Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques

Abstract

The near-term utility of quantum computers is hindered by hardware constraints in the form of noise. One path to achieving noise resilience in hybrid quantum algorithms is to decrease the required circuit depth -- the number of applied gates -- to solve a given problem. This work demonstrates how to reduce circuit depth by combining the transcorrelated (TC) approach with adaptive quantum ansätze and their implementations in the context of variational quantum imaginary time evolution (AVQITE). The combined TC-AVQITE method is used to calculate ground state energies across the potential energy surfaces of H${}_4$, LiH, and H${}_2$O. In particular, H${}_4$ is a notoriously difficult case where unitary coupled cluster theory, including singles and doubles excitations, fails to provide accurate results. Adding TC yields energies close to the complete basis set (CBS) limit while reducing the number of necessary operators -- and thus circuit depth -- in the adaptive ansätze. The reduced circuit depth furthermore makes our algorithm more noise-resilient and accelerates convergence. Our study demonstrates that combining the TC method with adaptive ansätze yields compact, noise-resilient, and easy-to-optimize quantum circuits that yield accurate quantum chemistry results close to the CBS limit.

References in corpus (64)

• A variational eigenvalue solver on a quantum processor
• Advances in Quantum Metrology
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Recent developments in the PySCF program package
• Predicting Many Properties of a Quantum System from Very Few Measurements
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Quantum algorithms for quantum chemistry and quantum materials science
• Quantum Fisher information matrix and multiparameter estimation
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Quantum Natural Gradient
• Theory of variational quantum simulation
• Training variational quantum algorithms is NP-hard
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Is there evidence for exponential quantum advantage in quantum chemistry?
• A Software Methodology for Compiling Quantum Programs
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods
• Geometry of variational methods: dynamics of closed quantum systems
• Efficient Formulation of Full Configuration Interaction Quantum Monte Carlo in a Spin Eigenbasis via the Graphical Unitary Group Approach
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
• Implementation of quantum imaginary-time evolution method on NISQ devices: Nonlocal approximation
• Prospects of Quantum Computing for Molecular Sciences
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
• Similarity transformation of the electronic Schrödinger equation via Jastrow factorisation
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems
• Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers
• Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Towards efficient and accurate \emph{ab initio} solutions to periodic systems via transcorrelation and coupled cluster theory
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• Transcorrelated Density Matrix Renormalization Group
• Variational quantum eigensolver techniques for simulating carbon monoxide oxidation
• Combined unitary and symmetric group approach applied to low-dimensional spin systems
• Quantum imaginary time evolution steered by reinforcement learning
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]-R12-Correction
• Optimizing Jastrow factors for the transcorrelated method
• Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
• Explicitly correlated electronic structure calculations with transcorrelated matrix product operators
• Error Bounds for Variational Quantum Time Evolution
• xTC: An efficient treatment of three-body interactions in transcorrelated methods
• Extension of selected configuration interaction for transcorrelated methods
• Eliminating the wave function singularity for ultracold atoms by similarity transformation
• A new form of transcorrelated Hamiltonian inspired by range-separated DFT
• Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity
• Transcorrelated coupled cluster methods. II. Molecular systems
• Nonunitary projective transcorrelation theory inspired by the F12 ansatz
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• Natural Gradient Optimization for Optical Quantum Circuits
• Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum Hardware
• TC++: First-principles calculation code for solids using the transcorrelated method
• Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian

Cited by in corpus (4)

• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
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• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Scaling up the transcorrelated density matrix renormalization group