Measurement-based quantum computation cannot avoid byproducts

TL;DR

Measurement-based quantum computation inherently involves byproducts due to fundamental physical principles, making it impossible to have a completely byproduct-free resource state.

Contribution

The paper proves that respecting the no-signaling principle prevents the existence of universal resource states without byproducts in measurement-based quantum computation.

Findings

Byproducts are unavoidable in measurement-based quantum computation.

No-signaling principle constrains the possibility of byproduct-free resource states.

Universal resource states must involve byproducts due to fundamental physics.

Abstract

Measurement-based quantum computation is a novel model of quantum computing where universal quantum computation can be done with only local measurements on each particle of a quantum many-body state, which is called a resource state. One large difference of the measurement-based model from the circuit model is the existence of byproducts. In the circuit model, a desired unitary U can be implemented deterministically, whereas the measurement-based model implements BU, where B is an additional operator, which is called a byproduct. In order to compensate byproducts, following measurement angles must be adjusted. Such a feed-forwarding requires some classical processing and tuning of the measurement device, which cause the delay of computation and the additional decoherence. Is there any byproduct-free resource state? Here we show that if we respect the no-signaling principle, which is one of the most fundamental principles of physics, no universal resource state can avoid byproducts.