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arXiv:2501.16776

Designing Minimalistic Variational Quantum Ansatz Inspired by Algorithmic Cooling

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

Published Jan 28, 2025• 0 citations
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Abstract

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-$1\%$ 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.

DOI
10.48550/arxiv.2501.16776

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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.
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.
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.
Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are two main approaches for VQEs: problem-agnostic and problem-specific. For problem-agnostic methods, they often suffer from trainability issues. For problem-specific methods, their performance usually relies upon the choice of initial reference states, which are often hard to determine. In this paper, we propose an entanglement-variational hardware-efficient ansatz (EHA), and numerically compare it with some widely used ansatzes by solving benchmark problems in quantum many-body systems and quantum chemistry. Our EHA is problem-agnostic and hardware-efficient, is especially suitable for NISQ devices, and has potential for wide applications. Our EHA can achieve a higher level of accuracy in finding ground states and their energies in most cases, even compared with problem-specific methods. The performance of the EHA is robust to the choice of initial states and to parameter initialization, and it has the ability to quickly adjust the entanglement to the required amount, which is also the fundamental reason for its superiority.
Quantum systems have historically been formidable to simulate using classical computational methods, particularly as the system size grows. In recent years, advancements in quantum computing technology have offered new opportunities for tackling complex quantum systems, potentially enabling the study and preparation of quantum states directly on quantum processors themselves. The Variational Quantum Eigensolver (VQE) algorithm is a system composed of a quantum circuit as well as a classical optimizer that can be used to efficiently prepare interesting many-body states on the current noisy intermediate-scale quantum (NISQ) devices. We assess the efficacy and scalability of VQE by preparing the ground states of the 1D generalized Heisenberg model, a pivotal model in understanding magnetic materials. We present an ansatz capable of preparing the ground states for all possible values of the coupling, including the critical states for the anisotropic XXZ model. This paper also aims to provide insights into the precision and time consumption involved in classical and optimized sampling approaches in the calculation of expectation values. In preparing the ground state for the Heisenberg models, this paper paves the way for more efficient quantum algorithms and contributes to the broader field of condensed matter physics.
The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.
Quantum computing has the potential to revolutionize quantum chemistry and material science by offering solutions to complex problems unattainable with classical computers. However, the development of efficient quantum algorithms that are efficient under noisy conditions remains a major challenge. This paper introduces the truncated Variational Hamiltonian Ansatz (tVHA), a novel circuit design for conducting quantum calculations on Noisy Intermediate-Scale Quantum (NISQ) devices. tVHA provides a promising approach for a broad range of applications by utilizing principles from the adiabatic theorem in solid state physics. Our proposed ansatz significantly reduces the parameter count and can decrease circuit size substantially, with a trade-off in accuracy. Thus, tVHA facilitates easier convergence within the variational quantum eigensolver framework compared to state-of-the-art ansätze such as Unitary Coupled Cluster (UCC) and Hardware-Efficient Ansatz (HEA). While this paper concentrates on the practical applications of tVHA in quantum chemistry, demonstrating its suitability for both weakly and strongly correlated systems and its compatibility with active space calculations, its underlying principles suggest a wider applicability extending to the broader field of material science computations on quantum computing platforms.