RQMP Research Seminar

Quantum coding with low-depth random circuits and targeted measurements

Michael Gullans

Princeton

Quantum computers offer computational advantages for the simulation of many-body quantum dynamics in near-term devices. Random quantum circuits have played a central role in establishing these results. Here, we revisit the study of quantum codes generated by low-depth random circuits. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge to zero failure probability below the channel capacity limit in any spatial dimension. These results improve upon previous bounds needed to achieve good coding with a local random circuit. We then introduce an “expurgation” algorithm that uses quantum measurements to remove logical operators that cause the code to fail. With such targeted measurements, we can surpass the depth O(log N) barrier to achieve good codes at sub-logarithmic depth O[(log N)^{1/D}] in D > 1 spatial dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices, which may significantly reduce the resource requirements to achieve fault-tolerance for near-term applications.