Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation

Abstract

Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to recent proposals for variational approaches to dynamical simulation. In this work, we aim to make variational dynamical simulation even more practical and near-term. We propose a new algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. VHD allows for fast forwarding, i.e., simulation beyond the coherence time of the quantum computer with a fixed-depth quantum circuit. It also removes Trotterization error and allows simulation of the entire Hilbert space. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. Moreover, we prove that the VHD cost function does not exhibit a shallow-depth barren plateau, i.e., its gradient does not vanish exponentially. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics.

7+5 pages, 4+1 figures

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Cited by in corpus (24)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Generalization in quantum machine learning from few training data
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• General parameter-shift rules for quantum gradients
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Theory of overparametrization in quantum neural networks
• Barren plateaus preclude learning scramblers
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Building spatial symmetries into parameterized quantum circuits for faster training
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Long-time simulations with high fidelity on quantum hardware
• Noisy intermediate-scale quantum algorithm for semidefinite programming
• Certified variational quantum algorithms for eigenstate preparation
• Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Quantum simulation of operator spreading in the chaotic Ising model
• Variational Quantum Algorithms for Trace Distance and Fidelity Estimation
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Adaptive shot allocation for fast convergence in variational quantum algorithms
• Assisted quantum simulation of open quantum systems
• NISQ algorithm for the matrix elements of a generic observable