Measurement-based quantum computation beyond the one-way model

TL;DR

This paper introduces new measurement-based quantum computing schemes utilizing many-body physics tools, demonstrating flexible resource states and novel computational methods beyond the traditional one-way model.

Contribution

It develops a framework combining many-body physics with measurement-based quantum computation, presenting new resource states and computational schemes with increased flexibility.

Findings

New measurement schemes differ from the original one-way model.

Resource states can have long-range correlations or be nearly pure.

Some resource states can be efficiently classically simulated.

Abstract

We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of tools from many-body physics - matrix product states, finitely correlated states or projected entangled pairs states - to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem - how to realize quantum computation - was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting, and present a large number of new examples. We find novel computational schemes, which differ from the original one-way computer for example in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may for example exhibit non-vanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.