Spin-free quantum computational simulations and symmetry adapted states

Abstract

The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. While the methods here represent adaptations of known quantum algorithms, they are the first to explicitly deal with preparing N-body symmetry-adapted states.

4+ pages. Submitted to JCP

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Cited by in corpus (12)

• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Scalable Quantum Simulation of Molecular Energies
• Adiabatic Quantum Simulation of Quantum Chemistry
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation
• Symmetry assisted preparation of entangled many-body states on a quantum computer
• Machine learning the derivative discontinuity of density-functional theory
• Filtering states with total spin on a quantum computer
• Quantum Simulations of Chemistry in First Quantization with any Basis Set
• Lowering Tomography Costs in Quantum Simulation with a Symmetry Projected Operator Basis