The development of various dynamic ansatz-constructing techniques has ushered in a new era, rendering the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, they exhibit substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretic measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework. The machine learning methodology is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This approach significantly enhances the feasibility of quantum simulations in molecular systems, paving the way for impactful advancements in quantum computational chemistry.
The development of various dynamic ansatz-constructing techniques has ushered in a new era, rendering the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, they exhibit substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretic measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework. The machine learning methodology is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This approach significantly enhances the feasibility of quantum simulations in molecular systems, paving the way for impactful advancements in quantum computational chemistry.
-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
Generative machine learning models like the Restricted Boltzmann Machine (RBM) provide a practical approach for ansatz construction within the quantum computing framework. This work introduces a method that efficiently leverages RBM and many-body perturbative measures to build a compact chemistry-inspired ansatz for determining accurate molecular energetics. By training on low-rank determinants derived from an approximate wave function, RBM predicts the key high-rank determinants that dominate the ground-state wave function. A shallow depth ansatz is constructed to explicitly incorporate these dominant determinants after dynamically decomposing them into low-rank components and applying many-body perturbative measures for further screening. The method requires no additional measurements beyond the initial training phase. Moreover, it incorporates Bayesian hyperparameter optimization for the RBM, ensuring efficient performance with minimal training data during its limited usage. This approach facilitates the efficient computation of molecular properties, paving the way for exploring new chemical phenomena with near-term quantum computers.
In recent times, a variety of hybrid quantum-classical algorithms have been developed that aim to calculate the ground state energies of molecular systems on Noisy Intermediate-Scale Quantum (NISQ) devices. Albeit the utilization of shallow depth circuits in these algorithms, the optimization of ansatz parameters necessitates a substantial number of quantum measurements, leading to prolonged runtimes on the scantly available quantum hardware. Through our work, we lay the general foundation for an interdisciplinary approach that can be used to drastically reduce the dependency of these algorithms on quantum infrastructure. We showcase these pertinent concepts within the framework of the recently developed Projective Quantum Eigensolver (PQE) that involves iterative optimization of the nonlinearly coupled parameters through repeated residue measurements on quantum hardware. We demonstrate that one may perceive such a nonlinear optimization problem as a collective dynamic interplay of fast and slow relaxing modes. As such, the synergy among the parameters is exploited using an on-the-fly supervised machine learning protocol that dynamically casts the PQE optimization into a smaller subspace by reducing the effective degrees of freedom. We demonstrate analytically and numerically that our proposed methodology ensures a drastic reduction in the number of quantum measurements necessary for the parameter updates without compromising the characteristic accuracy. Furthermore, the machine learning model may be tuned to capture the noisy data of NISQ devices, and thus the predicted energy is shown to be resilient under a given noise model.
Recent advances in quantum information and quantum science have inspired the development of various compact, dynamically structured ansätze that are expected to be realizable in Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus, they deviate significantly in the NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the ab initio many-body perturbation theory that requires no pre-circuit measurement and, thus, remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order, as desired, and, hence, are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count, and circuit depth, in comparison to the allied unitary coupled cluster based ansätze.
Recent advances in quantum information and quantum science have inspired the development of various compact dynamic structured ansätze that are expected to be realizable in the Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus they deviate significantly in NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources must be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the \textit{ab-initio} many-body perturbation theory that requires \textit{no} pre-circuit measurement and thus it remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order as desired and hence are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count and circuit depth, in comparison to the allied unitary coupled cluster based ansätze.
Despite significant efforts, the realization of the hybrid quantum-classical algorithms has predominantly been confined to proof-of-principles, mainly due to the hardware noise. With fault-tolerant implementation being a long-term goal, going beyond small molecules with existing error mitigation (EM) techniques with current noisy intermediate scale quantum (NISQ) devices has been a challenge. That being said, statistical learning methods are promising approaches to learning the noise and its subsequent mitigation. We devise a graph neural network and regression-based machine learning (ML) architecture for practical realization of EM techniques for molecular Hamiltonian without the requirement of the exponential overhead. Given the short coherence time of the quantum hardware, the ML model is trained with either ideal or mitigated expectation values over a judiciously chosen ensemble of shallow sub-circuits adhering to the native hardware architecture. The hardware connectivity network is mapped to a directed graph which encodes the information of the native gate noise profile to generate the features for the neural network. The training data is generated on-the-fly during ansatz construction thus removing the computational overhead. We demonstrate orders of magnitude improvements in predicted energy over a few strongly correlated molecules.