Filtering variational quantum algorithms for combinatorial optimization

Abstract

Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum Eigensolver (F-VQE) which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the Quantum Approximate Optimization Algorithm (QAOA). We also demonstrate the experimental feasibility of our algorithms on a Honeywell trapped-ion quantum processor.

14 pages, 9 figures, 2 tables, accepted version

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• The Variational Quantum Eigensolver: a review of methods and best practices
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• A case study of variational quantum algorithms for a job shop scheduling problem
• Barren plateaus in quantum tensor network optimization
• Optimizing resource efficiencies for scalable full-stack quantum computers
• Graph neural network initialisation of quantum approximate optimisation
• Error propagation in NISQ devices for solving classical optimization problems
• Variational quantum amplitude estimation
• NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
• An entanglement perspective on the quantum approximate optimization algorithm
• Protecting Expressive Circuits with a Quantum Error Detection Code
• Quantum Approximate Optimization Algorithm pseudo-Boltzmann states
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
• An introduction to variational quantum algorithms for combinatorial optimization problems
• State Preparation Boosters for Early Fault-Tolerant Quantum Computation
• Quantum Dropout: On and Over the Hardness of Quantum Approximate Optimization Algorithm
• Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm
• Quantum Gaussian filter for exploring ground-state properties
• Simulating time evolution on distributed quantum computers
• Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits
• Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions
• Accelerating variational quantum algorithms with multiple quantum processors