Quantum optimization algorithms for qubit-only and hybrid qubit-qumode devices
Brandon
Allen
RTX Technology Research Center
Talk
(Virtual)
Widely used quantum optimization methods, including quantum annealing and the quantum approximate optimization algorithm, are naturally suited to quadratic unconstrained binary optimization problems but struggle to systematically handle constraints, mixed discrete-continuous decision variables, barren plateaus, and hardware noise. In this talk, we present two complementary approaches for extending quantum optimization beyond standard QUBO formulations.
First, we introduce a hybrid classical–quantum framework that combines the alternating direction method of multipliers with QAOA. In this formulation, the constrained optimization problem is decomposed into an unconstrained discrete subproblem, solved as a QUBO on a quantum device, while continuous variables and constraint enforcement are handled classically. Compared with conventional penalty-based encodings, this approach avoids quantizing continuous variables, reduces the number of auxiliary qubits required to encode constraints, and lowers QAOA circuit depth, making it more suitable for near-term implementation. We further incorporate warm-start state initialization and conditional-value-at-risk objective estimation to improve convergence.
Second, we investigate hybrid qubit–qumode devices as an alternative platform for QUBO solving using the Echoed Conditional Displacement Variational Quantum Eigensolver. Motivated by circuit quantum electrodynamics architectures, we encode QUBO instances across multiple qumodes weakly coupled to a single qubit and extract binary solutions directly from photon-number measurements. We show that variational ECD ansätze can provide expressive state preparation with shallower circuits than comparable qubit-only constructions, highlighting the potential of qubit–qumode gates for quantum optimization.
We benchmark these approaches on a range of constrained combinatorial optimization problems using quantum simulators and noisy-device models, comparing solution quality, convergence behavior, resource requirements, and robustness to noise. Across representative benchmarks, the proposed methods reduce quantum resource requirements while maintaining competitive solution quality under realistic noise models, demonstrating a practical path toward more scalable quantum optimization for constrained and mixed-variable problems.
First, we introduce a hybrid classical–quantum framework that combines the alternating direction method of multipliers with QAOA. In this formulation, the constrained optimization problem is decomposed into an unconstrained discrete subproblem, solved as a QUBO on a quantum device, while continuous variables and constraint enforcement are handled classically. Compared with conventional penalty-based encodings, this approach avoids quantizing continuous variables, reduces the number of auxiliary qubits required to encode constraints, and lowers QAOA circuit depth, making it more suitable for near-term implementation. We further incorporate warm-start state initialization and conditional-value-at-risk objective estimation to improve convergence.
Second, we investigate hybrid qubit–qumode devices as an alternative platform for QUBO solving using the Echoed Conditional Displacement Variational Quantum Eigensolver. Motivated by circuit quantum electrodynamics architectures, we encode QUBO instances across multiple qumodes weakly coupled to a single qubit and extract binary solutions directly from photon-number measurements. We show that variational ECD ansätze can provide expressive state preparation with shallower circuits than comparable qubit-only constructions, highlighting the potential of qubit–qumode gates for quantum optimization.
We benchmark these approaches on a range of constrained combinatorial optimization problems using quantum simulators and noisy-device models, comparing solution quality, convergence behavior, resource requirements, and robustness to noise. Across representative benchmarks, the proposed methods reduce quantum resource requirements while maintaining competitive solution quality under realistic noise models, demonstrating a practical path toward more scalable quantum optimization for constrained and mixed-variable problems.