Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and correction is not feasible. VQAs can utilize noisy qubits in tandem with classical optimization algorithms to solve hard problems. However, VQAs are still slow relative to their classical counterparts. Hence, improving the performance of VQAs will be necessary to make them competitive. While VQAs are expected perform better as the problem sizes increase, increasing their performance will make them a viable option sooner. In this work we show that circuit-level concurrency provides a means to increase the performance of variational quantum algorithms on noisy quantum computers. This involves mapping multiple instances of the same circuit (program) onto the quantum computer at the same time, which allows multiple samples in a variational quantum algorithm to be gathered in parallel for each training iteration. We demonstrate that this technique provides a linear increase in training speed when increasing the number of concurrently running quantum circuits. Furthermore, even with pessimistic error rates concurrent quantum circuit sampling can speed up the quantum approximate optimization algorithm by up to 20x with low mapping and run time overhead.
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and correction is not feasible. VQAs can utilize noisy qubits in tandem with classical optimization algorithms to solve hard problems. However, VQAs are still slow relative to their classical counterparts. Hence, improving the performance of VQAs will be necessary to make them competitive. While VQAs are expected perform better as the problem sizes increase, increasing their performance will make them a viable option sooner. In this work we show that circuit-level concurrency provides a means to increase the performance of variational quantum algorithms on noisy quantum computers. This involves mapping multiple instances of the same circuit (program) onto the quantum computer at the same time, which allows multiple samples in a variational quantum algorithm to be gathered in parallel for each training iteration. We demonstrate that this technique provides a linear increase in training speed when increasing the number of concurrently running quantum circuits. Furthermore, even with pessimistic error rates concurrent quantum circuit sampling can speed up the quantum approximate optimization algorithm by up to 20x with low mapping and run time overhead.
Variational quantum algorithm (VQA), which is comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches for harvesting the power of quantum computers in the noisy intermediate scale quantum (NISQ) era. However, the deployment of VQAs on contemporary NISQ devices often faces considerable system and time-dependant noise and prohibitively slow training speeds. On the other hand, the expensive supporting resources and infrastructure make quantum computers extremely keen on high utilization. In this paper, we propose a virtualized way of building up a quantum backend for variational quantum algorithms: rather than relying on a single physical device which tends to introduce temporal-dependant device-specific noise with worsening performance as time-since-calibration grows, we propose to constitute a quantum ensemble, which dynamically distributes quantum tasks asynchronously across a set of physical devices, and adjusting the ensemble configuration with respect to machine status. In addition to reduced machine-dependant noise, the ensemble can provide significant speedups for VQA training. With this idea, we build a novel VQA training framework called EQC that comprises: (i) a system architecture for asynchronous parallel VQA cooperative training; (ii) an analytic model for assessing the quality of the returned VQA gradient over a particular device concerning its architecture, transpilation, and runtime conditions; (iii) a weighting mechanism to adjust the quantum ensemble's computational contribution according to the systems' current performance. Evaluations comprising 500K circuit evaluations across 10 IBMQ devices using a VQE and a QAOA applications demonstrate that EQC can attain error rates close to the most performant device of the ensemble, while boosting the training speed by 10.5x on average (up to 86x and at least 5.2x).
Variational quantum algorithms have promising applications in noisy intermediate-scale quantum (NISQ) devices. These algorithms rely on a classical optimization outer loop that minimizes a parameterized quantum circuit function. The optimization in variational quantum eigensolver (VQE) is NP-hard, meaning that finding the optimal solution is infeasible in the worst-case scenario. One way to address this challenge is through parallel optimization of parameters using multiple-parameterized quantum circuits. However, this approach is unsuitable for cloud-based quantum processing unit utilization due to the increased number of quantum circuit executions. Although NISQ devices have limitations in terms of gate depth, their size has been growing in recent years. Therefore, implementing multiple-parameterized quantum circuits in NISQ devices can suppress the increase in the number of executions. In this study, we propose a parallel-VQE, which leverages the parallel execution of parameterized quantum circuits to perform parallel parameter optimization in VQE, achieving convergence to solutions closer to the ground state. We validate the effectiveness of parallel-VQE in solving the random weighted max-cut problem using numerical simulations and a real quantum device. We present the results of running up to six circuits in parallel (120 qubits) and demonstrate the advantages of using multiple units to improve computational accuracy. This study provides a potential method for solving eigenvalue problems and combinatorial optimization problems for future quantum devices.
Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.
Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a parameterized quantum circuit (PQC). The goal is minimizing a cost function that depends on measurement outputs obtained from the PQC. Optimization is typically implemented via stochastic gradient descent (SGD). On NISQ computers, gate noise due to imperfections and decoherence affects the stochastic gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits, but they in turn cause an increase in the variance of the gradient estimates. This work studies the impact of quantum gate noise on the convergence of SGD for the variational eigensolver (VQE), a fundamental instance of VQAs. The main goal is ascertaining conditions under which QEM can enhance the performance of SGD for VQEs. It is shown that quantum gate noise induces a nonzero error-floor on the convergence error of SGD (evaluated with respect to a reference noiseless PQC), which depends on the number of noisy gates, the strength of the noise, as well as the eigenspectrum of the observable being measured and minimized. In contrast, with QEM, any arbitrarily small error can be obtained. Furthermore, for error levels attainable with or without QEM, QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently large, and a sufficiently large number of measurements is allowed at each SGD iteration. Numerical examples for a max-cut problem corroborate the main theoretical findings.
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.