RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers

• URL: http://arxiv.org/abs/2604.02569v1
• Date: Thu, 02 Apr 2026 22:44:10 GMT
• Title: RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers
• Abstract summary: RFOX (Rotated-Fieldy eXchange) is a parameter-free quantum algorithm for optimization.<n>We show that RFOX attains near-optimal, and in some exact, ground states using up to an order of fewer Trotter slices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization. RFOX combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive a closed-form effective Hamiltonian whose first-order term retains the full $XX$ driver, while the leading correction consists of a single qubit $Y$ field at high drive frequency. This structure ensures that the instantaneous spectral gap remains essentially flat, independent of both the interpolation parameter and the disorder strength, modulated only by a $δ$ parameter. This behavior stands in stark contrast to the unpredictable gap reductions, or even collapses, exhibited by the $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations on random-field Ising model (RFIM) instances with 7, 9, and 12 qubits, across three magnetic-field ranges, validate these spectral predictions: RFOX attains near-optimal, and in some cases exact, ground states using up to an order of magnitude fewer Trotter slices. Its performance advantage grows with increasing disorder, as conventional methods slow down near vanishing gaps, whereas RFOX maintains a constant runtime scaling of $T \propto Δ_{\min}^{-2}$. Hardware experiments on IBM Quantum processors (Eagle r3 and Heron r1, with 12, 15, and 20 physical qubits) reproduce similar performance rankings. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a promising, scalable, and tuning-free route toward quantum optimizers for combinatorial optimization problems.

Related papers

• Decay versus dephasing in Rydberg analog optimization: exchange rate, mechanism, and schedule design [0.05427878000393745]
  Noiseless Rydberg-atom optimization is studied in terms of decoherence and dephasing.<n>First-order perturbation theory reproduces $$ from noiseless propagation alone.<n>Because the whole cost model is noiseless, a schedule can be tuned to a device's channel mixture without any noisy simulation.
  arXiv  Detail & Related papers  (2026-08-30T15:41:02Z)
• 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)
• Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe [1.3537117504260623]
  We develop an algorithm that drops the assumption on $min_bmx in mathcalX.<n>The analysis extends to heavy-tailed noise oracles with bounded moments for $r$in (1, 2]$ and recovers the rates of the noise as the noise.
  arXiv  Detail & Related papers  (2026-05-14T19:20:22Z)
• The Spectral Edge Thesis: A Mathematical Framework for Intra-Signal Phase Transitions in Neural Network Training [0.0]
  We show that phase transitions in neural network training are controlled by the spectral gap of the rolling-window Gram matrix of parameter updates.<n>Adiabatic parameter $mathcalA = |G|_F / (, g2)$ controls circuit stability: $mathcalA ll 1$ (plateau), $mathcalA sim 1$ (phase transition), $mathcalA gg 1$ (forgetting)
  arXiv  Detail & Related papers  (2026-03-30T20:10:22Z)
• Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing [0.0]
  We propose an iterative framework based on Quadratic Un Binary Optimization (QUBO) for training the head of convolutional neural networks (CNNs)<n>A per-output decomposition splits the $C$-class problem into $C$ independent QUBOs, each with $(d+1)K$ binary variables, where $d$ is the feature dimension and $K$ is the bit precision.<n>We evaluate the method on six image-classification benchmarks (sklearn digits, MNIST, Fashion-MNIST, CIFAR-10, EMNIST, KMNIST)
  arXiv  Detail & Related papers  (2026-03-03T13:10:36Z)
• FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with $O(N\log N)$ Complexity [52.3171766248012]
  We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems.<n>We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results.<n>Our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.
  arXiv  Detail & Related papers  (2025-10-13T07:57:21Z)
• Programmable Quantum Matter: Heralding Large Cluster States in Driven Inhomogeneous Spin Ensembles [0.0]
  Atom-like emitters in solids are promising platforms for quantum sensing and information processing.<n>We present a framework that leverages this diversity to reduce the resources for generating optically heralded spin cluster states.<n>An optimized pulse sequence simultaneously corrects pulse-length and detuning errors, achieving single-qubit gate fidelities exceeding $99.99%$ for errors.
  arXiv  Detail & Related papers  (2025-09-03T03:59:22Z)
• Beyond likelihood ratio bias: Nested multi-time-scale stochastic approximation for likelihood-free parameter estimation [49.78792404811239]
  We study inference in simulation-based models where the analytical form of the likelihood is unknown.<n>We use a ratio-free nested multi-time-scale approximation (SA) method that simultaneously tracks the score and drives the parameter update.<n>We show that our algorithm can eliminate the original bias $Obig(sqrtfrac1Nbig)$ and accelerate the convergence rate from $Obig(beta_k+sqrtfracalpha_kNbig)$.
  arXiv  Detail & Related papers  (2024-11-20T02:46:15Z)
• Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping [2.6447353939786296]
  Noise-Directed Remapping (NDAR) is a algorithm for approximately solving binary optimization problems by leveraging certain types of noise.<n>We consider access to a noisy quantum processor with dynamics that features a global attractor state.<n>Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions.
  arXiv  Detail & Related papers  (2024-04-01T18:28:57Z)
• 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)
• Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing [0.0]
  We propose a quantum-signal-processing framework to overcome noise-induced limitations in quantum metrology. Our algorithm achieves an accuracy of $10-4$ radians in standard deviation for learning $theta$ in superconductingqubit experiments. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.
  arXiv  Detail & Related papers  (2022-09-22T17:47:21Z)
• Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization [116.89941263390769]
  We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $min_mathbfxmax_mathbfyF(mathbfx) + H(mathbfx,mathbfy)$, where one has access to first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. We present a emphaccelerated gradient-extragradient (AG-EG) descent-ascent algorithm that combines extragrad
  arXiv  Detail & Related papers  (2022-06-17T06:10:20Z)
• Reducing the Variance of Gaussian Process Hyperparameter Optimization with Preconditioning [54.01682318834995]
  Preconditioning is a highly effective step for any iterative method involving matrix-vector multiplication. We prove that preconditioning has an additional benefit that has been previously unexplored. It simultaneously can reduce variance at essentially negligible cost.
  arXiv  Detail & Related papers  (2021-07-01T06:43:11Z)
• Asynchronous Stochastic Optimization Robust to Arbitrary Delays [54.61797739710608]
  We consider optimization with delayed gradients where, at each time stept$, the algorithm makes an update using a stale computation - d_t$ for arbitrary delay $d_t gradient. Our experiments demonstrate the efficacy and robustness of our algorithm in cases where the delay distribution is skewed or heavy-tailed.
  arXiv  Detail & Related papers  (2021-06-22T15:50:45Z)

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.