Vincent Russo

Elijah Pelofske, Vincent Russo

Quantum circuit unoptimization is an algorithm that transforms a quantum circuit into a different circuit that uses more gate operations while maintaining the same unitary transformation. We demonstrate that this method can implement digital zero-noise extrapolation (ZNE), a quantum error mitigation technique. By employing quantum circuit unoptimization as a form of circuit folding, noise can be systematically amplified. The key advantages of this approach are twofold. First, its ability to generate an exponentially increasing number of distinct circuit variants as the noise level is amplified, which allows noise averaging over many circuit variants with slightly different circuit structure. Averaging over these variants can mitigate the effect of biased error propagation due to the significantly altered circuit structure from quantum circuit unoptimization, or biased noise sources on a quantum processor. Second, quantum circuit unoptimization by design resists circuit simplification back to the original unmodified circuit, making it plausible to use ZNE in contexts where circuit compiler optimization is applied server-side. We evaluate the effectiveness of quantum circuit unoptimization as a noise-scaling method for ZNE in two test cases using depolarizing noise numerical simulations: random quantum volume circuits, where the observable is the heavy output probability, and QAOA circuits for the (unweighted) maximum cut problem on random 3-regular graphs, where the observable is the cut value. We show that using quantum circuit unoptimization to perform ZNE can approximately recover signal from noisy quantum simulations.

Yanis Le Fur, Ethan Egger, Hong-Ye Hu et al.

Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on quantum hardware because of its two main drawbacks: (i) the number of samples increases exponentially in the circuit depth/noise level, and (ii) the classical processing generally grows exponentially in the code distance, though exceptions exist. Additionally, the constant (but often large) overhead of embedding the code and logical operations on hardware can make accuracy worse instead of better. In this work, we seek to provide a clear picture of these opportunities and challenges for scaling quantum error detection on hardware. We do so by performing a detailed benchmarking study on real and simulated noisy quantum computers, using the repetition code and triangular color code for memory experiments and logical computations with up to $74$ physical qubits. In addition to these benchmarks, we estimate the pseudothreshold of codes to map the frontier of error detection on current and future quantum computers. Despite the challenges, our results show strong promise for scaling quantum error detection on hardware.