theory dual of large-N thermal QCD. 7.5.4 Page Curve and An Exponential(-in-N) Hierarchy of Entanglement Entropies up to O(R4) Before/After the Page Time At the Page time, the entanglement entropies for the Hartman-Maldacena-like surface and the Island Surface are equal. This results in: Page time: Utilizing (7.99), (7.104) implies, Similarly, for the island surface O(β) contributions to the entanglement entropy is obtained as: Utilizing (7.99), (7.107) results in: From the equations (7.71), (7.100), (7.105) and (7.108), we obtained the following hierarchy: 7.6 Massless Graviton - the Physical reason for Exponentially Suppressed Entanglement Entropies Similar to [209], we can write the eleven-dimensional metric (7.19) as given below: We found that: the solution of above equation is: Since (7.121) is not well defined in the UV when m ̸= 0. Therefore, we need to consider m = 0 for which the graviton wave function is: Figure 7.8 plots the aforementioned potential for massless graviton (m = 0); this potential is “volcano”-like, with the massless graviton localized at the horizon on the ETW “brane”. This is analogous to [142], in which gravity can be localized on the end-of-the-world (ETW) brane with non-zero brane tension owing to the emergence of a “crater” in the “volcano” potential in the Schrödinger-like equation of motion of the graviton wave function. 7.7 Summary In this chapter, we constructed the doubly holographic setup from a top-down approach as discussed in 7.2. We have taken the external bath as thermal QCD in three dimension whose holographic dual is M-theory inclusive of O(R4) corrections [1], see chapter 1 for more detail of the same. The intermediate description of the doubly holographic setup constructed by us couples the black hole on the ETW-“brane” at x = 0 to thermal QCD bath via transparent boundary condition at the defect. We have addressed the effect of higher derivative terms in the context of top-down construction of double holography for the first time. First we obtained the Page curve without inclusion of O(R4) terms in the eleven-dimensional supergavity action in 7.4. To achieve the same, we computed the entanglement entropies associated with the Hartman-Maldacena-like (HM-like) and island surfaces and obtained the Page curve with the help of these entropies because the HM-like surface has Based on the viability of the Islands scenario, the M-theory dual of large-N thermal QCD at high temperature obtained in [15], [1] (based on [14]) produces the previously mentioned Page curve. The above-mentioned top-down M-theory dual, on the other hand, provides a number of new conceptual information: • Due to the lack of details of precise structures for boundary terms on the ETW-“brane” along with the presence of higher derivative terms, there exists relatively few works (e.g., [147]) in which the authors look into the doubly holographic setup in higher derivative theory of gravity. Remarkably we showed in 7.3.2 that the presence of the O(R4) terms generates no boundary terms. • As for as we know, our setup/(above-mentioned) M-theory dual appears either the sole one in existence (from M-theory) or one among the comparatively few top-down approaches that generate(s) the Page curve for massless graviton. • In our top-down M-theory dual, we find that ETW-“brane” to be a fluxed hypersurface W that is a warped product of an asymptotic AdS4 and a six-fold M6 where M6 is a warped product of the M-theory circle and a non-Einstenian generalization of T 1,1 ; the hypersurface W, can also be thought of as an effective ETW-“brane” corresponding to fluxed intersecting M5-brane wrapping a homologous sum of S 3×[0, 1] and S 2×S 2 in a warped product of R 2 and an SU(4)/Spin(7)-structure eight-fold. The ETW-“brane”, W, then has non-zero “tension” and a massless graviton localized near the horizon by a “volcano”-like potential. • Unlike largely other works in the literature, which compute the Page curve with a CFT bath, the external bath in our model is a non-CFT bath (thermal QCD). • Entanglement entropy contribution generated by a Hartman-Maldacena (HM)-like surface, which has been causing the growth of the Einstein-Rosen bridge in time, shows a Swiss-Cheese structure in the Large-N scenario (7.5.2) as discussed earlier. • By the presence of O(R4 ) terms in the action, our previously discussed M-theory dual produces a hierarchy in the entanglement entropies of the HM-like and Island surface (IS) with respect to a large-N exponential suppression factor, resulting physically via the presence of massless graviton mode on an ETW-brane. This suppression also suggests the fact that the addition of higher derivative terms - O(R4) in particular - has no effect on the Page curve. • To regulate the IR- and large-N enhancement in the IS entanglement entropy per unit BH entropy, a relationship involving the Planckian length and the non-extremality parameter (the horizon radius) has been shown to occur. • The positivity of the Page time, calculated in (refPage-time), has been showed to set an upper constraint on the non-extremality parameter, the black-hole horizon radius rh. This paper is under CC 4.0 license. available on arxiv

Entanglement Entropy and Page Curve From the M-Theory Dual of Thermal Qcd at Intermediate Coupling

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Acknowledgment PART I Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook PART II Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX B APPENDIX C Bibliography CHAPTER 3 - DECONFINEMENT PHASE TRANSITION IN THERMAL QCD-LIKE THEORIES AT INTERMEDIATE COUPLING IN THE ABSENCE AND PRESENCE OF ROTATION 3.1 Introduction We can compute the corrections to the infinite-’t Hooft-coupling limit as done in [100] using gauge/gravity duality, but this time using an AdS background. They used terms quartic in the Weyl tensor to include higher-derivative corrections on the gravity side. From the gauge theory point of view, there is a SU(N) supersymmetric Yang-Mills plasma with N = 4 SUSY at an intermediate ’t Hooft coupling. They provided an explanation for the transport peak that appeared in the spectral function of the stress-energy tensor at zero spatial momentum in the small frequency zone. This is a characteristic of perturbative plasma generally. In general theories of gravity, Wald provided a formula to determine black hole entropy [102]. He thought about the Lagrangian that results from the diffeomorphism invariant classical theory of gravity in n dimensions. Noether charge is a (n−2)-form in these theories of gravity, and the (n − 2)-form Noether charge’s integral across its bifurcate killing horizon will yield the black hole’s entropy. Therefore, for stationary black holes with bifurcate killing horizons, entropy equals Noether charge. A formula to calculate entropy for dynamical black holes was made in [103]. Every physical phenomenon has an energy/distance scale that defines it. RG group flow is used to move from UV to IR. However, short-range physics begins to interact with long-range physics in noncommutative field theories and string theory, a process known as UV/IR mixing. UV divergences in real ϕ 4 theory defined on commutative space are changed into infrared poles in the identical theory defined on noncommutative space as a result of UV/IR mixing, for example. There are further examples that are nicely explained in [104]. Theoretical models of gravity are nonlocal. As a result, UV/IR mixing might be present in such theories. In the gauge/gravity duality, the energy scale in the gauge theory side matches with the radial coordinate in gravitational theory. In the context of the AdS/CFT correspondence, the authors looked at the “I.R.-U.V.” connection and demonstrated how infrared phenomena in bulk theory are turned into ultravoilet phenomena in boundary theory [105]. In particular, the job of the ultraviolet regulator in the N = 4 super Yang Mills theory is played by the infrared regulator in the bulk theory. It’s fascinating that in our work, matching at the deconfinement temperature, M-theory actions dual to the thermal and black-hole backgrounds at the UV-cut-off, and obtaining a relationship between the O(R4 ) metric corrections in the IR, a specific type of UV-IR connection manifests itself. In noncentral relativistic heavy ion collisions (RHIC), a fluid known as quark-gluon plasma (QGP) is created. According to experimental findings from the RHIC collaboration, the angular momentum and angular velocity of this rotating fluid are on the order of 103ℏ and ω ∼ 6 MeV, respectively. In [108], the authors applied hydrodynamic simulations of heavy ion collisions and found ω ∼ 20−40 MeV. Considering the results mentioned above, a top-down analysis employing gauge-gravity duality of the effect of rotation on the deconfinement temperature of thermal QCD-like theories will be very interesting, with this motivation we obtained deconfinement temperature of thermal QCD from a top-down approach in [5]. The authors in [109] examined the consequences of rotating plasma on the deconfinement temperature of QCD in Hard wall and Soft wall models, and they discovered that deconfinement temperature of QCD decreases as angular velocity of the plasma increases. Similar works using a bottom-up method are available in [110–112]. 3.2 Deconfinement Phase Transition in Thermal QCDLike Theories in the Absence of Rotation In this section, we will discuss the deconfinement phase transition of thermal QCD-like theories at intermediate coupling without including the effect of rotation. 3.2.1 Tc from Semi-classical Method Here, we’ll detail how we implemented Witten’s proposal [4] to obtain the deconfinement temperature thermal QCD by applying the gauge/gravity duality and holographic renormalization of the eleven-dimensional supergravity action via 3.2.1.1, 3.2.1.2, and 3.2.1.3. The M-theory dual for high temperatures, that is, temperatures that are higher than the critical temperature T , will entail a black hole with the metric presented by: c that results in an EOM: 3.2.1.1 Black Hole Background Uplift (Relevant to T > T ) and Holographic Renormalization of On-Shell D = 11 Action c In this chapter, we worked near the Ouyang embedding implemented by the following coordinate patches [66]: The following expression is what we computed the IR Einstein-Hilbert term: Performing now the angular integration for the previously stated equation, which simplifies near (3.10) as given below: We derived the following expression for the action density (for Einstein-Hilbert term) in the IR by utilizing equation (3.13) and carrying out radial integration of (3.11): The version of the Einstein-Hilbert term pertaining to the ultraviolet (UV) region is: The following is the part that make up the EH action’s contribution to UV divergent: Up to O(β), the UV-finite boundary Gibbons-Hawking-York contribution is found to be: The GHY term’s UV-divergent contribution is as follows: We showed that the contribution from the higher derivative term is as follows, up to O(β ): 0 The higher derivative term that gives rise to the UV finite contribution was found to be: In addition, we observe that the surface counter term that neutralizes UV divergence is emerging via higher derivative term is provided by the expression that follows when r is held constant. Holographic Renormalization When T > T : It has been found that the form of the UV-divergent part of the on-shell action (3.9) for the black hole backdrop is as follows: c where the second term of (3.33) is worked out in (3.28), and 3.2.1.2 Thermal Background Uplift (Relevant to T < T ) and Holographic Renormalization of On-Shell = 11 Action c D In the limit of large N, as well as in the infrared, the fMN EOMs associated with the thermal background become algebraic. Writing below just those components that receive a non-trivial O(β) contributions, below is the O(β)-corrected MQGP metric for the thermal background in the IR in the ψ = 2nπ, n = 0, 1, 2-coordinate patches. The Einstein-Hilbert term pertaining to the thermal background, which works in the infrared close to (3.10), is: In the ultraviolet (UV), the equivalent Einstein-Hilbert term is: implying: Hence, the UV finite Einstein-Hilbert term, after carrying out the radial and angular integrals of the preceding equation is obtained as: The Einstein-Hilbert divergent term for the thermal background in the UV region is: For a thermal background up to (β), the UV-finite portion of the boundary GibbonsHawking-York term is calculated to be: O The Gibbons-Hawking-York term in thermal background has an additional UV divergence component, which is: implying: In addition, the contribution arising from the higher derivative term in the UV near (3.10) is: The UV-differential portion of the equation (3.46) was further deduced as: We found that: Let us assume the following in relation to (3.48) and the fourth equation in (3.49): The following can be deduced from (3.49): 3.2.1.3 T Inclusive of (R ) Corrections c O 4 Here, we’ll use the on-shell action comparison between black hole and thermal backgrounds to determine the deconfinement temperature using information gathered from 3.2.1.1 and 3.2.1.2. We will also describe a variant of the UV-IR connection that emerges from the O(R ) terms. 4 Following is the on-shell action that corresponds to the thermal background uplift: this results in, ) In the context of this discussion, the term “UV-IR connection” refers to the equations (3.62) and (3.59). Because this is providing a connection that connects the integration constant appearing in the O(R4 ) corrections to the thermal background along the M-theory circle and a specific combination of integration constants appearing in the O(R4 ) corrections to the black hole background. The combination figuring in the black hole background is along the compact part S3 of the non-compact four cycle (locally) Σ(4) = R+ × S 3 wrapping the flavor D7-branes of the type IIB dual [14], hence this has the information of flavor branes in M-theory uplift which has no branes and this is known as “Flavor Memory” effect in this context. We now turn to Green and Gutperle’s argument that a SL(2, Z) completion of an effective R4 interaction results into a fascinating non-renormalization theorem that prohibits perturbative corrections to this term beyond one loop in the zero-instanton sector [73]. term that occurs in (1.47) bilinear in the tensor tˆ bears the same structure just like terms that occur in the zero instanton sector via both the one-loop four-graviton amplitude and a (α ′ ) 3 effect at tree level [115]. Thus, in the Einstein frame, one gets the expression that follows for the total effective R4 action, which can be formally represented by: Non-Renormalization of the Deconfinement Temperature (Tc) from Semiclassical Method: wherein the summation denotes the sum of all positive and negative values except = 0. Now: p, n p = n The sum over , utilizing the Poisson resummation formula p 3.3 Wald Entropy, Tc from Entanglement Entropy and MχPT Compatibility 3.3.1 Wald Entropy As a result, we are able to notice that the contribution (iii) is the one that predominates in the MQGP limit, and the black hole entropy from the higher derivative terms is obtained as: As a result, we found that linear constraints must be placed on the constants of integration that appear in the solutions to the EOMs of the metric corrections at O(R4 ) in the directions that contain the “memory” of the compact part of the non-compact four-cycle “wrapped” by the flavor D7-branes in the type IIB dual [14] of the large-N thermal QCD-like theories. 3.3.2 Deconfinement from Entanglement Entropy where ϕ denotes the profile of the dilaton. Due to the absence of a dilaton in a M-theory dual, the equation (3.75) will be considered to be replaced with the following expression: Consider now the gravity dual’s metric in string frame, which may be stated as: Hence, where (r) is defined as: H Entanglement entropy will be reduced to the following using equations (3.81) and (3.83). Let us discuss the implications of (3.87). Equations (3.2) and (3.77) allow us to deduce the following: wherein λ1 and λ2 have been defined as follows: After that, rewriting σ(r) as follows: then The formula for the connected region entanglement entropy that takes into account both tiny l and large r is as follows: Entanglement Entropy: wherein: and, 3.3.3 MχPT Compatibility 3.4 Deconfinement Temperature of Rotating QGP at Intermediate Coupling from M-Theory This part is based on [5]. In this paper, we have obtained the deconfinement temperature of thermal QCD-like theories in the presence of rotation. We will discuss the holographic construction of rotating QGP from a top-down approach in 3.4.1. Using this holographic dual, we will discuss the calculation of Tc in the presence of rotation in 3.4.2 and UV-IR mixing, Flavor Memory effect, and non-renormalization of Tc in 3.4.3 3.4.1 Top-Down Holographic Dual of Rotating QGP When T > Tc on the gravity dual side and T < Tc on the gauge theory side, we could investigate the affect of rotation in thermal QCD-like theories by introducing a rotating cylindrical black hole and thermal backgrounds on the gravity dual side. In order to obtain the background of a rotating cylinder black hole, we need to make x 3 periodic by replacing it with lϕ, where l represents the length of the cylinder and 0 ≤ ϕ ≤ 2π. This will allow us to obtain the rotating cylinder black hole background. After completing the following Lorentz transformation around the cylinder of length l, one can obtain the holographic dual of rotating quark-gluon plasma. This can be done by following [116, 117]: where ω represents the angular velocity of the rotating cylindrical black hole in the gravity dual, which is connected to the rotation of quark-gluon plasma by means of the gauge-gravity duality. Only when ωl < 1, the Lorentz transformation, also known as the Lorentz-boost, considered to be trustworthy. Following the application of the Lorentz transformation, which is denoted by the equation (3.117), the equation (3.1) is rewritten as follows: In order to produce the rotating cylindrical thermal background, we substitute x3 by lϕ and carry out the Lorentz transformation (3.117) of (3.2) in the same manner as we did to the black hole background. As a result of these steps, the metric of the rotating cylindrical thermal background simplified as: 3.4.2 Deconfinement Temperature of Rotating QGP from M-Theory Dual Using a semi-classical method [4], we will compute the deconfinement temperature of a rotating QGP at intermediate coupling in this section similar to 3.2.1. On-shell action, in this case, will be the same as (3.9), and hence we computed the various terms appearing in (3.9) for the rotating cylindrical black hole (3.118) and thermal (3.122) backgrounds, and integrated over the angular coordinates similar to 3.2.1. In the upcoming pages, we will not discuss every step, and we will write the final results because the procedure is the same as 3.2.1. Only metric is different for the rotating cylindrical black hole and thermal backgrounds compared to 3.2.1. In a procedure analogous to that of 3.2.1, the UV-finite and holographic IR regularized on-shell action density for the M-theory rotating cylindrical black hole background (3.118) was calculated as follows: At the UV cut-off [3]: The following is a solution to the equation presented above: In the context of gauge-gravity duality, the Hawking Page phase transition, which occurs at T = TH(γ) on the gravity side between a thermal and black hole background is dual to the deconfinement phase transition, which occurs at T = Tc(γ) in gauge theories , i.e., The authors found identical behavior from NambuJona-Lansinio model in [120] because of chiral condensate suppression, which was investigated as well from lattice simulations in [121, 122]. Lattice simulations with different kinds of boundary conditions (open, periodic, and Dirichlet) have been carried out in rotating reference frames. In both gluodynamics and the theory of dynamical fermions, the authors investigated the impact of rotation on the critical temperature. The result found that the decrease in deconfinement temperature of thermal QCD from a rise of rotation of quark gluon plasma was previously studied using gauge-gravity duality from a bottom-up approach in [109–112]. In contrast to our finding and other holographic findings mentioned earlier, the critical temperature for gludynamics exhibits the opposite behavior. However, the authors found that the critical temperature for dynamical fermions decreases as rotation increases. The hard-wall and soft-wall models were used for the bottom-up holographic study in [109], and the Einstein-Maxwell-Dilaton system is involved in the gravity dual of [110]. The authors of [111, 112] considered the gravity dual of rotating QGP to be the Kerr-AdS black hole background in five dimensions. The deconfinement temperature of rotating QGP from a top-down model is not covered in any published article. Because top-down models compactify the initial type IIB/IIA string theory or M-theory on an internal manifold to produce four-dimensional QCD at finite temperature, they are more fundamental than bottom-up models. We successfully studied rotating QGP from a top-down holographic dual for the first time and were able to confirm the non-zero angular velocity of rotating QGP found in hydrodynamic simulation [108] and STAR collaboration [123]. Comparison with Other Models: 3.4.3 UV-IR Mixing, Flavor Memory Effect and Non-Renormalization of Tc in Rotating QGP Focusing on the outcomes presented in the appendix B.4. At O(β), the UV finite on-shell action densities for the rotating cylindrical black hole and thermal backgrounds are as follows: We got the following results using the equations (3.130) and (3.131): 3.5 Summary We obtained the following results in this chapter. During the computation of Tc from the semiclassical method [4], we obtained “UV-IR” mixing described as the connection between the O(β) corrections to the M-theory metric along the M-theory circle in thermal background and the O(β) correction to a specific combination of the M-theormetric components along the compact part of the four-cycle “wrapped” by the flavor D7-branes of the parent type IIB (warped resolved deformed) conifold geometry - the latter referred to as “Flavor Memory” in the M-theory uplift on equating the O(β) portion of the on-shell actions of the black hole and thermal backgrounds in the absence and presence of rotation both. • UV-IR Mixing and Flavor Memory: • Non-Renormalization of Tc: In the high-temperature M-theory dual, matching of O(R4 ) computation of Wald entropy with the black hole entropy puts a linear constraint on the same linear combination of the aforementioned integration constants. • Wald Entropy at O(R4): By applying Lorentz transformations (3.117) along (t, ϕ) coordinates on the gravity dual side, we are able to derive the rotating QGP on the gauge theory side via gauge-gravity duality. Therefore, for T > Tc and T < Tc on the gauge theory side (where Tc serves as the deconfinement temperature of thermal QCD-like theories), the gravity dual includes a rotating cylinder black hole and thermal backgrounds. • Holographic Dual of Rotating QGP: We found that the deconfinement temperature of rotating QGP (3.129) is inversely proportional to the Lorentz factor, γ, by equating the O(β 0 ) terms for the rotating cylindrical black hole and the cylindrical thermal backgrounds at the UV cut-off (3.125). This means that when the angular velocity of rotating QGP increases, the deconfinement temperature of thermal QCD-like theories decreases and vice-versa. Experimental results from the noncentral Relativistic Heavy Ion Collider (RHIC) have shown that the Quark Gluon Plasma created in these collisions has an angular velocity, and that the deconfinement temperature decreases with increasing rotation [123]. To ensure that the deconfinement temperature of rotating QGP computed using a top-down technique is in agreement with actual results, our study serves as a good check for the top-down duals of [14] and [1]. • Tc in Rotating QGP: This paper is under CC 4.0 license. available on arxiv

Deconfinement Phase Transition in Thermal Qcd-Like Theories at Intermediate Coupling

*** The History of Science Funding The scientist has always been a risky employee in terms of ROI.  They are trying to uncover truths about the universe, and oftentimes, the universe gives them the bird. Because experimenting means risking a lot of money and time on a possibly worthless idea, a scientist is a forever intern, until they make a breakthrough, then they become senior associates. That said, the scientist has been trying to make his own money. With the Alchemists, this was literal. While they invented Chemistry and catalyzed the birth of worldwide gold rushes, turning lead into gold was, alas, a wrong idea believed for centuries. The search consumed the lifetime of one person after another, with only dreams of wealth to get them through. But their tenacity was a testament to their resilience and patience. Patience meant, for the time being, remaining in the employ of someone who could afford the risk of backing science in the past. And that meant a King because they had gold/money collected from taxes. Wizards and fortune tellers didn’t make much sense, and they were comedians come to give the King a jolly time before he went to war. Though, while throwing guts on a wall may be stupid, it was mysterious and if they were right, doubly impressive. And here was this (broke) scientist, insisting that they knew a REAL strategy to help the King win. What was their credibility? Circa 200BC, the scientist is Archimedes and the King is the political head of Syracuse. Being a leader in those times largely meant you needed to win wars and as history had taught Kings the utter uselessness of charlatans, the scientist was given a chance to make his case. Archimedes made his case alright. It that he sunk the ships of the Romans with ingenious cranes and catapults that threw heavy stones. has been recounted Since his time, patronage from Kings, Princes, Bankers and Presidents to scientists has been immense. The scientist is respected, and all great scientists, even Leonardo da Vinci who was mostly fawned over for his impressive artwork, took off some time to design weapons. For weapons help the King win and hence, keep the scientist with a job. Scientists soon became ever more pivotal in war efforts. Especially Physicists and Chemists, who have designed countless forms of military hardware to date. However, the emergence of scientific methods in Economics, Sociology, Psychology, Biology, all riding on the power of statistical analysis and logical inference, quickly made the scientist important in every field of human endeavour. The problem however remained. To get a loan, the scientist usually had to, and still has to, rely on government funding because the government remains the biggest fish able to take on sufficient risk in the financial markets. Hate it all you want, but without credit from the government, be it debt or real money, a lot of scientific work would have stalled. Best example - SpaceX. However, governments and their ability to debase money and finance things on debt, made the world wars last longer to destroy the world much harder. It also led to economic depressions and after the 2008 financial crisis, Satoshi Nakamoto, a genius computer scientist, decided to create Bitcoin – a monetary tool outside the purview of government currency debasement. Birth of a financial model divorced from the King Bitcoin has been controversial from its inception. Of course, Kings and governments hate it. It is cutting into their business. A big part of the private sector also loathes its nature of priding in technological exclusivity, so that six years later, a hard fork was implemented to create Ethereum, a cryptocurrency built to provide extra blockchain services such as smart contracts. Many other hard forks quickly followed from the faithless. However, Bitcoin is still mainstream and has recently become interesting to Big Finance. The Bitcoin ETF proves as much. After 15 years of laughing at a thing that keeps building bigger and better, even the harshest critic will shut up and start listening more intimately. Because they now know they are missing something. Energy scientists are also starting to pay attention, with some claiming that Bitcoin mining may be our . are doing well selling cheaper electricity packages that have been subsidized by Bitcoin mining on the side. fast track to an energy transition Energy engineers But these are late to the party. Computer scientists have been earning well in Bitcoin, Ethereum, Doge for decades. And if any scientist has been comfortably living outside the need to get big budget funding from governments, that has been the computer scientist, from way back in the 20th century. While the field of Computer Science is much younger than Physics, Astronomy, Biology, many computer scientists quickly learned to earn big from private enterprise and individualized work, without begging the Kings and their Big Bankers for a loan. Futuristic Science Funding itself through Bitcoin Bitcoin is money for the people, and science has evolved to also be something done as a public good, on an open source plan, by dedicated people who put in their own time and money to make something good happen. As I mentioned, Computer Scientists now exist on the internet who are eagerly improving the Bitcoin ecosystem using the power of collaboration and their earnest efforts. These mostly come from the land of software development and after getting orange-pilled, decide to stay at Bitcoiner-land and build the Bitcoin ecosystem. However, there has not been much of an on-ramp for other types of scientists and this is the opportunity existing, wide open, for anybody to take. Currently, many a scientist in the Bitcoin world is a computer scientist of the type who builds zero-knowledge proofs, rollups, and more layers of the Bitcoin blockchain. But many more scientific people are needed. To re-iterate, I feel more electrical and power engineering scientists should be at the forefront of how Bitcoin mining equipment can provide electricity access to those without, making investments in clean, stranded energy sources much easier to manage. What better job than to be the electric engineer who designs their own job by bringing electricity to your people? Every university student of electrical engineering, whatever the developing country, should learn about this. Because developing countries in Africa, Asia and Latin America are struggling with scaling electricity usage from otherwise cheap energy sources, because of the high premiums that locals just cannot pay. The knowledge of using Bitcoin to subsidize electricity access from stranded energy sources should be spread as far and as widely as possible. Now, as an aspiring quantum information scientist, I feel there is also a place for me in the Bitcoin ecosystem. While the public might know how quantum information science threatens to undo the good that Bitcoin has done by potentially hacking it, I find that building quantum-resistant algorithms is far from scratching the surface of quantum capabilities. For example, quantum technologies could provide for Bitcoin nodes, allowing even weak signals to be successfully transmitted and ensure blocks are mined. better signal sensors Quantum computing could help guide better on how Bitcoin infrastructure could be better set up across nations and continents for optimum usage. solutions in logistics Quantum networks could provide better ways to securely. transmit Bitcoin information Some problems in the Bitcoin ecosystem could be (Bounded-error Quantum Polynomial) problems, which are the purview of quantum information science and these should be discovered and worked on using quantum computers. BQP Most importantly, quantum computers will be orders of magnitude better at mining proof-of-work cryptocurrencies than classical computers. When Bitcoin befriends Quantum Mechanics Moore’s law is coming to an end. IBM has already built transistors with only 5 atoms. To get smaller, it becomes harder to manage thermal noise and other nanoscale problems. To manage thermal noise, even more cooling will be done, the way it is done for qubits. Also, a 1-atom transistor is effectively a qubit. This is the quantum realm, and like it or not, more people will study quantum mechanics in the not-too-distant future, and by extension, quantum computing. The classical computing world can only scale by a multiplicity of the same technology, which will consume even more energy. The efficiency gains of quantum technologies like quantum computers will be needed. While , the science of building qubits is ramping upwards and systems are getting more powerful. There might not be an exponential growth in qubits with their own Moore’s law, but a linear growth in qubits leads to exponential computational power. Which kind of is a Moore’s law! I have said quantum computing is very expensive You remember this graph; If approximately 14 billion dollars in 2023 can bring in (logical qubits are the real qubits as manipulated in mathematical theory), by linear extrapolation, $125 billion by 2030 as seen above will bring in 428 logical qubits. 48 logical qubits But 7 years from now, Bitcoin itself might have ballooned to $200,000 per bitcoin which is a $4.2 trillion market cap. By linear extrapolation, $3 trillion is needed in global investments to take us to 10,000 logical qubits. As we can see, Bitcoin alone can pay for it over a 7-year span. Why 10,000 qubits? My Research Project Over the past three months, I have been studying QCourse551-1 which was offered in a collaboration between QWorld and Classiq Technologies. My research project was Project 11 - Bitcoin Mining using Grover’s Search Algorithm. The motivation for my project came from that shows that 10,000 logical qubits alone can do Bitcoin mining faster than any classical system using the same energy consumption. a research paper This is because 10,000 qubits can encode the full double SHA256 hashing process that goes into mining Bitcoin, but since they use Grover’s search algorithm, they effectively achieve quadratic speed-up by square_root(N) where N is the number of elements to check in an unstructured database. ASICs mining for bitcoins also check an unstructured database of random hashes for the nonce value. The question is, which one is faster? Most ASIC miners today are checking terahashes or For example checks 120TH/s. That is 120 million hashes every second. 1 million hashes every second. this miner Can a quantum computer beat that? Of course. square_root( 120 million) = only 10954 checks per second. A 1,095,400 % efficiency increase. And the more the competition, the more the quantum computer tears ahead in the race. The is rocketing upwards of 600 million million hashes per second. This is outputting enough heat to make climate scientists worried sick. But what if we replaced all those clunky ASICs with state-of-the-art QPUs from the year 2032, how many comparative hashes per second would they clock? square_root( 600 million million) = 24 million checks per second. A . current hash rate 2.4 billion % increase in efficiency If the above is not an attractive proposition, I don’t know what is. Bitcoin should fund quantum computing research. It will take a while, but when it happens, it will be glorious. It will be a more canonical event than the Moon landing. In our research, we were checking a much-simplified system with only 8-bit inputs and outputs, modeled on a Grover’s operator working with under 25 qubits. Given our really low hashing power, the advantages of Grover’s search could not be gleamed first hand, and could only be inferred with a relevant complexity analysis of the runs/depth of the Classical computer (my laptop) vs the depth of our Grover’s circuit executed on the Classiq Aer simulator. While it would have been good to model the energetics and the complexity graph of what this means, unfortunately, we ran out of time. However, we had some deliverables to show for our work. Below is what we had including the depth of each circuit. a) The simplified MD5 classical algorithm We modeled a simplified version of the MD5 (a most primitive cousin of SHA256) hashing 95 printable ASCII characters to find the nonce for hex values with difficulty = 1. Note: Our hex values were only 2-digit because we are working with 8-bit values. So our possible difficulty 1 values are only in 16 possibilities i.e. 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0a, 0b, 0c, 0d, 0e, 0f. 00 is also a difficulty 2 element. Hence the searching/hashing function is called simplified_MD5_8bit_difficulty_1or2. def simplified_MD5_8bit_difficulty_1or2():
    printables_list = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&\'()*+,-./:;<=>?@[\\]^_`{|}~'
    for i in printables_list:
        x2 = ord(i)

        x3 = bin(x2)[2:]

        if len(str(x3))==7:
            x4 = x3+'0'
        if len(str(x3))==6:
            x4 = x3+'00'

        x5 = list(x4)

        a0 = 2*int((x5[0]))
        a1 = int(x5[1])

        b0 = 2*int((x5[2]))
        b1 = int(x5[3])

        c0 = 2*int((x5[4]))
        c1 = int(x5[5])

        d0 = 2*int((x5[6]))
        d1 = int(x5[7])

        a = a0 + a1

        b = b0 + b1

        c = c0 + c1

        d = d0 + d1
    
        a = ((d ^ (b & (c ^ d))) + (c ^ (d & (b ^ c))) + (b ^ c ^ d) + (c ^ (b | ~(d))) + b)
        
        print()

        d1 = d//2
        d0 = d%2
        d = d1*(2**7) + d0*(2**6)

        a1 = a//2
        a0 = a%2
        a = a1*(2**5) + a0*(2**4)

        b1 = b//2
        b0 = b%2
        b = b1*(2**3) + b0*(2**2)

        c1 = c//2
        c0 = c%2
        c = c1*(2**1) + c0*(2**0)

        decimal_result = d + a + b + c
        binary_result = bin(decimal_result)[2:]
        print(binary_result)
        hex_result = hex(decimal_result)
        print(hex_result)

        if hex_result == '0x0':
            difficulty_2.append(hex_result)
            collisions_difficulty_2.append(i)
        if hex_result == ('0x1' or '0x2' or '0x3' or '0x4' or '0x5' or '0x6' or '0x7' or '0x8' or '0x9' or '0xa' or '0xb' or '0xc' or '0xd' or '0xe' or '0xf'):
            difficulty_1.append(hex_result)
            collisions_difficulty_1.append(i)

    print('Difficulty_1 list = ',difficulty_1)
    print('Difficulty_2 list = ',difficulty_2)
    print('Colliding inputs for difficulty 1 = ',collisions_difficulty_1)
    print('Colliding inputs for difficulty 2 = ',collisions_difficulty_2)
    
difficulty_2 = []
difficulty_1 = []     
collisions_difficulty_1 = []
collisions_difficulty_2 = []

import numpy as np
simplified_MD5_8bit_difficulty_1or2() As can be seen, to find the difficulty 1 (and by extension the difficulty 2) elements, we have to reiterate through 40 lines of code (ignoring spaces and printing in the for loop). There are 96 printable ASCII characters to hash and check hence 96 * 40 which gives us a circuit depth of 3840. However, this is run through fast by my laptop. Less than a few seconds. b) The simplified MD5 quantum algorithm We modeled a quantum version of our simplified MD5 algorithm to simulate finding the difficulty 1 nonce values no matter what the input ASCII character to the circuit was. This is possible because all we need is a zero at the beginning of our hex value. Since our hash set was small (only 96 ASCII characters), we tuned the system to ignore the input ASCII value so it is redundant, and to aim to capture all possible zeros given the Arithmetic expression; a == ((d ^ (b & (c ^ d))) + (c ^ (d & (b ^ c))) + (b ^ c ^ d) + (c ^ (b | ~(d))) + b) which is also in the classical Python algorithm. Notice that the 4 functions being added together are derived from the . original MD5 algorithm Since we want difficulty 1 values, we add and to the above function and then synthesize it in the Classiq platform. d = 0 a = 0 (Note: This is a shortcut thanks to the tireless work of the Classiq team. The Python code was also built in the Classiq Python SDK but it had a last-minute glitch. Hence we only have working Python SDK code for the Grover’s operator, but not for the Grover’s operator with a difficulty-1 hash/search, which is what you had to see here ) Hence our input Arithmetic expression is; a == ((d ^ (b & (c ^ d))) + (c ^ (d & (b ^ c))) + (b ^ c ^ d) + (c ^ (b | ~(d))) + b) and d == 0 and    a == 0 The resulting circuit has a depth of only 913 The quantum circuit wins! Endnote While the project time ended, our work is still a work in progress, to continue until we build a functional 10,000 qubit quantum bitcoin miner. Voluntary efforts to support us technically are most welcome. Some of our code is still glitchy and we have only scratched the surface of the Classiq platform’s capabilities. An ingenious software tool that takes away the cumbersome tinkering with gates, as would have been needed for anybody building the same project using Qiskit. Special thanks to Classiq and QWorld for the opportunity. And our mentor - Dr. Eyal Cornfeld, for the guidance. ***

Hash Rate Analysis Projections: Why Bitcoin Should Embrace Quantum Information Science

হ্যাশ রেট বিশ্লেষণ অনুমান: কেন বিটকয়েন কোয়ান্টাম তথ্য বিজ্ঞানকে আলিঙ্গন করা উচিত

Prognosen zur Hash-Rate-Analyse: Warum Bitcoin die Quanteninformationswissenschaft nutzen sollte

Proyecciones del análisis de la tasa de hash: por qué Bitcoin debería adoptar la ciencia de la información cuántica

Projections d'analyse du taux de hachage : pourquoi Bitcoin devrait adopter la science de l'information quantique

हैश दर विश्लेषण अनुमान: बिटकॉइन को क्वांटम सूचना विज्ञान को क्यों अपनाना चाहिए

ハッシュレート分析の予測: ビットコインが量子情報科学を採用すべき理由

해시레이트 분석 예측: 비트코인이 양자 정보 과학을 수용해야 하는 이유

Projeções de análise de taxa de hash: por que o Bitcoin deveria adotar a ciência da informação quântica

Прогнозы анализа скорости хэширования: почему Биткойн должен использовать квантовую информатику

Hash Rate Analizi Projeksiyonları: Bitcoin Neden Kuantum Bilgi Bilimini Kucaklamalı?

Dự đoán phân tích tỷ lệ băm: Tại sao Bitcoin nên áp dụng khoa học thông tin lượng tử

哈希率分析预测：为什么比特币应该拥抱量子信息科学

Dr. Sabine Hossenfelder’s is titled ‘ ’. latest YouTube video It looks like AI will kill Quantum Computing I would like to share why this shall not happen before this jab at quantum computers turns cold. Quantum Computers Are of Great Research Interest If you went away from the video with an earnest belief that AI shall indeed kill quantum computers by drying up its research funding, then you might as well believe that AI will kill particle physics, cosmology, and quantum gravity. And where the hell is the Higgs Boson hiding if it holds more mass-energy than a hydrogen atom? Just saying. Continuous progress in the theoretical and experimental realization of better quantum computers is of great interest to human beings because it is a real way to uncover computational truths about the universe. We are curious about building big, powerful quantum computers like we are curious about what happens inside a black hole. Shall a big powerful quantum computer hack RSA and uncover all those hashed-up secrets (about aliens)? I want to find out. Does a black hole teleport us into another Universe? Dr. Sabine is interested in this one. As AI makes big tech founders billions and soon to be trillions of dollars once we start putting servers on the moon, a lot of that newfound funding will go towards, take a guess, research in quantum computing. Computing Is Not Always About Speed The Graph We are always comparing the computational speed of quantum computers with that of classical computers in the graph below. The graph above starts with the line for quantum computing above that of classical computing. This means that classical computers are more efficient and take less time to do operations. Later on, there is a cross-over point, and classical computers take way more time to do the operations compared to a quantum computer. That cross-over point is when a quantum computer of modest size and complexity hacks classical encryption algorithms, simulation problems, and that no classical computers can hack. traveling problems Dr. Sabine argues that AI is shifting the lines and the cross-over point into the very far future, making Meta senior fellow and former tech chief Mike Schroepfer exactly right when he says “quantum computing being irrelevant to Meta right now”, quite prescient. …”(quantum machines) may come at some point, but it’s got such a long time horizon that it’s irrelevant to what we’re doing.” source But computing is not always about solving problems quickly. Modelling Computing is also about modeling problems. While the latest QC - the - is not gargantuan enough for the computational problems that most people are paying for, the fact that you would need a supercomputing complex to model what it can model should be impressive enough. 433 qubit IBM Osprey Know what, we should do it. Let us model something impressive in Osprey and also try to model it on See which one uses less electricity. This modeling contest can be appreciated as high art and designed to get people entertained. Where there is entertainment, people are willing to pay for it. Frontier. On a more practical note, quantum sensors built at the measurement side of quantum computers are a peak into the universe that classical computational sensors have no hope of seeing. Of note are LIGO and Atomic clocks. The latter can see and count atomic zeptoseconds using minimum energy periodically cycled by continuously exciting an atom. Telling time very accurately helps us keep an accurate, albeit . clunky calendar The former can see gravitational waves using a variation of the Mach-Zehnder interferometer. In the quantum computing world, this is just a singular CNOT gate. So, if one CNOT gate can see gravitational waves, wonder what our elaborate algorithms can see. We need to find out. The measurement-computing use cases for quantum computing shall only get more impressive. I hope to one day measure the Hamiltonian of the . smallest Bitcoin miner possible AI Might Love Quantum Computing We need to realize that AI might love quantum computing, because AI loves learning. AI might be pushing the boundaries of classical computers to make them develop heuristic powers that people who train AI models also marvel over. But no matter how hard you push a car, it will never be a boat. While AI is still poor at explaining quantum mechanics compared to most human physicists, that might change once we keep pumping AI with quantum computing data. Machine Learning of Quantum (MLQ, not which is ) technology should be of interest to Meta because the road to developing better quantum computers will also develop better nanomaterials relevant to the classical computing world. QML Quantum Machine Learning The quantum computing world, like the classical computing world, is now parked at the nanoscale. Being neighbors, they could benefit from each other. They will. P.S. >> Quantum Computers also have their finger on improving battery technology because an entanglement of atoms packs more energy than if you did not have an entanglement. Admit it; these quantum computers are interesting.

AI Will Not Kill Quantum Computing

এআই কোয়ান্টাম কম্পিউটিংকে হত্যা করবে না

KI wird Quantencomputing nicht töten

La IA no acabará con la computación cuántica

L’IA ne tuera pas l’informatique quantique

एआई क्वांटम कंप्यूटिंग को खत्म नहीं करेगा

AI は量子コンピューティングを破壊しない

AI는 양자 컴퓨팅을 죽이지 않을 것이다

A IA não acabará com a computação quântica

ИИ не убьет квантовые вычисления

Yapay Zeka Kuantum Bilişimi Öldürmeyecek

AI sẽ không giết chết máy tính lượng tử

人工智能不会杀死量子计算

Quantum Computing is Dead - Long Live Quantum Processing!

কোয়ান্টাম কম্পিউটিং মৃত - দীর্ঘজীবী কোয়ান্টাম প্রসেসিং!

Quantencomputing ist tot – Es lebe die Quantenverarbeitung!

La computación cuántica ha muerto: ¡larga vida al procesamiento cuántico!

L’informatique quantique est morte – Vive le traitement quantique !

क्वांटम कंप्यूटिंग ख़त्म हो चुकी है - क्वांटम प्रोसेसिंग लंबे समय तक जीवित रहेगी!

量子コンピューティングは死んだ - 量子処理万歳!

양자 컴퓨팅은 끝났습니다 - 양자 처리가 오래 지속됩니다!

A computação quântica está morta - viva o processamento quântico!

Квантовые вычисления мертвы – да здравствуют квантовые вычисления!

Kuantum Bilişim Öldü - Yaşasın Kuantum İşleme!

Máy tính lượng tử đã chết - Xử lý lượng tử tồn tại lâu dài!

量子计算已死——量子处理万岁！

Explaining the Infinite Potential of Quantum Computing in Marvel-lous English (No Math)

মার্ভেল-লাউস ইংলিশে কোয়ান্টাম কম্পিউটিং এর অসীম সম্ভাবনা ব্যাখ্যা করা (কোন গণিত নয়)

Erklären Sie das unendliche Potenzial des Quantencomputings in wunderbarem Englisch (keine Mathematik)

Explicando el potencial infinito de la computación cuántica en un inglés bastante divertido (sin matemáticas)

Expliquer le potentiel infini de l'informatique quantique dans un anglais plutôt drôle (pas de mathématiques)

क्वांटम कंप्यूटिंग की अनंत संभावनाओं को मज़ेदार अंग्रेजी में समझाना (कोई गणित नहीं)

量子コンピューティングの無限の可能性を面白い英語で説明する (数学なし)

놀라운 영어로 양자 컴퓨팅의 무한한 잠재력 설명(수학 없음)

Explicando o potencial infinito da computação quântica em inglês bastante engraçado (sem matemática)

Kuantum Hesaplamanın Sonsuz Potansiyelini Harika İngilizceyle Açıklamak (Matematiksiz)

Giải thích tiềm năng vô hạn của máy tính lượng tử bằng tiếng Anh khá hài hước (Không có toán học)

用相当有趣的英语解释量子计算的无限潜力（无数学）

Why consciousness? The quest to understand consciousness and develop artificial general intelligence has long been a topic of fascination and study in the fields of computer science and neuroscience. It is also a complex and elusive phenomenon that has puzzled scientists and philosophers for centuries. In this note, we will explore the ways in which the fields of neuroscience, neurosymbolic AI, neuromorphic computing, and quantum theory can contribute to our understanding of consciousness and the potential for the development of artificial general intelligence. A word for Neuroscience Neuroscience is the study of the structure and function of the nervous system, including the brain and the spinal cord. By studying the brain, neuroscientists have gained a better understanding of how the brain processes information and how it generates the experience of consciousness. For example, neuroimaging techniques such as fMRI have allowed researchers to identify specific brain regions that are involved in consciousness, such as the prefrontal cortex and the posterior cingulate cortex. Neurosymbolic AI; the best of both worlds Neurosymbolic artificial intelligence, also known as hybrid AI, is a type of artificial intelligence that combines the strengths of both symbolic AI and connectionist AI. Symbolic AI, also known as "good old-fashioned AI," uses a rule-based approach to problem-solving and decision-making, while connectionist AI, also known as "machine learning” and “deep learning" uses neural networks and large amounts of data to learn and adapt. Neurosymbolic AI combines these two approaches, allowing for more flexible and adaptable AI systems. One way that neurosymbolic AI can contribute to the study of consciousness is by allowing for the creation of more complex and realistic models of the brain. These models can be used to simulate the processes involved in conscious thought and decision-making, providing insight into the underlying mechanisms of consciousness. Additionally, neurosymbolic AI can be used to develop more advanced AI systems that can exhibit human-like consciousness and intelligence, bringing us closer to the goal of developing artificial general intelligence. Neuromorphic Computing architectures as the physical substrates (beyond Von Neumann) Neuromorphic computing, also known as "brain-inspired computing," is a type of computing that is based on the principles of the human brain. Unlike traditional computing systems, which use a von Neumann architecture with separate memory and processing units, neuromorphic computing systems use a more brain-like architecture with distributed memory and computing. This allows for more efficient and energy-efficient computation, as well as the ability to process complex and unstructured data. One way that neuromorphic computing can contribute to the study of consciousness is by providing a more realistic and efficient platform for simulating brain processes. These simulations can be used to study the dynamics of large-scale neural networks, providing insight into the neural basis of consciousness. Additionally, neuromorphic computing systems can be used to develop AI systems that are better able to mimic the flexibility and adaptability of the human brain, bringing us closer to the goal of developing artificial general intelligence. And then it goes Quantum… Quantum theory is a branch of physics that deals with the behavior of matter and energy at the atomic and subatomic levels. Quantum mechanics is the mathematical framework that describes this behavior, and it has been incredibly successful at explaining the behavior of the smallest building blocks of the universe. In recent years, researchers have begun to explore the potential applications of quantum mechanics to the study of consciousness and the development of artificial general intelligence. One way that quantum theory can contribute to the study of consciousness is by providing a framework for understanding the relationship between the brain and the mind. Many theories of consciousness, such as the integrated information theory, suggest that consciousness arises from the complex interactions of large numbers of neurons in the brain. Quantum mechanics may provide a way to model these interactions and understand how they give rise to consciousness. Additionally, the unique properties of quantum systems, such as superposition and entanglement, may provide a way to create more advanced and intelligent AI systems that can exhibit human-like consciousness. The takeaways In conclusion, neuroscience, neurosymbolic AI, neuromorphic computing, and Quantum theory are fields that hold great promise for the study of consciousness. By combining the strengths of these technologies and recent advances in neuroscience we can create more complex and realistic models of the brain, and develop more advanced and flexible AI systems that are capable of adapting to a wide range of tasks and environments. Ultimately, the potential is to gain a deeper understanding of the complex and elusive phenomenon of consciousness and make progress towards developing AGI systems with artificial consciousness, someday…

Quantum neuroAI and Its Role in the Quest for Artificial Consciousness

NeuroIA cuántica y su papel en la búsqueda de la conciencia artificial

La neuroIA quantique et son rôle dans la quête de la conscience artificielle

कृत्रिम चेतना की खोज में क्वांटम न्यूरोएआई और इसकी भूमिका

量子ニューロAIと人工意識の探求におけるその役割

NeuroAI quântica e seu papel na busca pela consciência artificial

Quantum neuroAI và vai trò của nó trong việc tìm kiếm ý thức nhân tạo

量子神经人工智能及其在探索人工意识中的作用

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