A Quantum Approximate Optimization Algorithm

Abstract

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit that implements the algorithm consists of unitary gates whose locality is at most the locality of the objective function whose optimum is sought. The depth of the circuit grows linearly with p times (at worst) the number of constraints. If p is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing. If p grows with the input size a different strategy is proposed. We study the algorithm as applied to MaxCut on regular graphs and analyze its performance on 2-regular and 3-regular graphs for fixed p. For p = 1, on 3-regular graphs the quantum algorithm always finds a cut that is at least 0.6924 times the size of the optimal cut.

References in corpus (1)

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• Simulator Demonstration of Large Scale Variational Quantum Algorithm on HPC Cluster
• QContext: Context-Aware Decomposition for Quantum Gates
• Quantum annealing-based computed tomography using variational approach for a real-number image reconstruction
• Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow
• Stochastic Approximation of Variational Quantum Imaginary Time Evolution
• EQC : Ensembled Quantum Computing for Variational Quantum Algorithms
• Graph Cut Segmentation Methods Revisited with a Quantum Algorithm
• Planning for Compilation of a Quantum Algorithm for Graph Coloring
• A quantum algorithm for solving 0-1 Knapsack problems
• Mixed-Integer Programming Using a Bosonic Quantum Computer
• Noise reduction using past causal cones in variational quantum algorithms
• The Inductive Bias of Quantum Kernels
• Incentivising Demand Side Response through Discount Scheduling using Hybrid Quantum Optimization
• Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
• Classical Quantum Optimization with Neural Network Quantum States
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• MLQAOA: Graph Learning Accelerated Hybrid Quantum-Classical Multilevel QAOA
• Flexibility of the factorized form of the unitary coupled cluster ansatz
• Quantum Approximate Optimization Algorithm with Sparsified Phase Operator
• Using the Parameterized Quantum Circuit combined with Variational-Quantum-Eigensolver (VQE) to create an Intelligent social workers' schedule problem solver
• Diagrammatic Analysis for Parameterized Quantum Circuits
• A Multilevel Framework for Partitioning Quantum Circuits
• Minimizing state preparation times in pulse-level variational molecular simulations
• Large-scale Quantum Approximate Optimization via Divide-and-Conquer
• Variational quantum simulation of long-range interacting systems
• Experimental pairwise entanglement estimation for an N-qubit system :A machine learning approach for programming quantum hardware
• Quantum Computation for Pricing the Collateralized Debt Obligations
• Engineering the Cost Function of a Variational Quantum Algorithm for Implementation on Near-Term Devices
• Neural network accelerator for quantum control
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Tensor Networks for Simulating Quantum Circuits on FPGAs
• Inter-temperature Bandwidth Reduction in Cryogenic QAOA Machines
• Qompress: Efficient Compilation for Ququarts Exploiting Partial and Mixed Radix Operations for Communication Reduction
• Toward a quantum computing algorithm to quantify classical and quantum correlation of system states
• Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks
• Connection between single-layer Quantum Approximate Optimization Algorithm interferometry and thermal distributions sampling
• A quantum algorithm to count weighted ground states of classical spin Hamiltonians
• Reducing the Compilation Time of Quantum Circuits Using Pre-Compilation on the Gate Level
• Evaluating Three Levels of Quantum Metrics on Quantum-Inspire Hardware
• Quantum and quantum-inspired optimization for solving the minimum bin packing problem
• BBQ-mIS: a parallel quantum algorithm for graph coloring problems
• A framework for optimal quantum spatial search using alternating phase-walks
• An example of use of Variational Methods in Quantum Machine Learning
• Constant Depth Code Deformations in the Parity Architecture
• Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
• Circuit lower bounds for low-energy states of quantum code Hamiltonians
• Variational Optimization for Quantum Problems using Deep Generative Networks
• Toward a standardized methodology for constructing quantum computing use cases
• QuTracer: Mitigating Quantum Gate and Measurement Errors by Tracing Subsets of Qubits
• A framework for randomized benchmarking over compact groups
• Sequence of penalties method to study excited states using VQE
• Reinforcement Learning Enhanced Quantum-inspired Algorithm for Combinatorial Optimization
• Hierarchical Multigrid Ansatz for Variational Quantum Algorithms
• Single entanglement connection architecture between multi-layer bipartite Hardware Efficient Ansatz
• Forecasting Election Polls with Spin Systems
• Using quantum computers in control: interval matrix properties
• Quantum mean value approximator for hard integer value problems
• Quantum Neural Networks: Concepts, Applications, and Challenges
• Quantum annealer accelerates the variational quantum eigensolver in a triple-hybrid algorithm
• LX-mixers for QAOA: Optimal mixers restricted to subspaces and the stabilizer formalism
• Minimizing polynomial functions on quantum computers
• Pitfalls of the sublinear QAOA-based factorization algorithm
• Accelerating the training of single-layer binary neural networks using the HHL quantum algorithm
• Quantum-Classical Hybrid Algorithm for Solving the Learning-With-Errors Problem on NISQ Devices
• QFCNN: Quantum Fourier Convolutional Neural Network
• Quantum Spectral Clustering through a Biased Phase Estimation Algorithm
• Quantum Integer Programming (QuIP) 47-779: Lecture Notes
• Out of the Loop: Structural Approximation of Optimisation Landscapes and non-Iterative Quantum Optimisation
• Sampling Problems on a Quantum Computer
• Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm
• Posiform Planting: Generating QUBO Instances for Benchmarking
• Hamiltonian Switching Control of Noisy Bipartite Qubit Systems
• Towards Efficient Superconducting Quantum Processor Architecture Design
• TILT: Achieving Higher Fidelity on a Trapped-Ion Linear-Tape Quantum Computing Architecture
• QuOp_MPI: a framework for parallel simulation of quantum variational algorithms
• Neural optimization for quantum architectures: graph embedding problems with Distance Encoder Networks
• Quantum Technology for Military Applications
• Towards solving the BCS Hamiltonian gap in Near-Term Quantum Computers
• Realization of arbitrary doubly-controlled quantum phase gates
• Experimental Demonstration of Fermionic QAOA with One-Dimensional Cyclic Driver Hamiltonian
• Algorithm for Finding the Maximum Clique Based on Continuous Time Quantum Walk
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Quantum Computing Approach for Energy Optimization in a Prosumer Community
• Quantum Annealing with chaotic driver Hamiltonians
• Switching Time Optimization for Binary Quantum Optimal Control
• An explicit vector algorithm for high-girth MaxCut
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Quantum gradient estimation of Gevrey functions
• A Quantum Circuit Obfuscation Methodology for Security and Privacy
• Addition and Differentiation of ZX-diagrams
• Accelerating variational quantum algorithms with multiple quantum processors
• Continuous black-box optimization with quantum annealing and random subspace coding
• Limits of Short-Time Evolution of Local Hamiltonians
• Quantum Approximation Optimization Algorithm for the Trellis based Viterbi Decoding of Classical Error Correcting Codes
• Energy levels estimation on a quantum computer by evolution of a physical quantity
• Comparing Quantum Service Offerings
• Q-Profile: Profiling Tool for Quantum Control Stacks applied to the Quantum Approximate Optimization Algorithm
• Quantum Software Ecosystem Design
• Tighter Lower Bounds on Quantum Annealing Times
• Perspectives on Utilization of Measurements in Quantum Algorithms
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology
• Detecting Entanglement Generating Circuits in Cloud-Based Quantum Computing
• BGLS: A Python Package for the Gate-by-Gate Sampling Algorithm to Simulate Quantum Circuits
• Quantum Approximation for Wireless Scheduling
• Quantum Adiabatic Theorem Revisited
• The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion
• Ab initio nuclear structure via quantum adiabatic algorithm
• Normalized Gradient Descent for Variational Quantum Algorithms
• Computability and Complexity of Unconventional Computing Devices
• Quantum evolution kernel : Machine learning on graphs with programmable arrays of qubits
• Ising formulations of routing optimization problems
• A Critical and Moving-Forward View on Quantum Image Processing
• qLEET: Visualizing Loss Landscapes, Expressibility, Entangling Power and Training Trajectories for Parameterized Quantum Circuits
• Lower Bounds on Circuit Depth of the Quantum Approximate Optimization Algorithm
• NISQ algorithm for the matrix elements of a generic observable
• Bayesian machine learning for Boltzmann machine in quantum-enhanced feature spaces
• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
• "Proper" Shift Rules for Derivatives of Perturbed-Parametric Quantum Evolutions
• Formulation of the Electric Vehicle Charging and Routing Problem for a Hybrid Quantum-Classical Search Space Reduction Heuristic
• Approximate Phase Search and Eigen Estimation using Modified Grover's Algorithm
• Quantum-data-driven dynamical transition in quantum learning
• Dynamical transition in controllable quantum neural networks with large depth
• On Sampling and Inference using Quantum Algorithms
• Quick design of feasible tensor networks for constrained combinatorial optimization
• ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum Algorithms
• Quantum-Assisted Graph Clustering and Quadratic Unconstrained D-ary Optimisation
• Generating Compilers for Qubit Mapping and Routing
• Generative flow-based warm start of the variational quantum eigensolver
• Modularized and Scalable Compilation for Double Quantum Dot Quatum Computing
• Harnessing Inferior Solutions For Superior Outcomes: Obtaining Robust Solutions From Quantum Algorithms
• Laplacian Eigenmaps with variational circuits: a quantum embedding of graph data
• Benchmarking a heuristic Floquet adiabatic algorithm for the Max-Cut problem
• Electron cloud design for Rydberg multi-qubit gates
• Improving the Quantum Approximate Optimization Algorithm with postselection
• Fairness evaluation during the conceptual design of heat grids with quantum annealers
• Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem
• State of practice: evaluating GPU performance of state vector and tensor network methods
• Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models
• Improving Parameter Training for VQEs by Sequential Hamiltonian Assembly
• QPack: Quantum Approximate Optimization Algorithms as universal benchmark for quantum computers
• Quantum Noise Sensing by generating Fake Noise
• Error Mitigation in Quantum Computers through Instruction Scheduling
• Maritime Just-in-time navigation with Quantum algorithms
• Hamiltonian formulations of centroid-based clustering
• Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Training
• The quantum version of the shifted power method and its application in quadratic binary optimization
• Quantum circuit to estimate pi using quantum amplitude estimation
• On quantum ensembles of quantum classifiers
• Low overhead universality and quantum supremacy using only $Z$-control
• The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline
• Towards a Pattern Language for Quantum Algorithms
• The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions
• Symmetry-based quantum algorithms for open-shop scheduling with hard constraints
• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice
• Optimising Rolling Stock Planning including Maintenance with Constraint Programming and Quantum Annealing
• Optimizing Quantum Variational Circuits with Deep Reinforcement Learning
• Classical algorithms for Forrelation
• Bayesian ACRONYM Tuning
• EVA: a quantum Exponential Value Approximation algorithm
• Introductory Tutorial for SPSA and the Quantum Approximation Optimization Algorithm
• Towards a NISQ Algorithm to Simulate Hermitian Matrix Exponentiation
• Efficient Quantum Circuit Simulation by Tensor Network Methods on Modern GPUs
• A Quantum Annealing Approach to Reduce Covid-19 Spread on College Campuses
• Fast suppression of classification error in variational quantum circuits
• Robust decompositions of quantum states
• An unsupervised feature learning for quantum-classical convolutional network with applications to fault detection
• Multiple Query Optimization using a Hybrid Approach of Classical and Quantum Computing
• Exploring Airline Gate-Scheduling Optimization Using Quantum Computers
• Exploiting Long-Distance Interactions and Tolerating Atom Loss in Neutral Atom Quantum Architectures
• Optimized fermionic SWAP networks with equivalent circuit averaging for QAOA
• Quantum Model-Discovery
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states
• Quantum Computation
• Large Scale Diverse Combinatorial Optimization: ESPN Fantasy Football Player Trades
• Application of graph theory in quantum computer science
• Electric Power Demand Portfolio Optimization by Fermionic QAOA with Self-Consistent Local Field Modulation
• Depth Optimized Ansatz Circuit in QAOA for Max-Cut
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks
• Software mitigation of coherent two-qubit gate errors
• The Rise of Quantum Computing -- Take a BITE for Built Environment and Urban Microclimate Research
• Quantum Optimization for Electromagnetics: Physics-Informed QAOA for Reconfigurable Intelligent Surfaces
• Hybrid Path-Sums for Hybrid Quantum Programs
• Considering Decoherence Errors in the Simulation of Quantum Circuits Using Decision Diagrams
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits
• Sampling (noisy) quantum circuits through randomized rounding
• Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing
• An Analysis of the Quantum Approximation Optimisation Algorithm
• From Hope to Heuristic: Realistic Runtime Estimates for Quantum Optimisation in NHEP
• Logical Abstractions for Noisy Variational Quantum Algorithm Simulation
• An upper bound on the Universality of the Quantum Approximate Optimization Algorithm
• Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation
• Resiliency Analysis and Improvement of Variational Quantum Factoring in Superconducting Qubit
• Encodings of the weighted MAX k-CUT on qubit systems
• Quantum Alternating Operator Ansatz for the Preparation and Detection of Long-Lived Singlet States in NMR
• A combined quantum-classical method applied to material design: optimization and discovery of photochromic materials for photopharmacology applications
• QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation
• Finding the optimal Nash equilibrium in a discrete Rosenthal congestion game using the Quantum Alternating Operator Ansatz
• On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ansätze