Quantum state preparation with optimal T-count
Abstract
How many T gates are needed to approximate an arbitrary n-qubit quantum state to within
a given precision ϵ? Improving prior work of Low, Kliuchnikov and Schaeffer, we show that the
optimal asymptotic scaling is Θ(sqrt{2^n log(1/ε)} + log(1/ε)) if we allow an unlimited number of ancilla qubits. We also show that this is the optimal T-count for implementing an arbitrary
diagonal n-qubit unitary to within error ϵ. We describe an application to batched synthesis of
single-qubit unitaries: we can approximate a tensor product of m = O(log log(1/ϵ)) arbitrary
single-qubit unitaries to within error ϵ with the same asymptotic T-count as is required to
approximate just one single-qubit unitary.
a given precision ϵ? Improving prior work of Low, Kliuchnikov and Schaeffer, we show that the
optimal asymptotic scaling is Θ(sqrt{2^n log(1/ε)} + log(1/ε)) if we allow an unlimited number of ancilla qubits. We also show that this is the optimal T-count for implementing an arbitrary
diagonal n-qubit unitary to within error ϵ. We describe an application to batched synthesis of
single-qubit unitaries: we can approximate a tensor product of m = O(log log(1/ϵ)) arbitrary
single-qubit unitaries to within error ϵ with the same asymptotic T-count as is required to
approximate just one single-qubit unitary.
