Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer.

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for solving quantum mechanical problems.
• Solving the electronic structure problem on quantum computers requires addressing symmetry constraints.
• Ignoring symmetries can lead to convergence to incorrect, symmetry-broken states.

Purpose of the Study:

• To introduce and assess methods for incorporating physical symmetries into the VQE framework.
• To compare the efficiency and feasibility of symmetry projectors against constraint optimization procedures.
• To improve the accuracy of variational wavefunction ansatze in quantum electronic structure calculations.

Main Methods:

• Development and application of exact and approximate symmetry projectors.
• Constraining the VQE search to irreducible eigensubspaces.
• Comparison of projector methods with symmetry constraint optimization.

Main Results:

• Symmetry projectors improve the accuracy of variational wavefunctions without additional unitary transformations.
• Projectors generally require more terms for VQE measurement than constraint approaches.
• The projection formalism offers benefits for reducing quantum circuit depths.

Conclusions:

• Symmetry projectors are a viable and effective method for enhancing VQE accuracy in electronic structure calculations.
• The trade-off between measurement overhead and circuit depth reduction should be considered when choosing between projectors and constraint methods.
• This work advances the application of quantum computing for solving fundamental problems in chemistry and physics.