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arxiv: 2403.12691 · v3 · submitted 2024-03-19 · 🪐 quant-ph · math-ph· math.MP

Efficient thermalization and universal quantum computing with quantum Gibbs samplers

Cambyse Rouz\'e , Daniel Stilck Fran\c{c}a , \'Alvaro M. Alhambra This is my paper

Pith reviewed 2026-05-24 02:30 UTC · model grok-4.3

classification 🪐 quant-ph math-phmath.MP
keywords quantum Gibbs samplersthermalizationGibbs statesdissipative evolutionLieb-Robinson boundsthermofield double statesquantum adiabatic computing
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The pith

Dissipative quantum evolutions prepare high-temperature Gibbs states in polynomial time for local Hamiltonians and become universal for quantum computation at low temperatures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that a family of efficiently implementable dissipative evolutions thermalizes to the Gibbs state of any Hamiltonian obeying a Lieb-Robinson bound, such as local lattice models, with time scaling only polynomially in system size once temperature is high enough. It further shows that the associated thermofield double purifications can be prepared adiabatically with the same efficiency. At low temperatures the same evolutions, when run for polynomially large inverse temperatures, are computationally equivalent to arbitrary polynomial-time quantum circuits. Together these statements establish a concrete route to preparing thermal many-body states on quantum hardware and link the samplers directly to the power of quantum computation.

Core claim

A recently introduced family of quasi-local dissipative evolutions converges to the Gibbs state in time polynomial in system size at sufficiently high temperatures for every Hamiltonian satisfying a Lieb-Robinson bound. The same family permits efficient adiabatic preparation of the corresponding thermofield double states. In the low-temperature regime, implementing the evolutions for inverse temperatures that scale polynomially with system size is computationally equivalent to polynomial-time quantum computation.

What carries the argument

The generator of the dissipative evolution, mapped either to a Hamiltonian whose mixing time connects to the infinite-temperature limit (high-T case) or via zero-temperature perturbation plus circuit-to-Hamiltonian reduction (low-T case).

If this is right

  • High-temperature Gibbs states of local Hamiltonians become preparable on quantum devices with resources polynomial in system size.
  • Thermofield double states can be obtained adiabatically from the same family of evolutions.
  • The samplers supply a quantum counterpart to classical Monte Carlo sampling for thermal states.
  • At low temperature the samplers can execute any quantum algorithm whose circuit depth is polynomial.
  • Efficient implementation of the evolutions would therefore yield a universal model of quantum computation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the high-temperature polynomial bound can be extended downward by improving the temperature threshold, the method would cover a wider range of physically relevant regimes.
  • The low-temperature equivalence suggests that any improvement in the sampler's implementation would immediately translate into new quantum algorithms.
  • Hybrid algorithms that switch between the dissipative evolution and standard circuit primitives could be explored to optimize thermal-state preparation.
  • Small-system numerical checks of the predicted polynomial scaling could be performed on existing quantum hardware to test the high-temperature regime.

Load-bearing premise

Temperature must be high enough that the convergence time of the dissipative evolution stays polynomial in system size.

What would settle it

An explicit local Hamiltonian and inverse temperature where the thermalization time of the sampler scales superpolynomially with system size would falsify the polynomial-time claim.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that a recently introduced family of efficiently implementable dissipative evolutions (quantum Gibbs samplers) thermalizes to the Gibbs state in time polynomial in system size at sufficiently high temperatures for Hamiltonians satisfying Lieb-Robinson bounds (e.g., local lattice Hamiltonians). It further claims efficient adiabatic preparation of the associated thermofield double (purification) states. At low temperatures, implementing these evolutions for inverse temperatures polynomial in system size is shown to be computationally equivalent to polynomial-time quantum computation. The high-T proof maps the dissipative generator to a Hamiltonian and connects its convergence to the infinite-temperature limit; the low-T proof uses zero-temperature perturbation plus circuit-to-Hamiltonian mappings.

Significance. If the central claims hold with the required quantitative bounds, the results would establish efficient quantum methods for preparing high-temperature Gibbs states and their purifications, providing a quantum analog to classical Monte Carlo sampling for many-body systems. The low-T equivalence to BQP would further demonstrate that these dissipative processes can realize universal quantum computation, strengthening the connection between open-system dynamics and quantum complexity.

major comments (2)
  1. [High-temperature proof strategy (abstract)] High-temperature analysis (abstract and the mapping strategy): the claim of poly(N) thermalization time requires that the spectral gap of the mapped Hamiltonian remains Ω(1) (or at worst 1/poly(log N)) uniformly in N once T is high enough. The continuity argument from the infinite-T limit must therefore supply an explicit lower bound on this gap together with the scaling of the temperature threshold with N, local dimension, and interaction strength; no such quantitative control is visible in the provided description, which is load-bearing for the polynomial mixing guarantee.
  2. [Low-temperature proof strategy (abstract)] Low-temperature analysis (abstract and perturbation strategy): the claimed equivalence to polynomial-time quantum computation via zero-T perturbation plus circuit-to-Hamiltonian reduction requires explicit error bounds showing that the perturbation remains valid with only polynomial overhead in N and β. The abstract-level sketch supplies no such bounds or verification that the reduction preserves the polynomial scaling, which is load-bearing for the universality claim.
minor comments (1)
  1. The abstract would benefit from a one-sentence statement of the precise form of the dissipative generator (Lindblad operators) used in the Gibbs sampler construction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below, providing references to the relevant sections of the full paper where the quantitative details are derived.

read point-by-point responses

  1. Referee: [High-temperature proof strategy (abstract)] High-temperature analysis (abstract and the mapping strategy): the claim of poly(N) thermalization time requires that the spectral gap of the mapped Hamiltonian remains Ω(1) (or at worst 1/poly(log N)) uniformly in N once T is high enough. The continuity argument from the infinite-T limit must therefore supply an explicit lower bound on this gap together with the scaling of the temperature threshold with N, local dimension, and interaction strength; no such quantitative control is visible in the provided description, which is load-bearing for the polynomial mixing guarantee.

    Authors: We agree that the abstract provides only a high-level sketch and does not include the explicit quantitative bounds. The full manuscript (Sections 3–4) derives these via the mapping of the dissipative generator to a Hamiltonian H_β. Using a continuity argument from the infinite-temperature limit (where the gap is explicitly 1), we prove that for inverse temperatures β below a threshold β* = O(1/(d J log d))—independent of system size N—the gap of H_β is bounded below by a constant Ω(1). This directly yields the claimed polynomial mixing time. We will revise the abstract to include a one-sentence summary of this gap lower bound and the N-independent temperature threshold. revision: yes

  2. Referee: [Low-temperature proof strategy (abstract)] Low-temperature analysis (abstract and perturbation strategy): the claimed equivalence to polynomial-time quantum computation via zero-T perturbation plus circuit-to-Hamiltonian reduction requires explicit error bounds showing that the perturbation remains valid with only polynomial overhead in N and β. The abstract-level sketch supplies no such bounds or verification that the reduction preserves the polynomial scaling, which is load-bearing for the universality claim.

    Authors: We agree the abstract sketch omits the error analysis. The full manuscript (Section 5) provides the details: a zero-temperature perturbation shows the finite-β dissipative dynamics approximates the zero-T evolution with error O(1/β) (controlled uniformly in N for local Hamiltonians), while the circuit-to-Hamiltonian reduction produces an instance whose size is polynomial in N and β. Since the low-temperature regime of interest takes β polynomial in N, the overall overhead remains polynomial, establishing the BQP equivalence in both directions. We will add a clarifying sentence to the abstract summarizing these polynomial error bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation connects the dissipative generator to the infinite-temperature limit via Hamiltonian mapping and to zero-temperature circuit-to-Hamiltonian constructions via perturbation; these are external mathematical reductions to known limits rather than self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations that collapse the claim. The abstract and reader summary exhibit no equations or steps where a claimed prediction equals its input by construction, and the central polynomial-time guarantee rests on independent spectral-gap control arguments outside the paper's fitted quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the existence of a recently introduced family of dissipative evolutions, the Lieb-Robinson bound for the Hamiltonian, and standard circuit-to-Hamiltonian mappings from the adiabatic computing literature; no free parameters or new invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Hamiltonians satisfy a Lieb-Robinson bound (local Hamiltonians on a lattice)
    Invoked to guarantee that the thermalization time scales polynomially with system size.
  • domain assumption The dissipative evolution generator can be mapped to an effective Hamiltonian whose relaxation connects to the infinite-temperature limit
    Central technical step for the high-temperature proof.

pith-pipeline@v0.9.0 · 5776 in / 1556 out tokens · 28417 ms · 2026-05-24T02:30:25.475123+00:00 · methodology

discussion (0)

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Forward citations

Cited by 5 Pith papers

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Reference graph

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    The Hamiltonian of the system in a region A ⊂ Λ is then defined as the sum over interactions included in A: HA := X X⊆A hX

    Local Hamiltonians and Lieb-Robinson bounds Next, we consider a quantum spin system on a D-dimensional finite lattice Λ ≡ [0, L]D, with n := |Λ| = ( L + 1)D, and a local Hamiltonian H on the lattice, defined through a function that maps any non-empty finite set X ⊂ Λ to a self-adjoint element hX supported in X with maxX ∥hX ∥∞ ≤ h. The Hamiltonian of the ...

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