Gate fidelity of arbitrary single-qubit gates constrained by conservation laws

TL;DR

This paper derives an upper bound on the fidelity of any single-qubit gate constrained by conservation laws, considering the geometry of the law, the gate's action, and ancilla size, extending previous results beyond specific gates.

Contribution

It generalizes the understanding of conservation law constraints to all single-qubit gates, providing a universal fidelity bound based on geometric and system parameters.

Findings

Derived an upper bound for gate fidelity under conservation laws.

Extended previous constraints from specific gates to all single-qubit gates.

The bound depends on conservation law geometry, gate action, and ancilla size.

Abstract

Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the size of the ancilla.