Quantum Gibbs State Preparation

Short answer: A Gibbs state is the thermal state of a quantum system at a given temperature. Preparing it on a quantum computer is useful for simulating matter and for estimating quantities such as partition functions. Recent theory papers study quantum Gibbs samplers, algorithms modelled on how a system thermalizes through contact with a heat bath, and prove that they work efficiently in some regimes. The results are proofs about algorithms, with the strongest ones at high temperature, and none is a hardware demonstration.

Why thermal states matter

A 2023 arXiv paper (2303.18224) says preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. It notes that, despite the hope for practical quantum advantage in simulation, popular state preparation approaches have been challenged, and that Monte Carlo-style quantum Gibbs samplers have emerged as an alternative, though earlier proposals were unsatisfactory because of technical obstacles rooted in energy-time uncertainty. The authors say that Gibbs sampling approaches the problem in the way a system in nature thermalizes when coupled to a thermal bath, so the line between the physical process and the algorithm is blurred.

Continuous-time Gibbs samplers

The 2023 paper introduces simple continuous-time quantum Gibbs samplers that overcome those obstacles by efficiently simulating quantum master equations known as Lindbladians. They also construct what they describe as the first provably accurate and efficient algorithm for preparing certain purified Gibbs states, called thermal field double states, for rapidly thermalizing systems, with a quantum walk speedup. The cost has a provable dependence on temperature, accuracy and the mixing time, or spectral gap, of the Lindbladian. They complete what they call the first rigorous proof of finite-time thermalization for physically derived Lindbladians. Given the success of classical Markov chain Monte Carlo, the authors anticipate that quantum Gibbs sampling will become indispensable in quantum computing, which is their expectation and not a result.

Efficiency at high and low temperature

A 2024 arXiv paper (2403.12691) studies a dissipative evolution introduced in earlier work. It proves that, at high enough temperatures, the evolution thermalizes to the Gibbs state in time scaling polynomially with system size, for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. It also shows efficient adiabatic preparation of the associated purifications, called thermofield double states. At low temperature, the authors show that implementing this family of evolutions for inverse temperatures polynomial in system size is computationally equivalent to standard quantum computations, which means it is not expected to be easy in general. They state the potential to mirror the success of classical Monte Carlo methods for many-body states.

Rapid mixing

A paper in Physical Review Letters tightens the high-temperature result. It proves that, at high enough temperatures, the same type of evolution reaches the Gibbs state in time scaling logarithmically with system size, for Hamiltonians satisfying the Lieb-Robinson bound, including long-range systems. The authors say these are the first results rigorously establishing rapid mixing for high-temperature quantum Gibbs samplers, which gives the fastest possible speed of thermalization in the many-body setting. They apply it to estimating partition functions at high temperature, showing improved performance over previous classical and quantum algorithms.

What this does not tell you

These are proofs under stated conditions, mostly at high temperature, where the physics is easier. The low-temperature result shows the problem can be as hard as general quantum computation. None of the papers reports running the algorithms on a quantum computer, and a speedup in a proof does not tell you what the cost would be on real hardware.

FAQ

What is a Gibbs state?

The thermal state of a system at a given temperature.

What is a quantum Gibbs sampler?

An algorithm that mimics thermalization through contact with a heat bath to prepare the Gibbs state.

When is it efficient?

The papers prove efficiency at high enough temperature for Hamiltonians satisfying a Lieb-Robinson bound.

What about low temperature?

One paper shows the task is computationally equivalent to standard quantum computations.

Has it been run on hardware?

These papers do not report that.