SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation

Abstract

The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{{\epsilon }^2})$ to $O(\frac{1}{{\epsilon }^2})$ for a system of $N$ qubits and accuracy $\epsilon$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{{\epsilon }^2})$ to $O(\frac{N^3}{{\epsilon }^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem.

References in corpus (57)

• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Error mitigation for short-depth quantum circuits
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Scalable Quantum Simulation of Molecular Energies
• Towards Quantum Chemistry on a Quantum Computer
• Hartree-Fock on a superconducting qubit quantum computer
• Towards Practical Quantum Variational Algorithms
• NWChem: Past, Present, and Future
• Efficient variational quantum simulator incorporating active error minimisation
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Practical Quantum Error Mitigation for Near-Future Applications
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Variational Quantum Computation of Excited States
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Generalized Jordan-Wigner Transformations
• Quantum Supremacy of Many-Particle Thermal Machines
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Entanglement Devised Barren Plateau Mitigation
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Efficient quantum circuits for quantum computational chemistry
• Lowering qubit requirements for quantum simulations of fermionic systems
• Machine learning quantum states in the NISQ era
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Accuracy and Resource Estimations for Quantum Chemistry on a Near-term Quantum Computer
• Precise measurement of quantum observables with neural-network estimators
• Hamiltonian variational ansatz without barren plateaus
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
• Efficient estimation of trainability for variational quantum circuits
• PANSATZ: Pulse-based Ansatz for Variational Quantum Algorithms
• Variational Quantum-Neural Hybrid Error Mitigation
• Development of Zero-Noise Extrapolated Projection Based Quantum Algorithm for Accurate Evaluation of Molecular Energetics in Noisy Quantum Devices
• Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols
• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Linear Ascending Metrological Algorithm
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Calculation of core-excited and core-ionized states using variational quantum deflation method and applications to photocatalyst modelling
• Hardware-efficient entangled measurements for variational quantum algorithms
• Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation
• On The Study Of Partial Qubit Hamiltonian For Efficient Molecular Simulation Using Variational Quantum Eigensolvers

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