Abstract
The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE.
Highlights
Quantum computing is expected to revolutionize computational chemistry by achieving polynomial scaling in both the number of quantum particles and the quality of the description of the system [1,2]
PermVQE for 2D grid architecture Up to this point, we have demonstrated the beneficial effect of qubit permutations for small molecular systems implemented on a linear qubit connectivity quantum chip
In this work we show that encoding strongly interacting spin-orbitals of molecular systems into proximal qubits on a linear or 2D grid architecture chain architecture quantum chip naturally reduces the circuit depth needed to prepare the ground state for the quantum chemistry electronic structure problem with hardware-efficient ansatz
Summary
Quantum computing is expected to revolutionize computational chemistry by achieving polynomial scaling in both the number of quantum particles and the quality of the description of the system (e.g., the number of orbital basis functions or numerical grid points) [1,2]. This concern arises since increased circuit depth leads to smaller gradients [12,13,14,15,16,17,18], and accurate estimation of small gradients on a quantum computer requires a large number of runs (or “shots”) These two issues are related as the accumulation of hardware noise leads to smaller gradients [19]. Permutations significantly reduce the circuit depth required to reach a given energy accuracy, relative to the unpermuted case To realize this permutation technique, we introduce the PermVQE algorithm, an added layer on top Molecule (xyz, basis set). We demonstrate the beneficial effect of qubit permutations to build fermionic–adaptive derivative assembled pseudo-Trotter (ADAPT) ansatz [30] for the implementation on a linear nearest-neighbor quantum chip architecture [47]
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