Optimized Clifford Noise Reduction: Theory, Simulations and Experiments (2504.13356v1)

Abstract: We propose several optimizations of the CliNR partial error correction scheme which implements Clifford circuits by consuming a resource state. Errors are corrected by measuring a sequence of Pauli operators that we refer to as the verification sequence. We first propose a global optimization algorithm searching for a verification sequence resulting in a low logical error rate using tabu search. Then, we introduce a proxy for the logical error rate which is easier to evaluate and we design a two-step optimization algorithm. First, a verification sequence minimizing the proxy is computed, then this sequence is refined by reintroducing the logical error rate. Finally, we identify a large group of automorphisms of the search space which preserve the proxy and we use this symmetry to reduce the size of the search space. This results in a 168 $\times$ (respectively 20,160 $\times$) reduction of the size of the search space for the optimization of verification sequences with three (respectively four) Pauli operators. Our numerical simulations for 20-qubit Clifford circuits with size 400 under the ion chain model show that our optimization algorithms improve the performance of CliNR by 25% and that the two-step optimization achieves the same results as the global optimization with 64% fewer evaluations of the logical error rate. Finally, we perform experiments on a 36-qubit trapped ion quantum computer, without mid-circuit measurements, showing that the CZNR variant of CliNR is at breakeven.

Overview of Optimized Clifford Noise Reduction

The paper, titled "Optimized Clifford Noise Reduction: Theory, Simulations and Experiments," by Edwin Tham and Nicolas Delfosse, presents advancements in the domain of quantum error mitigation through partial error correction schemes. Specifically, the authors focus on optimizing the Clifford Noise Reduction (CliNR) scheme, which is pertinent for implementing Clifford circuits supplemented by a resource state.

Optimization Strategies

The core contribution of the paper is the introduction of several algorithms aimed at minimizing logical error rates during the deployment of the CliNR scheme. The authors propose a global optimization algorithm utilizing tabu search to find verification sequences, sequences of Pauli operator measurements, that result in a minimized logical error rate. In practice, these sequences verify the integrity of resource states before they are consumed in computations.

Two distinct optimization approaches are explored:

1. Global Tabu Search Optimization: This heuristic approach iteratively searches for verification sequences with the lowest logical error rate, leveraging tabu lists to avoid redundant evaluations and minimize computational overhead.
2. Two-step Optimization Using Proxy: To further streamline the process, the paper introduces a proxy for the logical error rate. This proxy correlates with the error rate but is computationally efficient. The authors advance a two-step algorithm where initially, the proxy is minimized, followed by incorporation of actual logical error rate metrics.

Search Space Reduction

A notable theoretical contribution is identifying automorphisms within the verification sequence search space, which preserve the proxy metrics. This symmetry enables a significant reduction in search space dimensions, enhancing computational efficiency. For instances of verification sequences incorporating three Pauli operators, a 168-fold reduction is achieved, and for those with four operators, a reduction by a factor of 20,160 is realized.

Numerical and Experimental Results

Numerical simulations with 20-qubit Clifford circuits under an ion chain noise model reveal that the optimization algorithms proposed improve logical error rates by 25%, compared to previously reported CliNR implementations. Furthermore, the two-step optimization achieves comparable results to global optimization with 64% fewer computations.

On the experimental front, a test was conducted on a 36-qubit trapped ion quantum computer where the CZNR variant of the CliNR scheme demonstrated breakeven performance when employed for verifying resource states. The experiments highlight the practical applicability of CliNR in real-world quantum computing environments, illustrating its efficacy even without mid-circuit measurements.

Implications and Future Work

The findings delineated in this paper have significant implications for quantum computing, suggesting an avenue for reduced qubit overhead amidst non-fault-tolerant regimes. While traditional quantum error correction protocols demand substantial computational resources, the optimized CliNR scheme offers a pragmatic alternative with lower overhead, suitable for near-term implementations.

Future research could focus on refining the proxy metrics to align closely with diverse noise models encountered in various quantum architectures. Additionally, exploring machine learning techniques for dynamic optimization of verification sequences in continuously evolving noise environments could present further improvements in logical error rates.

In summary, this paper contributes valuable methodologies within quantum error reduction, providing a framework that balances computational efficiency with state verification rigor, poised for integration into next-generation quantum computing systems.