Hybrid quantum-classical algorithms and quantum error mitigation (2011.01382v1)

Abstract: Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies.

• The paper introduces hybrid quantum-classical approaches by integrating variational quantum algorithms with error mitigation techniques to optimize NISQ device performance.
• It details methods including VQE, QAOA, Richardson extrapolation, and quasi-probability correction to address practical computational challenges.
• The research outlines future directions for enhancing quantum simulations and machine learning applications in near-term quantum systems.

Overview of "Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation"

The paper "Hybrid quantum-classical algorithms and quantum error mitigation" provides a comprehensive review of methodologies and techniques designed for exploiting noisy intermediate-scale quantum (NISQ) devices. The authors, Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan, identify two primary categories of algorithms that can be executed on these near-term quantum devices: variational quantum algorithms and quantum error mitigation strategies. These methods are crucial in pushing the boundaries of what current quantum technology can achieve, given its inherent limitations due to noise and the lack of fault-tolerant universal quantum computation.

Hybrid Quantum-Classical Algorithms

1. Variational Quantum Algorithms (VQAs):

VQAs are pivotal in leveraging NISQ devices by integrating quantum processes with classical computational methods to solve optimization problems. The paper discusses multiple instances of VQAs such as the Variational Quantum Eigensolver (VQE) for finding ground state energies, and the Quantum Approximate Optimization Algorithm (QAOA), which is designed for addressing combinatorial optimization problems.

• Variational Quantum Eigensolver: Used for quantum chemistry and material science, VQE utilizes parameterized quantum circuits to approximate ground state energies of Hamiltonians.
• Quantum Approximate Optimization Algorithm: Aims at solving classical optimization problems by encoding them into Hamiltonian form, providing a structure suitable for NISQ deployment.

1. Applications Beyond Optimization:

VQAs also extend to tasks like simulating time evolution (variational quantum simulations), simulating open quantum systems, and preparing Gibbs states. These applications align closely with both practical simulations of physical systems and fundamental research areas in quantum computing.

1. Machine Learning and Beyond:

Besides optimization and simulation, there is an exploration of VQAs in machine learning contexts, such as quantum neural networks and generative models which are designed to harness quantum advantages for data-driven tasks.

Quantum Error Mitigation Techniques

Given the noise present in NISQ devices, quantum error mitigation strategies are integral to extracting reliable and valid computational results from quantum processors.

1. Error Extrapolation Methods:

Techniques like Richardson extrapolation are discussed, which aim to infer zero-noise results by running circuits at multiple effective noise levels and extrapolating the outcomes.

1. Quasi-Probability Methods:

These are strategies that attempt to negate noise by effectively inverting the noise channels through controlled applications of corrective operations, albeit with increased measurement overhead.

1. Symmetry Verification and Subspace Expansion:

Utilizing inherent symmetries of quantum systems to perform error checks and corrections is another proposed method for improving the fidelity of achieved outcomes from quantum algorithms.

1. Measurement Error Mitigation:

Specific techniques that address errors introduced during the measurement phase, ensuring that readouts reflect the intended quantum states as accurately as possible.

Implications and Future Directions

The research documented in this paper has significant implications for both the theoretical and practical execution of quantum algorithms. By establishing methodologies to mitigate errors and optimize hybrid algorithms, the paper underscores a pathway to demonstrating quantum advantages on existing architectures. Importantly, these efforts support the move towards more extensive, accurate, and reliable quantum computations, enfolding these benefits into broader areas such as quantum chemistry, materials science, and even emerging quantum machine learning fields.

Future research is likely to focus on enhancing these techniques' efficiency, potentially integrating them within more complex quantum systems, and exploring their applicability across increasingly complex problem domains. The hybrid nature of these algorithms ensures that they remain relevant even as fully fault-tolerant quantum computing continues to develop.