Smallest Fault-Tolerant Universal Quantum Computer via Code Switching

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the Eastin-Knill theorem, which prohibits a universal set of transversal gates within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the [[8, 3, 2]] code, where one version offers weakly fault-tolerant logical Hadamard and phase gates, and the other version implements a logical CCZ gates with transversal T/T^{\dagger} gates and logical CNOT gates with SWAP gates. Because both codes have distance 2, this scheme detects all weight-1 errors, enabling universal, post-selected fault-tolerant computation. This strategy can be generalized to a general code-switching protocol between the [[n, n-2, 2]] and the [[2^D, D, 2]] code families. We also study the performance of our protocol on Grover's algorithm, which illustrates the applicability of our scheme on early fault-tolerant quantum computers.