Retrieving information from a black hole using quantum machine learning

Leone, Lorenzo; Oliviero, Salvatore F. E.; Stefano, Piemontese,; True, Sarah; Hamma, Alioscia

doi:10.1103/physreva.106.062434

Cited by 16 publications

(4 citation statements)

References 79 publications

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“…Therefore, in the case of a t-doped Clifford circuit, there is no distinction between the stabilizer entropy of V |0〉 and |V 〉 for sufficiently large d. It is worth noting that the relation of 4-OTOC fluctuations with the averaged 8-OTOC has been studied in Ref. [44]. In contrast, here we describe the relationship to 2-Renyi entropy.…”

Section: The Stabilizer Renyi Entropy and Otocmentioning

confidence: 88%

Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

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Section: The Stabilizer Renyi Entropy and Otocmentioning

confidence: 88%

Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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“…The complexity gap between the efficient classical simulation of Clifford unitary circuits, and that of generic unitaries suggests it may be instructive to study the controlled introduction of non-Clifford gates into structured circuits. To that end, a framework known as doped random circuits proved to be useful in gradually obtaining unitary designs via magic doping [45,46], and in capturing the role of magic in quantum chaos [44,[47][48][49][50][51] and many-body entanglement spectrum statistics [52,53].…”

Section: Doping Random Quantum Circuits With Magical Resourcesmentioning

confidence: 99%

Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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Recently, cat states have been used to heuristically improve the runtime of a classical simulator of quantum circuits based on the diagrammatic ZX-calculus. Here we investigate the use of cat-state injection within the quantum circuit model. We explore a family of cat states, $\left| \mathrm{cat}_m^* \right>$, and describe circuit gadgets using them to concurrently inject non-stabilizerness (also known as magic) and entanglement into any quantum circuit. We provide numerical evidence that cat-state injection does not lead to speed-up in classical simulation. On the other hand, we show that our gadgets can be used to widen the scope of compelling applications of cat states. Specifically, we show how to leverage them to achieve savings in the number of injected qubits, and also to induce scrambling dynamics in otherwise non-entangling Clifford circuits in a controlled manner.

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“…Scrambling has flourished by connecting diverse areas, including quantum many-body physics ( 3 – 5 ), black hole physics ( 7 – 12 ), and quantum information ( 7 ). It has become a prevalent ingredient in many information processing problems found in quantum machine learning ( 13 – 17 ), shadow tomography with classical shadows ( 18 – 23 ), quantum error correction ( 24 , 25 ), encryption ( 26 ), and emergent quantum state designs ( 27 ).…”

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confidence: 99%

Resource theory of quantum scrambling

Garcia

Jaffe

2023

Proc. Natl. Acad. Sci. U.S.A.

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Quantum chaos has become a cornerstone of physics through its many applications. One trademark of quantum chaotic systems is the spread of local quantum information, which physicists call scrambling. In this work, we introduce a mathematical definition of scrambling and a resource theory to measure it. We also describe two applications of this theory. First, we use our resource theory to provide a bound on magic, a potential source of quantum computational advantage, which can be efficiently measured in experiment. Second, we also show that scrambling resources bound the success of Yoshida’s black hole decoding protocol.

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Retrieving information from a black hole using quantum machine learning

Cited by 16 publications

References 79 publications

Quantifying non-stabilizerness via information scrambling

Quantifying non-stabilizerness via information scrambling

Non-stabilizerness and entanglement from cat-state injection

Resource theory of quantum scrambling

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