scholarly journals Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code

2012 ◽  
Vol 12 (11&12) ◽  
pp. 1034-1080
Author(s):  
Adam Paetznick ◽  
Ben W. Reichardt
Keyword(s):  
Error Propagation ◽  
Fault Tolerant ◽  
Error Correcting Code ◽  
Block Size ◽  
Golay Code ◽  
Important Target ◽  
Noise Threshold ◽  
The Cost ◽  
Quantum Error ◽  
Logical Qubit

In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In consequence, large codes that are otherwise very efficient have found limited fault-tolerance applications. Fault-tolerant preparation circuits therefore are an important target for optimization. We study the Golay code, a $23$-qubit quantum error-correcting code that protects the logical qubit to a distance of seven. In simulations, even using a na{\"i}ve ancilla preparation procedure, the Golay code is competitive with other codes both in terms of overhead and the tolerable noise threshold. We provide two simplified circuits for fault-tolerant preparation of Golay code-encoded ancillas. The new circuits minimize error propagation, reducing the overhead by roughly a factor of four compared to standard encoding circuits. By adapting the malignant set counting technique to depolarizing noise, we further prove a threshold above $\threshOverlap$ noise per gate.

scholarly journals Magic state distillation with the ternary Golay code

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200187 ◽  
Author(s):  
Shiroman Prakash
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Fault Tolerant ◽  
Error Correcting Code ◽  
Error Correcting Codes ◽  
High Threshold ◽  
Golay Code ◽  
Quadratic Error ◽  
Quantum Error ◽  
Error Suppression

The ternary Golay code—one of the first and most beautiful classical error-correcting codes discovered—naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the ‘most magic’ qutrit state—an eigenstate of the qutrit Fourier transform known as the strange state —with cubic error suppression and a remarkably high threshold. It also distils the ‘second-most magic’ qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

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 Quantum teleportation of physical qubits into logical code spaces

2021 ◽  
Vol 118 (36) ◽  
pp. e2026250118
Author(s):  
Yi-Han Luo ◽  
Ming-Cheng Chen ◽  
Manuel Erhard ◽  
Han-Sen Zhong ◽  
Dian Wu ◽  
...  
Keyword(s):  
Quantum Information ◽  
Large Scale ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Quantum Circuits ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Universal Quantum ◽  
Quantum Error ◽  
Logical Qubit

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

scholarly journals Fault-tolerant detection of a quantum error

Science ◽  
2018 ◽  
Vol 361 (6399) ◽  
pp. 266-270 ◽  
Author(s):  
S. Rosenblum ◽  
P. Reinhold ◽  
M. Mirrahimi ◽  
Liang Jiang ◽  
L. Frunzio ◽  
...  
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
Critical Component ◽  
Detection Scheme ◽  
Dephasing Time ◽  
Order Of Magnitude ◽  
Quantum Error ◽  
Specific Error ◽  
Logical Qubit

A critical component of any quantum error–correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.

scholarly journals DISTRIBUTED QUANTUM COMPUTATION ARCHITECTURE USING SEMICONDUCTOR NANOPHOTONICS

2010 ◽  
Vol 08 (01n02) ◽  
pp. 295-323 ◽  
Author(s):  
RODNEY VAN METER ◽  
THADDEUS D. LADD ◽  
AUSTIN G. FOWLER ◽  
YOSHIHISA YAMAMOTO
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Quantum Communication ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Cluster State ◽  
Laser Pulses ◽  
Resource Requirements ◽  
The Cost ◽  
Quantum Error

In a large-scale quantum computer, the cost of communications will dominate the performance and resource requirements, place many severe demands on the technology, and constrain the architecture. Unfortunately, fault-tolerant computers based entirely on photons with probabilistic gates, though equipped with "built-in" communication, have very large resource overheads; likewise, computers with reliable probabilistic gates between photons or quantum memories may lack sufficient communication resources in the presence of realistic optical losses. Here, we consider a compromise architecture, in which semiconductor spin qubits are coupled by bright laser pulses through nanophotonic waveguides and cavities using a combination of frequent probabilistic and sparse determinstic entanglement mechanisms. The large photonic resource requirements incurred by the use of probabilistic gates for quantum communication are mitigated in part by the potential high-speed operation of the semiconductor nanophotonic hardware. The system employs topological cluster-state quantum error correction for achieving fault-tolerance. Our results suggest that such an architecture/technology combination has the potential to scale to a system capable of attacking classically intractable computational problems.

scholarly journals Dynamically Generated Logical Qubits

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 564
Author(s):  
Matthew B. Hastings ◽  
Jeongwan Haah
Keyword(s):  
Fault Tolerant ◽  
Error Correcting Code ◽  
Quantum Memory ◽  
Two Dimensional ◽  
Logical Qubits ◽  
Quantum Error ◽  
Toric Code

We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a two-qubit Pauli measurement.

scholarly journals Logical-qubit operations in an error-detecting surface code

2021 ◽  
Author(s):  
Jorge Marques ◽  
Boris Varbanov ◽  
Miguel Moreira ◽  
Hany Ali ◽  
Nandini Muthusubramanian ◽  
...  
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
The Road ◽  
Logical Operations ◽  
The Difference ◽  
Surface Code ◽  
On The Road ◽  
Qubit Operations ◽  
Quantum Error ◽  
Logical Qubit

Abstract Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

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