Parallel Quantum Simulation of Large Systems on Small Quantum Computers

Abstract

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translate infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution arbitrary one-dimensional systems. Illustrative simulated output of these codes for achievable circuit sizes is given.

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• A class of quantum many-body states that can be efficiently simulated
• Real- and imaginary-time evolution with compressed quantum circuits
• Sequential Generation of Matrix-Product States in Cavity QED

Cited by in corpus (70)

• Variational Quantum Algorithms
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Hardware-efficient variational quantum algorithms for time evolution
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Holographic quantum algorithms for simulating correlated spin systems
• The Variational Power of Quantum Circuit Tensor Networks
• Quantum simulation with hybrid tensor networks
• Classically optimized Hamiltonian simulation
• Fast quantum circuit cutting with randomized measurements
• Hybrid quantum-classical reservoir computing of thermal convection flow
• Riemannian optimization of isometric tensor networks
• Variational Quantum Eigensolver with Reduced Circuit Complexity
• Holographic dynamics simulations with a trapped ion quantum computer
• Data compression for quantum machine learning
• Sequential generation of projected entangled-pair states
• Error-Mitigated Simulation of Quantum Many-Body Scars on Quantum Computers with Pulse-Level Control
• Characterizing a non-equilibrium phase transition on a quantum computer
• Optimised Trotter Decompositions for Classical and Quantum Computing
• Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Tensor networks for quantum machine learning
• Algebraic Bethe Circuits
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation
• Perturbative quantum simulation
• Entanglement from tensor networks on a trapped-ion QCCD quantum computer
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Holographic quantum simulation of entanglement renormalization circuits
• Quench dynamics of the Schwinger model via variational quantum algorithms
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Holographic simulation of correlated electrons on a trapped ion quantum processor
• Tensor networks for quantum computing
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Variational dynamics as a ground-state problem on a quantum computer
• Quantum algorithms for scientific computing
• Pauli path simulations of noisy quantum circuits beyond average case
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Tensor-network-assisted variational quantum algorithm
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Probing critical states of matter on a digital quantum computer
• Time Evolution of Uniform Sequential Circuits
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Integrable spin chains and the Clifford group
• Adaptive projected variational quantum dynamics
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Finite-depth scaling of infinite quantum circuits for quantum critical points
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• QuYBE -- An Algebraic Compiler for Quantum Circuit Compression
• Machine learning of quantum channels on NISQ devices
• Sequential quantum simulation of spin chains with a single circuit QED device
• Variational Quantum Simulation of Valence-Bond Solids
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Trotterless Simulation of Open Quantum Systems for NISQ Quantum Devices
• Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Error detection without post-selection in adaptive quantum circuits