Shadow Ansatz for the Many-Fermion Wave Function in Scalable Molecular Simulations on Quantum Computing Devices

TL;DR

This paper introduces a shadow tomography-based ansatz for many-fermion wave functions that enables scalable quantum simulations with fewer measurements and shallower circuits, demonstrated on H3 molecules.

Contribution

The paper develops an exact, measurement-efficient ansatz for many-fermion wave functions using shadow tomography, linking measurement outcomes to the Schrödinger equation residuals.

Findings

Exact ansatz derived from shadow tomography for many-electron systems.

Fewer measurements and shallower circuits needed for simulations.

Successful demonstration on simulators and a quantum device for H3.

Abstract

Here we show that shadow tomography can generate an efficient and exact ansatz for the many-fermion wave function on quantum devices. We derive the shadow ansatz -- a product of transformations applied to the mean-field wave function -- by exploiting a critical link between measurement and preparation. Each transformation is obtained by measuring a classical shadow of the residual of the contracted Schr\"odinger equation (CSE), the many-electron Schr\"odinger equation (SE) projected onto the space of two electrons. We show that the classical shadows of the CSE vanish if and only if the wave function satisfies the SE and, hence, that randomly sampling only the two-electron space yields an exact ansatz regardless of the total number of electrons. We demonstrate the ansatz's advantages for scalable simulations -- fewer measurements and shallower circuits -- by computing H$_{3}$ on simulators and a quantum device.