Limitations of tensor network approaches for optimization and sampling: A comparison against quantum and classical Ising machines

• URL: http://arxiv.org/abs/2411.16431v1
• Date: Mon, 25 Nov 2024 14:35:14 GMT
• Title: Limitations of tensor network approaches for optimization and sampling: A comparison against quantum and classical Ising machines
• Authors: Anna Maria Dziubyna, Tomasz Śmierzchalski, Bartłomiej Gardas, Marek M. Rams, Masoud Mohseni,
• Abstract summary: We develop an algorithm to reveal the low-energy spectrum of Ising spin-glass systems with interaction graphs. Our deterministic approach combines a branch-and-bound search strategy with an approximate calculation of marginals. We benchmark our approach on random problems defined on Pegasus and Zephyr graphs with up to a few thousand spins.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor-network-based algorithm to reveal the low-energy spectrum of Ising spin-glass systems with interaction graphs relevant to present-day quantum annealers. Our deterministic approach combines a branch-and-bound search strategy with an approximate calculation of marginals via tensor-network contractions. Its application to quasi-two-dimensional lattices with large unit cells of up to 24 spins, realized in current quantum annealing processors, requires a dedicated approach that utilizes sparse structures in the tensor network representation and GPU hardware acceleration. We benchmark our approach on random problems defined on Pegasus and Zephyr graphs with up to a few thousand spins, comparing it against the D-Wave Advantage quantum annealer and Simulated Bifurcation algorithm, with the latter representing an emerging class of classical Ising solvers. Apart from the quality of the best solutions, we compare the diversity of low-energy states sampled by all the solvers. For the biggest considered problems with over 5000 spins, the state-of-the-art tensor network approaches lead to solutions that are $0.1\%$ to $1\%$ worse than the best solutions obtained by Ising machines while being two orders of magnitude slower. We attribute those results to approximate contraction failures. While all three methods can output diverse low-energy solutions, e.g., differing by at least a quarter of spins with energy error below $1\%$, our deterministic branch-and-bound approach finds sets of a few such states at most. On the other hand, both Ising machines prove capable of sampling sets of thousands of such solutions.

Related papers

• Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking [1.6385815610837167]
  We investigate making posiform planted QUBOs computationally harder by fusing many smaller random discrete coefficient spin-glass Ising models. We benchmark the capabilities of three D-Wave superconducting qubit quantum annealing processors. We find that the D-Wave QPU ground-state sampling success rate does not change with respect to the size of the random QUBOs we employ.
  arXiv  Detail & Related papers  (2024-11-06T02:46:33Z)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Quantum Circuit Simulation with Fast Tensor Decision Diagram [10.24745264727704]
  We present a novel open-source framework that harnesses tensor decision diagrams to eliminate overheads and achieve significant speedups. We introduce a new linear-complexity rank simplification algorithm, Tetris, and edge-centric data structures for tensor decision diagram operations.
  arXiv  Detail & Related papers  (2024-01-21T01:24:29Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Validation and benchmarking of quantum annealing technology [0.0]
  This thesis focuses on the problem of benchmarking and validating quantum annealers. We propose two algorithms for solving real-world problems and test how they perform on the current generation of quantum annealers.
  arXiv  Detail & Related papers  (2023-12-06T14:56:45Z)
• Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models [8.463477025989542]
  We take advantage of a digitized-counterdiabatic quantum optimization (DCQO) algorithm to find an optimal solution of the $p$-spin model up to 4-local interactions. By further optimizing parameters using variational methods, we solve with unit accuracy 2-spin, 3-spin, and 4-spin problems for $100%$, $93%$, and $83%$ of instances, respectively.
  arXiv  Detail & Related papers  (2023-11-11T22:49:16Z)
• Block belief propagation algorithm for two-dimensional tensor networks [0.0]
  We propose a block belief propagation algorithm for contracting two-dimensional tensor networks and approximating the ground state of $2D$ systems. As applications, we use our algorithm to study the $2D$ Heisenberg and transverse Ising models, and show that the accuracy of the method is on par with state-of-the-art results.
  arXiv  Detail & Related papers  (2023-01-14T07:37:08Z)
• Comparing Three Generations of D-Wave Quantum Annealers for Minor Embedded Combinatorial Optimization Problems [1.0878040851638]
  We report benchmarks across three generations of D-Wave quantum annealers. The Ising, or equivalently QUBO, formulation of these problems do not require auxiliary variables for order reduction.
  arXiv  Detail & Related papers  (2023-01-08T10:02:56Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• 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)
• Optimizing Tensor Network Contraction Using Reinforcement Learning [86.05566365115729]
  We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges.
  arXiv  Detail & Related papers  (2022-04-18T21:45:13Z)
• 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)
• A Hybrid Quantum-Classical Algorithm for Robust Fitting [47.42391857319388]
  We propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs. We present results obtained using an actual quantum computer.
  arXiv  Detail & Related papers  (2022-01-25T05:59:24Z)
• Sampling diverse near-optimal solutions via algorithmic quantum annealing [0.3506539188356145]
  One of the main open problems is the lack of ergodicity, or mode collapse, for typical Monte Carlo solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems.
  arXiv  Detail & Related papers  (2021-10-20T13:33:37Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids [63.75363908696257]
  The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully.
  arXiv  Detail & Related papers  (2021-06-11T09:43:09Z)
• GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models [62.997667081978825]
  We introduce a new framework that leverages machine learning models known as generative models to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines. We show its superior performance when the goal is to find the best minimum given a fixed budget for the number of function calls.
  arXiv  Detail & Related papers  (2021-01-15T18:18:38Z)

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.