Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure

Abstract

Due to their non-iterative nature, fixed Unitary Coupled-Cluster (UCC) ansätze are attractive for performing quantum chemistry Variational Quantum Eigensolver (VQE) computations as they avoid pre-circuit measurements on a quantum computer. However, achieving chemical accuracy for strongly correlated systems with UCC requires further inclusion of higher-order fermionic excitations beyond triples increasing circuit depth. We introduce $k$-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster compact ansatz, based on specific $"k"$ sets of "qubit" excitations, eliminating the needs for fermionic-type excitations. These elements scale linearly ($\mathcal{O}(n)$) by leveraging Lie algebraic structures, with $n$ being the number of qubits. The key excitations are screened through specific selection criteria, including the enforcement of all symmetries, to ensure the construction of a robust set of generators. NI-DUCC employs $"k"$ products of the exponential of $\mathcal{O}(n)$- anti-Hermitian Pauli operators, where each operator has a length $p$. This results in a fewer two-qubit CNOT gates circuit, $\mathcal{O}(knp)$, suitable for hardware implementations. Tested on LiH, H${}_6$ and BeH${}_2$, NI-DUCC-VQE achieves both chemical accuracy and rapid convergence even for molecules deviating significantly from equilibrium. It is hardware-efficient, reaching the exact Full Configuration Interaction energy solution at specific layers, while reducing significantly the VQE optimization steps. While NI-DUCC-VQE effectively addresses the gradient measurement bottleneck of ADAPT-VQE-like iterative algorithms, the classical computational cost of constructing the $\mathcal{O}(n)$ set of excitations increases exponentially with the number of qubits. We provide a first implementation for constructing the generators' set able to handle up to 20 qubits and discuss the efficiency perspectives.

References in corpus (42)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Quantum algorithms for quantum chemistry and quantum materials science
• Elucidating Reaction Mechanisms on Quantum Computers
• Hartree-Fock on a superconducting qubit quantum computer
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Theory of overparametrization in quantum neural networks
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Fast Semistochastic Heat-Bath Configuration Interaction
• Qubit-excitation-based adaptive variational quantum eigensolver
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• Simulating Quantum Materials with Digital Quantum Computers
• The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze
• Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze
• On the order problem in construction of unitary operators for the Variational Quantum Eigensolver
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Unitary Selective Coupled-Cluster Method
• Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
• Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing
• Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations
• Estimation of electrostatic interaction energies on a trapped-ion quantum computer
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• Quantum computational study of chloride ion attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes

Cited by in corpus (1)

• Energy Landscape Plummeting in Variational Quantum Eigensolver: Subspace Optimization, Non-iterative Corrections and Generator-informed Initialization for Improved Quantum Efficiency