Solving Constrained Optimization Problems Using Hybrid Qubit-Qumode Quantum Devices

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Optimization

Background:

• Variational Quantum Algorithms (VQAs) are a key approach for near-term quantum hardware.
• Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various scientific and industrial domains.
• Hybrid qubit-qumode systems offer a novel platform for quantum computation.

Purpose of the Study:

• To demonstrate the efficacy of hybrid qubit-qumode devices for solving QUBO problems.
• To introduce and apply the Echoed Conditional Displacement Variational Quantum Eigensolver (ECD-VQE) for optimization.
• To compare ECD-VQE performance against existing quantum algorithms like QAOA.

Main Methods:

• Utilizing circuit quantum electrodynamics (cQED) architectures for hybrid qubit-qumode implementation.
• Encoding QUBO instances across multiple qumodes coupled to a single qubit.
• Extracting binary solutions via photon-number measurements.
• Applying the ECD-VQE algorithm to the Binary Knapsack Problem.

Main Results:

• ECD-VQE on hybrid qubit-qumode devices achieved higher-quality solutions than QAOA on conventional qubit circuits.
• The ECD-VQE approach required significantly fewer resources compared to QAOA.
• Demonstrated applicability of ECD-VQE to chemistry problems, specifically active-space selection.
• Showcased shallower circuit depths for state preparation using variational ECD ansatz.

Conclusions:

• Hybrid qubit-qumode platforms are efficient for solving NP-hard and chemistry-related optimization problems.
• ECD-VQE on qubit-qumode systems offers a promising advantage over qubit-only architectures.
• Qubit-qumode gates are strong candidates for constrained optimization in early fault-tolerant quantum computing.