Retrieving information from a black hole using quantum machine learning

Abstract

In a seminal paper[JHEP09(2007)120], Hayden and Preskill showed that information can be retrieved from a black hole that is sufficiently scrambling, assuming that the retriever has perfect control of the emitted Hawking radiation and perfect knowledge of the internal dynamics of the black hole. In this paper, we show that for $t-$doped Clifford black holes - that is, black holes modeled by random Clifford circuits doped with an amount $t$ of non-Clifford resources - an information retrieval decoder can be learned with fidelity scaling as $\exp (-\alpha t)$ using quantum machine learning while having access only to out-of-time-order correlation functions. We show that the crossover between learnability and non-learnability is driven by the amount of non-stabilizerness present in the black hole and sketch a different approach to quantum complexity.

References in corpus (29)

• Black holes as mirrors: quantum information in random subsystems
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Stabilizer Rényi entropy
• Effect of barren plateaus on gradient-free optimization
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Jarzynski-like equality for the out-of-time-ordered correlator
• Quantum chaos and thermalization in gapped systems
• Large gradients via correlation in random parameterized quantum circuits
• Variational Quantum State Eigensolver
• Barren plateaus preclude learning scramblers
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Optimizing quantum process tomography with unitary 2-designs
• Measuring magic on a quantum processor
• Quantum Chaos is Quantum
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Transitions in entanglement complexity in random quantum circuits by measurements
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Transitions in Entanglement Complexity in Random Circuits
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• Quantum scrambling and the growth of mutual information
• Isospectral twirling and quantum chaos
• Random Matrix Theory of the Isospectral twirling
• Hayden-Preskill protocol and decoding Hawking radiation at finite temperature
• Quantum self-learning Monte Carlo with quantum Fourier transform sampler

Cited by in corpus (18)

• Resource theory of quantum scrambling
• Stabilizer entropy dynamics after a quantum quench
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Unscrambling Quantum Information with Clifford decoders
• Stabilizer entropy in non-integrable quantum evolutions
• Phase transition in Stabilizer Entropy and efficient purity estimation
• Magic of quantum hypergraph states
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Quantifying non-stabilizerness via information scrambling
• Stabilizer entropy of quantum tetrahedra
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Maximal Magic for Two-qubit States
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Non-stabilizerness and entanglement from cat-state injection
• Magic of discrete lattice gauge theories
• Harvesting stabilizer entropy and non-locality from a quantum field
• Disentangling quantum autoencoder