Quantum computing encompasses a variety of computation models, including gate-based (GB), topological, quantum annealing, and measurement-based (MB). MB performs computation through single-qubit measurements on a highly entangled cluster state and is proposed to offer some practical advantages on near-term quantum hardware in terms of circuit depth. In this work, we propose MB-VQITE, which leverages the MB model for solving optimization problems using the variational quantum imaginary time evolution (VQITE) algorithm. We apply MB-VQITE to the molecular docking problem, which is relevant in pharmaceutical research. We perform direct comparisons between the MB and GB computing paradigms on IBM Cleveland quantum hardware and perform optimization procedures on noisy simulators. We find that MB-VQITE outperforms GB-VQITE on current quantum hardware by reducing circuit depth, thus decreasing noise to allow for smoother optimization.
Quantum computing encompasses a variety of computation models, including gate-based (GB), topological, quantum annealing, and measurement-based (MB). MB performs computation through single-qubit measurements on a highly entangled cluster state and is proposed to offer some practical advantages on near-term quantum hardware in terms of circuit depth. In this work, we propose MB-VQITE, which leverages the MB model for solving optimization problems using the variational quantum imaginary time evolution (VQITE) algorithm. We apply MB-VQITE to the molecular docking problem, which is relevant in pharmaceutical research. We perform direct comparisons between the MB and GB computing paradigms on IBM Cleveland quantum hardware and perform optimization procedures on noisy simulators. We find that MB-VQITE outperforms GB-VQITE on current quantum hardware by reducing circuit depth, thus decreasing noise to allow for smoother optimization.
Abstract Variational quantum imaginary time evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that requiring the imaginary-time evolution to be correct only when projected onto a chosen set of operators allows to achieve a twofold reduction in circuit depth by bypassing fidelity estimations, and reduces measurement complexity from quadratic to linear in the number of parameters. We demonstrate by a simulation of the transverse-field Ising model that our algorithm achieves a several orders of magnitude improvement in the number of measurements required for the same accuracy.
Preparing ground states of correlated molecules on near-term quantum computers requires algorithms that are both accurate and resource-efficient. We introduce the qubit-adaptive variational quantum imaginary time evolution (QAITE) algorithm, which synthesizes the systematic convergence of imaginary-time evolution with hardware-efficient, adaptive ansatz construction. By integrating the linear-scaling qubit operator pool into the adaptive variational quantum imaginary time evolution framework, QAITE deterministically constructs a compact ansatz without costly classical optimization loops. Numerical simulations for molecular systems (H4, LiH, H2O, BeH2), benchmarked against our own implementations of established adaptive algorithms under identical conditions, show that QAITE achieves chemical accuracy with a 15-45% reduction in CNOT gates compared to the standard adaptive variational quantum imaginary time evolution (AVQITE) method. For hydrogen chains (RHH = 1.5 Å, N = 6-16 qubits), QAITE's circuit complexity grows approximately quadratically and remains the lowest of the four methods at every system size, reaching 31% fewer CNOT gates than AVQITE at 16 qubits─a saving of 1322 gates. This efficiency extends to heterogeneous (LiH)n and (HBe)n chains, where QAITE maintains a CNOT gate ratio below 1 for all sizes studied (e.g., 0.81 for (LiH)2). We further show that the deterministic parameter update is numerically robust: the results are insensitive to the regularization of the quantum geometric tensor over at least 4 orders of magnitude, and chemical accuracy is retained under realistic shot noise applied to both the quantum geometric tensor and the force vector. By outperforming established adaptive algorithms in both absolute gate count and scaling, QAITE establishes a promising, scalable pathway for quantum molecular simulations on noisy intermediate-scale quantum devices.
Maxwells equations are fundamental to our understanding of electromagnetic fields, but their solution can be computationally demanding, even for high-performance computing clusters. Quantum computers offer a promising alternative for solving these equations, as they can simulate larger and more complex systems more efficiently both in time and resources. In this paper we investigate the potential of using the variational quantum imaginary time evolution (VarQITE) algorithm on near-term quantum hardware to solve for the Maxwells equations. Our objective is to analyze the trade-off between the accuracy of the simulated fields and the depth of the quantum circuit required to implement the VarQITE algorithm. We demonstrate that VarQITE can efficiently approximate the solution of these equations with high accuracy, and show that its performance can be enhanced by optimizing the quantum circuit depth. Our findings suggest that VarQITE on near-term quantum devices could provide a powerful tool for solving PDEs in electromagnetics and other fields.
The Schwinger model serves as a benchmark for testing non-perturbative algorithms in quantum chromodynamics (QCD), emphasizing its similarities to QCD in strong coupling regimes, primarily due to the phenomena such as confinement and charge screening. However, classical algorithms encounter challenges when simulating the Schwinger model, such as the "sign problem" and the difficulty in handling large-scale systems. These limitations motivate the exploration of alternative simulation approaches, including quantum computing techniques, to overcome the obstacles. While existing variational quantum algorithms (VQAs) methods for simulating the Schwinger model primarily rely on mathematical gradient-based optimization, which sometimes fail to provide intuitive and physically-guided optimization pathways. In contrast, the Variational Quantum Imaginary Time Evolution (VQITE) method offers a physically-inspired optimization approach. Therefore, we introduce that VQITE holds promise as a potent tool for simulating the Schwinger model. However, the standard VQITE method is not sufficiently stable, as it encounters difficulties with the non-invertible matrix problem. To address this issue, we have proposed a regularized version of the VQITE, which we have named the Regularized-VQITE (rVQITE) method, as it incorporates a truncation-based approach. Through numerical simulations, we demonstrate that our proposed rVQITE approach achieves better performance and exhibits faster convergence compared to other related techniques. We employ the rVQITE method to simulate the phase diagrams of various physical observables in the Schwinger model, and the resulting phase boundaries are in agreement with those obtained from an exact computational approach.
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational advantages. To address this we present a variational quantum algorithm for solving combinatorial optimization problems with linear-depth circuits. Our algorithm uses an ansatz composed of Hamiltonian generators designed to control each term in the target combinatorial function, along with parameter updates following a modified version of quantum imaginary time evolution. We evaluate this ansatz in numerical simulations that target solutions to the MAXCUT problem. The state evolution is shown to closely mimic imaginary time evolution, and its optimal-solution convergence is further improved using adaptive transformations of the classical Hamiltonian spectrum. With these innovations, the algorithm consistently converges to optimal solutions, with interesting highly-entangled dynamics along the way. We further demonstrate the success of this approach by performing optimization of a truncated version of our ansatz with up to 32 qubits in a trapped-ion quantum computer, using measurements from the quantum computer to train the ansatz and prepare optimal solutions with high fidelity in the majority of cases we consider. The success of these large-scale quantum circuit optimizations, in the presence of realistic hardware constraints and without error mitigation, mark significant progress on the path towards solving combinatorial problems using quantum computers. We conclude our performant and resource-minimal approach is a promising candidate for potential quantum computational advantages.
Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ansätze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and XY-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with 27 and 127 qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.