PME SPECIAL QUANTUM SEMINAR: Quantum Computing at the Physical Layer

Quantum computing is ultimately implemented on physical devices. However, there is a lack of systematic research into the following two fundamental questions: 1. What quantum operations can be implemented on a given hardware device? 2. How do we use these operations for computational tasks? In this talk, we give answers for two-qubit operations used for circuit synthesis. Given the two-qubit Hamiltonian of a physical device, we explore the diverse space of two-qubit operations that it can support and mathematically evaluate their corresponding compilation capabilities. We in particular show that a general class of device Hamiltonians can support all possible two-qubit operations modulo single-qubit operations. We also formulate a necessary novel single-qubit gate compilation scheme that is compatible with general two-qubit gates, thereby enabling universal quantum computation.