Qubit fidelity under stochastic Schrödinger equations driven by colored noise

Abstract

Environmental noise on a controlled quantum system is generally modeled by a dissipative Lindblad equation. This equation describes the average state of the system via the density matrix $\rho$. One way of deriving this Lindblad equation is by introducing a stochastic operator evolving under white noise in the Schrödinger equation. However, white noise, where all noise frequencies contribute equally in the power spectral density, is not a realistic noise profile as lower frequencies generally dominate the spectrum. Furthermore, the Lindblad equation does not fully describe the system as a density matrix $\rho$ does not uniquely describe a probabilistic ensemble of pure states $\{{\psi }_j{\}}_j$. In this work, we introduce a method for solving for the full distribution of qubit fidelity driven by important stochastic Schrödinger equation cases, where qubits evolve under more realistic noise profiles, e.g. Ornstein-Uhlenbeck noise. This allows for predictions of the mean, variance, and higher-order moments of the fidelities of these qubits, which can be of value when deciding on the allowed noise levels for future quantum computing systems, e.g. deciding what quality of control systems to procure. Furthermore, these methods will prove to be integral in the optimal control of qubit states under (classical) control system noise.

arXiv comment14 pages, 7 figures

References in corpus (36)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A short introduction to the Lindblad Master Equation
• 1/f noise: implications for solid-state quantum information
• Quantum simulation and computing with Rydberg-interacting qubits
• Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Arbitrary quantum control of qubits in the presence of universal noise
• Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
• Stochastic Schrodinger equations
• Density-matrix simulation of small surface codes under current and projected experimental noise
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• A simple derivation of the Lindblad equation
• Optimizing Rydberg Gates for Logical Qubit Performance
• Stochastic jump processes for non-Markovian quantum dynamics
• Compilation by stochastic Hamiltonian sparsification
• Sensitivity of quantum gate fidelity to laser phase and intensity noise
• Creation of 2000-atom Greenberger-Horne-Zeilinger states by entanglement amplification
• Robust control and optimal Rydberg states for neutral atom two-qubit gates
• Improving qubit coherence using closed-loop feedback
• Simple master equations for describing driven systems subject to classical non-Markovian noise
• Stochastic Schrödinger equations with coloured noise
• Lindblad Decoherence in Atomic Clocks
• Semi-martingale driven variational principles
• Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation
• Pulse based Variational Quantum Optimal Control for hybrid quantum computing
• A novel approach to noisy gates for simulating quantum computers
• Fast shuttling of a particle under weak spring-constant noise of the moving trap
• The effect of fast noise on the fidelity of trapped-ions quantum gates
• Stochastic Schrödinger Equations for Markovian and non-Markovian cases
• Impacts of Noise and Structure on Quantum Information Encoded in a Quantum Memory
• Characterizing low-frequency qubit noise
• Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels
• Modeling and simulation of a quantum thermal noise on the qubit
• Master Equation Emulation and Coherence Preservation with Classical Control of a Superconducting Qubit
• Control limit on quantum state preparation under decoherence

Cited by in corpus (5)

• Fidelity-Enhanced Variational Quantum Optimal Control
• Engineering the uncontrollable: Steering noisy spin-correlated radical-pairs with coherent and incoherent control
• On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians
• Fidelity Relations in an Array of Neutral Atom Qubits -- Experimental Validation of Control Noise
• Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach