Parity Quantum Optimization: Encoding Constraints

Abstract

Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to the spin encoding, translates the problem to a representation using only parity variables that encodes products of spin variables. In combining exchange interaction and single spin flip terms in the parity representation, constraints on sums and products of arbitrary k-body terms can be implemented without additional overhead in two-dimensional quantum systems.

References in corpus (46)

• Many-Body Physics with Ultracold Gases
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Quantum information with Rydberg atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Adiabatic Quantum Computing
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Quantum Annealing and Analog Quantum Computation
• Interfacing spin qubits in quantum dots and donors - hot, dense and coherent
• Schrieffer-Wolff transformation for quantum many-body systems
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Perspectives of quantum annealing: Methods and implementations
• Quantum computing with neutral atoms
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• A four-qubit germanium quantum processor
• Silicon CMOS architecture for a spin-based quantum computer
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• A case study in programming a quantum annealer for hard operational planning problems
• $XY$-mixers: analytical and numerical results for QAOA
• Consistency of the Adiabatic Theorem
• Quantum Speedup by Quantum Annealing
• Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
• Application of Quantum Annealing to Nurse Scheduling Problem
• Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management
• Deterministic Preparation of Dicke States
• Quantum Annealing Correction with Minor Embedding
• Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
• Quantum Annealing for Constrained Optimization
• Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems
• Divide and concur: A general approach to constraint satisfaction
• Dynamics of reverse annealing for the fully-connected $p$-spin model
• Two-Dimensional Arrays of RF Ion Traps with Addressable Interactions
• Driver Hamiltonians for constrained optimization in quantum annealing
• The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover
• Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing
• Single-electron spin resonance in a nanoelectronic device using a global field
• Quantum optimization via four-body Rydberg gates
• Demonstration of tunable three-body interactions between superconducting qubits
• Error correction for encoded quantum annealing
• Simulated Quantum Annealing with Two All-to-All Connectivity Schemes
• Programmable Superpositions of Ising Configurations

Cited by in corpus (11)

• Quantum Annealing for Industry Applications: Introduction and Review
• Quantum computing for finance
• Encoding-Independent Optimization Problem Formulation for Quantum Computing
• Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates
• Parity Quantum Computing as YZ-Plane Measurement-Based Quantum Computing
• Constructive plaquette compilation for the parity architecture
• Quantum optimization with linear Ising penalty functions for customer data science
• Flexible constraint compilation in the parity architecture
• Minimally Universal Parity Quantum Computing
• Four-body coupler for superconducting qubits based on Josephson parametric oscillators
• Spin Model for Quantum Annealing with Kerr Parametric Oscillators