Bootstrap Embedding on a Quantum Computer

Abstract

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

58+24 pages, 8+9 figures

References in corpus (8)

• Simulated Quantum Computation of Molecular Energies
• Efficient quantum state tomography
• Bloch vectors for qudits
• Quantum embedding theories
• Fixed-point quantum search with an optimal number of queries
• Speed-up via Quantum Sampling
• On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules
• Energetics and Dipole Moment of Transition Metal Monoxides by Quantum Monte Carlo

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• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
• Bootstrap Embedding for Interacting Electrons in Phonon Coherent-state Mean Field