Scalable ROM-PRUs imply a positive resolution to the Aaronson-Kuperberg unitary synthesis problem, with any such algorithm requiring a classical oracle of input length (2-o(1))log d that rules out existing candidates.
How to Construct Random Unitaries
8 Pith papers cite this work, alongside 123 external citations. Polarity classification is still indexing.
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Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
Random dimension reduction replaces full dimension with max rank in sample complexity for symmetric quantum state properties and connects to but differs from random purification.
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.
Pure-state BNMR is an intrinsic function of the nonzero Schmidt spectrum via dimension reduction, yielding quadratic perturbation response, Haar-random profiles localized at symmetric cuts, and closed forms for rank-2 states.
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.
citing papers explorer
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On Scalable Pseudorandom Unitaries and the Unitary Synthesis Problem
Scalable ROM-PRUs imply a positive resolution to the Aaronson-Kuperberg unitary synthesis problem, with any such algorithm requiring a classical oracle of input length (2-o(1))log d that rules out existing candidates.
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Distributed Property Testing with (Quantum) Carrier Pigeons: Tight Bounds on State Certification
Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
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Random dimension reduction and learning symmetric properties of quantum states
Random dimension reduction replaces full dimension with max rank in sample complexity for symmetric quantum state properties and connects to but differs from random purification.
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Quantum Nonlinear Properties from a Single Measurement Setting
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
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Accessible Quantum Correlations Under Complexity Constraints
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.
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Intrinsic spectral structure of bipartite nonlocal magic resource
Pure-state BNMR is an intrinsic function of the nonzero Schmidt spectrum via dimension reduction, yielding quadratic perturbation response, Haar-random profiles localized at symmetric cuts, and closed forms for rank-2 states.
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Lecture Notes on Replica Tensor Networks for Random Quantum Circuits
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
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Quantum Dynamics in Krylov Space: Methods and Applications
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.