Determination of Chain Strength induced by Embedding in D-Wave Quantum Annealer

• URL: http://arxiv.org/abs/2209.12166v1
• Date: Sun, 25 Sep 2022 06:59:10 GMT
• Title: Determination of Chain Strength induced by Embedding in D-Wave Quantum Annealer
• Abstract summary: D-wave quantum annealer requires embedding with ferromagnetic (FM) chains connected by several qubits. determination of the chain strength $J_c$ required to sustain FM order of qubits in the chains is crucial for the accuracy of quantum annealing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The D-wave quantum annealer requires embedding with ferromagnetic (FM) chains connected by several qubits, because it cannot capture exact long-range coupling between qubits, and retains the specific architecture that depends on the hardware type. Therefore, determination of the chain strength $J_c$ required to sustain FM order of qubits in the chains is crucial for the accuracy of quantum annealing. In this study, we devise combinatorial optimization problems with ordered and disordered qubits for various embeddings to predict appropriate $J_c$ values. We analyze the energy interval $\Delta_s$ and $\Delta_c$ between ground and first excited states in the combinatorial optimization problems without and with chains respectively, using the exact approach. We also measure the probability $p$ that the exact ground energy per site $E_g$ is observed in many simulated annealing shots. We demonstrate that the determination of $J_c$ is increasingly sensitive with growing disorder of qubits in the combinatorial optimization problems. In addition, the values of appropriate $J_c$, where the values of $p$ are at a maximum, increase with decreasing $\Delta_s$. Finally, the appropriate value of $J_c$ is shown to be observed at approximately $\Delta_c/\Delta_s=0.25$ and $2.1 E_g$ in the ordered and disordered qubits, respectively.

Related papers

• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence [41.64418624570687]
  We study first-order methods for objectives satisfying the Polyak-ojasiewicz (PL) condition when samples are generated by an Markov chain.<n>In the lighttailed setting, prior uniform-in-time high-probability bounds for ordinary Gradient Descent (SGD) under a standard growth envelope scale as $widetildeO(t_mix/k)$.<n>We prove this linear dependence on the mixing time is optimal via a matching $(2 t_mix/k)$ lower bound on a quadratic objective driven by a persistent two
  arXiv  Detail & Related papers  (2026-06-24T19:00:56Z)
• OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing [0.0]
  We establish that orbital-angular-momentum encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled.<n>Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $ell$, the lattice aspect ratio $r$, and the finite-energy envelope $$ to maximise quantum Fisher information.
  arXiv  Detail & Related papers  (2026-05-13T09:49:16Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• Probing Quantum Entanglement in $τ^+τ^-$ Pairs via the $ππ$ Channel at STCF [7.941172053476731]
  Quantum entanglement and Bell-inequality violation in $+-$ pairs provide a sensitive probe of quantum correlations in high-energy interactions.<n>Super Tau-Charm Facility can provide a competitive platform for precision studies of quantum correlations in $$-lepton pairs.
  arXiv  Detail & Related papers  (2026-05-02T04:10:09Z)
• Lambert W Function Framework for Graphene Nanoribbon Quantum Sensing: Theory, Verification, and Multi-Modal Applications [0.0]
  We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy.<n>We demonstrate that operating near the branch point at $z = -1/e$ yields sensitivity enhancement factors scaling as $_textenh propto (z - z_c)-1/2$, achieving 35-fold enhancement at $= 0.001$.
  arXiv  Detail & Related papers  (2026-01-15T08:32:47Z)
• Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing [52.124267908936396]
  The model is composed of $M$ arms and $K$ plays.<n>Each arm has a number of capacities, and each unit of capacity is associated with a reward function.<n>When multiple plays compete for the arm capacity, the arm capacity is allocated in a larger priority weight first manner.
  arXiv  Detail & Related papers  (2025-12-25T11:19:09Z)
• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Convergence Rate Analysis of LION [54.28350823319057]
  LION converges iterations of $cal(sqrtdK-)$ measured by gradient Karush-Kuhn-T (sqrtdK-)$. We show that LION can achieve lower loss and higher performance compared to standard SGD.
  arXiv  Detail & Related papers  (2024-11-12T11:30:53Z)
• Determination of Optimal Chain Coupling made by Embedding in D-Wave Quantum Annealer [0.0]
  The qubits in a D-wave quantum annealer (D-wave QA) are designed on a Pegasus graph that is different from structure of an optimization problem. Weak and strong $J_c$ values induce chain breaking and enforcement of chain energy. We present an algorithm howJ_ctextoptimal$ with the maximum probabilityp$ for observing the possible lowest energy is determined.
  arXiv  Detail & Related papers  (2024-06-05T15:18:22Z)
• Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation [0.0]
  Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables.<n>In this paper, we propose a method to divide $U_X(t)$ based on orthogonal series density estimation.<n>Our method achieves the circuit depth and total query complexity scaling as $O(sqrtN)$ and $O(N3/2)$, respectively.
  arXiv  Detail & Related papers  (2024-06-04T01:50:21Z)
• Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives [50.24983453990065]
  This article is devoted to developing an approach for manipulating the von Neumann entropy $S(rho(t))$ of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy $S(rho(T))$; (b) steering $S(rho(T))$ to a given target value; (c) steering $S(rho(T))$ to a target value and satisfying the pointwise state constraint $S(
  arXiv  Detail & Related papers  (2024-05-10T10:01:10Z)
• 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)
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors [46.76612530830571]
  We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (detectors'') We explore the dynamics of density and of entanglement entropy in the chain, for various values of $rho_a$ and $M$.
  arXiv  Detail & Related papers  (2023-11-21T21:41:11Z)
• Contextual Combinatorial Bandits with Probabilistically Triggered Arms [55.9237004478033]
  We study contextual bandits with probabilistically triggered arms (C$2$MAB-T) under a variety of smoothness conditions. Under the triggering modulated (TPM) condition, we devise the C$2$-UC-T algorithm and derive a regret bound $tildeO(dsqrtT)$.
  arXiv  Detail & Related papers  (2023-03-30T02:51:00Z)
• Precision of quantum simulation of all-to-all coupling in a local architecture [0.0]
  We find an analytic relation between the values $J_ij$ of the desired interaction and the parameters of the 2d circuit. For the relative error to be a constant $epsilon$, one requires an energy scale growing as $n6$ in the number of qubits. Our proof is based on the Schrieffer-Wolff transformation and generalizes to any hardware.
  arXiv  Detail & Related papers  (2023-02-05T18:54:28Z)
• Approximate Function Evaluation via Multi-Armed Bandits [51.146684847667125]
  We study the problem of estimating the value of a known smooth function $f$ at an unknown point $boldsymbolmu in mathbbRn$, where each component $mu_i$ can be sampled via a noisy oracle. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-delta$ returns an $epsilon$ accurate estimate of $f(boldsymbolmu)$.
  arXiv  Detail & Related papers  (2022-03-18T18:50:52Z)
• Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution [5.789743084845758]
  In a ubiquitous $SU(2)$ dynamics, achieving the simultaneous optimal estimation of multiple parameters is difficult. We propose a method, characterized by the nested cross-products of the coefficient vector $mathbfX$ of $SU(2)$ generators. Our work reveals that quantum control is not always functional in improving the estimation precision.
  arXiv  Detail & Related papers  (2022-02-08T06:05:20Z)
• Periodically driven Rydberg chains with staggered detuning [0.0]
  We study the stroboscopic dynamics of a driven finite Rydberg chain with staggered ($Delta$) and time-dependent uniform ($lambda(t)$) detuning terms using exact diagonalization (ED) We show that at intermediate drive ($omega_D$), the presence of a finite $Delta$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density density correlation function at specific $omega_D
  arXiv  Detail & Related papers  (2021-12-29T19:04:07Z)
• Power-like potentials: from the Bohr-Sommerfeld energies to exact ones [77.34726150561087]
  Bohr-Sommerfeld Energies (BSE) extracted explicitly from the Bohr-Sommerfeld quantization condition are compared with the exact energies. For physically important cases $m=1,4,6$ for the $100$th excited state BSE coincide with exact ones in 5-6 figures.
  arXiv  Detail & Related papers  (2021-07-31T21:37:50Z)
• Spectral density estimation with the Gaussian Integral Transform [91.3755431537592]
  spectral density operator $hatrho(omega)=delta(omega-hatH)$ plays a central role in linear response theory. We describe a near optimal quantum algorithm providing an approximation to the spectral density.
  arXiv  Detail & Related papers  (2020-04-10T03:14:38Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)

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.