Application of fermionic marginal constraints to hybrid quantum algorithms

TL;DR

This paper leverages fermionic $n$-representability conditions to optimize measurement strategies in hybrid quantum algorithms, significantly reducing measurement overhead and improving physicality in quantum chemistry simulations.

Contribution

It introduces fermionic $n$-representability conditions into quantum computation and develops techniques to enhance measurement efficiency and accuracy in quantum chemistry applications.

Findings

Reduced measurement requirements by over an order of magnitude for medium-sized systems.

Restored physical energy curves in noisy quantum simulations of hydrogen.

Demonstrated applicability in pre-fault tolerant quantum chemistry experiments.

Abstract

Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic $n$-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. We show that one can use fermionic $n$-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. We also demonstrate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments.