Abstract
A major challenge in quantum computing lies in our ability to efficiently perform computations fault-tolerantly. Schemes for such fault-tolerance often rely on quantum error-correcting codes with two key properties, namely (1) low-weight stabilizers (i.e. parity-checks), and (2) transversal non-Clifford gates (which provide a sort of algebraic structure). Yet these properties have proven difficult to obtain. Indeed, the first asymptotically good codes achieving either property (1) or (2) alone were only recently constructed. Asymptotically good codes achieving both properties simultaneously, which could lead to new fault-tolerance protocols with improved efficiency and error resilience, have remained out of reach.
In this talk, we describe new code constructions providing progress on this problem. We present the first known asymptotically good quantum codes with sublinear-weight checks that support transversal non-Clifford gates. We also obtain new constructions of (nearly) asymptotically good quantum codes with constant or subpolynomial-weight checks that are not based on the lifted/balanced product operation used in prior constructions. Instead, our codes are based on the much more elementary tensor product.
Based on joint work with Venkatesan Guruswami.