Hierarchical Clifford transformations to reduce entanglement in quantum chemistry wavefunctions

Abstract

The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress in the field. So far, tools from theoretical quantum information have been not thoroughly explored for this task. Here we take a step in this direction by presenting efficiently computable Clifford similarity transformations for quantum chemistry Hamiltonians, which expose bases with reduced entanglement in the corresponding molecular ground states. These transformations are constructed via block diagonalization of a hierarchy of truncated molecular Hamiltonians, preserving the full spectrum of the original problem. We show that the bases introduced here allow for more efficient classical and quantum computation of ground state properties. First, we find a systematic reduction of bipartite entanglement in molecular ground states as compared to standard problem representations. This entanglement reduction has implications in classical numerical methods such as ones based on the density matrix renormalization group. Then, we develop variational quantum algorithms that exploit the structure in the new bases, showing again improved results when the hierarchical Clifford transformations are used.

14 pages, 11 figures

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Tapering off qubits to simulate fermionic Hamiltonians
• A canonical transformation theory from extended normal ordering
• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?
• Improving the accuracy of quantum computational chemistry using the transcorrelated method

Cited by in corpus (11)

• Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Doped stabilizer states in many-body physics and where to find them
• Disentangling critical quantum spin chains with Clifford circuits
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Simulation of a Diels-Alder Reaction on a Quantum Computer
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Adiabatic state preparation from general initial states
• Simple Diagonal State Designs with Reconfigurable Real-Time Circuits