Filter Function Formalism and Software Package to Compute Quantum Processes of Gate Sequences for Classical Non-Markovian Noise

Abstract

Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of noise on sequences of quantum gates cannot be described by concatenating isolated quantum operations if the environmental correlation times are on the scale of the typical gate durations. The filter function formalism has been successful in characterizing the decay of coherence under the influence of such classical, non-Markovian environments and here we show it can be applied to describe unital evolution within the quantum operations formalism. We find exact results for the quantum process and a simple composition rule for a sequence of operations. This enables the detailed study of effects of noise correlations on algorithms and periodically driven systems. Moreover, we point out the method's suitability for numerical applications and present the open-source Python software package filter_functions. Amongst other things, it facilitates computing the noise-averaged transfer matrix representation of a unital quantum operation in the presence of universal classical noise for arbitrary control sequences. We apply the presented methods to selected examples.

arXiv comment35 pages, 8 figures. In-depth article accompanying arXiv:2103.02385. Open-source software available at https://github.com/qutech/filter_functions. v2: published version

References in corpus (82)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Quantum Computation with Quantum Dots
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Quantum Computing
• Charge insensitive qubit design derived from the Cooper pair box
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• The Magnus expansion and some of its applications
• Two-Bit Gates are Universal for Quantum Computation
• Randomized Benchmarking of Quantum Gates
• An addressable quantum dot qubit with fault-tolerant control fidelity
• A >99.9%-fidelity quantum-dot spin qubit with coherence limited by charge noise
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Prescription for experimental determination of the dynamics of a quantum black box
• A single-atom electron spin qubit in silicon
• Demonstration of a small programmable quantum computer with atomic qubits
• Robust randomized benchmarking of quantum processes
• Quantum Error Correction for Beginners
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
• Optimized Dynamical Decoupling in a Model Quantum Memory
• 1/f noise: implications for solid-state quantum information
• Quantum CNOT Gate for Spins in Silicon
• How to Enhance Dephasing Time in Superconducting Qubits
• The Bloch Vector for N-Level Systems
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• Ion-trap measurements of electric-field noise near surfaces
• Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
• Chopped random-basis quantum optimization
• Bloch vectors for qudits
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit
• An approximate Fourier transform useful in quantum factoring
• Universal dynamical control of quantum mechanical decay: Modulation of the coupling to the continuum
• Dynamical decoupling noise spectroscopy
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Quantification and Characterization of Leakage Errors
• Randomized Benchmarking with Confidence
• Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
• Origin and Suppression of $1/f$ Magnetic Flux Noise
• Qubit noise spectroscopy for non-Gaussian dephasing environments
• Rotating-frame relaxation as a noise spectrum analyzer of a superconducting qubit undergoing driven evolution
• Experimental noise filtering by quantum control
• Arbitrary quantum control of qubits in the presence of universal noise
• Investigating the limits of randomized benchmarking protocols
• Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
• Measurement of the Noise Spectrum Using a Multiple-Pulse Sequence
• Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• The impact of classical control electronics on qubit fidelity
• Observation of Floquet states in a strongly driven artificial atom
• Environmental noise spectroscopy with qubits subjected to dynamical decoupling
• A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
• Combining dynamical decoupling with fault-tolerant quantum computation
• Local observation of antibunching in a trapped Fermi gas
• Analog control of open quantum systems under arbitrary decoherence
• Notch filtering the nuclear environment of a spin qubit
• Robust Extraction of Tomographic Information via Randomized Benchmarking
• Robustness of composite pulses to time-dependent control noise
• Spectrum of the Nuclear Environment for GaAs Spin Qubits
• Introduction to Quantum Gate Set Tomography
• The effect of noise correlations on randomized benchmarking
• High-order noise filtering in nontrivial quantum logic gates
• Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage
• Non-exponential Fidelity Decay in Randomized Benchmarking with Low-Frequency Noise
• Fault-tolerant quantum computation versus Gaussian noise
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Achieving High-Fidelity Single-Qubit Gates in a Strongly Driven Charge Qubit with $1/f$ Charge Noise
• Experimental quantum verification in the presence of temporally correlated noise
• Estimating the coherence of noise in quantum control of a solid-state qubit
• Microscopic models for charge-noise-induced dephasing of solid-state qubits
• High-fidelity gate set for exchange-coupled singlet-triplet qubits
• Dynamically corrected gates suppress spatio-temporal error correlations as measured by randomized benchmarking
• Pulse sequence designed for robust C-phase gates in SiMOS and Si/SiGe double quantum dots
• Filter Functions for Quantum Processes under Correlated Noise
• Analytic Filter Function Derivatives for Quantum Optimal Control
• Self-Consistent Calibration of Quantum Gate Sets
• Efficient continuous wave noise spectroscopy beyond weak coupling
• On the Matrix Representation of Quantum Operations