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Physical Review A

Hardware-efficient variational quantum algorithm in a trapped-ion quantum computer

J.-Z. Zhuang, Yukai Wu, L.-M. Duan

Published Dec 9, 2024• 7 citations
Publisher

Abstract

We study a hardware-efficient ansatz tailored for a trapped-ion quantum simulator (HEA-TI), utilizing single-qubit rotations and global spin-spin interactions to reduce the reliance on resource-intensive multiqubit gates typical of conventional gate-based approaches. This ansatz also allows streamlined experimental control sequences with continuous global interaction and insertions of single-qubit gates. We examine the scaling behavior of quantum resources required by HEA-TI. We also apply it to the ground-state calculation of chemical molecules and examine its performance under realistic experimental noise and statistical fluctuations. Our results demonstrate that HEA-TI achieves competitive efficiency with other commonly used variational ansatzes, such as UCCSD, while offering significant implementation advantages for trapped-ion platforms.

DOI
10.1103/physreva.110.062414

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We study a hardware-efficient ansatz tailored for a trapped-ion quantum simulator (HEA-TI), utilizing single-qubit rotations and global spin-spin interactions to reduce the reliance on resource-intensive multiqubit gates typical of conventional gate-based approaches. This ansatz also allows streamlined experimental control sequences with continuous global interaction and insertions of single-qubit gates. We examine the scaling behavior of quantum resources required by HEA-TI. We also apply it to the ground-state calculation of chemical molecules and examine its performance under realistic experimental noise and statistical fluctuations. Our results demonstrate that HEA-TI achieves competitive efficiency with other commonly used variational ansatzes, such as UCCSD, while offering significant implementation advantages for trapped-ion platforms.
We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules H2\mathrm{H_{2}}H2​, LiH\mathrm{LiH}LiH and F2\mathrm{F_{2}}F2​. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer.
Abstract Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ’s Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters—the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.
Abstract Quantum simulation on noisy intermediate-scale quantum (NISQ) hardware is limited by short coherence time and gate errors. We present a universal variational compilation optimization method (VCOM) that directly leverages the native gate set of trapped-ion processors, namely single-qubit rotations and global Ising-type XX interactions, to construct shallow circuits for simulating molecular Hamiltonians. Specifically, VCOM employs a hybrid optimization strategy combining genetic algorithms with gradient-based refinement to compile Pauli string evolution operators e −i Pt , thereby substantially reducing circuit depth and multi-qubit gate overhead in Hamiltonian simulation. Applied to hydrogen chains, the compiled circuits achieve fidelities comparable to standard decompositions while reducing the proportion of two-qubit operations to only 1.9%–4.6% of the total native gates, a significant improvement over the standard second-order Trotter–Suzuki product formula. Under experimentally motivated laser-intensity and phase-noise models, the proposed scheme maintains high fidelity and exhibits significantly slower degradation than direct native gate decompositions of conventional circuits. These results establish native-gate-based variational compilation as a scalable and practical approach for digital quantum simulation on trapped-ion platforms, with potential extensions to strongly correlated systems and non-equilibrium dynamics.
Abstract Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our findings demonstrate a significant reduction in single- and two-qubit gate counts, suggesting a reliable circuit architecture for noisy intermediate-scale quantum devices. Building on this foundation, we tested our low-depth scheme to investigate the expressive capacity of the proposed parameterized ansatz in simulating nonlinear Burgers’ dynamics. The resulting variational quantum states faithfully capture the shockwave feature of the turbulent regime and maintain high overlaps with classical benchmarks, underscoring the practical effectiveness of our framework. Furthermore, we evaluate the effect of hardware noise by modeling the error properties of real quantum processors and by executing the variational algorithm on a trapped-ion-based IBEX Q1 device. The outcomes of our demonstrations highlight the resilience of our low-depth scheme in the turbulent regime, consistently preparing high-fidelity variational states that exhibit strong agreement with classical benchmarks. Our work contributes to the advancement of resource-efficient strategies for quantum computation, offering a robust framework for tackling a range of computationally intensive problems across numerous applications.
Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.
ABSTRACT We propose a variational quantum regression (VQR) algorithm using a hardware‐efficient ansatz (HEA) structure. This approach enables the quantum state to directly encode classical tabular data with variational parameters corresponding to real‐valued regression coefficients, ensuring high interpretability and efficient optimization without sacrificing expressiveness. By combining a variational quantum circuit with a classical optimizer, our method predicts the ground‐state energy of a hydrogen molecule using full configuration interaction (FCI) data. We quantify the expressibility of the VQR HEA circuit via the Kullback–Leibler (KL) divergence D KL and show the advantages of our R y − R x gate sequence in balancing expressibility. Performed for pennylane using an idealized quantum simulator, our 4‐qubit, 5‐layer HEA‐based VQR model achieves an accuracy of ∼0.99, mean squared error (MSE) < 10 −6 Hartree 2 , and mean absolute error (MAE) around 0.1 × 10 −2 Hartree compared to FCI benchmarks. We further demonstrate how qubit number and layer depth influence model accuracy, providing insights for task‐specific quantum circuit design. Our results advance practical applications of quantum computing for electronic structure problems by introducing an expressive, interpretable ansatz tailored for high‐precision simulations.