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

• URL: http://arxiv.org/abs/2308.10719v1
• Date: Mon, 21 Aug 2023 13:39:58 GMT
• Title: Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All
• Authors: Dibyendu Mondal and Rahul Maitra
• Abstract summary: Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in quantum devices. We propose a unified VQE framework that treats the ground and excited states in the same footings. We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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