Halving the cost of quantum multiplexed rotations

TL;DR

This paper presents a method to significantly reduce the quantum resource costs, specifically T gates and qubits, for implementing multiplexed quantum rotations, thereby enhancing the efficiency of quantum algorithms like electronic structure simulations.

Contribution

It introduces a novel approach that halves the T gate count and reduces qubit requirements for multiplexed rotations, improving quantum algorithm efficiency.

Findings

Halves the T gate count for quantum multiplexed rotations.

Reduces qubit requirements by up to a factor of two.

Improves efficiency of electronic structure simulation algorithms.

Abstract

We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn b})$, and reduce the number of qubits needed by up to a factor of two. This generic quantum circuit primitive is found in many quantum algorithms, and our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations. We achieve this by extending recent ideas on stochastic compilation of quantum circuits to classical data and discuss space-time trade-offs and concentration of measure in its implementation.