Quantum approximate optimization of finite-state bosonic systems

Abstract

There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may be exponentially larger. To exclude the infeasible subspace, one common approach relies on penalizing the objective function. However, this strategy can be inefficient as the size of the illegitimate subspace grows. Here we propose to employ the Hamiltonian-based quantum approximate optimization algorithm (QAOA) through devising appropriate mixing Hamiltonians such that the infeasible configuration space is ruled out. We investigate this idea by employing binary, symmetric, and unary mapping techniques. It is shown that the standard mixing Hamiltonian (sum of the bit-flip operations) is the optimal option for symmetric mapping, where the controlled-NOT gate count is used as a measure of implementation cost. In contrast, the other two encoding schemes witness a $p$-fold increase in this figure for a $p$-layer QAOA. We apply this framework to quantum approximate thermalization and find the ground state of the repulsive Bose-Hubbard model in the strong and weak interaction regimes.

16 pages, 5 figures, 1 table (accepted version)

References in corpus (41)

• Quantum Computing in the NISQ era and beyond
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Variational Quantum Algorithms
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• The logarithmic negativity: A full entanglement monotone that is not convex
• Quantum many-body systems out of equilibrium
• Logical quantum processor based on reconfigurable atom arrays
• Invariant Variation Problems
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Qudits and high-dimensional quantum computing
• Tools for quantum simulation with ultracold atoms in optical lattices
• High-threshold and low-overhead fault-tolerant quantum memory
• Training variational quantum algorithms is NP-hard
• Quantum Boltzmann Machine
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Effect of barren plateaus on gradient-free optimization
• Barren Plateaus in Variational Quantum Computing
• Thermalization dynamics of a gauge theory on a quantum simulator
• $XY$-mixers: analytical and numerical results for QAOA
• How robust is a quantum gate in the presence of noise?
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Variational Thermal Quantum Simulation via Thermofield Double States
• Quantum Annealing for Constrained Optimization
• Improving Hamiltonian encodings with the Gray code
• Coherent Optomechanical State Transfer between Disparate Mechanical Resonators
• Product Spectrum Ansatz and the Simplicity of Thermal States
• Driver Hamiltonians for constrained optimization in quantum annealing
• Variational Quantum Algorithm for Non-equilibrium Steady States
• Programmable Quantum Annealers as Noisy Gibbs Samplers
• Quantum approximate optimization algorithm for qudit systems
• Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions
• Quantum Approximate Optimization Algorithm pseudo-Boltzmann states
• Observation of quantum thermalization restricted to Hilbert space fragments
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• Crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators
• Iterative Layerwise Training for Quantum Approximate Optimization Algorithm
• Performance of Quantum Approximate Optimization with Quantum Error Detection
• Field induced non-BEC transitions in frustrated magnets
• End-to-End Protocol for High-Quality QAOA Parameters with Few Shots