Error Bounds for Variational Quantum Time Evolution

Abstract

Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We derive global phase agnostic error bounds for the state simulation accuracy with variational quantum time evolution that improve the tightness of fidelity estimates over existing error bounds. These analysis tools are practically crucial for assessing the quality of the simulation and making informed choices about simulation hyper-parameters. The efficient, a posteriori evaluation of the bounds can be tightly integrated with the variational time simulation and, hence, results in a minor resource overhead which is governed by the system's energy variance. The performance of the novel error bounds is demonstrated on numerical examples.

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• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Provable bounds for noise-free expectation values computed from noisy samples
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Gate-based quantum simulation of Gaussian bosonic circuits on exponentially many modes
• Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Performance and scaling analysis of variational quantum simulation
• Practical limitations of quantum data propagation on noisy quantum processors
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Exponential Separation Criteria for Quantum Iterative Power Algorithms
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations
• Error and Resource Estimates of Variational Quantum Algorithms for Solving Differential Equations Based on Runge-Kutta Methods