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arXiv:2606.20551

Benchmark of quantum algorithms for ground state preparation in the presence of noise

Daniel Molpeceres, Sirui Lu, J. Ignacio Cirac, Barbara Kraus

quant-phSubmitted Jun 18, 2026• Announced Jun 19, 2026• 0 citations
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Abstract

We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise. Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, we derive the scaling of the achievable relative energy as a function of the noise rate and support these results with numerical simulations. The Hamiltonian exhibits two phases, separated by a quantum phase transition. As expected, the performance of the different algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm, as proposed in [1], becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. We further present numerical results for the quantum approximate optimization algorithm [2], showing that it performs competitively with cooling in the trivial phase but is typically outperformed in the topological regime. Finally, we show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation. The analytical approach developed here, in conjunction with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.

Comments
14+12 pages, 11 figures

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We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise. Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, we derive the scaling of the achievable relative energy as a function of the noise rate and support these results with numerical simulations. The Hamiltonian exhibits two phases, separated by a quantum phase transition. As expected, the performance of the different algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm, as proposed in [1], becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. We further present numerical results for the quantum approximate optimization algorithm [2], showing that it performs competitively with cooling in the trivial phase but is typically outperformed in the topological regime. Finally, we show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation.
The analytical approach developed here, in conjunction with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.
We consider the problem of preparing thermal equilibrium states at finite temperature on quantum computers. Assuming thermalization, we show that states that are locally at thermal equilibrium can be prepared by evolving adiabatically an initial thermal Gibbs state of a simple Hamiltonian with an interpolating time-dependent Hamiltonian, identically to adiabatic ground state preparation. We argue that the entropy density of local density matrices is conserved during the adiabatic evolution in the thermodynamic limit, so that both the entropy and energy of the final state can be computed, and thus the final temperature too. We show that in the presence of hardware noise, the entropy created by the noisy evolution can be precisely benchmarked with mirror circuits. We give numerical evidence that the resulting thermal state preparation protocol is noise-resilient for depolarizing noise, in the sense that the energy-temperature curve measured on a noisy quantum computer is remarkably insensitive to the amplitude of depolarizing noise in the state preparation. We finally propose a protocol to estimate the lack of adiabaticity in a given actual Trotter implementation of the dynamics. We test our protocol on Quantinuum’s H1-1 ion-trap device. We measure that a circuit with 640 two-qubit gates implemented on hardware generates an entropy per site of 0.166 ± 0.0045, giving a benchmark metric for this state preparation. We report the preparation of a thermal state with temperature 2.56 ± 0.26 of the Ising model in size 5 × 4.
Noise and errors are unavoidable in any realistic quantum process, including processes designed to reduce noise and errors in the first place. In particular, quantum thermodynamical protocols for cooling can be significantly affected, potentially altering both their performance and efficiency. Analytically characterizing the impact of such errors becomes increasingly challenging as the system size grows, particularly in deep quantum circuits where noise can accumulate in complex ways. To address this, we introduce a general framework for approximating the cumulative effect of gate-dependent noise using a global depolarizing channel. We specify the regime in which this approximation provides a reliable description of the noisy dynamics. Applying our framework to the thermodynamical two-sort algorithmic cooling (TSAC) protocol, we analytically derive its asymptotic cooling limit in the presence of noise. Using the cooling limit, the optimal cooling performance is achieved by a finite number of qubits--distinguished from the conventional noiseless TSAC protocol by an infinite number of qubits--and fundamental bounds on the achievable ground-state population are derived. This approach opens new avenues for exploring noisy quantum thermodynamical processes.
Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed-matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for instance, on variational and adiabatic principles, or on dissipative state preparation. In this work, we investigate a set of cooling algorithms in a simple, solvable fermionic model that allows us to identify the mechanisms that underlie the cooling process and, also, those that prevent it. We derive analytical expressions for the cooling dynamics, steady states, and cooling rates in the weak-coupling limit. We find that multifrequency and randomized cycle strategies can significantly enhance the performance of the quantum algorithm and circumvent some of the obstacles. We also analyze the effects of noise and evaluate the conditions under which cooling remains feasible. Furthermore, we present optimized cooling protocols that can significantly enhance cooling performance in the presence of noise. Additionally, we compare cooling and dissipative state preparation and show that, in the model analyzed here, cooling generally achieves lower energies and is more resilient to noise.
Simulating many-body systems is one of the most promising applications of near-term quantum computers. An important open question is how to efficiently prepare the ground states of arbitrary fermionic Hamiltonians, especially those with nontrivial topology. Here, we propose an efficient protocol for preparing low-energy states of fermionic Hamiltonians on a noisy bosonic quantum simulator by adiabatic cooling using a simulated bath. We arrange the couplings such that the simulated system and bath together obtain a local fermionic description in which fermionic excitations can be extracted individually, via coherent hopping to the bath, rather than in pairs as would otherwise be required by fermion parity conservation. This approach thus achieves a linear (rather than quadratic) scaling of the cooling rate vs. excitation density at low densities. We show that certain topological phases such as the chiral (non-Abelian) phase of the Kitaev honeycomb model can be prepared efficiently using our protocol. Our protocol performs favorably in the presence of noise, making it suitable for execution on near-term quantum devices. Simulating many-body systems is a promising application of near-term quantum computers; however, preparing ground states of fermions on a quantum computer is challenging, especially if the ground state is topologically non-trivial. The authors propose a protocol to prepare the ground state of arbitrary fermionic Hamiltonians, which is particularly suitable for topological chiral states.
Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative evolution. A recent experiment with a Google superconducting quantum processor [X. Mi , Science 383, 1332 (2024)] demonstrated a cooling algorithm utilizing auxiliary degrees of freedom that are periodically reset to remove quasiparticles from the system, thereby driving it towards its ground state. In this work, we develop a kinetic-theory framework to describe quasiparticle cooling dynamics, and employ it to compare the efficiency of different cooling algorithms. In particular, we introduce a protocol where coupling to auxiliaries is modulated in time to minimize heating processes, and demonstrate that it allows a high-fidelity preparation of ground states in different quantum phases. We verify the validity of the kinetic-theory description by an extensive comparison with numerical simulations for the examples of a one-dimensional transverse-field Ising model, the transverse-field Ising model with an additional integrability-breaking field, and a nonintegrable antiferromagnetic Heisenberg spin ladder. In all cases, we are able to efficiently cool into the many-body ground state. The effects of noise, which limits efficiency of variational quantum algorithms in near-term quantum processors, are investigated through the lens of the kinetic theory: we show how the steady-state quasiparticle populations depend on the noise rate, and we establish maximum noise values for achieving high-fidelity ground states. This work establishes quasiparticle cooling algorithms as a practical, robust method for many-body state preparation on near-term quantum processors.
Quantum computers represent a relatively new and promising development in computing technology. One of the applications of quantum computers is modelling quantum many-body systems, which describe interactions between particles on atomic and subatomic scales. Such systems are highly complex and challenging to model with classical computers due to the vast number of possible states and entanglement of the particles. In this dissertation, we examine the extent to which quantum computers can accelerate the modelling of quantum many-body systems compared to classical computers. Specifically, this dissertation presents research on adiabatic state preparation: a quantum algorithmic technique that uses the adiabatic principle from quantum mechanics to approximate eigenstates. We describe three new techniques that fall within this category and, in certain cases, offer advantages over standard methods. First, we consider cases of ground state preparation for fermionic many-body systems, where standard direct interpolation between the initial and final hamiltonian is hindered by level crossings due to discrete symmetries. As an alternative to direct interpolation, we propose adiabatic paths in a higher-dimensional space, which break the relevant symmetries. Next, we present an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. We show that the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement. Finally, we propose a general, fully gate-based and nonvariational quantum algorithm for counterdiabatic driving. We provide a rigorous quantum gate complexity upper bound in terms of the minimum gap Δ\DeltaΔ around this eigenstate. We find that, in the worst case, the algorithm can be run with at most O~(Δ−(3+o(1))ϵ−(1+o(1)))\tilde O(\Delta^{-(3 + o(1))} \epsilon^{-(1 + o(1))})O~(Δ−(3+o(1))ϵ−(1+o(1))) quantum gates such that a target state fidelity of at least 1−ϵ21 - \epsilon^21−ϵ2 is achieved. In certain cases, the gap dependence can be improved to quadratic.