Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code
- URL: http://arxiv.org/abs/2411.04974v2
- Date: Tue, 03 Dec 2024 05:34:12 GMT
- Title: Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code
- Authors: F. Setiawan, Campbell McLauchlan,
- Abstract summary: We propose the X$3$Z$3$ Floquet code, a type of dynamical code with improved performance under biased noise.
Our work establishes the X$3$Z$3$ code as a prime quantum error-correcting code candidate.
- Score: 0.0
- License:
- Abstract: We propose the X$^3$Z$^3$ Floquet code, a type of dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent symmetry under infinitely biased noise, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that a general dynamical code with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature resulting in the high performance of bias-tailored stabiliser codes. Despite this limitation, we demonstrate through our comprehensive numerical simulations that the symmetry of the X$^3$Z$^3$ Floquet code renders its performance under biased noise far better than several leading Floquet code candidates. Furthermore, to maintain high-performance implementation in hardwares without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X$^3$Z$^3$ code as a prime quantum error-correcting code candidate, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.
Related papers
- Quantum XYZ cyclic codes for biased noise [5.197632326399701]
In some quantum computing architectures, Pauli noise is highly biased. Tailoring Quantum error-correcting codes to the biased noise may benefit reducing the physical qubit overhead without reducing the logical error rate.
We propose a family of quantum XYZ cyclic codes, which are the only one family of quantum cyclic codes with code distance increasing with code length.
arXiv Detail & Related papers (2025-01-28T10:06:31Z) - Demonstrating dynamic surface codes [138.1740645504286]
We experimentally demonstrate three time-dynamic implementations of the surface code.
First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three.
Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors.
Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
arXiv Detail & Related papers (2024-12-18T21:56:50Z) - Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements [44.99833362998488]
Floquet codes provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware.
This is an under-studied issue of crucial importance for running such codes on realistic hardware.
We introduce a new method of accommodating defective qubits on a wide range of two-dimensional Floquet codes.
arXiv Detail & Related papers (2024-05-24T18:00:05Z) - Estimating the Decoding Failure Rate of Binary Regular Codes Using Iterative Decoding [84.0257274213152]
We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder.
We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
arXiv Detail & Related papers (2024-01-30T11:40:24Z) - The Near-optimal Performance of Quantum Error Correction Codes [2.670972517608388]
We derive the near-optimal channel fidelity, a concise and optimization-free metric for arbitrary codes and noise.
Compared to conventional optimization-based approaches, the reduced computational cost enables us to simulate systems with previously inaccessible sizes.
We analytically derive the near-optimal performance for the thermodynamic code and the Gottesman-Kitaev-Preskill (GKP) code.
arXiv Detail & Related papers (2024-01-04T01:44:53Z) - 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) - Performance of surface codes in realistic quantum hardware [0.24466725954625884]
Surface codes are generally studied based on the assumption that each of the qubits that make up the surface code lattice suffers noise that is independent and identically distributed (i.i.d.)
We introduce independent non-identically distributed (i.ni.d.) noise model, a decoherence model that accounts for the non-uniform behaviour of the docoherence parameters of qubits.
We consider and describe two methods which enhance the performance of planar codes under i.ni.d. noise.
arXiv Detail & Related papers (2022-03-29T15:57:23Z) - Improved decoding of circuit noise and fragile boundaries of tailored
surface codes [61.411482146110984]
We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes.
Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC.
We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
arXiv Detail & Related papers (2022-03-09T18:48:54Z) - Bias-tailored quantum LDPC codes [3.565124653091339]
We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods.
We show that bias-tailored quantum low density parity check codes can be similarly bias-tailored.
Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression.
arXiv Detail & Related papers (2022-02-03T17:11:10Z) - 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) - Efficient and robust certification of genuine multipartite entanglement
in noisy quantum error correction circuits [58.720142291102135]
We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME)
We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME.
We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
arXiv Detail & Related papers (2020-10-06T18:00:07Z)
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.