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Journal of the Korean Physical Society

Designing minimalistic variational quantum ansatz inspired by algorithmic cooling

Soyoung Shin, Ha Eum Kim, Jaewan Kim, Hyeonjun Yeo, Wonho Jhe, Kabgyun Jeong

Published Mar 30, 2026• 0 citations
Publisher

Abstract

Abstract Variational quantum algorithms offer a practical route to low-energy state preparation on near-term hardware, but performance depends strongly on ansatz design. We introduce the Heat-Exchange (HE) ansatz, a compact circuit family inspired by heat-bath algorithmic cooling and built from a tunable exchange interaction between a system qubit and an auxiliary bath qubit. On superconducting processors the exchange evolution $$U_{\textrm{HE}}(\theta )=\exp [-i\theta (XX+YY)/2]$$ U HE ( θ ) = exp [ - i θ ( X X + Y Y ) / 2 ] is implemented digitally as a shallow compiled gate sequence, requiring no mid-circuit reset, measurement, or feedback. We benchmark HE on two complementary tasks: weighted MaxCut on random complete graphs (noise-free simulation and hardware runs on with readout error mitigation) and a one-dimensional Heisenberg chain with a pinned site within a dissipative-VQE-style workflow (noise-free simulation). HE increases the probability of sampling the best cut compared with a hardware-efficient baseline and QAOA under limited evaluation budgets and yields ground-state energies with sub-percent relative error for the impurity chain. These results highlight exchange-driven cooling blocks as compact, parameter-efficient, hardware-compatible primitives for near-term variational workflows.

DOI
10.1007/s40042-026-01627-3

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Abstract Variational quantum algorithms offer a practical route to low-energy state preparation on near-term hardware, but performance depends strongly on ansatz design. We introduce the Heat-Exchange (HE) ansatz, a compact circuit family inspired by heat-bath algorithmic cooling and built from a tunable exchange interaction between a system qubit and an auxiliary bath qubit. On superconducting processors the exchange evolution UHE(θ)=exp⁡[−iθ(XX+YY)/2]U_{\textrm{HE}}(\theta )=\exp [-i\theta (XX+YY)/2]UHE​(θ)=exp[−iθ(XX+YY)/2] U HE ( θ ) = exp [ - i θ ( X X + Y Y ) / 2 ] is implemented digitally as a shallow compiled gate sequence, requiring no mid-circuit reset, measurement, or feedback. We benchmark HE on two complementary tasks: weighted MaxCut on random complete graphs (noise-free simulation and hardware runs on with readout error mitigation) and a one-dimensional Heisenberg chain with a pinned site within a dissipative-VQE-style workflow (noise-free simulation). HE increases the probability of sampling the best cut compared with a hardware-efficient baseline and QAOA under limited evaluation budgets and yields ground-state energies with sub-percent relative error for the impurity chain. These results highlight exchange-driven cooling blocks as compact, parameter-efficient, hardware-compatible primitives for near-term variational workflows.
This study introduces a novel minimalistic variational quantum ansatz inspired by algorithmic cooling principles. The proposed Heat Exchange algorithmic cooling ansatz (HE ansatz) facilitates efficient population redistribution without requiring bath resets, simplifying implementation on noisy intermediate-scale quantum (NISQ) devices. The HE ansatz achieves superior approximation ratios with the complete network \textsc{Maxcut} optimization problem compared to the conventional Hardware efficient and QAOA ansatz. We also proposed a new variational algorithm that utilize HE ansatz to compute the ground state of impure dissipative-system variational quantum eigensolver (dVQE) which achieved a sub-1%1\%1% error in ground-state energy calculations of the 1D Heisenberg chain with impurity and successfully simulates the edge effect of impure spin chain, highlighting its potential for applications in quantum many-body physics. These results underscore the compatibility of the ansatz with hardware-efficient implementations, offering a scalable approach for solving complex quantum problems in disordered and open quantum systems.
The performance of the variational quantum eigensolver depends critically on the choice of ansatz. In this work, we experimentally evaluate the emergent-coupling-based ansatz (ECBA), a physically motivated variational ansatz for disordered systems. The ECBA is based on a renormalization (semi-)group approach to determine the dominant effective couplings, resulting in shallow circuits that capture the essential long-range entanglement structure while balancing local correlations. We implement the ECBA on superconducting quantum processors and benchmark it on disordered Heisenberg chain models. Using classically pre-optimized parameters and error mitigation techniques, we study systems of up to 30 qubits and observe an experimental relative energy accuracy of 96.41% for the largest system. Furthermore, we find that the ECBA can be efficiently embedded on hardware with two-dimensional square-lattice connectivity. We compare to commonly used hardware efficient ansätze and observe that the ECBA achieves significantly higher accuracy at a similar gate count.
Variational quantum algorithms often adapt the ansätze (ansatz) to the target Hamiltonian, leading to deep or hardware-incompatible circuits. In this work we demonstrate an opposite approach: choosing a hardware-efficient CNOT-ladder ansatz and calibrating the Hamiltonian to compensate for its expressibility to solve ground-state energy problem of 100+ site lattice on real quantum computer. This ansatz-calibrated Hamiltonian framework enables two key advantages: (1) it allows restructuring the algorithm into smaller sub-problems which can independently solved off-line classically, leaving quantum computer tasked with recombining partial solutions into full state-vector with fewer parameters to optimize and (2) it leverages circuit-specific error statistics to de-noise observable readouts with nominal noise-mitigation overhead. We simulate the spin-1/2 antiferromagnetic Heisenberg model over a 103-site flat Kagome lattice using IBM’s Heron r1 and r2 processors. The obtained per-site ground-state energy of −0.4172 J-0.4172\,J−0.4172J , which approaches the benchmark −0.4386 J-0.4386\,J−0.4386J after open boundary correction and approximate error mitigation. Our experiments reveal a peculiar distribution of bond energies when the ansatz is executed on the quantum processor, in contrast to its classical simulation, which merits further investigation.
Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve a potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely used hardware-efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that, compared with conventional hardware-efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise and hence is more likely to be implemented on near-term devices.
Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.
We develop a hardware-efficient ansatz for variational optimization, derived from existing ansatze in the literature, that parametrizes subsets of all interactions in the Cost Hamiltonian in each layer. We treat gate orderings as a variational parameter and observe that doing so can provide significant performance boosts in experiments. We carried out experimental runs of a compilation-optimized implementation of fully-connected Sherrington-Kirkpatrick Hamiltonians on a 50-qubit linear-chain subsystem of Rigetti’s Aspen-M-3 transmon processor. Our results indicate that, for the best circuit designs tested, the average performance at optimized angles and gate orderings increases with circuit depth (using more parameters), despite the presence of a high level of noise. We report performance significantly better than using a random guess oracle for circuits involving up to ≃ 5, 000 two-qubit and ≃ 5, 000 one-qubit native gates. We additionally discuss various takeaways of our results toward more effective utilization of current and future quantum processors for optimization.