Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes

• URL: http://arxiv.org/abs/2406.02427v2
• Date: Wed, 30 Oct 2024 20:09:04 GMT
• Title: Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes
• Authors: Kenneth Goodenough, Aqil Sajjad, Eneet Kaur, Saikat Guha, Don Towsley,
• Abstract summary: We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an associated stabilizer code. We find stabilizer states that are resilient against noise, allowing for more robust entanglement distribution in near-term quantum networks.
• Score: 8.59730790789283
• License:
• Abstract: Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states across a bipartition. We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an associated stabilizer code. In particular, this allows us to show that the coherent information is related to the so-called syndrome entropy of the underlying code. We use this viewpoint to find stabilizer states that are resilient against noise, allowing for more robust entanglement distribution in near-term quantum networks. We specialize our results to the case of graph states, where the found connections with stabilizer codes reduces back to classical linear codes for dephasing noise. On our way we provide an alternative proof of the fact that every qubit stabilizer code is equivalent up to single-qubit Clifford gates to a graph code.

Related papers

• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties [2.1438108757511958]
  We find the best stabilizer approximations to the true ground states of molecules up to 36 qubits in size. Our work represents a promising step toward designing algorithms for early fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2024-10-28T15:28:15Z)
• Clifford Manipulations of Stabilizer States: A graphical rule book for Clifford unitaries and measurements on cluster states, and application to photonic quantum computing [0.9935277311162707]
  We develop a rule-book and a tableau simulator for arbitrary stabilizer manipulations of cluster states. We extend our graphical rule-book to include dual-rail photonic-qubit cluster state manipulations. We show how stabilizer descriptions of multi-qubit fusions can be mapped linear optical circuits.
  arXiv  Detail & Related papers  (2023-12-04T22:40:24Z)
• Bases for optimising stabiliser decompositions of quantum states [14.947570152519281]
  We introduce and study the vector space of linear dependencies of $n$-qubit stabiliser states. We construct elegant bases of linear dependencies of constant size three. We use them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques.
  arXiv  Detail & Related papers  (2023-11-29T06:30:05Z)
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes [0.0]
  We propose a prototype quantum circuit model for classification of classical data. A quantum neural network (QNN) layer is realized by a stabilizer code which consists of many stabilizers. We also consider the first challenge to most applications of quantum computers, including data classification.
  arXiv  Detail & Related papers  (2023-09-18T19:02:54Z)
• Efficient quantum algorithms for stabilizer entropies [0.0]
  We efficiently measure stabilizer entropies (SEs) for integer R'enyi index $n>1$ via Bell measurements. We provide efficient bounds of various nonstabilizerness monotones which are intractable to compute beyond a few qubits. Our results open up the exploration of nonstabilizerness with quantum computers.
  arXiv  Detail & Related papers  (2023-05-30T15:55:04Z)
• Quantum error correction with dissipatively stabilized squeezed cat qubits [68.8204255655161]
  We propose and analyze the error correction performance of a dissipatively stabilized squeezed cat qubit. We find that for moderate squeezing the bit-flip error rate gets significantly reduced in comparison with the ordinary cat qubit while leaving the phase flip rate unchanged.
  arXiv  Detail & Related papers  (2022-10-24T16:02:20Z)
• 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)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Shannon theory for quantum systems and beyond: information compression for fermions [68.8204255655161]
  We show that entanglement fidelity in the fermionic case is capable of evaluating the preservation of correlations. We introduce a fermionic version of the source coding theorem showing that, as in the quantum case, the von Neumann entropy is the minimal rate for which a fermionic compression scheme exists.
  arXiv  Detail & Related papers  (2021-06-09T10:19:18Z)
• Transmon platform for quantum computing challenged by chaotic fluctuations [55.41644538483948]
  We investigate the stability of a variant of a many-body localized (MBL) phase for system parameters relevant to current quantum processors. We find that these computing platforms are dangerously close to a phase of uncontrollable chaotic fluctuations.
  arXiv  Detail & Related papers  (2020-12-10T19:00:03Z)
• 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)

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.