Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

Abstract

Quantum imaginary time evolution (QITE) is one of the promising candidates for finding eigenvalues and eigenstates of a Hamiltonian. However, the original QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary time evolution by real time evolution, suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Phys. Rev. Lett 123, 070503 (2019)], which randomly draws a Pauli term out of the approximated unitary operation generators of QITE according to the strength and rescales that term by the total strength of the Pauli terms. We show that this drifting scheme removes the depth dependency on size of the operator pool and converges inverse linearly to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. Meanwhile, we introduce an efficient measurement reduction scheme across Trotter steps, which removes its cost dependence on the number of iterations, and a measurement distribution protocol for different observables within each time step. We also analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance, and faithfulness of measurement reduction approximation of our algorithms on LiH, BeH${}_2$ and N${}_2$ molecules. In particular, the results on LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver~(VQE) methods while requiring much fewer measurements.

References in corpus (18)

• A Quantum Approximate Optimization Algorithm
• Noisy intermediate-scale quantum (NISQ) algorithms
• Simulated Quantum Computation of Molecular Energies
• Training variational quantum algorithms is NP-hard
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
• Experimental quantum state measurement with classical shadows
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• A Hybrid Classical/Quantum Approach for Large-Scale Studies of Quantum Systems with Density Matrix Embedding Theory
• Perturbative quantum simulation
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• Quantum imaginary time evolution steered by reinforcement learning
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Universal quantum algorithmic cooling on a quantum computer
• Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting

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• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Halving the Cost of Quantum Algorithms with Randomization
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Simulating the non-Hermitian dynamics of financial option pricing with quantum computers
• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time