Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models

• URL: http://arxiv.org/abs/2311.02151v2
• Date: Thu, 05 Dec 2024 12:17:08 GMT
• Title: Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models
• Authors: Elisabeth Wybo, Martin Leib,
• Abstract summary: parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA) We show that for fixed number of parity-encoded QAOA layers, the performance or the output energy vanishes towards zero. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA.
• Score: 0.0
• License:
• Abstract: The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size $N$ as $N^{-1/2}$. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances.

Related papers

• Performance of Parity QAOA for the Signed Max-Cut Problem [0.0]
  We investigate the performance of the Quantum Approximate Algorithm Optimization on the Parity architecture (Parity QAOA) By comparing the algorithms at fixed circuit depth, we demonstrate that Parity QAOA outperforms conventional QAOA implementations based on SWAP networks.
  arXiv  Detail & Related papers  (2024-09-23T08:00:03Z)
• Hybrid Classical-Quantum Simulation of MaxCut using QAOA-in-QAOA [0.0]
  In this work, an implementation of the QAOA2 method for the scalable solution of the MaxCut problem is presented. The limits of the Goemans-Williamson (GW) algorithm as a purely classical alternative to QAOA are investigated. Results from large-scale simulations of up to 33 qubits are presented, showing the advantage of QAOA in certain cases and the efficiency of the implementation.
  arXiv  Detail & Related papers  (2024-06-25T09:02:31Z)
• An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation [0.23999111269325263]
  The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve optimisation problems. While QAOA can be implemented on NISQ devices, physical limitations can limit circuit depth and decrease performance. This work introduces the eXpressive QAOA (XQAOA) that assigns more classical parameters to the ansatz to improve its performance at low depths.
  arXiv  Detail & Related papers  (2023-02-09T07:47:06Z)
• Solving boolean satisfiability problems with the quantum approximate optimization algorithm [0.05076419064097732]
  We study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to quantum computing problems. We develop analytic bounds on the average success probability of QAOA over random formulae at the satisfiability threshold. We find that for around 14 ansatz layers, QAOA matches the scaling performance of the highest-performance classical solver.
  arXiv  Detail & Related papers  (2022-08-14T20:39:48Z)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• 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)
• Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach [94.37521840642141]
  We study the correlation clustering problem using the quantum approximate optimization algorithm (QAOA) and qudits. Specifically, we consider a neutral atom quantum computer and propose a full stack approach for correlation clustering. We show the qudit implementation is superior to the qubit encoding as quantified by the gate count.
  arXiv  Detail & Related papers  (2021-06-22T11:07:38Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Evaluation of QAOA based on the approximation ratio of individual samples [0.0]
  We simulate the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives. Because of the evolving QAOA computational complexity-theoretic guidance, we utilize a framework for the search for quantum advantage.
  arXiv  Detail & Related papers  (2020-06-08T18:00:18Z)

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.