Not all physical errors can be linear CPTP maps in a correlation space

TL;DR

This paper reveals that not all physical errors in measurement-based quantum computation can be represented as linear CPTP maps in the correlation space, challenging assumptions in fault-tolerance simulations.

Contribution

It demonstrates that physical errors do not always translate into linear CPTP errors in the correlation space, highlighting limitations in fault-tolerance modeling.

Findings

Not all physical errors are linear CPTP maps in correlation space.

Fault-tolerance theories assuming such errors may not be directly applicable.

Challenges in simulating fault-tolerant circuits with general resource states.

Abstract

In the framework of quantum computational tensor network, which is a general framework of measurement-based quantum computation, the resource many-body state is represented in a tensor-network form, and universal quantum computation is performed in a virtual linear space, which is called a correlation space, where tensors live. Since any unitary operation, state preparation, and the projection measurement in the computational basis can be simulated in a correlation space, it is natural to expect that fault-tolerant quantum circuits can also be simulated in a correlation space. However, we point out that not all physical errors on physical qudits appear as linear completely-positive trace-preserving errors in a correlation space. Since the theories of fault-tolerant quantum circuits known so far assume such noises, this means that the simulation of fault-tolerant quantum circuits in a correlation space is not so straightforward for general resource states.