scholarly journals Bias-preserving gates with stabilized cat qubits

2020 ◽  
Vol 6 (34) ◽  
pp. eaay5901 ◽  
Author(s):  
Shruti Puri ◽  
Lucas St-Jean ◽  
Jonathan A. Gross ◽  
Alexander Grimm ◽  
Nicholas E. Frattini ◽  
...  
Keyword(s):  
Phase Space ◽  
Lower Bound ◽  
Error Correction ◽  
Fault Tolerant ◽  
Nonlinear Oscillators ◽  
Continuous Variable ◽  
High Threshold ◽  
Code Capacity ◽  
Cat States ◽  
Phase Space Topology

The code capacity threshold for error correction using biased-noise qubits is known to be higher than with qubits without such structured noise. However, realistic circuit-level noise severely restricts these improvements. This is because gate operations, such as a controlled-NOT (CX) gate, which do not commute with the dominant error, unbias the noise channel. Here, we overcome the challenge of implementing a bias-preserving CX gate using biased-noise stabilized cat qubits in driven nonlinear oscillators. This continuous-variable gate relies on nontrivial phase space topology of the cat states. Furthermore, by following a scheme for concatenated error correction, we show that the availability of bias-preserving CX gates with moderately sized cats improves a rigorous lower bound on the fault-tolerant threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of five. Our results open a path toward high-threshold, low-overhead, fault-tolerant codes tailored to biased-noise cat qubits.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

scholarly journals A novel error correction protocol for continuous variable quantum key distribution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kadir Gümüş ◽  
Tobias A. Eriksson ◽  
Masahiro Takeoka ◽  
Mikio Fujiwara ◽  
Masahide Sasaki ◽  
...  
Keyword(s):  
Error Correction ◽  
Quantum Key Distribution ◽  
Ldpc Codes ◽  
Key Distribution ◽  
Continuous Variable ◽  
Early Termination ◽  
Parity Check ◽  
Secret Key ◽  
Ldpc Decoder ◽  
And Performance

AbstractReconciliation is a key element of continuous-variable quantum key distribution (CV-QKD) protocols, affecting both the complexity and performance of the entire system. During the reconciliation protocol, error correction is typically performed using low-density parity-check (LDPC) codes with a single decoding attempt. In this paper, we propose a modification to a conventional reconciliation protocol used in four-state protocol CV-QKD systems called the multiple decoding attempts (MDA) protocol. MDA uses multiple decoding attempts with LDPC codes, each attempt having fewer decoding iteration than the conventional protocol. Between each decoding attempt we propose to reveal information bits, which effectively lowers the code rate. MDA is shown to outperform the conventional protocol in regards to the secret key rate (SKR). A 10% decrease in frame error rate and an 8.5% increase in SKR are reported in this paper. A simple early termination for the LDPC decoder is also proposed and implemented. With early termination, MDA has decoding complexity similar to the conventional protocol while having an improved SKR.

scholarly journals Phase-space studies of backscattering diffraction of defective Schrödinger cat states

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Damian Kołaczek ◽  
Bartłomiej J. Spisak ◽  
Maciej Wołoszyn
Keyword(s):  
Phase Space ◽  
Dispersive Medium ◽  
Wigner Distribution ◽  
Interference Term ◽  
Wigner Distribution Function ◽  
The Subject ◽  
Schrödinger Cat ◽  
Cat States ◽  
Schrodinger Cat State ◽  
Space Approach

AbstractThe coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.

scholarly journals Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

2021 ◽  
Author(s):  
Dongsheng Wang ◽  
Yunjiang Wang ◽  
Ningping Cao ◽  
Bei Zeng ◽  
Raymond Lafflamme
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Valence Bond ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Exact Quantum ◽  
Valence Bond Solid ◽  
Quantum Error

Abstract In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

scholarly journals SOFTWARE IMPLEMENTED HARDWARE-TRANSIENT FAULTS DETECTION

2014 ◽  
pp. 26-30
Author(s):  
Goutam Kumar Saha
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Low Cost ◽  
Transient Faults ◽  
Fault Tolerant System ◽  
Cost Approach ◽  
Run Time ◽  
Commodity Systems ◽  
Fail Safe ◽  
Register Error

This paper examines a software implemented self-checking technique that is capable of detecting processorregisters' hardware-transient faults. The proposed approach is intended to detect run-time transient bit-errors in memory and processor status register. Error correction is not considered here. However, this low-cost approach is intended to be adopted in commodity systems that use ordinary off-the-shelf microprocessors, for the purpose of operational faults detection towards gaining fail-safe kind of fault tolerant system.

scholarly journals Hamming Codes: Error Reducing Techniques

2021 ◽  
Vol 9 (11) ◽  
pp. 1972-1974
Author(s):  
Rohitkumar R Upadhyay
Keyword(s):  
Lower Bound ◽  
Error Correction ◽  
Coding Theory ◽  
Hamming Distance ◽  
Error Reduction ◽  
Error Correcting Codes ◽  
Significant Other ◽  
Hamming Codes ◽  
Decoding Algorithms ◽  
Reducing Properties

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

scholarly journals Phase space structure of generalized Gaussian cat states

2010 ◽  
Vol 374 (43) ◽  
pp. 4385-4392 ◽  
Author(s):  
Fernando Nicacio ◽  
Raphael N.P. Maia ◽  
Fabricio Toscano ◽  
Raúl O. Vallejos
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Phase Space Structure ◽  
Cat States
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