Multiscale Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2312.06181v1
• Date: Mon, 11 Dec 2023 07:47:16 GMT
• Title: Multiscale Quantum Approximate Optimization Algorithm
• Authors: Ping Zou
• Abstract summary: The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to optimization problems. We propose a new version of QAOA that incorporates the capabilities of QAOA and the real-space renormalization group transformation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an active area of research to exhibit its speedup over classical algorithms. The performance of the QAOA at low depths is limited, while the QAOA at higher depths is constrained by the current techniques. We propose a new version of QAOA that incorporates the capabilities of QAOA and the real-space renormalization group transformation, resulting in enhanced performance. Numerical simulations demonstrate that our algorithm can provide accurate solutions for certain randomly generated instances utilizing QAOA at low depths, even at the lowest depth. The algorithm is suitable for NISQ devices to exhibit a quantum advantage.

Related papers

• Distributed Quantum Approximate Optimization Algorithm on Integrated High-Performance Computing and Quantum Computing Systems for Large-Scale Optimization [1.7099366779394252]
  Quantum approximated optimization algorithm (QAOA) has shown promise for solving optimization problems by providing quantum speedup on gate-based quantum computing systems. We propose a distributed QAOA (DQAOA), which leverages a high-performance computing-quantum computing integrated system. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible with our strategies.
  arXiv  Detail & Related papers  (2024-07-29T17:42:25Z)
• Depth scaling of unstructured search via quantum approximate optimization [0.0]
  Variational quantum algorithms have become the de facto model for current quantum computations. One such problem is unstructured search which consists on finding a particular bit of string. We trotterize a CTQW to recover a QAOA sequence, and employ recent advances on the theory of Trotter formulas to bound the query complexity.
  arXiv  Detail & Related papers  (2024-03-22T18:00:03Z)
• QAOA Performance in Noisy Devices: The Effect of Classical Optimizers and Ansatz Depth [0.32985979395737786]
  The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) This paper presents an investigation into the impact realistic noise on the classical vectors. We find that while there is no significant difference in the performance of classicals in a state simulation, the Adam and AMSGrads perform best in the presence of shot noise.
  arXiv  Detail & Related papers  (2023-07-19T17:22:44Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Mean-Field Approximate Optimization Algorithm [0.17812428873698405]
  Mean-field Approximate Optimization Algorithm (mean-field AOA) developed by replacing quantum evolution of QAOA with classical spin dynamics. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick (SK) model and the partition problem. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot.
  arXiv  Detail & Related papers  (2023-03-01T08:47:06Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits [15.279642278652654]
  We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
  arXiv  Detail & Related papers  (2021-12-21T12:41:31Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection [80.28858481461418]
  Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices. Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
  arXiv  Detail & Related papers  (2021-07-11T10:56:24Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.