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.
Efficient thermalization and universal quantum computing with quantum Gibbs samplers
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abstract
The preparation of thermal states of matter is a crucial task in quantum simulation. In this work, we prove that a recently introduced, efficiently implementable dissipative evolution thermalizes to the Gibbs state in time scaling polynomially with system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. Furthermore, we show the efficient adiabatic preparation of the associated purifications or ``thermofield double'' states. These results establish the efficient preparation of high-temperature Gibbs states and their purifications. In the low-temperature regime, we show that implementing this family of dissipative evolutions for inverse temperatures polynomial in the system's size is computationally equivalent to polynomial time quantum computations. On a technical level, for high temperatures, our proof makes use of the mapping of the generator of the evolution into a Hamiltonian, and then connecting its convergence to that of the infinite temperature limit. For low temperature, we instead perform a perturbation at zero temperature and resort to circuit-to-Hamiltonian mappings akin to the proof of universality of quantum adiabatic computing. Taken together, our results show that a family of quasi-local dissipative evolutions efficiently prepares a large class of quantum many-body states of interest, and has the potential to mirror the success of classical Monte Carlo methods for quantum many-body systems.
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representative citing papers
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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.
Introduces local-circuit approximations to quasilocal dissipative processes for efficient, provably convergent quantum Gibbs sampling at high temperatures.
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
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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.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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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.
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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.
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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.