Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states

TL;DR

This paper introduces a measurement-based quantum computation scheme using hypergraph states that allows massive parallelization of certain gates, leading to a new trade-off between space and time complexity in quantum circuits.

Contribution

It develops a deterministic universal measurement-based quantum computation scheme with enhanced parallelization and a novel space-time complexity trade-off using hypergraph states.

Findings

Massive parallelization of CCZ and SWAP gates in the scheme

Logarithmic-depth implementation of controlled-Z gates

New trade-off between space and time complexity in quantum computation

Abstract

While the circuit model of quantum computation defines its logical depth or "computational time" in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical gates. By developing techniques to analyze Pauli measurements on multi-qubit hypergraph states generated by the Controlled-Controlled-Z (CCZ) gates, we introduce a deterministic scheme of universal measurement-based computation. In contrast to the cluster-state scheme, where the Clifford gates are parallelizable, our scheme enjoys massive parallelization of CCZ and SWAP gates, so that the computational depth grows with the number of global applications of Hadamard gates, or, in other words, with the number of changing computational bases. A logarithmic-depth implementation of an N-times Controlled-Z gate illustrates a novel trade-off between space and time complexity.