Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized...

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• The Schrödinger equation is central to understanding molecular behavior.
• Quantum computers offer a potential pathway to solve complex quantum chemistry problems.
• Current quantum eigensolvers face challenges with convergence and noise.

Purpose of the Study:

• To accelerate the convergence of the contracted quantum eigensolver (CQE).
• To improve the accuracy and efficiency of quantum simulations for the Schrödinger equation.
• To explore classical optimization techniques for quantum algorithms.

Main Methods:

• Applied classical optimization theory, specifically quasi-Newton and nonlinear conjugate gradient methods.
• Treated the CQE algorithm as an optimization problem in a local parameter space.
• Utilized a general product ansatz of two-body exponential unitary transformations.

Main Results:

• Achieved superlinear convergence of the wave function to a solution of the anti-Hermitian contracted Schrödinger equation (ACSE).
• Demonstrated the effectiveness of classical optimization for accelerating CQE.
• Showcased heuristic implementations for cost reduction and compared with variational quantum eigensolvers.

Conclusions:

• Classical optimization significantly enhances CQE performance.
• Accelerated CQE minimizes noise on near-term quantum devices and improves accuracy on future fault-tolerant systems.
• The developed methods offer a more efficient route to solving the many-electron Schrödinger equation.