Method for efficient implementation of diagonal operators over CLIFFORD+T basis

Abstract

Quantum circuits and circuit designs are based on factorizations of diagonal unitaries using a phase context. The cost / complexity of phase sparse / phase dense approximations is compared, and a suitable implementation is selected. For phase sparse implementations in the Clifford+T basis, required entangling circuits are defined based on a number of occurrences of a phase in the phase context in a factor of the diagonal unitary.

Description

technical field [0001] This disclosure relates to quantum computing. Background technique [0002] Diagonal operators appear in a variety of different quantum computing algorithms, and their efficient implementation is crucial for creating practical implementations on the proposed quantum computing architecture. In the case of an exact diagonal operator factorization with exact approximation precision, the exact factorization exhibits the property that all entanglement occurs by using elementary CNOT gates with a small error-tolerance cost. This results in the completeness of the quantum resource complexity placed in the number of per-qubit spins, which in these approaches typically has exponential scaling. In some cases, exact factorization of the diagonal operator yields single-qubit rotations that are difficult or impossible to achieve precisely by using Clifford+T general-purpose gate ensembles. Therefore, single-qubit approximation methods are often required. [0003...

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Problems solved by technology

However, since these approaches lead to zero-fault-tolerant implementation costs in entanglement operations, the fault-tolerance cost of circuits can quickly grow to the point where it is not feasible in practical implementations of quantum computing architectures.

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