Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
Quantum algorithms for Gibbs sampling and hitting-time estimation
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in $\log(1/\epsilon)$, where $N$ is the Hilbert space dimension, $\beta$ is the inverse temperature, ${\cal Z}$ is the partition function, and $\epsilon$ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on $1/\epsilon$ and quadratically improves the dependence on $\beta$ of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix $P$, it runs in time almost linear in $1/(\epsilon \Delta^{3/2})$, where $\epsilon$ is the absolute precision in the estimation and $\Delta$ is a parameter determined by $P$, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on $1/\epsilon$ and $1/\Delta$ of the analog classical algorithm for hitting-time estimation. Both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.
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quant-ph 3representative citing papers
A variational framework assisted by matrix product states prepares approximate thermal Gibbs states for 1D lattices up to 30 sites and 2D lattices up to 6x6 using up to 44 qubits, with a demonstration on IBM Heron hardware.
Adiabatic evolution prepares local thermal states from initial Gibbs states while conserving entropy density in the thermodynamic limit, with mirror-circuit benchmarking of hardware noise entropy demonstrated experimentally on a 5x4 Ising model.
citing papers explorer
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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
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Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States
A variational framework assisted by matrix product states prepares approximate thermal Gibbs states for 1D lattices up to 30 sites and 2D lattices up to 6x6 using up to 44 qubits, with a demonstration on IBM Heron hardware.
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Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers
Adiabatic evolution prepares local thermal states from initial Gibbs states while conserving entropy density in the thermodynamic limit, with mirror-circuit benchmarking of hardware noise entropy demonstrated experimentally on a 5x4 Ising model.