Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2-3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.
Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2-3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.
Variational Quantum Algorithms (VQA) have been identified as a promising candidate for the demonstration of near-term quantum advantage in solving optimization tasks in chemical simulation, quantum information, and machine learning. The standard model of training requires a significant amount of quantum resources, which led researchers to use classical shadows to devise an alternative that consumes exponentially fewer quantum resources. However, the approach only works when the observables are local and the ansatz is the shallow Alternating Layered Ansatz (ALA), thus severely limiting its potential in solving problems such as quantum state preparation, where the ideal state might not be approximable with an ALA. In this work, we present a protocol based on shallow shadows that achieves similar levels of savings for almost any shallow ansatz studied in the literature, when combined with observables of low Frobenius norm. We show that two important applications in quantum information for which VQAs can be a powerful option, namely variational quantum state preparation and variational quantum circuit synthesis, are compatible with our protocol. We also experimentally demonstrate orders of magnitude improvement in comparison to the standard VQA model.
We introduce a general framework called neural-network- (NN) encoded variational quantum algorithms (VQAs), or NNVQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NNVQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NNVQA can accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pretrained NN. To concretely illustrate the merits of NNVQA, we present results on a NN variational quantum eigensolver (VQE) for solving the ground state of parameterized XXZ spin models in one and two dimensions. Our results demonstrate that NNVQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of the given Hamiltonian. We also employ an active learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NNVQAs offer an alternative hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.
Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over 6× fewer parameters, and for VQE on H2 we achieve UCCSD-like accuracy at substantially reduced circuit complexity.
Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is [Formula: see text]. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.
Variational quantum algorithms (VQAs) have emerged as the leading strategy for using these noisy devices to achieve an advantage over their classical counterparts.VQAs use a hybrid quantum-classical framework, in which one employs the quantum computer to prepare a parameterized quantum state and outsource the optimization to a classical subroutine. VQAs have been proposed for applications in various fields, including physics, quantum chemistry, machine learning, and optimization. Nevertheless, many challenges must be addressed before we can use them for practical tasks. In this dissertation, we propose strategies to overcome some challenges in implementing VQAs. We first look at the issue of trainability for VQAs and propose three methods for optimizing them.The first method is based on natural evolutionary strategies (NES) and can alleviate the issue of vanishing gradients for randomly initialized parameterized quantum circuits (PQCs). The second method is based on the notion of information flow in PQCs and uses a mutual information-based distance metric to define paths for stochastic optimization of VQAs. Finally, we develop gradient evaluation procedures for optimizing objectives with the unitary coupled-cluster ansatz. Next, we study the issue of expressibility of PQCs used in variational algorithms.First, using the theory of quantum optimal control we define a notion of reachability of general ans\"atze used in VQAs. Next, using a variational autoencoder (VAE) coupled with a regression model, we try to gain a better understanding of the parameterization of PQCs. Finally, we attempt to remedy the inefficient usage of quantum resources for storing quantum data using evolutionary strategies to design quantum circuits for compressing quantum data. We present numerical evidence that the work presented here can increase trainability, efficiency, and understanding of VQAs.We believe our work is of interest to the quantum computing community as we continue to push the limits of NISQ devices for solving practical problems.
Abstract Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various approaches have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of the approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of the NN-based BP mitigation approach by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the approach’s utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.