Fitting quantum noise models to tomography data

Abstract

The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavourable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes. In the case of dynamics consistent with Markovian evolution, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition. We provide a Python implementation of all our algorithms, and benchmark these on a range of 1- and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate values of non-Markovianity that match analytical calculations.

arXiv commentpublished version, 36 + 24 pages, merging material from arXiv:2303.08936. Code available at: https://gitlab.com/TamaraKohler/non-markovianity

References in corpus (38)

• Quantum Computing in the NISQ era and beyond
• On the Measurement of Qubits
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Assessing non-Markovian dynamics
• Quantum state estimation
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Measure for the Non-Markovianity of Quantum Processes
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Optimal, reliable estimation of quantum states
• On the degree of non-Markovianity of quantum evolution
• Concepts of quantum non-Markovianity: a hierarchy
• Quantum certification and benchmarking
• Non-Markovian quantum jumps
• Dividing Quantum Channels
• Operational Markov condition for quantum processes
• Geometrical characterization of non-Markovianity
• Fault-tolerant quantum computation with long-range correlated noise
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Finding the Kraus decomposition from a master equation and vice versa
• Comparative study of non-Markovianity measures in exactly solvable one and two qubit models
• Contractivity of positive and trace preserving maps under $L_p$ norms
• Completely Positive Divisibility Does Not Mean Markovianity
• An alternative non-Markovianity measure by divisibility of dynamical map
• Machine learning non-Markovian quantum dynamics
• Detecting and tracking drift in quantum information processors
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Fault-tolerant quantum computation versus Gaussian noise
• Is there a Floquet Lindbladian?
• Lindblad Tomography of a Superconducting Quantum Processor
• Quantum advantage in simulating stochastic processes
• Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
• High-frequency expansions for time-periodic Lindblad generators
• Learning Non-Markovian Quantum Noise from Moiré-Enhanced Swap Spectroscopy with Deep Evolutionary Algorithm
• The Complexity of Divisibility
• Non-Markovianity as a Resource for Quantum Technologies

Cited by in corpus (8)

• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Accurate and Honest Approximation of Correlated Qubit Noise
• Almost All Quantum Channels Are Diagonalizable
• Quantum noise modeling through Reinforcement Learning
• Response kinetic uncertainty relation for Markovian open quantum systems
• Neural Network Based Qubit Environment Characterization