Accurate and Honest Approximation of Correlated Qubit Noise
arXiv:2311.09305 · doi:10.22331/q-2025-04-09-1701
Abstract
Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the number of qubits. We propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, we first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual noise channel into components based on interqubit correlation degree. We generate a -th order approximate noise channel by truncating the cluster expansion and incorporating noise components with correlations up to the -th degree. We require that the approximate noise channels must be accurate and also ``honest", i.e., the actual errors are not underestimated in our physical models. As an example application, we apply our method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,2]] codeword, which is one of the four Bell states. We find that, for realistic noise strength typical for fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic characterization of multi-qubit noise correlations, it enables the potential for accurate, honest and scalable approximations to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient yet still retain essential noise features of the entire device.
arXiv comment13 pages + 8 pages of Appendix, 11 figures
References in corpus (42)
- Good Quantum Error-Correcting Codes Exist
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- The Magnus expansion and some of its applications
- Reliable Quantum Computers
- A Theory of Fault-Tolerant Quantum Computation
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- Robust randomized benchmarking of quantum processes
- Quantum Error Correction for Beginners
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- Scalable Noise Estimation with Random Unitary Operators
- Procedure for systematically tuning up crosstalk in the cross resonance gate
- A simple all-microwave entangling gate for fixed-frequency superconducting qubits
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Building a fault-tolerant quantum computer using concatenated cat codes
- Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
- Symmetrised Characterisation of Noisy Quantum Processes
- The XZZX Surface Code
- Efficient learning of quantum noise
- Gate Set Tomography
- Quantification and Characterization of Leakage Errors
- A fast, low-leakage, high-fidelity two-qubit gate for a programmable superconducting quantum computer
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- First-principles analysis of cross-resonance gate operation
- Quantum process tomography and Linblad estimation of a solid state qubit
- Detecting and tracking drift in quantum information processors
- Improved quantum algorithms for linear and nonlinear differential equations
- Experimentally scalable protocol for identification of correctable codes
- Non-Markovian Dynamics of Open Quantum Systems: Stochastic Equations and their Perturbative Solutions
- Modeling quantum noise for efficient testing of fault-tolerant circuits
- Lindblad Tomography of a Superconducting Quantum Processor
- Comparison of a quantum error correction threshold for exact and approximate errors
- Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
- Simple master equations for describing driven systems subject to classical non-Markovian noise
- Smoking-gun signatures of non-Markovianity of a superconducting qubit
- Learning correlated noise in a 39-qubit quantum processor
- Open systems dynamics: Simulating master equations in the computer
- Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging
- Fitting quantum noise models to tomography data
- Testing complementarity on a transmon quantum processor
- Fitting time-dependent Markovian dynamics to noisy quantum channels