Quantum computing offers a potential for algorithmic speedups for applications, such as large-scale simulations in chemistry and physics. However, these speedups must yield results that are sufficiently accurate to predict realistic outcomes of experiments precisely. Delivering on the promise of high accuracy and precision requires methods to evaluate the computational accuracy of the quantum computing devices. We develop a framework to estimate the computational accuracy of near-term noisy, intermediate scale quantum (NISQ) computing devices using a quantum chemistry application. Application benchmarks that run on NISQ devices require techniques for mitigating errors to improve accuracy and precision. We use device agnostic error-mitigation schemes, quantum error detection and readout error detection, with post-selection to mitigate the dominant sources of noise. We evaluate the framework by simulating the ground state of molecular hydrogen with the variational quantum eigensolver (VQE) algorithm, estimating the energy and calculating the precision of the estimate using numerical simulations with realistic noise models. We first quantify the improvement in the logical error rate and state fidelity of the VQE application when encoded with the [[4,2,2]] quantum error detection code. When additionally encoded with readout error detection, we show that compared to the unencoded simulation, the encoded simulation yields a more accurate estimate by more than 1 mHa (0.027 eV) with comparable precision and higher state fidelity. Additionally, unlike the best estimate from the unencoded simulations, the results from the encoded simulation fall within the chemical accuracy threshold of 1.6 mHa of the exact energy. The estimated accuracy and precision indicate that current quantum computers can achieve error rates that yield useful outcomes for chemical applications.
Quantum computing offers a potential for algorithmic speedups for applications, such as large-scale simulations in chemistry and physics. However, these speedups must yield results that are sufficiently accurate to predict realistic outcomes of experiments precisely. Delivering on the promise of high accuracy and precision requires methods to evaluate the computational accuracy of the quantum computing devices. We develop a framework to estimate the computational accuracy of near-term noisy, intermediate scale quantum (NISQ) computing devices using a quantum chemistry application. Application benchmarks that run on NISQ devices require techniques for mitigating errors to improve accuracy and precision. We use device agnostic error-mitigation schemes, quantum error detection and readout error detection, with post-selection to mitigate the dominant sources of noise. We evaluate the framework by simulating the ground state of molecular hydrogen with the variational quantum eigensolver (VQE) algorithm, estimating the energy and calculating the precision of the estimate using numerical simulations with realistic noise models. We first quantify the improvement in the logical error rate and state fidelity of the VQE application when encoded with the [[4,2,2]] quantum error detection code. When additionally encoded with readout error detection, we show that compared to the unencoded simulation, the encoded simulation yields a more accurate estimate by more than 1 mHa (0.027 eV) with comparable precision and higher state fidelity. Additionally, unlike the best estimate from the unencoded simulations, the results from the encoded simulation fall within the chemical accuracy threshold of 1.6 mHa of the exact energy. The estimated accuracy and precision indicate that current quantum computers can achieve error rates that yield useful outcomes for chemical applications.
New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)-an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.
Abstract Quantum computers promise to solve electronic structure, lattice dynamics, and strongly correlated problems beyond classical reach. However, near-term noisy intermediate scale quantum (NISQ) processors require systematic benchmarking to establish where variational algorithms with error mitigation can achieve chemical accuracy and cor rectly predict physical phenomena. Here we present 28 quantum material simula tions implemented with Qiskit, spanning molecular hydrogen (H 2 ) through the iron molybdenum cofactor (FeMoco), one-dimensional Hubbard chains, Kitaev honeycomb spin liquids, topological insulators (SSH model), BCS superconductors, and disordered Anderson insulators. Using the variational quantum eigensolver (VQE) with UCCSD ansatz, we achieve chemical accuracy (±1.6 mHa) for H 2 across the full dissociation curve and recover exact ground-state energies for H4 within 9 mHa after zero-noise extrapolation (ZNE) — reducing raw VQE errors from 152 mHa to 9 mHa. We accu rately identify the transverse-field Ising quantum critical point (h c = J) with 4 qubits, resolve Majorana Dirac dispersions in the Kitaev spin liquid, and reproduce the Mott transition in the Fermi-Hubbard model at U c = 6t. Resource estimation for FeMoco reveals O(N 2.5 ) scaling, projecting chemical accuracy with ∼200 logical qubits. Across all benchmarks, we quantify the accuracy-circuit depth tradeoff, demonstrating that depth-6 VQE ans¨atze achieve chemical accuracy for small molecules while depth-10 is required for correlated lattices. These results establish a comprehensive benchmark suite for evaluating quantum hardware, error mitigation protocols, and variational al gorithms for materials science on NISQ processors.
Abstract The inherent noise in current Noisy Intermediate-Scale Quantum (NISQ) devices presents a major obstacle to the accurate implementation of quantum algorithms such as the Variational Quantum Eigensolver (VQE) for quantum chemistry applications. This study examines the impact of error mitigation strategies on VQE performance. We show that, for small molecular systems, an older-generation 5-qubit quantum processing unit (IBMQ Belem), when combined with optimized Twirled Readout Error Extinction (T-REx), achieves ground-state energy estimations an order of magnitude more accurate than those obtained from a more advanced 156-qubit device (IBM Fez) without error mitigation. Our findings demonstrate that T-REx, a computationally inexpensive error mitigation technique, substantially improves VQE accuracy not only in energy estimation, but more importantly in optimizing the variational parameters that characterize the molecular ground state. Consequently, state-vector simulated energies suggest that the accuracy of the optimized variational parameters provides a more reliable benchmark of VQE performance than quantum hardware energy estimates alone. Our results point to the critical role of error mitigation in extending the utility of noisy quantum hardware for molecular simulations.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state energy of a target molecule. Although VQE has a potential to achieve a higher accuracy than classical approximation methods in QCC, it is challenging to achieve it on current NISQ computers due to the significant impact of noises. Density matrix embedding theory (DMET) is a well-known technique to divide a molecule into multiple fragments, which is available to mitigate the noise impact on VQE. However, our preliminary evaluation shows that the naive combination of DMET and VQE does not outperform a gold standard classical method. In this work, we present three approaches to mitigate the noise impact for the DMET+VQE combination. (1) The size of quantum circuits used by VQE is decreased by reducing the number of bath orbitals which represent interactions between multiple fragments in DMET. (2) Reduced density matrices (RDMs), which are used to calculate a molecular energy in DMET, are calculated accurately based on expectation values obtained by executing quantum circuits using a noise-less quantum computer simulator. (3) The parameters of a quantum circuit optimized by VQE are refined with mathematical post-processing. The evaluation using a noisy quantum computer simulator shows that our approaches significantly improve the accuracy of the DMET+VQE combination. Moreover, we demonstrate that on a real NISQ device, the DMET+VQE combination applying our three approaches achieves a higher accuracy than the gold standard classical method.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.
Abstract Quantum computers are expected to be highly beneficial for chemistry simulations, promising significant improvements in accuracy and speed. The most prominent algorithm for chemistry simulations on NISQ devices is the Variational Quantum Eigensolver (VQE). It is a hybrid quantum-classical algorithm which calculates the ground state energy of a Hamiltonian based on parametrized quantum circuits, while a classical optimizer is used to find optimal parameter values. However, quantum hardware is affected by noise, and it needs to be understood to which extent it can degrade the performance of the VQE algorithm. In this paper, we study the impact of noise on the example of the hydrogen molecule. First, we compare the VQE performance for a set of various optimizers, from which we find NFT to be the most suitable one. Next, we quantify the effect of different noise sources by systematically increasing their strength. The noise intensity is varied around values common to superconducting devices of IBM Q, and curve fitting is used to model the relationship between the obtained energy values and the noise magnitude. Since the amount of noise in a circuit highly depends on its architecture, we perform our studies for different ansatzes, including both hardware-efficient and chemistry-inspired ones. Finally, we compare our results from noisy simulations with experiments on different IBM hardware devices.