Hybrid quantum-classical algorithms and error mitigation

Thesis

These days, research groups such as Google, Microsoft, and Rigetti are working towards fabricating quantum devices which have hundreds to thousands of qubits. In recently proposed quantum algorithms, i.e. hybrid quantum-classical algorithms, such quantum devices are used as subroutines for calculation of classically intractable tasks. However, the applicability of hybrid algorithms was quite limited, for example, the search of the ground state, and simulation of the dynamics of quan- tum systems. In addition, near-term quantum devices are expected to be quite noisy, impairing the precision of computation seriously and removing any potential advantages with quantum computers. Therefore, it is necessary to extend the applicability of hybrid algorithms and mitigate errors on quantum computers.

In this thesis, we describe the generalisation of hybrid algorithms so that they can be applied to variety of problems, such as search of the spectrum of quantum systems, simulation of open quantum systems and even general mathematical tasks. The algorithm for finding spectra is useful for applications such as new drug discovery, design of batteries. Generally speaking, quantum systems of interest to physicists, chemists, and materials scientists inevitably interact with their environments, and quantum states are decohered. Therefore, to investigate quantum phenomena, new algorithms simulating open quantum systems are described in this thesis. Algorithms for general mathematical tasks such as matrix multiplication to a vector and solving linear equations, useful for a large number of problems, such as machine learning, are also presented.

Furthermore, in order to make hybrid algorithms useful, we also invented a practical error mitigation method for suppressing physical errors, which may make hybrid algorithms useful. We showed that errors can be suppressed for a quantum system with over 50 qubits for the current achievable error rate, which is believed to be hard to simulate with classical computers. Also, we generalised the error mitigation technique to be applied to mitigate algorithmic errors, which may enhance the accuracy of Hamiltonian simulation.

Authors: Endo, S; Benjamin, S

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Near term quantum computing
• Subjects: Quantum computing