A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product
Codes
- URL: http://arxiv.org/abs/2002.06257v1
- Date: Fri, 14 Feb 2020 21:40:44 GMT
- Title: A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product
Codes
- Authors: Muyuan Li, Theodore J. Yoder
- Abstract summary: We show that hypergraph product codes can be obtained by entangling the gauge qubits of two SHP codes.
For circuit noise, a BBS code and a SHP code have pseuds of $2times10-3$ and $8times10-4$, respectively.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We provide a numerical investigation of two families of subsystem quantum
codes that are related to hypergraph product codes by gauge-fixing. The first
family consists of the Bravyi-Bacon-Shor (BBS) codes which have optimal code
parameters for subsystem quantum codes local in 2-dimensions. The second family
consists of the constant rate "generalized Shor" codes of Bacon and Cassicino
\cite{bacon2006quantum}, which we re-brand as subsystem hypergraph product
(SHP) codes. We show that any hypergraph product code can be obtained by
entangling the gauge qubits of two SHP codes. To evaluate the performance of
these codes, we simulate both small and large examples. For circuit noise, a
$[[21,4,3]]$ BBS code and a $[[49,16,3]]$ SHP code have pseudthresholds of
$2\times10^{-3}$ and $8\times10^{-4}$, respectively. Simulations for
phenomenological noise show that large BBS and SHP codes start to outperform
surface codes with similar encoding rate at physical error rates $1\times
10^{-6}$ and $4\times10^{-4}$, respectively.
Related papers
- SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes.
Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes.
We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
arXiv Detail & Related papers (2024-07-12T16:50:01Z) - Constructions and performance of hyperbolic and semi-hyperbolic Floquet
codes [5.33024001730262]
We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces.
We also construct semi-hyperbolic Floquet codes, which have improved distance scaling.
arXiv Detail & Related papers (2023-08-07T17:54:45Z) - Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.
We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
arXiv Detail & Related papers (2023-03-24T00:29:15Z) - Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space.
We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit.
We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
arXiv Detail & Related papers (2023-01-24T14:17:07Z) - Classical product code constructions for quantum Calderbank-Shor-Steane codes [1.4699455652461726]
We introduce a new product code construction which is a natural generalisation of classical product codes to quantum codes.
We show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors.
arXiv Detail & Related papers (2022-09-27T15:48:37Z) - Distance bounds for generalized bicycle codes [0.7513100214864644]
Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices.
We have done an exhaustive enumeration of GB codes for certain prime circulant sizes in a family of two-qubit encoding codes with row weights 4, 6, and 8.
The observed distance scaling is consistent with $A(w)n1/2+B(w)$, where $n$ is the code length and $A(w)$ is increasing with $w$.
arXiv Detail & Related papers (2022-03-31T17:43:34Z) - Tailored XZZX codes for biased noise [60.12487959001671]
We study a family of codes having XZZX-type stabilizer generators.
We show that these XZZX codes are highly qubit efficient if tailored to biased noise.
arXiv Detail & Related papers (2022-03-30T17:26:31Z) - Morphing quantum codes [77.34726150561087]
We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate.
We construct a family of hybrid color-toric codes by morphing the color code.
arXiv Detail & Related papers (2021-12-02T17:43:00Z) - Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit
Topological Codes [3.9962751777898955]
We show that trellis decoders have strong structure, extend the results using classical coding theory as a guide, and demonstrate a canonical form from which the structural properties of the decoding graph may be computed.
The modified decoder works for any stabilizer code $S$ and separates into two parts: a one-time, offline which builds a compact, graphical representation of the normalizer of the code, $Sperp$, and a quick, parallel, online computation using the Viterbi algorithm.
arXiv Detail & Related papers (2021-06-15T16:01:42Z) - Low overhead fault-tolerant quantum error correction with the
surface-GKP code [60.44022726730614]
We propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits.
We show that a low logical failure rate $p_L 10-7$ can be achieved with moderate hardware requirements.
arXiv Detail & Related papers (2021-03-11T23:07:52Z) - Decoding Across the Quantum LDPC Code Landscape [4.358626952482686]
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes.
We run numerical simulations of the decoder applied to three families of hypergraph product code: topological codes, fixed-rate random codes and a new class of codes that we call semi-topological codes.
arXiv Detail & Related papers (2020-05-14T14:33:08Z)
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.