Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

• URL: http://arxiv.org/abs/2409.20561v1
• Date: Mon, 30 Sep 2024 17:59:01 GMT
• Title: Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage
• Authors: Cheng-Ju Lin, Zi-Wen Liu, Victor V. Albert, Alexey V. Gorshkov,
• Abstract summary: We show that a subset of the basis for the irreducible representations of the total $SU(2)$ rotation forms a covariant approximate quantum error-correcting code with $U(1)$ logical gates.
• Score: 0.9499648210774583
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a subset of the basis for the irreducible representations of the total $SU(2)$ rotation forms a covariant approximate quantum error-correcting code with transversal $U(1)$ logical gates. Using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy against generic noise on any known $d$ sites and against heralded $d$-local erasures, generalizing and improving previous works on the ``thermodynamic code" to general local spin and different irreducible representations. We demonstrate that this family of codes can host and protect a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the $U(1)$ logical gate.

Related papers

• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Universal transversal gates [0.0]
  A long-standing challenge in quantum error correction is the infeasibility of universal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model.
  arXiv  Detail & Related papers  (2024-10-09T16:34:47Z)
• Qudit-based quantum error-correcting codes from irreducible representations of SU(d) [0.0]
  Qudits naturally correspond to multi-level quantum systems, but their reliability is contingent upon quantum error correction capabilities. We present a general procedure for constructing error-correcting qudit codes through the irreducible representations of $mathrmSU(d)$ for any odd integer $d geq 3.$ We use our procedure to construct an infinite class of error-correcting codes encoding a logical qudit into $(d-1)2$ physical qudits.
  arXiv  Detail & Related papers  (2024-10-03T11:35:57Z)
• Approximate quantum error correcting codes from conformal field theory [0.0]
  We consider generic 1+1D CFT codes under extensive local dephasing channels. We show that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.
  arXiv  Detail & Related papers  (2024-06-13T19:40:36Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes [1.2183405753834557]
  We consider the quantum error correction capability of random covariant codes. In particular, we show that $U(1)$-covariant codes generated by Haar random $U(1)$-symmetric unitaries saturate the fundamental limits to leading order. Our results hold for symmetric variants of unitary 2-designs, and comment on the convergence problem of charge-conserving random circuits.
  arXiv  Detail & Related papers  (2021-02-23T18:11:15Z)
• Optimal Universal Quantum Error Correction via Bounded Reference Frames [8.572932528739283]
  Error correcting codes with a universal set of gates are a desideratum for quantum computing. We show that our approximate codes are capable of efficiently correcting different types of erasure errors. Our approach has implications for fault-tolerant quantum computing, reference frame error correction, and the AdS-CFT duality.
  arXiv  Detail & Related papers  (2020-07-17T18:00:03Z)

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.