Towards adiabatic quantum computing using compressed quantum circuits

Abstract

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization.

13 pages, 10 figures

References in corpus (63)

• The density-matrix renormalization group
• Variational Quantum Algorithms
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• Barren plateaus in quantum neural network training landscapes
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Noisy intermediate-scale quantum (NISQ) algorithms
• Adiabatic Quantum Computing
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Parameterized quantum circuits as machine learning models
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The ITensor Software Library for Tensor Network Calculations
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Efficient variational quantum simulator incorporating active error minimisation
• Shortcut to adiabatic passage in two and three level atoms
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Perspectives of quantum annealing: Methods and implementations
• Theory of variational quantum simulation
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Sequential generation of entangled multi-qubit states
• Time-evolving a matrix product state with long-ranged interactions
• Variational quantum algorithms for nonlinear problems
• Geometry and non-adiabatic response in quantum and classical systems
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Minimal Universal Two-qubit Quantum Circuits
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Algorithms for finite Projected Entangled Pair States
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Hardware-efficient variational quantum algorithms for time evolution
• Adiabatic tracking of quantum many-body dynamics
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Barren plateaus preclude learning scramblers
• Tensor Network Algorithms: a Route Map
• Sequential Generation of Matrix-Product States in Cavity QED
• Unifying Projected Entangled Pair States contractions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Digitized-counterdiabatic quantum approximate optimization algorithm
• Preparation of matrix product states with log-depth quantum circuits
• The Variational Power of Quantum Circuit Tensor Networks
• Classically optimized Hamiltonian simulation
• Barren plateaus in quantum tensor network optimization
• Counterdiabatic Optimised Local Driving
• Digitized-Counterdiabatic Quantum Algorithm for Protein Folding
• Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms
• Multigrid Renormalization
• Digitized-Counterdiabatic Quantum Optimization
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Simulation of many-qubit quantum computation with matrix product states
• Optimal compression of quantum many-body time evolution operators into brickwall circuits
• Renormalization algorithm with graph enhancement
• A variational method based on weighted graph states
• Systematic construction of density functionals based on matrix product state computations
• Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations
• Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm
• Tensor network methods with graph enhancement
• Variational adiabatic transport of tensor networks

Cited by in corpus (44)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Quantum Machine Learning for Digital Health? A Systematic Review
• Nonlinear dynamics as a ground-state solution on quantum computers
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
• Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Geometric Floquet theory
• Digitized Counterdiabatic Quantum Algorithms for Logistics Scheduling
• Bias-field digitized counterdiabatic quantum optimization
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Variational adiabatic transport of tensor networks
• Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
• Tensor-based quantum phase difference estimation for large-scale demonstration
• Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
• Counterdiabatic Driving with Performance Guarantees
• Practicality of quantum adiabatic algorithm for chemistry applications
• Quantum circuit compilation with quantum computers
• Riemannian quantum circuit optimization based on matrix product operators
• Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Reversing adiabatic state preparation in few-level quantum systems
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Quantum Shortcut to Adiabaticity for State Preparation in a Finite-Sized Jaynes-Cummings Lattice
• Shortcuts to adiabaticity in open quantum critical systems
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Benchmarking a heuristic Floquet adiabatic algorithm for the Max-Cut problem
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• Noise Effects on Diabatic Quantum Annealing Protocols
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Energy-saving fast-forward scaling
• Time evolution of controlled many-body quantum systems with matrix product operators
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
• Ancillary entangling Floquet kicks for accelerating quantum algorithms
• Tensor-based phase difference estimation on time series analysis
• Quantum coherence and counterdiabatic quantum computing
• Improving adiabatic quantum factorization via chopped random-basis optimization
• Hidden local adiabatic ramp in the modulated time evolution and the quantum approximate optimization algorithm