Variational Quantum Eigensolver with Fewer Qubits

Abstract

We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of qubits smaller than the physical degrees of freedom. By increasing the qubits number, one can exponentially increase the bond dimension of the tensor network variational ansatz on a quantum computer. Moreover, we construct circuits blocks which respect U(1) and SU(2) symmetries of the physical system and show that they can significantly speed up the training process and alleviate the gradient vanishing problem. To demonstrate the feasibility of the qubit efficient variational quantum eigensolver in a practical setting, we perform first principle classical simulation of differentiable programming of the circuits. Using only $6$ qubits one can obtain the ground state of a $4\times 4$ square lattice frustrated Heisenberg model with fidelity over 97%. Arbitrarily long ranged correlations can also be measured on the same circuit after variational optimization.

github page: https://github.com/GiggleLiu/QuantumPEPS.jl

References in corpus (23)

• Quantum Computing in the NISQ era and beyond
• The density-matrix renormalization group in the age of matrix product states
• Barren plateaus in quantum neural network training landscapes
• Quantum Circuit Learning
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Evaluating analytic gradients on quantum hardware
• Efficient quantum state tomography
• DMRG and periodic boundary conditions: a quantum information perspective
• Criticality, the area law, and the computational power of PEPS
• Experimental Comparison of Two Quantum Computing Architectures
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Towards Quantum Machine Learning with Tensor Networks
• Differentiable Learning of Quantum Circuit Born Machine
• Continuous Matrix Product States for Quantum Fields
• Effective Extensible Programming: Unleashing Julia on GPUs
• Quantum algorithms to simulate many-body physics of correlated fermions
• Methodology for replacing indirect measurements with direct measurements
• Sequential Generation of Matrix-Product States in Cavity QED
• Simulating Quantum Fields with Cavity QED
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Solving search problems by strongly simulating quantum circuits

Cited by in corpus (98)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum algorithms for quantum chemistry and quantum materials science
• Solving nonlinear differential equations with differentiable quantum circuits
• Exploiting symmetry in variational quantum machine learning
• Doubling the size of quantum simulators by entanglement forging
• Quantum Machine Learning for Chemistry and Physics
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• Quantum Power Method by a Superposition of Time-Evolved States
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Neural Predictor based Quantum Architecture Search
• Holographic quantum algorithms for simulating correlated spin systems
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• The Variational Power of Quantum Circuit Tensor Networks
• Symmetry-adapted variational quantum eigensolver
• Quantum simulation with hybrid tensor networks
• Simulating Quantum Materials with Digital Quantum Computers
• Barren plateaus in quantum tensor network optimization
• Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Variational Quantum-Neural Hybrid Eigensolver
• Holographic dynamics simulations with a trapped ion quantum computer
• Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Building spatial symmetries into parameterized quantum circuits for faster training
• Quantum variational optimization: The role of entanglement and problem hardness
• Markovian Quantum Neuroevolution for Machine Learning
• Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Probabilistic Nonunitary Gate in Imaginary Time Evolution
• Symmetry enhanced variational quantum spin eigensolver
• Qubit-efficient entanglement spectroscopy using qubit resets
• Quantum algorithms for estimating quantum entropies
• Probing many-body localization by excited-state VQE
• Entanglement from tensor networks on a trapped-ion QCCD quantum computer
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Variational thermal quantum simulation of the lattice Schwinger model
• Hamiltonian operator approximation for energy measurement and ground state preparation
• Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits
• Filtering states with total spin on a quantum computer
• Entanglement-guided architectures of machine learning by quantum tensor network
• Quantum State Discrimination Using Noisy Quantum Neural Networks
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Selected topics of quantum computing for nuclear physics
• Training variational quantum algorithms with random gate activation
• Entanglement Production and Convergence Properties of the Variational Quantum Eigensolver
• Collective optimization for variational quantum eigensolvers
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Here comes the SU(N): multivariate quantum gates and gradients
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Quantum algorithms for scientific computing
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Improved variational quantum eigensolver via quasi-dynamical evolution
• Q${}^2$Chemistry: A quantum computation platform for quantum chemistry
• Variational Quantum-Neural Hybrid Error Mitigation
• Assessment of the variational quantum eigensolver: application to the Heisenberg model
• Quantum Gaussian filter for exploring ground-state properties
• Overhead-constrained circuit knitting for variational quantum dynamics
• Differentiable Programming of Isometric Tensor Networks
• Entanglement Diagnostics for Efficient Quantum Computation
• Numerical hardware-efficient variational quantum simulation of a soliton solution
• Hybrid quantum-classical algorithms for solving quantum chemistry in Hamiltonian-wavefunction space
• Variational quantum state preparation via quantum data buses
• Fermionic Simulators for Enhanced Scalability of Variational Quantum Simulation
• Variational adiabatic transport of tensor networks
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Universal imaginary-time critical dynamics on a quantum computer
• An RNN-policy gradient approach for quantum architecture search
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Exponential Qubit Reduction in Optimization for Financial Transaction Settlement
• Detection of energy levels of a spin system on a quantum computer by probe spin evolution
• Improving the Performance of Digitized Counterdiabatic Quantum Optimization via Algorithm-Oriented Qubit Mapping
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits
• Generation of photonic tensor network states with Circuit QED
• Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning
• Sequential quantum simulation of spin chains with a single circuit QED device
• Variational Quantum Simulation of Valence-Bond Solids
• Efficient parameterised compilation for hybrid quantum programming
• Resource-efficient Generalized Quantum Subspace Expansion
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Variational post-selection for ground states and thermal states simulation
• Quantum Active Learning
• Tangent Space Excitation Ansatz for Quantum Circuits
• Energy levels estimation on a quantum computer by evolution of a physical quantity
• Efficient Large-Scale Quantum Optimization via Counterdiabatic Ansatz
• Correcting and extending Trotterized quantum many-body dynamics
• Distributed variational quantum computing with deterministic entanglement tuning