Circuit Optimization for Universality Transformation

TL;DR

This paper presents a shorter circuit for transforming a universal gate set to a strictly universal one, eliminating the need for non-imaginary ancillary qubits, and extends the approach to continuous gate sets.

Contribution

It introduces a more efficient circuit for universality transformation and generalizes the method to continuous multi-qubit unitary generation.

Findings

Successfully reduces circuit complexity for universality transformation.

Extends the transformation to continuous multi-qubit unitary generation.

Demonstrates exact generation of any multi-qubit unitary with a specific gate set.

Abstract

It is known that a computationally universal gate set $\{H,CCZ\}$ can be transformed to a strictly universal one $\{H, \Lambda(S)\}$ using one maximally imaginary state $|+i \rangle$ and non-imaginary ancillary qubits. We succeed this transformation with a shorter circuit that eliminates non-imaginary ancillary qubits. We further extend this to the continuous gate-set setting, showing that any multi-qubit unitary can be exactly generated by real single-qubit unitary gates, $CCZ$ gates and $|0 \rangle |+i \rangle$.