Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All

TL;DR

This paper introduces a unified variational quantum eigensolver framework capable of accurately computing both ground and excited molecular states with symmetry considerations, suitable for near-term quantum devices.

Contribution

The authors develop a state-specific VQE method that simultaneously targets ground and excited states using symmetry-adapted multi-determinantal references and a spin-scalar unitary, avoiding high circuit depth.

Findings

Achieves direct access to excited states without cumulative errors.

Maintains state purity and avoids variational collapse.

Compatible with near-term quantum hardware.

Abstract

Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in near-term quantum devices. While the VQE is traditionally tailored to determine the ground state wavefunction with the underlying Rayleigh-Ritz principle, the access to specific symmetry-adapted excited states remains elusive. This often requires high depth circuit or additional ancilla qubits along with prior knowledge of the ground state wavefunction. We propose a unified VQE framework that treats the ground and excited states in the same footings. With the knowledge of the irreducible representations of the spinorbitals, we construct a multi-determinantal reference that is adapted to a given spatial symmetry where additionally, the determinants are entangled through appropriate Clebsch-Gordan coefficients to ensure the desired spin-multiplicity. We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization. The state-selectivity safeguards the method against any variational collapse while leading to any targeted low-lying eigenroot of arbitrary symmetry. The direct access to the excited states shields our approach from the cumulative error that plagues excited state calculations in a quantum computer and with few parameter count, it is expected to be realized in near-term quantum devices.