Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings

• URL: http://arxiv.org/abs/2011.08165v2
• Date: Thu, 12 May 2022 23:23:03 GMT
• Title: Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings
• Authors: Joel Rajakumar, Jai Moondra, Bryan Gard, Swati Gupta, and Creston D. Herold
• Abstract summary: We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.
• Score: 3.2622301272834524
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with $n\le8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.

Related papers

• Imaginary Hamiltonian variational ansatz for combinatorial optimization problems [3.14105061893604]
  We introduce a tree arrangement of the parametrized quantum gates, enabling the exact solution of arbitrary tree graphs using the one-round $i$HVA. Our ansatz solves MaxCut exactly for graphs with up to 24 nodes and $D leq 5$, whereas only approximate solutions can be derived by the classical near-optimal Goemans-Williamson algorithm.
  arXiv  Detail & Related papers  (2024-08-17T03:34:17Z)
• Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations [5.451583832235867]
  We develop new approximate compilation schemes to solve the Max-Cut problem. Results are based on principles of graph sparsification and decomposition. We demonstrate significant reductions in noise are obtained in our new compilation approaches.
  arXiv  Detail & Related papers  (2024-06-20T14:00:09Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• 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)
• Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models [15.857373057387669]
  We prove concentration properties at any constant level (number of layers) on ensembles of random optimization problems in the infinite size limit. Our analysis can be understood via a saddle-point approximation of a sum-over-paths integral. We show that the performance of the QAOA at constant levels is bounded away from optimality for pure $q$-spin models when $qge 4$ and is even.
  arXiv  Detail & Related papers  (2022-04-21T17:40:39Z)
• The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model [0.0]
  The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to optimization problems. We give an iterative formula to evaluate performance for any $D$ at any depth $p$. We make an optimistic conjecture that the QAOA, as $p$ goes to infinity, will achieve the Parisi value.
  arXiv  Detail & Related papers  (2021-10-27T06:35:59Z)
• 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)
• Minimax Optimization with Smooth Algorithmic Adversaries [59.47122537182611]
  We propose a new algorithm for the min-player against smooth algorithms deployed by an adversary. Our algorithm is guaranteed to make monotonic progress having no limit cycles, and to find an appropriate number of gradient ascents.
  arXiv  Detail & Related papers  (2021-06-02T22:03:36Z)
• The Min-Max Complexity of Distributed Stochastic Convex Optimization with Intermittent Communication [61.60069865891783]
  We resolve the min-max complexity of distributed convex optimization (up to a log factor) in the intermittent communication setting. We present a novel lower bound with a matching upper bound that establishes an optimal algorithm.
  arXiv  Detail & Related papers  (2021-02-02T16:18:29Z)
• Hybrid quantum-classical algorithms for approximate graph coloring [65.62256987706128]
  We show how to apply the quantum approximate optimization algorithm (RQAOA) to MAX-$k$-CUT, the problem of finding an approximate $k$-vertex coloring of a graph. We construct an efficient classical simulation algorithm which simulates level-$1$ QAOA and level-$1$ RQAOA for arbitrary graphs.
  arXiv  Detail & Related papers  (2020-11-26T18:22:21Z)
• Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving [1.0660480034605238]
  "spectral sparsification" reduces number of edges to near-linear in number of nodes. We show a quantum speedup for spectral sparsification and many of its applications. Our algorithm implies a quantum speedup for solving Laplacian systems.
  arXiv  Detail & Related papers  (2019-11-17T17:29:40Z)

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.