Stabilizer Entanglement Enhances Magic Injection

• URL: http://arxiv.org/abs/2503.20873v3
• Date: Wed, 24 Sep 2025 03:49:42 GMT
• Title: Stabilizer Entanglement Enhances Magic Injection
• Authors: Zong-Yue Hou, ChunJun Cao, Zhi-Cheng Yang,
• Abstract summary: We show that entanglement acts as a conduit that teleports magic across the system, thereby enhancing magic injection.<n>We extend our analysis to tripartite stabilizer entanglement, non-stabilizer entanglement, and magic injection via shallow-depth brickwork circuits.
• Score: 8.474797307449121
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-stabilizerness is a key resource for fault-tolerant quantum computation, yet its interplay with entanglement in dynamical settings remains underexplored. We address this by analyzing a well-controlled, analytically tractable setup, where we show that entanglement acts as a conduit that teleports magic across the system, thereby enhancing magic injection. Using exact calculations, we prove that when a Haar-random unitary $U_A$ is applied to a subsystem $A$ of an entangled stabilizer state, the total injected magic increases with the entanglement between $A$ and its complement. More generally, for any unitary $U_A$, we show that this enhancement is maximized when $A$ is maximally entangled with its complement, in which case the total injected magic is exactly given by the unitary stabilizer R\'enyi entropy we introduce. This quantity provides both a directly computable measure of unitary magic and a lower bound on the minimum number of $T$ gates required to synthesize $U_A$. We further extend our analysis to tripartite stabilizer entanglement, non-stabilizer entanglement, and magic injection via shallow-depth brickwork circuits, finding that the qualitative picture remains unchanged.

Related papers

• Predicting Magic from Very Few Measurements [0.0]
  We show that nonstabilizerness can be witnessed and quantified using any set of $m$ $n$-qubit Pauli measurements.<n>We also prove that deciding membership in the corresponding reduced stabilizer polytope is NP-hard.<n>In particular, unless $mathrmP = mathrmNP$, no algorithm in $m$ can solve the problem in full generality.
  arXiv  Detail & Related papers  (2026-02-21T19:13:43Z)
• Rise and fall of nonstabilizerness via random measurements [0.0]
  We investigate the dynamics of nonstabilizerness in quantum circuits composed of random Clifford unitaries and local projective measurements.<n>For measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness.<n>Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics.
  arXiv  Detail & Related papers  (2025-07-15T18:01:02Z)
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation [0.0]
  We investigate how the stabilizer formalism, in particular highly-entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity.<n>The resulting stabilizer ground state is found to capture to a large extent both bi-partite and collective multi-partite entanglement features.
  arXiv  Detail & Related papers  (2025-05-05T18:01:20Z)
• Non-stabilizerness in open XXZ spin chains: Universal scaling and dynamics [0.0]
  We investigate magic in the open XXZ spin chain under either boundary gain and loss, or bulk dephasing.<n>We develop a novel, highly efficient algorithm for computing $M$ within the matrix product states formalism.<n>These findings position magic as a powerful diagnostic tool for probing universality and dynamics in open quantum systems.
  arXiv  Detail & Related papers  (2025-04-15T12:41:52Z)
• Non-stabilizerness of Neural Quantum States [41.94295877935867]
  We introduce a methodology to estimate non-stabilizerness or "magic", a key resource for quantum complexity, with Neural Quantum States (NQS)<n>We study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite non-stabilizerness besides large entanglement.
  arXiv  Detail & Related papers  (2025-02-13T19:14:15Z)
• Towards a Sharp Analysis of Offline Policy Learning for $f$-Divergence-Regularized Contextual Bandits [49.96531901205305]
  We analyze $f$-divergence-regularized offline policy learning.<n>For reverse Kullback-Leibler (KL) divergence, we give the first $tildeO(epsilon-1)$ sample complexity under single-policy concentrability.<n>We extend our analysis to dueling bandits, and we believe these results take a significant step toward a comprehensive understanding of $f$-divergence-regularized policy learning.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits [1.1517315048749441]
  We study the emergence of complexity in deep random $N$--qubit $T$gate doped Clifford circuits.<n>For pure (undoped) Clifford circuits, a unique periodic orbit structure in the space of Pauli strings implies peculiar spectral correlations and level statistics with large degeneracies.
  arXiv  Detail & Related papers  (2024-12-20T14:04:51Z)
• Stabilizer Tensor Networks with Magic State Injection [0.4934360430803066]
  We report a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford operations.<n>Specifically, for random $T$-doped $N$-qubit Clifford circuits the computational cost of circuits prepared with magic state injection scales as $mathcalO(textpoly(N))$ when the circuit has $t lesssim N$ $T$-gates.
  arXiv  Detail & Related papers  (2024-11-19T13:03:27Z)
• Magic spreading in random quantum circuits [0.0]
  We show how rapidly do generic many-body dynamics generate magic resources under the constraints of locality and unitarity.<n>We demonstrate that magic resources equilibrate on timescales logarithmic in the system size, akin to anti-concentration and Hilbert space delocalization phenomena.<n>As random circuits are minimal models for chaotic dynamics, we conjecture that our findings describe the phenomenology of magic resources growth in a broad class of chaotic many-body systems.
  arXiv  Detail & Related papers  (2024-07-04T13:43:46Z)
• Nonstabilizerness via matrix product states in the Pauli basis [0.0]
  We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPS) Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer R'enyi entropies, stabilizer nullity, and Bell magic. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays.
  arXiv  Detail & Related papers  (2024-01-29T19:12:10Z)
• Learning the stabilizer group of a Matrix Product State [0.0]
  We present a novel classical algorithm designed to learn the stabilizer group of a given Matrix Product State (MPS) We benchmark our method on $T$-doped states randomly scrambled via Clifford unitary dynamics. Our method, thanks to a very favourable scaling $mathcalO(chi3)$, represents the first effective approach to obtain a genuine magic monotone for MPS.
  arXiv  Detail & Related papers  (2024-01-29T19:00:13Z)
• Critical behaviors of non-stabilizerness in quantum spin chains [0.0]
  Non-stabilizerness measures the extent to which a quantum state deviates from stabilizer states. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains.
  arXiv  Detail & Related papers  (2023-09-01T18:00:04Z)
• Quantifying nonstabilizerness of matrix product states [0.0]
  We show that nonstabilizerness, as quantified by the recently introduced Stabilizer R'enyi Entropies (SREs), can be computed efficiently for matrix product states (MPSs) We exploit this observation to revisit the study of ground-state nonstabilizerness in the quantum Ising chain, providing accurate numerical results up to large system sizes.
  arXiv  Detail & Related papers  (2022-07-26T17:50:32Z)
• Magic-state resource theory for the ground state of the transverse-field Ising model [0.0]
  We study the behavior of the stabilizer R'enyi entropy in the integrable transverse field Ising spin chain. We show that the locality of interactions results in a localized stabilizer R'enyi entropy in the gapped phase.
  arXiv  Detail & Related papers  (2022-05-04T18:00:03Z)
• Improved Graph Formalism for Quantum Circuit Simulation [77.34726150561087]
  We show how to efficiently simplify stabilizer states to canonical form. We characterize all linearly dependent triplets, revealing symmetries in the inner products. Using our novel controlled-Pauli $Z$ algorithm, we improve runtime for inner product computation from $O(n3)$ to $O(nd2)$ where $d$ is the maximum degree of the graph.
  arXiv  Detail & Related papers  (2021-09-20T05:56:25Z)
• Robust Online Control with Model Misspecification [96.23493624553998]
  We study online control of an unknown nonlinear dynamical system with model misspecification. Our study focuses on robustness, which measures how much deviation from the assumed linear approximation can be tolerated.
  arXiv  Detail & Related papers  (2021-07-16T07:04:35Z)
• Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory [85.29718245299341]
  We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR) We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We propose an efficient data dependent algorithm -- textsceXploration -- that with high probability quickly identifies a stabilizing controller.
  arXiv  Detail & Related papers  (2020-06-19T08:58:57Z)
• Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent [55.85456985750134]
  We introduce a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting. To our best knowledge, this gives the firstever-known stability and generalization for SGD with even non-differentiable loss functions.
  arXiv  Detail & Related papers  (2020-06-15T06:30:19Z)
• Sparse Identification of Nonlinear Dynamical Systems via Reweighted $\ell_1$-regularized Least Squares [62.997667081978825]
  This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear systems from noisy state measurements. The aim of this work is to improve the accuracy and robustness of the method in the presence of state measurement noise.
  arXiv  Detail & Related papers  (2020-05-27T08:30:15Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)
• Naive Exploration is Optimal for Online LQR [49.681825576239355]
  We show that the optimal regret scales as $widetildeTheta(sqrtd_mathbfu2 d_mathbfx T)$, where $T$ is the number of time steps, $d_mathbfu$ is the dimension of the input space, and $d_mathbfx$ is the dimension of the system state. Our lower bounds rule out the possibility of a $mathrmpoly(logT)$-regret algorithm, which had been
  arXiv  Detail & Related papers  (2020-01-27T03:44:54Z)
• Improper Learning for Non-Stochastic Control [78.65807250350755]
  We consider the problem of controlling a possibly unknown linear dynamical system with adversarial perturbations, adversarially chosen convex loss functions, and partially observed states. Applying online descent to this parametrization yields a new controller which attains sublinear regret vs. a large class of closed-loop policies. Our bounds are the first in the non-stochastic control setting that compete with emphall stabilizing linear dynamical controllers.
  arXiv  Detail & Related papers  (2020-01-25T02:12:48Z)

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.