Scalable Method Improves Quantum Processor Accuracy

Quantum computers are advancing rapidly, but their performance is often limited by errors that occur during computation. In the noisy intermediate-scale quantum (NISQ) era, devices with tens of qubits are accessible, yet errors in state preparation and measurement (SPAM) can undermine their reliability. Characterizing these errors is crucial for improving accuracy, but traditional methods require an exponential number of experiments as qubit counts increase, making them impractical for large systems. This study introduces a scalable technique to approximate measurement fidelity matrices (MFMs), which describe how errors affect quantum states, by focusing on correlations among small groups of qubits.

The researchers found that MFMs can be constructed using a cumulant expansion method, which leverages low-order correlations from one- and two-qubit measurements to approximate larger matrices. This approach significantly reduces the number of required experiments compared to full MFM determination, which grows exponentially with qubit count. For instance, on a 5-qubit system, the cumulant method used measurements from smaller subsystems to build an approximate MFM, achieving results close to those from direct measurements without the high cost.

The methodology involved executing quantum circuits on superconducting processors like IBM's ibmq_valencia and ibmq_5_yorktown. Circuits prepared specific quantum states and measured outcomes to estimate conditional probabilities for MFMs. The team compared approximations built from vendor calibration data, direct one- and two-qubit MFMs, and expansions including higher-order terms. They also employed spectator qubits—additional qubits manipulated with Hadamard gates—to randomize noise and improve accuracy in some cases. Metrics such as the Frobenius norm difference (||K - ~K||F) and fidelity differences (Δf) quantified how well approximations matched full MFMs.

Results showed that the cumulant-based reconstructions captured key error patterns without full scalability limitations. For example, on ibmq_valencia, the 5-qubit MFM approximation using one- and two-qubit data had a ||K - ~K||F value of 0.658, indicating reasonable accuracy. Cluster product methods, which combine MFMs from disjoint qubit groups, further improved fidelity in systems like ibmq_johannesburg, where 8-qubit approximations reduced Δf to as low as 0.002. The scalar correlation factor (SCF) metric identified statistically significant qubit correlations, such as strong links between qubits 1 and 4 on ibmq_valencia, highlighting error hotspots. However, accuracy varied by device; on ibmq_cambridge, some reconstructions overestimated errors, underscoring dependence on the specific noise environment.

The study's motivation stems from the need for scalable benchmarks in NISQ computing, where end users require efficient error characterization to enhance application performance. By enabling better identification of correlated errors, this method supports applications like spatial multiplexing, where uncorrelated qubit subsets can be used simultaneously to boost computational efficiency. The authors emphasize that this approach helps quantify error locations and strengths, aiding in error mitigation strategies without full tomography.

Limitations include the method's reliance on low-order correlations, which may miss higher-order effects in noisier systems. The authors note that accuracy depends on the degree of correlation captured by subsystems, and in cases like ibmq_johannesburg, adding spectator qubits did not consistently improve results. Statistical uncertainties from measurement outcomes also impose bounds on correlation detection, requiring sufficient sample sizes for reliability.

References: [1] K. E. Hamilton et al., arXiv:2006.01805v1 [quant-ph] (2020).