Two-qubit Projective Measurements are Universal for Quantum Computation

TL;DR

This paper proves that universal quantum computation can be achieved using only 2-qubit projective measurements, improving previous methods that required measurements on up to 4 qubits.

Contribution

It introduces a new approach that reduces the measurement complexity to 2-qubits, establishing both sufficiency and necessity for universality.

Findings

2-qubit measurements are sufficient for universal quantum computation

A method to partially collapse the $C_k$-hierarchy in gate construction

Identification of discrete universal sets of 2-qubit measurements

Abstract

Nielsen [quant-ph/0108020] showed that universal quantum computation is possible given quantum memory and the ability to perform projective measurements on up to 4-qubits. We describe an improved method that requires only 2-qubit measurements, which are both sufficient and necessary. We present a method to partially collapse the $C_k$-hierarchy in the indirect construction of unitary gates [Gottesman and Chuang, Nature, {\bf 402} 309 (1999)], and apply the method to find discrete universal sets of 2-qubit measurements.