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arXiv:2202.13714 · Physical Review A

Robust resource-efficient quantum variational ansatz through an evolutionary algorithm

Yuhan Huang, Qingyu Li, Xiaokai Hou, Re-Bing Wu, Man‐Hong Yung, Abolfazl Bayat, Xiaoting Wang

Published May 10, 2022• 48 citations
arXivHTMLPDF

Abstract

Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve a potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely used hardware-efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that, compared with conventional hardware-efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise and hence is more likely to be implemented on near-term devices.

DOI
10.1103/physreva.105.052414

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Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve a potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely used hardware-efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that, compared with conventional hardware-efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise and hence is more likely to be implemented on near-term devices.
Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to 18.6×18.6\times18.6× shallower and use up to 12×12\times12× fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least 3.6×3.6\times3.6× less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.
Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to 18.6×18.6\times18.6× shallower and use up to 12×12\times12× fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least 3.6×3.6\times3.6× less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.
Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.
Quantum variational algorithms (VQAs) are highly promising to realize quantum advantages on near-term quantum devices. Existing VQAs based on a manually fixed quantum are computationally inefficient due to noise and the limited coupling maps of these devices. Previous work considers various quantum architecture search (QAS) algorithms to autodesign a quantum based on specific questions to improve the performance of VQAs. Compared to manual design, autodesign can more efficiently explore the large space of a possible and achieve better performance. However, two main challenges in utilizing QAS to design quantum circuits efficiently are the tremendous amount of space required for candidate quantum circuits, and the disconnection between quantum devices and autodesign in terms of qubit mapping and quantum noise. To address these issues, we propose an adaptive diversity-based quantum search algorithm to efficiently generate the optimal quantum circuit based on device qubit mapping and noise. By considering the diversity among different candidate circuits and adaptively adding circuit depths, our approach only needs to focus on a small optimization space at each iteration step. In addition, the synchronization of optimizing circuit structure and aligning qubit mapping enables us to generate quantum circuits while avoiding additional mapping overhead. We evaluate the performance of our algorithm on simulators and real quantum devices for quantum eigenvalue problems and classification tasks. Results demonstrate that quantum circuits generated by our method outperform both a fixed hardware-efficient and randomly generated quantum circuits in terms of final performance and resource-saving. Our algorithm provides a flexible way to efficiently generate excellent quantum circuits for significantly improving the performances of VQAs on near-term quantum devices. Published by the American Physical Society 2024
Abstract Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS cannot only alleviate the influence of quantum noise and barren plateaus but also outperforms VQAs with pre-selected ansatze.