Universal quantum circuits for quantum chemistry

Abstract

Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01⟩,|10⟩$, while leaving other states unchanged -- a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.

11 pages, 12 figures

References in corpus (5)

• Estimating the gradient and higher-order derivatives on quantum hardware
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Preparation of many-body states for quantum simulation
• Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
• Universal extensions of restricted classes of quantum operations

Cited by in corpus (10)

• Exploiting symmetry in variational quantum machine learning
• Variational approaches to constructing the many-body nuclear ground state for quantum computing
• T-count and T-depth of any multi-qubit unitary
• Quantum simulation of molecules in solution
• Differentiable quantum computational chemistry with PennyLane
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
• Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
• Variational Quantum Simulation of Valence-Bond Solids
• Basis set generation and optimization in the NISQ era with Quiqbox.jl
• Chemistry beyond the Hartree-Fock limit via quantum computed moments