Inequality constraints in variational quantum circuits with qudits
arXiv:2410.07674 · doi:10.1103/3l96-41xf
Abstract
Quantum optimization is emerging as a prominent candidate for exploiting the capabilities of near-term quantum devices. Many application-relevant optimization tasks require the inclusion of inequality constraints, usually handled by enlarging the Hilbert space through the addition of slack variables. This approach, however, requires significant additional resources especially when considering multiple constraints. Here, we study an alternative direct implementation of these constraints within the QAOA algorithm, achieved using qudit-SUM gates, and compare it to the slack variable method generalized to qudits. We benchmark these approaches on three paradigmatic optimization problems. We find that the direct implementation of the inequality penalties vastly outperforms the slack variables method, especially when studying real-world inspired problems with many constraints. Within the direct penalty implementation, a linear energy penalty for unfeasible states outperforms other investigated functional forms, such as the canonical quadratic penalty. The proposed approach may thus be an enabling step for approaching realistic industry-scale and fundamental science problems with large numbers of inequality constraints.
References in corpus (32)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Variational Quantum Algorithms
- Ising formulations of many NP problems
- Noisy intermediate-scale quantum (NISQ) algorithms
- The Variational Quantum Eigensolver: a review of methods and best practices
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- Perspectives of quantum annealing: Methods and implementations
- Simulating Lattice Gauge Theories within Quantum Technologies
- A Review on Quantum Approximate Optimization Algorithm and its Variants
- A universal qudit quantum processor with trapped ions
- Quantum Information Scrambling in a Superconducting Qutrit Processor
- Barren Plateaus in Variational Quantum Computing
- Challenges and Opportunities in Quantum Optimization
- Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
- Native qudit entanglement in a trapped ion quantum processor
- Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas
- Hybrid quantum-classical algorithms for approximate graph coloring
- On the representation of Boolean and real functions as Hamiltonians for quantum computing
- Domain wall encoding of discrete variables for quantum annealing and QAOA
- Universal qudit gate synthesis for transmons
- Penalty methods for variational quantum eigensolver
- Constrained mixers for the quantum approximate optimization algorithm
- Polymer Physics by Quantum Computing
- Engineering random spin models with atoms in a high-finesse cavity
- Constrained Optimization via Quantum Zeno Dynamics
- Quantum approximate optimization algorithm for qudit systems
- Universal quantum control in irreducible state-space sectors: application to bosonic and spin-boson systems
- Data re-uploading with a single qudit
- On the role of entanglement in qudit-based circuit compression
- Multiobjective variational quantum optimization for constrained problems: an application to Cash Management
- Qudit Machine Learning
- Many-Qudit representation for the Travelling Salesman Problem Optimisation