Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver

Abstract

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz (HVA) aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate the effectiveness, efficiency, and advantages of the two-dimensional Heisenberg model and the Fermi-Hubbard chain. Numerical experiments show that MBHVA is expected to reduce resource overhead compared to quantum circuits, especially in the presence of large multi-qubit rotation operations. Furthermore, when compared to Measurement-based Hardware Efficient Ansatz (MBHEA), MBHVA also demonstrates superior performance. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in terms of both resource efficiency and error mitigation, particularly for photonic platforms.

23 pages, 8 figures

References in corpus (39)

• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• Quantum Teleportation is a Universal Computational Primitive
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Measurement-based quantum computation with cluster states
• Improved Simulation of Stabilizer Circuits
• Superconducting Qubits: Current State of Play
• Error mitigation for short-depth quantum circuits
• Detecting Single Infrared Photons with 93% System Efficiency
• The Variational Quantum Eigensolver: a review of methods and best practices
• Multi-party entanglement in graph states
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Towards Practical Quantum Variational Algorithms
• Photonic quantum information processing: a review
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum optimization using variational algorithms on near-term quantum devices
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Large-scale silicon quantum photonics implementing arbitrary two-qubit processing
• Training variational quantum algorithms is NP-hard
• Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
• Graphical description of the action of local Clifford transformations on graph states
• Error-mitigated digital quantum simulation
• Universal resources for measurement-based quantum computation
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Efficient variational simulation of non-trivial quantum states
• On barren plateaus and cost function locality in variational quantum algorithms
• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• A measurement-based variational quantum eigensolver
• Hamiltonian variational ansatz without barren plateaus
• Variational Quantum Eigensolver for Frustrated Quantum Systems
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• A native measurement-based QAOA algorithm, applied to the MAX K-CUT problem
• Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Hybrid Quantum Computation
• Physical Realization of Measurement Based Quantum Computation
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model

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