State Preparation Boosters for Early Fault-Tolerant Quantum Computation

Abstract

Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization landscape, make state preparation through ansatz optimization unreliable. In this work, we introduce the method of ground state boosting, which uses a limited-depth quantum circuit to reliably increase the overlap with the ground state. This circuit, which we call a booster, can be used to augment an ansatz from VQE or be used as a stand-alone state preparation method. The booster converts circuit depth into ground state overlap in a controllable manner. We numerically demonstrate the capabilities of boosters by simulating the performance of a particular type of booster, namely the Gaussian booster, for preparing the ground state of $N_2$ molecular system. Beyond ground state preparation as a direct objective, many quantum algorithms, such as quantum phase estimation, rely on high-quality state preparation as a subroutine. Therefore, we foresee ground state boosting and similar methods as becoming essential algorithmic components as the field transitions into using early fault-tolerant quantum computers.

Comparison with related works and more detailed proofs are added

References in corpus (8)

• Simulated Quantum Computation of Molecular Energies
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Fixed-point quantum search with an optimal number of queries
• Optimal Quantum Measurements of Expectation Values of Observables
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Computing Ground State Properties with Early Fault-Tolerant Quantum Computers
• Quantum Gaussian filter for exploring ground-state properties

Cited by in corpus (13)

• Early Fault-Tolerant Quantum Computing
• Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision
• Initial state preparation for quantum chemistry on quantum computers
• Sparse Quantum State Preparation for Strongly Correlated Systems
• Quantum Gaussian filter for exploring ground-state properties
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
• Option pricing under stochastic volatility on a quantum computer
• On proving the robustness of algorithms for early fault-tolerant quantum computers
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation