Leakage benchmarking with decohering subgroups in the presence of preparation and measurement errors
Abstract
A common problem with physical qubits is that the state can leak outside the computational subspace. To characterize the problem, it is desirable to measure both the leakage probability and the fidelity of gates inside the computational subspace. Randomized benchmarking is a readily accessible method for estimating average gate fidelities and can be modified to account for leakage. However, in the presence of state preparation and measurement errors (SPAM) there are parameter degeneracies, and fidelities and leakage become underdetermined. We study the example of qudits with any number of leakage levels under the assumption of gate-independent noise. We show that randomized benchmarking sequences with leakage level decoherence can be analyzed as a Markov process with noisy classical preparations and measurements. This result generalizes to randomized benchmarking with random gates from an arbitrary group that contains a phase-decohering subgroup. We characterize the parameter degeneracy in inferring the Markov process, preparations and measurements. Based on this characterization we develop a measurement and inference method taking advantage of known conservative bounds on SPAM to constrain fidelity, leakage and other parameters of the Markov process, state preparations and measurements. As part of our study, we experimentally implemented the measurement method for a qubit defined on the one-excitation subspace of two transmons, for which there are two leakage levels. We determined confidence intervals accounting for parameter degeneracy for a number of performance parameters of the system. For leakage and fidelity, we compare these intervals to those obtained for several conventional methods for leakage benchmarking.
Related
- Initial-State Preparation for Strongly Correlated Molecules from Matrix Product States: Benchmarking and Environment-Aware Divide-and-Conquer Compilation
- On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse
- Benchmarking Single-Photon Sources for Measurement-Device-Independent Quantum Key Distribution
- Experimental Measurement-Device-Independent Quantum Key distribution with Flawed State-Preparation over 300 km
- Less precise but less noisy: local circuits for momentum-space state preparation and measurement
BibTeX
@misc{geller2026leakage,
title = {{Leakage benchmarking with decohering subgroups in the presence of preparation and measurement errors}},
author = {Shawn Geller and Tongyu Zhao and Alex Kwiatkowski and Scott Glancy and Raymond W. Simmonds and Emanuel Knill},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19304},
eprint = {2610.19304},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19304},
}
RIS
TY - UNPB
TI - Leakage benchmarking with decohering subgroups in the presence of preparation and measurement errors
AU - Shawn Geller
AU - Tongyu Zhao
AU - Alex Kwiatkowski
AU - Scott Glancy
AU - Raymond W. Simmonds
AU - Emanuel Knill
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19304
UR - https://arxiv.org/abs/2610.19304
AB - A common problem with physical qubits is that the state can leak outside the computational subspace. To characterize the problem, it is desirable to measure both the leakage probability and the fidelity of gates inside the computational subspace. Randomized benchmarking is a readily accessible method for estimating average gate fidelities and can be modified to account for leakage. However, in the presence of state preparation and measurement errors (SPAM) there are parameter degeneracies, and fidelities and leakage become underdetermined. We study the example of qudits with any number of leakage levels under the assumption of gate-independent noise. We show that randomized benchmarking sequences with leakage level decoherence can be analyzed as a Markov process with noisy classical preparations and measurements. This result generalizes to randomized benchmarking with random gates from an arbitrary group that contains a phase-decohering subgroup. We characterize the parameter degeneracy in inferring the Markov process, preparations and measurements. Based on this characterization we develop a measurement and inference method taking advantage of known conservative bounds on SPAM to constrain fidelity, leakage and other parameters of the Markov process, state preparations and measurements. As part of our study, we experimentally implemented the measurement method for a qubit defined on the one-excitation subspace of two transmons, for which there are two leakage levels. We determined confidence intervals accounting for parameter degeneracy for a number of performance parameters of the system. For leakage and fidelity, we compare these intervals to those obtained for several conventional methods for leakage benchmarking.
ER -