Abstract Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low-rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling nonlocal Jordan–Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground-state energies of strongly correlated electronic systems.
Abstract Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low-rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling nonlocal Jordan–Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground-state energies of strongly correlated electronic systems.
As a hybrid quantum-classical algorithm, the variational quantum eigensolver is widely applied in quantum chemistry simulations, especially in computing the electronic structure of complex molecular systems. However, on existing noisy intermediate-scale quantum devices, some factors such as quantum decoherence, measurement errors, and gate operation imprecisions are unavoidable. To overcome these challenges, this study proposes an efficient noise-mitigating variational quantum eigensolver for accurate computation of molecular ground state energies in noisy environments. We design the quantum circuit with reference to the structure of matrix product states and utilize it to pre-train the circuit parameters, which ensures circuit stability and mitigates fluctuations caused by initialization. We also employ zero-noise extrapolation to mitigate quantum noise and combine it with neural networks to improve the accuracy of the noise-fitting function, which significantly eliminates noise interference. Furthermore, we implement an intelligent grouping strategy for measuring Hamiltonian Pauli strings, which not only reduces measurement errors but also improves sampling efficiency. We perform numerical simulations to solve the ground state energy of the H4molecule by using MindSpore Quantum framework, and the results demonstrate that our algorithm can constrain noise errors within the range of O(10−2)∼O(10−1), outperforming mainstream variational quantum eigensolvers. This work provides a new strategy for high-precision quantum chemistry calculations on near-term noisy quantum hardware.
Abstract Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational quantum algorithms, which require deep entangling quantum circuit ansatzes to capture correlations, to small molecules. Here we demonstrate a variational NISQ-friendly algorithm that generates a set of Hartree–Fock ansatzes using multiple shallow circuits with depth linear in the number of qubits to estimate electronic correlation energies via perturbation theory up to the second order. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. The number of shallow circuits required for our algorithms scales O ( N 5 ) , with N being the system size, thus enabling the study of larger molecules compared to other approaches, where circuit depth or number of qubits required become prohibitive for NISQ devices.
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
Quantum computers exist today that are capable of performing calculations that challenge the largest classical supercomputers. Now the great challenge is to make use of these devices, or their successors, to perform calculations of independent interest. This thesis focuses on a family of algorithms that aim to accomplish this goal, known as variational quantum algorithms, and the challenges that they face. We frame these challenges in terms of two kinds of resources, the number of operations that we can afford to perform in a single quantum circuit, and the overall number of circuit repetitions required. Before turning to our specific contributions, we provide a review of the electronic structure problem, which serves as a central example for our work. We also provide a self-contained introduction to the field of quantum computing and the notion of a variational quantum algorithm.We begin the main body of the thesis by studying a generalization of the standard unitary coupled cluster ansatz. We present a sparse version of unitary coupled cluster and show that it can accurately represent the ground and excited states of small molecular systems using fewer quantum gates than the full unitary coupled cluster. We then introduce a strategy for representing molecular ground states as linear combinations of parameterized wavefunctions, allowing for a tradeoff between the number of operations required for each circuit and the number of circuit repetitions. We provide circuit primitives that allow for the efficient measurement of the required matrix elements between these wavefunctions. Subsequently, we show how the cost of estimating the energy of a quantum chemical wavefunction on a near-term quantum computer can be dramatically reduced by using a factorization of the two-electron integraltensor. Furthermore, we explain how this measurement strategy helps mitigate against errors during state preparation and measurement. We then present a Monte Carlo version of a classical algorithm for calculating the partition function of two-dimensional lattice models that shows a similar kind of tradeoff between two resources, albeit in a different context. Finally, we show how ideas based on tensor networks can inform the design of quantum circuits for machine learning tasks. We argue that this application is especially tolerant to noise and present numerical data substantiating this argument. We conclude by explaining explicitly how our work addresses the problems of the limited resources available to near-term quantum computers and offering some optimism about the future of the field.
Simulating molecular systems on quantum computers requires efficient mappings from Fermionic operators to qubit operators. Traditional mappings such as Jordan-Wigner or Bravyi-Kitaev often produce high-weight Pauli terms, increasing circuit depth and measurement complexity. Although several local qubit mappings have been proposed to address this challenge, most are specialized for structured models like the Hubbard Hamiltonian and perform poorly for realistic chemical systems with dense two-body interactions. In this work, we utilize a suite of techniques to construct compact and noise-resilient Fermion-to-qubit mappings suitable for general molecular Hamiltonians. Building on the Generalized Superfast Encoding (GSE) and other similar works, we demonstrate that it outperforms prior encodings in both accuracy and hardware efficiency for molecular simulations. Our improvements include path optimization within the Hamiltonian's interaction graph to minimize operator weight, introduction of multi-edge graph structures for enhanced error detection without added circuit depth, and a stabilizer measurement framework that directly maps logical terms and stabilizers to the Z-basis using Clifford simulation. Applying these methods to simulations of (H2)2 and (H2)3 systems yields significantly improved absolute and correlation energy estimates under realistic hardware noise, with further accuracy gains achieved by increasing code distance. We also propose a [[2N, N, 2]] variant of GSE compatible with square-lattice and (quasi-)linear hardware topologies, demonstrating a twofold reduction in RMSE for orbital rotations on IBM Kingston hardware. These results establish GSE as a very attractive mapping for molecular quantum simulations.
Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. Quantum computers suffer from high readout errors, making quantum simulations with high accuracy requirements particularly challenging. This paper implements practical techniques to reach accuracies essential for quantum chemistry by addressing key overheads and noise sources. Specifically, we leverage locally biased random measurements for reducing shot overhead, repeated settings with parallel quantum detector tomography for reducing circuit overhead and mitigating readout errors, and blended scheduling for mitigating time-dependent noise. We demonstrate these techniques via molecular energy estimation of the BODIPY molecule on a Hartree-Fock state on an IBM Eagle r3, obtaining a reduction in measurement errors by an order of magnitude from 1-5% to 0.16%. These strategies pave the way for more reliable quantum computations, particularly for applications requiring precise molecular energy calculations.