Quantum compiler: quantum circuit synthesis using optimal control theory

IQC Special Seminar - Sahel Ashhab, National Institute of Information and Communications, Japan

We use numerical optimal-control-theory methods to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. In the first set of calculations, we consider all possible gate configurations for a given number of qubits and a given number of CNOT gates, and we determine the maximum achievable fidelity for the specified parameters. This information allows us to identify the minimum number of gates needed to perform a specific target operation.

It also allows us to enumerate the different gate configurations that can be used for a perfect implementation of the target operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. This last result motivates the second set of calculations, in which we consider only a small fraction of the super-exponentially large number of possible gate configurations for an increasing number of qubits. We find that the fraction of gate configurations that allow us to achieve the desired target operation increases rapidly as soon as the number of gates exceeds the theoretical lower bound for the required number of gates. As a result, a random search can be a highly efficient approach for quantum circuit synthesis. Our results demonstrate the important role that numerical optimal control theory can play in the development of quantum compilers.

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