Latency in local, two-dimensional, fault-tolerant quantum computing

2009 ◽  
Vol 9 (7&8) ◽  
pp. 666-682
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Error Rates ◽  
Error Threshold ◽  
Two Dimensional ◽  
Memory Errors

(pp0666-0682) F.M. Spedalieri and V.P. Roychowdhury We analyze the latency of fault-tolerant quantum computing based on the 9-qubit Bacon-Shor code using a local, two-dimensional architecture. We embed the data qubits in a 7 by 7 array of physical qubits, where the extra qubits are used for ancilla preparation and qubit transportation by means of a SWAP chain. The latency is reduced with respect to a similar implementation using Steane's 7-qubit code~\cite{svore2007a}. Furthermore, the error threshold is also improved to $2.02 \times 10^{-5}$, when memory errors are taken to be one tenth of the gate error rates.

scholarly journals Performance and error analysis of Knill's postselection scheme in a two-dimensional architecture

2014 ◽  
Vol 14 (9&10) ◽  
pp. 807-822
Author(s):  
Ching-Yi Lai ◽  
Gerardo Paz ◽  
Martin Suchara ◽  
Todd A. Brun
Keyword(s):  
Fault Tolerant ◽  
Error Rates ◽  
Error Threshold ◽  
Noise Model ◽  
Concatenated Codes ◽  
Two Dimensional ◽  
Memory Error ◽  
Computation Scheme ◽  
Quantum Architecture ◽  
With Memory

Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of $3\%$ over the depolarizing channel. We show how to use Knill's postselection scheme in a practical two-dimensional quantum architecture that we designed with the goal to optimize the error correction properties, while satisfying important architectural constraints. In our 2D architecture, one logical qubit is embedded in a tile consisting of $5\times 5$ physical qubits. The movement of these qubits is modeled as noisy SWAP gates and the only physical operations that are allowed are local one- and two-qubit gates. We evaluate the practical properties of our design, such as its error threshold, and compare it to the concatenated Bacon-Shor code and the concatenated Steane code. Assuming that all gates have the same error rates, we obtain a threshold of $3.06\times 10^{-4}$ in a local adversarial stochastic noise model, which is the highest known error threshold for concatenated codes in 2D. We also present a Monte Carlo simulation of the 2D architecture with depolarizing noise and we calculate a pseudo-threshold of about $0.1\%$. With memory error rates one-tenth of the worst gate error rates, the threshold for the adversarial noise model, and the pseudo-threshold over depolarizing noise, are $4.06\times 10^{-4}$ and $0.2\%$, respectively. In a hypothetical technology where memory error rates are negligible, these thresholds can be further increased by shrinking the tiles into a $4\times 4$ layout.

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 multi-commodity network model for optimal quantum reversible circuit synthesis

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0253140
Author(s):  
Jihye Jung ◽  
In-Chan Choi
Keyword(s):  
Quantum Computing ◽  
Network Flow ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Error Rates ◽  
Quantum Circuits ◽  
Circuit Synthesis ◽  
Multiple Control ◽  
Proposed Model ◽  
Implementation Costs

Quantum computing is a newly emerging computing environment that has recently attracted intense research interest in improving the output fidelity, fully utilizing its high computing power from both hardware and software perspectives. In particular, several attempts have been made to reduce the errors in quantum computing algorithms through the efficient synthesis of quantum circuits. In this study, we present an application of an optimization model for synthesizing quantum circuits with minimum implementation costs to lower the error rates by forming a simpler circuit. Our model has a unique structure that combines the arc-subset selection problem with a conventional multi-commodity network flow model. The model targets the circuit synthesis with multiple control Toffoli gates to implement Boolean reversible functions that are often used as a key component in many quantum algorithms. Compared to previous studies, the proposed model has a unifying yet straightforward structure for exploiting the operational characteristics of quantum gates. Our computational experiment shows the potential of the proposed model, obtaining quantum circuits with significantly lower quantum costs compared to prior studies. The proposed model is also applicable to various other fields where reversible logic is utilized, such as low-power computing, fault-tolerant designs, and DNA computing. In addition, our model can be applied to network-based problems, such as logistics distribution and time-stage network problems.

scholarly journals Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher Chamberland ◽  
Kyungjoo Noh
Keyword(s):  
Quantum Computing ◽  
Nearest Neighbor ◽  
Fault Tolerant ◽  
Error Correcting Code ◽  
Error Rates ◽  
High Quality ◽  
Color Code ◽  
Order Of Magnitude ◽  
Computing Platforms ◽  
Classical Computing

Abstract Fault-tolerant quantum computing promises significant computational speedup over classical computing for a variety of important problems. One of the biggest challenges for realizing fault-tolerant quantum computing is preparing magic states with sufficiently low error rates. Magic state distillation is one of the most efficient schemes for preparing high-quality magic states. However, since magic state distillation circuits are not fault-tolerant, all the operations in the distillation circuits must be encoded in a large distance error-correcting code, resulting in a significant resource overhead. Here, we propose a fault-tolerant scheme for directly preparing high-quality magic states, which makes magic state distillation unnecessary. In particular, we introduce a concept that we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. We apply such schemes to a planar architecture of the triangular color code family and demonstrate that our scheme requires at least an order of magnitude fewer qubits and space–time overhead compared to the most competitive magic state distillation schemes. Since our scheme requires only nearest-neighbor interactions in a planar architecture, it is suitable for various quantum computing platforms currently under development.

Efficient reversible quantum design of sig-magnitude to two's complement converters

2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon
Keyword(s):  
Quantum Computing ◽  
Scientific Community ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
State Of The Art ◽  
The Other ◽  
Quantum Computers ◽  
Binary Number ◽  
Quantum Cost ◽  
The One

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.

Fault-tolerant blind quantum computing using GHZ states over depolarization channel

2021 ◽  
Vol 20 (9) ◽  
Author(s):  
Xiaoqing Tan ◽  
Hong Tao ◽  
Xiaoqian Zhang ◽  
Xiaodan Zeng ◽  
Qingshan Xu
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Ghz States
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