Quantum error mitigation via structural encoding with classical error correction codes

Bridging the gap between today’s noisy quantum hardware and future fault-tolerant systems requires practical error management strategies that go beyond statistical mitigation. We propose a scheme that embeds quantum algorithms within the structure of classical error correction codes, offering a step toward fault-tolerance without the full overhead of quantum error correction. Our approach targets the asymmetric structure of many key algorithms, where complex, problem-defining diagonal operators (e.g., oracles) are paired with simple, fixed non-diagonal operators (e.g., diffusion operators). The core of our scheme is an encoding that commutes with the diagonal operators, obviating any associated overhead, while confining the main computational overhead of encoding and decoding to the non-diagonal components. This approach concentrates error resilience where it is most needed. Noisy simulations demonstrate that our scheme substantially improves the probability of success, providing a viable strategy to enhance quantum algorithmic performance pending the arrival of full-scale fault-tolerance.