Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models

• URL: http://arxiv.org/abs/2311.06682v1
• Date: Sat, 11 Nov 2023 22:49:16 GMT
• Title: Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models
• Authors: Huijie Guan, Fei Zhou, Francisco Albarr\'an-Arriagada, Xi Chen, Enrique Solano, Narendra N. Hegade, He-Liang Huang
• Abstract summary: 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.
• Score: 8.463477025989542
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers from limited hardware coherence times. In this sense, counterdiabatic quantum protocols provide a shortcut to this process, steering the system along its ground state with fast-changing Hamiltonian. In this work, we take full advantage of a digitized-counterdiabatic quantum optimization (DCQO) algorithm to find an optimal solution of the $p$-spin model up to 4-local interactions. We choose a suitable scheduling function and initial Hamiltonian such that a single-layer quantum circuit suffices to produce a good ground-state overlap. 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. As a particular case of the latter, we also solve factorization problems involving 5, 9, and 12 qubits. Due to the low computational overhead, our compact approach may become a valuable tool towards quantum advantage in the NISQ era.

Related papers

• 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)
• Qubit-efficient quantum combinatorial optimization solver [0.0]
  We develop a qubit-efficient algorithm that overcomes the limitation by mapping a candidate bit solution to an entangled wave function of fewer qubits. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.
  arXiv  Detail & Related papers  (2024-07-22T11:02:13Z)
• 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)
• Pre-optimizing variational quantum eigensolvers with tensor networks [1.4512477254432858]
  We present and benchmark an approach where we find good starting parameters for parameterized quantum circuits by simulating VQE. We apply this approach to the 1D and 2D Fermi-Hubbard model with system sizes that use up to 32 qubits. In 2D, the parameters that VTNE finds have significantly lower energy than their starting configurations, and we show that starting VQE from these parameters requires non-trivially fewer operations to come down to a given energy.
  arXiv  Detail & Related papers  (2023-10-19T17:57:58Z)
• Alleviating the quantum Big-$M$ problem [0.237499051649312]
  Classically known as the "Big-$M$" problem, it affects the physical energy scale. We take a systematic, encompassing look at the quantum big-$M$ problem, revealing NP-hardness in finding the optimal $M$. We propose a practical translation algorithm, based on SDP relaxation, that outperforms previous methods in numerical benchmarks.
  arXiv  Detail & Related papers  (2023-07-19T18:00:05Z)
• Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm [0.7046417074932257]
  We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers. We find that classical solvers are capable of producing high-quality approximate solutions in linear time complexity. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.
  arXiv  Detail & Related papers  (2022-06-07T20:59:19Z)
• 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)
• Efficiently Solve the Max-cut Problem via a Quantum Qubit Rotation Algorithm [7.581898299650999]
  We introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA) The approximate solution of the max-cut problem can be obtained with probability close to 1. We compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.
  arXiv  Detail & Related papers  (2021-10-15T11:19:48Z)
• 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)
• 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.