Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions (1805.04340v1)

Abstract: In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

• The paper applies a particle-hole transformation to streamline electronic structure computations and improve trial wavefunction accuracy.
• It develops an enhanced q-UCC method via VQE, incorporating exchange-type gates to achieve low-depth quantum circuits.
• Numerical results on simple molecules like H₂ and H₂O show that a single Trotter step can accurately approximate molecular ground state energies.

Quantum Algorithms for Electronic Structure Calculations: Particle/Hole Hamiltonian and Optimized Wavefunction Expansions

The paper presents a detailed investigation into optimizing quantum algorithms to improve the efficiency and scalability of electronic structure calculations in quantum chemistry. The principal approach involves applying a particle-hole (p/h) transformation to the electronic structure Hamiltonian within the framework of second quantization. This transformation ostensibly provides a refined starting point for developing trial wavefunctions that explore the computationally relevant sector of molecular Fock space effectively.

The significant thrust of this work is on parameterization techniques that identify the most efficient ways to represent the molecular ground state. A key component of the approach is the application of quantum circuits enriched by exchange-type gates, which are designed to maintain accuracy in results while minimizing circuit complexity or depth.

The authors develop a noteworthy enhancement in the implementation of the Unitary Coupled Cluster (UCC) method via the Variational Quantum Eigensolver (VQE) approach. This combination, referred to as q-UCC, leverages the advantages of quantum computation strategies like low circuit depth while addressing notable pitfalls in classical mechanics, such as demanding exponential resources for exact wavefunction solutions.

Numerical demonstrations underscore tangible gains in efficient extrapolation of molecular ground state energies. For instance, the paper reports that a single Trotter step can adequately replicate the ground state energies for simplistic molecular systems, marking a significant advancement in computational efficiency.

Practical implementations are explored using quantum circuits crafted in the p/h framework, highlighting the potential to bypass classical computational limitations often encountered in quantum chemical methods. Application of these techniques to simple molecules like hydrogen (H₂) and water (H₂O) showcases robustness, supporting faster convergence and reduced instance complexity.

From a theoretical perspective, the paper's findings suggest promising future research directions and practical applications, particularly where quantum simulations are necessary. The importance of this work lies in its advancements in the modification of trial wavefunction strategies and computational methods to refine the precision of quantum chemistry calculations while preserving computational resources. Further exploration could involve expanding these methodologies toward more complex molecular architectures and testing robustness in increasingly sophisticated quantum systems.

This research forms part of a broader dialogue regarding the role of quantum computing in simulating quantum physical systems, offering new methodologies that could eventually bridge current gaps in simulating larger, multi-electronic molecular environments. The insights furnished by this paper could herald more efficient algorithms that might outperform classical simulations, hence presenting a vital stride toward broader applications in quantum-assisted computational chemistry.