Blind Symmetry Matching in Quantum States with Application to Shot-Count Reduction

• URL: http://arxiv.org/abs/2606.19196v1
• Date: Wed, 17 Jun 2026 15:36:12 GMT
• Title: Blind Symmetry Matching in Quantum States with Application to Shot-Count Reduction
• Abstract summary: A basis adapted to a symmetry it carries reduces the repeated measurements needed to read a statistical answer.<n>Two conditions are treated, both detected by the same score with a different projection.<n>Blind symmetry matching is a practical primitive for the common case where the matched basis cannot be written down in advance.
• Score: 1.3537117504260623
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Measuring a quantum computation in a basis adapted to a symmetry it carries reduces the repeated measurements, commonly referred to as ``shots'', needed to read a statistical answer. Detecting the symmetry a quantum state carries has many uses: certifying a claimed symmetry, identifying a conserved-charge sector, flagging symmetry-breaking as an error signature, and selecting a compression or readout basis; shot-count reduction is developed here as one exemplary case. Existing methods assume the symmetry is known in advance; we remove that assumption. When it is unknown, the carried symmetry is discovered from the data by a symmetry test that scores candidate groups, and the largest passing group is exploited as the measurement basis. We state the pipeline precisely, prove the selection rule is unbiased, and charge discovery in full. Two conditions are treated, both detected by the same score with a different projection: a weak condition, commutation with the representation, and a strong condition, confinement to a single charge sector, the distinction drawn in the quantum-reference-frame literature. A single circuit, a controlled twirl followed by a SWAP test, discovers both: discarding the group register tests the weak condition, post-selecting it the strong one. The framework is general over finite groups, with cyclic (Fourier), dihedral, and symmetric-group (Schur-Weyl) examples; strong confinement to the symmetric, or Dicke, subspace is an exponential reduction. Seeded demonstrations show the loop wins net of discovery: weak matching on momentum readout reduces shots by a factor widening from ten to several thousand, and strong matching on a two-system target by a further factor of the subsystem size. Blind symmetry matching is a practical primitive for the common case where the matched basis cannot be written down in advance.

Related papers

• Statistical Symmetry Release for Equivariant Quantum Learning [12.042012916861829]
  Hard symmetry constraints reduce model complexity, but can also erase label information.<n> Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint.
  arXiv  Detail & Related papers  (2026-09-10T12:38:27Z)
• Symmetry Constrained Quantum Error Mitigation for the Schwinger Model [39.146761527401424]
  We exploit the parity and fermion-number symmetries of a gauge theory under depolarising noise.<n>We investigate symmetry verification under digital quantum simulation.
  arXiv  Detail & Related papers  (2026-08-21T13:49:11Z)
• Symmetry-initialized quantum Gibbs sampling: a non-Abelian asymmetry cascade [0.0]
  For a quantum Gibbs sampler whose mixing bottleneck is a weakly broken symmetry, I prove a general speedup-versus-factor dichotomy.<n>I then show that when the bottleneck is a weakly broken symmetry, the otherwise exponentially expensive bottleneck eigenvector is the symmetry charge.<n>I verify these results analytically and numerically in an $SU(2)$ Davies sampler.
  arXiv  Detail & Related papers  (2026-07-27T06:03:15Z)
• A homotopy-type-theoretic generalization of neurosymbolic inference [46.36639624013224]
  neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $$-structures.<n>We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts.
  arXiv  Detail & Related papers  (2026-06-16T12:22:12Z)
• Observable signatures of exceptional points from left-right eigenstate distinction [17.925787462168707]
  Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems.<n>We develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian.<n>Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points.
  arXiv  Detail & Related papers  (2026-06-09T18:12:27Z)
• Statistical-Geometric Degeneracy in UAV Search: A Physics-Aware Asymmetric Filtering Approach [23.49656058107753]
  Post-disaster survivor localization using Unmanned Aerial Vehicles (UAVs) faces a fundamental physical challenge.<n>Unlike standard Gaussian noise, signal reflection from debris introduces strictly non-negative ranging biases.<n>Existing robust estimators, typically designed with symmetric loss functions, implicitly rely on the assumption of error symmetry.<n>We propose a physically-grounded solution, the AsymmetricHuberEKF, which explicitly incorporates the non-negative physical prior of NLOS biases.
  arXiv  Detail & Related papers  (2026-02-11T08:33:56Z)
• Discovering Lie Groups with Flow Matching [35.127962200638756]
  We propose learning symmetries directly from data via flow matching on Lie groups.<n>We formulate symmetry discovery as learning a distribution over a larger hypothesis group.<n>Experiments on 2D and 3D point clouds demonstrate the successful discovery of discrete groups.
  arXiv  Detail & Related papers  (2025-12-23T04:27:35Z)
• Euclidean Distance Matrix Completion via Asymmetric Projected Gradient Descent [25.846262685970164]
  This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization.<n>It reconstructs the point set configuration from partial Euclidean distance measurements.
  arXiv  Detail & Related papers  (2025-04-28T07:13:23Z)
• Topological response in open quantum systems with weak symmetries [0.0]
  In open quantum systems, the interaction of the system with its environment gives rise to two types of symmetry.<n>We show that weak symmetries can protect topological responses that distinguish different phases of matter.<n>In particular, we show that the coupling to the environment can induce a phase transition to a state protected by weak symmetries.
  arXiv  Detail & Related papers  (2025-04-03T18:00:10Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements [11.213906010203264]
  Recent developments have highlighted a novel symmetry-breaking pattern.<n>Strong-to-weak symmetry breaking is typically detected using multi-replica correlation functions, such as the R'enyi-2 correlator.<n>We propose a practical protocol for detecting strong-to-weak symmetry breaking in experiments using the randomized measurement toolbox.
  arXiv  Detail & Related papers  (2024-12-24T12:41:38Z)
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits [0.0]
  Under symmetry-respective decoherence, spontaneous strong-to-weak symmetry breaking can occur. This work provides a scheme to describe S SSB and other decoherence phenomena in the mixed state by employing the stabilizer formalism and the efficient numerical algorithm of Clifford circuits.
  arXiv  Detail & Related papers  (2024-08-08T06:03:23Z)
• Symmetric Neural-Collapse Representations with Supervised Contrastive Loss: The Impact of ReLU and Batching [26.994954303270575]
  Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced data, this symmetry breaks under class imbalances. This paper presents an intriguing discovery: the introduction of a ReLU activation at the final layer effectively restores the symmetry in SCL-learned representations.
  arXiv  Detail & Related papers  (2023-06-13T17:55:39Z)
• Generative Adversarial Symmetry Discovery [19.098785309131458]
  LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.
  arXiv  Detail & Related papers  (2023-02-01T04:28:36Z)
• Quantum Error Mitigation using Symmetry Expansion [0.0]
  Noise remains the biggest challenge for the practical applications of any near-term quantum devices. We develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification.
  arXiv  Detail & Related papers  (2021-01-08T18:30:48Z)

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.