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 Schrödinger equation (CSE), the many-electron Schrödinger 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 ${\mathrm{H}}_3$ on simulators and a quantum device.

Close

PrevNext

View figure in article

• Electronic structure of atoms & molecules
• Quantum algorithms & computation
• Quantum simulation
• Quantum tomography
• Density matrix methods