Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

Abstract

Fermionic ansatz state preparation is a critical subroutine in many quantum algorithms such as Variational Quantum Eigensolver for quantum chemistry and condensed matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scale at least linearly with respect to the system size $N$. Inspired by data-loading circuits developed for quantum machine learning, we propose an alternate paradigm that provides shallower, yet scalable $\mathcal{O}(d{\log }_2^{2}N)$ two-qubit gate depth circuits to prepare such states with d-fermions, offering a subexponential reduction in $N$ over existing approaches in second quantization, enabling high-accuracy studies of $d\ll \mathcal{O}\left(N/{\log }_2^{2}N\right)$ fermionic systems with larger basis sets on near-term quantum devices.

arXiv commentrevised, 5+8 pages, 5+1 figures

References in corpus (27)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Noisy intermediate-scale quantum (NISQ) algorithms
• Superconducting Qubits: Current State of Play
• Simulated Quantum Computation of Molecular Energies
• Trapped-Ion Quantum Computing: Progress and Challenges
• The Variational Quantum Eigensolver: a review of methods and best practices
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Quantum algorithms for quantum chemistry and quantum materials science
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Hartree-Fock on a superconducting qubit quantum computer
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Training variational quantum algorithms is NP-hard
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Quantum Algorithms for Fermionic Simulations
• Solving strongly correlated electron models on a quantum computer
• Is there evidence for exponential quantum advantage in quantum chemistry?
• A Quantum Computing View on Unitary Coupled Cluster Theory
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Emerging quantum computing algorithms for quantum chemistry
• Quantum algorithms to simulate many-body physics of correlated fermions
• Efficient quantum circuits for quantum computational chemistry
• Universal quantum circuits for quantum chemistry
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation
• Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry
• Exterior calculus and fermionic quantum computation

Cited by in corpus (4)

• Multireference error mitigation for quantum computation of chemistry
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Resource-Efficient Hadamard Test Tailored Variational Framework for Nonlinear Dynamics on Quantum Computers
• Comment on arXiv:2307.08384 "Efficient Quantum State Preparation with Walsh Series"