Using Device Physics and Error Mitigation to Improve the Performance of Quantum Computers

Quantum computers have seen rapid development over the last two decades. Despite this, they are not yet scalable or fault-tolerant (i.e. we cannot address arbitrarily many error-corrected qubits). Therefore, improvements that include consideration of the underlying physics are paramount. To do this, we must reduce existing errors and understand how algorithms perform without error correction. In this dissertation, we provide contributions toward these goals. We organize these efforts into three groups.

Firstly, we focus on quantum control. We introduce a novel scheme for performing entangling gates on superconducting qubits. We create fast, high-fidelity entangling operations and single-qubit gates to implement arbitrary quantum operations. Then, we implement entangling gates on real transmon qubits. Finally, we develop new techniques for entangling gates on spin qubits. In total, we improve low-level device performance with high-fidelity entangling operations.

Secondly, we focus on quantum simulation algorithms. First, we apply error mitigation techniques to a quantum simulation algorithm while simultaneously performing device characterization. Then we take advantage of known symmetries of the input Hamiltonian to improve the same algorithm. Then, we demonstrate that this reduces resources compared to other approaches in the presence of noise. Then we compare this technique with state-of-the-art approaches. Then, we improve this algorithm with approaches from quantum control. Finally, we develop a novel algorithm to simulate spin chains on a quantum processor with improved resources compared to other techniques. In total, we improve quantum simulation algorithms, with the aim of better utilizing current devices.

Thirdly, we consider the ADAPT-VQE algorithm, which is used to construct quantum circuits for preparing trial states in quantum simulation. In total, we improve gate counts for the algorithm, improve a separate algorithm by utilizing the gradient criterion, and leverage the repeating structure of an input Hamiltonian to improve performance. Finally, we provide a deeper understanding of ADAPT-VQE and demonstrate its robustness to scaling issues of competing algorithms. In total, we improve the algorithm and its applicability. Thus, we improve quantum simulation algorithms that can be run in the near term.