High-Rate Surgery: towards constant-overhead logical operations

Abstract: Scalable quantum computation requires not only quantum codes with low memory overhead but also encoded operations with low space-time overhead. High rate quantum low-density parity-check (qLDPC) codes address the former by achieving a high information-encoding rate, yet existing methods for implementing logical operations often suffer from a low information-processing rate, leading to substantial space-time costs. Here, we introduce high-rate surgery, a general scheme that can perform extensive, addressable logical Pauli-product measurements in parallel on arbitrary qLDPC codes using a shared ancilla system, attaining nearly constant space-time overhead. We develop both algebraic and randomized ancilla constructions and demonstrate, using the $[[144, 12, 12]]$ Gross code and new instances of qLDPC codes (e.g., $[[1125, 245, \leq 10]]$) with encoding rate up to $25\%$, that up to hundreds of randomly sampled logical measurements can be executed simultaneously with a total space-time overhead around a factor of two of that of memory experiments. Our results address a major bottleneck for performing complex, addressable logical operations on qLDPC codes in practice, advancing the prospect of scalable, constant-overhead fault-tolerant quantum computation.