Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality

Bouland, Adam; Fefferman, Bill; Vazirani, Umesh

doi:10.48550/arxiv.1910.14646

Cited by 29 publications

(49 citation statements)

References 23 publications

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“…Since entropy is an important quantity of interest in AdS/CFT, we discuss potential implications of our result for this duality 21 In particular we propose a gedankenexperiment based on our results that gives evidence for certain instances of AdS/CFT having the AdS dictionary be computationally intractable to compute, unless LWE is tractable. A similar result was obtained by Bouland et al [BFV19], in the context of the wormhole growth paradox. Their result also uses cryptographic techniques in the form of pseudorandom quantum states.…”

Section: Applications To Holographysupporting

confidence: 88%

“…That is, in some sense, quantum gravitational systems cannot be simulated efficiently by a quantum computer. Bouland, Fefferman and Vazirani have also explored this challenge to the thesis from the perspective of the wormhole growth paradox using the tools of computational complexity [BFV19]. In particular, they showed that one can prepare computationally pseudorandom states on the boundary CFT.…”

Section: Discussion and Open Questionsmentioning

confidence: 99%

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Estimating the entropy of shallow circuit outputs is hard

Gheorghiu,

Hoban

2020

Preprint

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Calculating relevant entropic quantities of probability distributions and quantum states is a fundamental task in information processing. The decision problem version of estimating the Shannon entropy is the Entropy Difference problem (ED): given descriptions of two circuits, determine which circuit produces more entropy in its output when acting on a uniformly random input. The analogous problem with quantum circuits (QED) is to determine which circuit produces the state with greater von Neumann entropy, when acting on a fixed input state and after tracing out part of the output. Based on plausible complexity-theoretic assumptions, both of these problems are believed to be intractable for polynomial-time quantum computation.In this paper, we investigate the hardness of these problems in the case where the circuits under consideration have logarithmic (ED log and QED log ) and constant depth (ED O(1) and QED O(1) ), respectively. We first show that, relative to an oracle, these problems cannot be as hard as their counterparts with polynomial-size circuits. Furthermore, we show that if a certain type of reduction from QED to QED log exists, it implies that any polynomial-time quantum computation can be performed in log depth. While this suggests that having shallow circuits makes entropy estimation easier, we give indication that the problem remains intractable for polynomial-time quantum computation by proving a reduction from Learning-With-Errors (LWE) to ED O(1) .We then consider a potential application of our results to quantum gravity research via the AdS/CFT correspondence. First, we introduce HQED, a Hamiltonian version of QED, where one is given two local Hamiltonians and asked to estimate the entanglement entropy difference in their ground states. We show that this problem is at least as hard as the circuit version by providing a reduction from QED to HQED. With these results, we then discuss a potential experiment that would make use of AdS/CFT in order to solve LWE efficiently. We conjecture that unless the AdS/CFT bulk to boundary map is exponentially complex, this experiment would violate the intractability assumption of LWE.

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Section: Applications To Holographysupporting

confidence: 88%

Section: Discussion and Open Questionsmentioning

confidence: 99%

Estimating the entropy of shallow circuit outputs is hard

Gheorghiu,

Hoban

2020

Preprint

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“…Finally we would like to discuss observational difficulties in detecting the Python's lunch degrees of freedom (see [50] for some related discussions). In our setup, a computationally bounded observer performs relatively simple operations that are limited to the Hilbert space H i introduced above.…”

Section: Complexity Reconstruction and Ghostly Interactionsmentioning

confidence: 99%

Python's Lunches in Jackiw-Teitelboim gravity with matter

Bak,

Kim,

et al. 2021

Preprint

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We study Python's lunch geometries in the two-dimensional Jackiw-Teitelboim model coupled to a massless scalar field in the semiclassical limit. We show that all extrema including the minimal quantum extremal surface, bulges and appetizers lie inside the horizon. We obtain fully back-reacted general bulk solutions with a massless scalar field, which can be understood as deformations of black holes. The temperatures of the left/right black holes become in general different from each other. Moreover, in the presence of both state and source deformations at the same time, the asymptotic black hole spacetime is further excited from that of the vacuum solution. We provide information-theoretic interpretation of deformed geometries including Python's lunches, minimal quantum extremal surface and appetizers according to the entanglement wedge reconstruction hypothesis. By considering the restricted circuit complexity associated with Python's lunch geometries and the operator complexity of the Petz map reconstructing a code space operation, we show that the observational probability of Python's lunch degrees of freedom from the boundary is exponentially suppressed. Thus, any bulk causality violation effects related with Python's lunch degrees are suppressed nonperturbatively.

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“…This is of theoretical interest as it shows an alternative way for achieving quantum pseudorandomness which is different from current approaches based on post-quantum and computational assumptions. Apart from the cryptography perspective, having a different set of assumptions for PRS and PRU can find potential applications in physics [44]. Another interesting future direction would be to further explore the relationship between unclonability and quantum pseudorandomness that has been initially proposed in [9], relying upon our new results.…”

Section: Conclusion and Discussionmentioning

confidence: 93%

On the Connection Between Quantum Pseudorandomness and Quantum Hardware Assumptions

Doosti¹,

Kashefi²,

Chakraborty³

2021

Preprint

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This paper, for the first time, addresses the questions related to the connections between the quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that the efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for the universally unforgeable qPUF, improving the previous existing constructions that are based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain PRS from the hardware assumptions. Moreover, we provide a sufficient condition (in terms of the diamond norm) that a set of unitaries should have to be a PRU in order to construct a universally unforgeable qPUF, giving yet another novel insight into the properties of the PRUs. Later, as an application of our results, we show that the efficiency of an existing qPUF-based client-server identification protocol can be improved without losing the security requirements of the protocol.

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Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality

Cited by 29 publications

References 23 publications

Estimating the entropy of shallow circuit outputs is hard

Estimating the entropy of shallow circuit outputs is hard

Python's Lunches in Jackiw-Teitelboim gravity with matter

On the Connection Between Quantum Pseudorandomness and Quantum Hardware Assumptions

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