Citation: Morvan, Alexis, et al. "Phase transition in random circuit sampling." arXiv preprint arXiv:2304.11119 (2023).
Web: https://arxiv.org/abs/2304.11119
Tags: Phase-transition, Hardware, Error-correcting-codes
This paper discuss the act of sampling random circuits on a noisy quantum computer. The idea is as follows. Consider a high-depth quantum circuit on a noisy quantum computer. The circuit will try to explore and exploit coherent long-range correlations in the computer. However, because the computer is noisy it will not have any long-range coherent correlations! Thus, the circuit will not depend on long-range correlations. Thus, insofar as the outputs of the circuits are concerned, The larger quantum system can be essentially modeled as a collection of several smaller decoupled quantum systems.
In a regime where the circuit depth is deep, the number of qubits is large, and the error rate is large, this approximation of the system as several decoupled subsystems is accurate. When the number of qubits is small and the error rate is small, this approximation will not be accurate as well! In other words, as the error rate changes there is a quantum phase transition in the behavior of the output of the systems.
This paper also identifies a second interesting phase transition.
The reason I like this paper is as follows. I am interested in studying topological quantum systems. These systems undergo phase transitions, have gaps, symmetries, and all sorts of other interesting phenomena. An important point is that error corrected quantum computers are topological quantum systems. They really do have topological entanglement. In that way, we can study error corrected quantum computers not as a technology to use for applications but as a scientific object of interest in its own right. Non error corrected quantum computers are not particularly interesting - they can be simulated classically, as discussed in this paper. They only get interesting when they become topological. This paper is a perfect example of what I mean when I say that you can study error corrected quantum computers intrinsically and unbiased by your desired for them, as lovely topological systems which can undergo phase transitions like any other.