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.
Hermitian and non-Hermitian thermal Hamiltonians
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abstract
Thermal density matrices can be described by a pure quantum state within the thermofield formalism. Here we show how to construct a class of Hamiltonians realizing a thermofield state as their ground state. These Hamiltonians are frustration-free, and can be Hermitian or non-Hermitian, allowing one to use ground-state methods to understand the thermodynamic properties of the system. In particular this approach gives an explicit mapping of thermal phase transitions into quantum phase transitions. In the non-Hermitian case, the quantum phase transition is not accompanied by a change in the spectrum of the Hamiltonian, which remains gapped. We illustrate these ideas for the classical 2D Ising model.
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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.
citing papers explorer
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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.
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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.