A factorization of the parent Hamiltonian into noncommutative first-order operators enables a walk-free QSVT algorithm with quadratic gap improvement for preparing purified Gibbs states under exact KMS detailed balance.
hub Canonical reference
Quantum Thermal State Preparation
Canonical reference. 83% of citing Pith papers cite this work as background.
25
Pith papers citing it
Background
83% of classified citations
abstract
Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged. Monte Carlo-style quantum Gibbs samplers have emerged as an alternative, but prior proposals have been unsatisfactory due to technical obstacles rooted in energy-time uncertainty. We introduce simple continuous-time quantum Gibbs samplers that overcome these obstacles by efficiently simulating Nature-inspired quantum master equations (Lindbladians). In addition, we construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states (called thermal field double states in high-energy physics) of rapidly thermalizing systems; this algorithm also benefits from a quantum walk speedup. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time (or spectral gap) of the relevant Lindbladian. We complete the first rigorous proof of finite-time thermalization for physically derived Lindbladians by developing a general analytic framework for nonasymptotic secular approximation and approximate detailed balance. Given the success of classical Markov chain Monte Carlo (MCMC) algorithms and the ubiquity of thermodynamics, we anticipate that quantum Gibbs sampling will become indispensable in quantum computing.
hub tools
citation-role summary
background 5
method 1
citation-polarity summary
representative citing papers
Quantum algorithm with rigorous truncation error bounds and spectral gap guarantees for free energy estimation in finite-temperature Coulomb quantum systems via Markovian Gibbs sampling.
A new rigorous Gibbs sampling method is given for bosonic models by proving that their dissipative generators have positive spectral gaps, enabling efficient quantum preparation of thermal states for Bose-Hubbard Hamiltonians.
Symmetry classification of measurement-inclusive fermionic dynamics with equivalence between many-body and single-particle schemes, plus post-selection-free adaptive circuits for topological states in four classes.
Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
Introduces gauge-invariant QMETTS using mutually unbiased physical bases derived from stabilizer formalism for Z2 LGT at finite T and density, with single-shot sampling shown near-optimal and numerical validation in 1+1D.
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
Quantum Gibbs samplers thermalize to Gibbs states in polynomial time at high temperatures for Lieb-Robinson bounded Hamiltonians and are BQP-complete at low temperatures via circuit-to-Hamiltonian reductions.
ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
The strong Markov property holds if and only if the state has correlation decay for suitable observables, enabling single-copy multi-observable estimation and forcing local marginals of such states to be close or well-separated.
Proves KMS detailed balance on the transition part of an approximate Lindbladian suffices for the fixed point to approach the Gibbs state arbitrarily closely regardless of Lamb shift structure, giving O(ε^{-1}) thermalization complexity.
High-temperature Gibbs states with arbitrary external fields admit O(log n) quantum mixing via a detailed-balance Lindbladian and exhibit classical sampling hardness for β < 1.
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
Sudden quenches in a pair of coupled oscillators produce exact or approximate thermalization of a quantum harmonic oscillator to arbitrary temperatures via solvable equations on the Gaussian covariance matrix.
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.
Quantum trajectory algorithm achieves additive O(T + log(1/ε)) query complexity for simulating dissipative Lindbladians.
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.
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
A simplified version of quantum dynamical entropy is introduced, its growth rate is computed from correlation functions in the thermodynamic limit, and a Planckian bound on the rate is conjectured.
Introduces local-circuit approximations to quasilocal dissipative processes for efficient, provably convergent quantum Gibbs sampling at high temperatures.
A quantum MCMC algorithm leveraging the MBL phase and its thermal-to-localized transition to tune acceptance rates and sample thermal distributions on programmable quantum simulators for combinatorial optimization.
Cholesky-based circuit synthesis methods for arbitrary and sparse mixed quantum states with approximation options for lower complexity.
A comprehensive review of scaling paths for superconducting quantum computers, with resource and sensitivity analyses for utility-scale applications under realistic error distributions.
citing papers explorer
-
Accelerating quantum Gibbs sampling without quantum walks
A factorization of the parent Hamiltonian into noncommutative first-order operators enables a walk-free QSVT algorithm with quadratic gap improvement for preparing purified Gibbs states under exact KMS detailed balance.
-
Computing the free energy of quantum Coulomb gases and molecules via quantum Gibbs sampling
Quantum algorithm with rigorous truncation error bounds and spectral gap guarantees for free energy estimation in finite-temperature Coulomb quantum systems via Markovian Gibbs sampling.
-
Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
A new rigorous Gibbs sampling method is given for bosonic models by proving that their dissipative generators have positive spectral gaps, enabling efficient quantum preparation of thermal states for Bose-Hubbard Hamiltonians.
-
Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
Symmetry classification of measurement-inclusive fermionic dynamics with equivalence between many-body and single-particle schemes, plus post-selection-free adaptive circuits for topological states in four classes.
-
Typical Mixing and Rare-State Bottlenecks in Open Quantum Systems
Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
-
Gauge-invariant QMETTS with mutually unbiased physical bases for $Z_2$ lattice gauge theories at finite temperature and density
Introduces gauge-invariant QMETTS using mutually unbiased physical bases derived from stabilizer formalism for Z2 LGT at finite T and density, with single-shot sampling shown near-optimal and numerical validation in 1+1D.
-
Exponential Lindbladian fast forwarding and exponential amplification of certain Gibbs state properties
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
-
Efficient thermalization and universal quantum computing with quantum Gibbs samplers
Quantum Gibbs samplers thermalize to Gibbs states in polynomial time at high temperatures for Lieb-Robinson bounded Hamiltonians and are BQP-complete at low temperatures via circuit-to-Hamiltonian reductions.
-
Estimating Green's functions with a robust quantum Arnoldi method
ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.
-
Preparing High-Fidelity Thermofield Double States
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
-
Note on Strong Quantum Markov Properties
The strong Markov property holds if and only if the state has correlation decay for suitable observables, enabling single-copy multi-observable estimation and forcing local marginals of such states to be close or well-separated.
-
Overcoming the Lamb Shift in System-Bath Interaction Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interactions
Proves KMS detailed balance on the transition part of an approximate Lindbladian suffices for the fixed point to approach the Gibbs state arbitrarily closely regardless of Lamb shift structure, giving O(ε^{-1}) thermalization complexity.
-
Rapid mixing for high-temperature Gibbs states with arbitrary external fields
High-temperature Gibbs states with arbitrary external fields admit O(log n) quantum mixing via a detailed-balance Lindbladian and exhibit classical sampling hardness for β < 1.
-
Quantum Gibbs sampling through the detectability lemma
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
-
Thermalization from quenching in coupled oscillators
Sudden quenches in a pair of coupled oscillators produce exact or approximate thermalization of a quantum harmonic oscillator to arbitrary temperatures via solvable equations on the Gaussian covariance matrix.
-
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.
-
Quantum algorithms based on quantum trajectories
Quantum trajectory algorithm achieves additive O(T + log(1/ε)) query complexity for simulating dissipative Lindbladians.
-
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.
-
Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
-
Planckian bound on quantum dynamical entropy
A simplified version of quantum dynamical entropy is introduced, its growth rate is computed from correlation functions in the thermodynamic limit, and a Planckian bound on the rate is conjectured.
-
Efficient Quantum Gibbs Sampling with Local Circuits
Introduces local-circuit approximations to quasilocal dissipative processes for efficient, provably convergent quantum Gibbs sampling at high temperatures.
-
Quantum Markov chain Monte Carlo method with programmable quantum simulators
A quantum MCMC algorithm leveraging the MBL phase and its thermal-to-localized transition to tune acceptance rates and sample thermal distributions on programmable quantum simulators for combinatorial optimization.
-
Quantum circuit synthesis for the preparation of arbitrary and highly sparse mixed quantum states
Cholesky-based circuit synthesis methods for arbitrary and sparse mixed quantum states with approximation options for lower complexity.
-
How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits
A comprehensive review of scaling paths for superconducting quantum computers, with resource and sensitivity analyses for utility-scale applications under realistic error distributions.
-
Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
Review of quantum computing methods and potential for non-ground-state quantum chemistry including reaction dynamics, mechanisms, and finite temperatures.