FET: Small: Improving Quantum Computing and Classical Communication using Discrete Sets of Unitary Matrices

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Quantum computers promise to be more capable than any classical computer at solving certain problems and these devices are moving out of the lab and becoming generally programmable. The different physical implementations of qubits have quite different strengths and weaknesses, and it is essential to consider these characteristics when designing a quantum computer. This project uses the error characteristics of trapped-ion qubits to align algorithm design and hardware implementation for this physical architecture. The research program combines abstract mathematics, quantum physics, and signal processing; it is highly interdisciplinary. Research experience at the interface of engineering physics and signal processing will provide students with the skills needed to build bridges between these disciplines in either academia or industry. Code released on GitHub will encourage use by different research communities.This project will design new algorithms that optimize the realization of logical operators acting on encoded qubits, and that use the error characteristics of trapped-ion qubits to choose appropriate realizations for this architecture. Phase 1 will develop tools for manipulating Pauli operators, including stabilizer groups (with signs), Clifford operators, and diagonal gates represented by symmetric matrices over rings. The software that is developed will be compatible with commonly used software for quantum circuit optimization. Phase 2 will implement efficient algorithms to synthesize stabilizer codes that support transversal small-angle rotations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.