Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations

Abstract

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wave function, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides the best compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.

References in corpus (33)

• A variational eigenvalue solver on a quantum processor
• 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 computational chemistry
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Validating quantum computers using randomized model circuits
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Direct visualization of current induced spin accumulation in topological insulators
• Variational Quantum Computation of Excited States
• Robust determination of molecular spectra on a quantum processor
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Subspace-search variational quantum eigensolver for excited states
• Variational quantum algorithms for discovering Hamiltonian spectra
• Accelerated Variational Quantum Eigensolver
• From transistor to trapped-ion computers for quantum chemistry
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Witnessing eigenstates for quantum simulation of Hamiltonian spectra
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Low rank representations for quantum simulation of electronic structure
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Electron-Phonon Systems on a Universal Quantum Computer
• Digital quantum simulation of molecular vibrations
• Digital quantum computation of fermion-boson interacting systems
• Vibrational Density Matrix Renormalization Group
• Non-unitary operations for ground-state calculations in near term quantum computers
• Optimization of highly excited matrix product states with an application to vibrational spectroscopy
• Ground-state energy estimation of the water molecule on a trapped ion quantum computer
• Variational Quantum Simulation of Ultrastrong Light-Matter Coupling

Cited by in corpus (44)

• The Variational Quantum Eigensolver: a review of methods and best practices
• A Quantum Computing View on Unitary Coupled Cluster Theory
• Hardware-efficient variational quantum algorithms for time evolution
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Prospects of Quantum Computing for Molecular Sciences
• Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur Batteries
• Universal qudit gate synthesis for transmons
• Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Molecular spin qudits for quantum simulation of light-matter interactions
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
• Microcanonical and finite temperature ab initio molecular dynamics simulations on quantum computers
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Exact quantum dynamics developments for floppy molecular systems and complexes
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• Towards a variational Jordan-Lee-Preskill quantum algorithm
• The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors
• TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era
• HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems
• Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes
• Partitioning Quantum Chemistry Simulations with Clifford Circuits
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Coarse grained intermolecular interactions on quantum processors
• Quantum computing for classical problems: Variational Quantum Eigensolver for activated processes
• Simulating Vibrational Dynamics on Bosonic Quantum Devices
• Graph Optimization Perspective for Low-Depth Trotter-Suzuki Decomposition
• Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra
• Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis
• Exploiting subspace constraints and ab initio variational methods for quantum chemistry
• Trotter simulation of vibrational Hamiltonians on a quantum computer
• Advantage of discrete variable representation in variational quantum eigensolvers for vibrational energy calculations
• Simulating quantum field theories on gate-based quantum computers
• Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model
• Rovibrational energy levels of H${}_2$O by quantum computing
• Resource-efficient encoding algorithm for variational bosonic quantum simulations
• Mapping quantum chemical dynamics problems onto spin-lattice simulators
• Analog quantum simulation of non-Condon effects in molecular spectroscopy
• The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers