Lindblad-like quantum tomography for non-Markovian quantum dynamical maps
arXiv:2403.19799 · doi:10.1038/s41534-025-01044-7
Abstract
We introduce Lindblad-like quantum tomography (LQT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss LQT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of LQT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.
References in corpus (74)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Quantum computational advantage using photons
- Introduction to Quantum Noise, Measurement and Amplification
- Non-Markovian dynamics in open quantum systems
- Error mitigation for short-depth quantum circuits
- Quantum Error Correction for Quantum Memories
- Trapped-Ion Quantum Computing: Progress and Challenges
- Suppressing quantum errors by scaling a surface code logical qubit
- Logical quantum processor based on reconfigurable atom arrays
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Quantum information processing with superconducting circuits: a review
- Universal dynamical decoupling of a single solid-state spin from a spin bath
- Keeping a Quantum Bit Alive by Optimized -Pulse Sequences
- Assessing non-Markovian dynamics
- Quantum Error Mitigation
- Fault-Tolerant Quantum Dynamical Decoupling
- Demonstration of the trapped-ion quantum-CCD computer architecture
- How to Enhance Dephasing Time in Superconducting Qubits
- Quantum process tomography of a controlled-NOT gate
- Canonical form of master equations and characterization of non-Markovianity
- Realization of the quantum Toffoli gate with trapped ions
- Concepts of quantum non-Markovianity: a hierarchy
- Realization of an Error-Correcting Surface Code with Superconducting Qubits
- Quantum simulation and computing with Rydberg-interacting qubits
- Non-Markovian quantum processes: complete framework and efficient characterisation
- Quantum certification and benchmarking
- Demonstration of fault-tolerant universal quantum gate operations
- Dynamical decoupling noise spectroscopy
- Decoherence-Free Subspaces and Subsystems
- Complete methods set for scalable ion trap quantum information processing
- Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
- Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits
- Dynamically Error-Corrected Gates for Universal Quantum Computation
- Fault-tolerant quantum computation with long-range correlated noise
- Process tomography of ion trap quantum gates
- Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
- Dynamical decoupling sequence construction as a filter-design problem
- Quantum Process Tomography of the Quantum Fourier Transform
- Quantum inference of states and processes
- Exact Results on Dynamical Decoupling by -Pulses in Quantum Information Processes
- Pure quantum dephasing of a solid state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions
- Entanglement of two superconducting qubits in a waveguide cavity via monochromatic two-photon excitation
- Theory of quantum system certification: a tutorial
- Measurement of the Noise Spectrum Using a Multiple-Pulse Sequence
- Diagnosis, prescription and prognosis of a Bell-state filter by quantum process tomography
- Quantum process tomography and Linblad estimation of a solid state qubit
- Encoding a magic state with beyond break-even fidelity
- Universal dynamical decoherence control of noisy single-and multi-qubit systems
- A Robust Method for Estimating the Lindblad Operators of a Dissipative Quantum Process from Measurements of the Density Operator at Multiple Time Points
- Non-Markovian Quantum Process Tomography
- Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits
- Direct Measurement of the System-Environment Coupling as a Tool For Understanding Decoherence and Dynamical Decoupling
- Fault-tolerant quantum computation versus Gaussian noise
- Quantum Error Correction in Spatially Correlated Quantum Noise
- Dissipation-Assisted Quantum Information Processing with Trapped Ions
- Dynamical decoupling efficiency versus quantum non-Markovianity
- Learning the dynamics of open quantum systems from their steady states
- Lindblad Tomography of a Superconducting Quantum Processor
- Dissipative ground-state preparation of a spin chain by a structured environment
- Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection
- QInfer: Statistical inference software for quantum applications
- Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
- Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
- Frame-Based Filter-Function Formalism for Quantum Characterization and Control
- Relationship between costs for quantum error mitigation and non-Markovian measures
- Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit
- Characterizing non-Markovian Off-Resonant Errors in Quantum Gates
- Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction
- Practical and reliable error bars for quantum process tomography
- Quantum Transport of Energy in Controlled Synthetic Quantum Magnets
- Compressed gate characterization for quantum devices with time-correlated noise
- Dynamical quantum maps for single-qubit gates under universal non-Markovian noise