scholarly journals Upper Bounds on the Noise Threshold for Fault-Tolerant Quantum Computing

2008 ◽  
pp. 845-856 ◽  
Author(s):  
Julia Kempe ◽  
Oded Regev ◽  
Falk Unger ◽  
Ronald de Wolf
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Upper Bounds ◽  
Noise Threshold

scholarly journals A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing

2006 ◽  
Vol 6 (3) ◽  
pp. 193-212 ◽  
Author(s):  
K.M. Svore ◽  
A.W. Cross ◽  
I.L. Chuang ◽  
A.V. Aho
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Upper Bounds ◽  
Component Failure ◽  
Simulation Procedure ◽  
Component Failure Rates ◽  
Flow Map ◽  
Noise Models

An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent estimates of the threshold are near some experimentally achieved gate fidelities. However, the landscape of threshold estimates includes pseudothresholds, threshold estimates based on a subset of components and a low level of the recursion. In this paper, we observe that pseudothresholds are a generic phenomenon in fault-tolerant computation. We define pseudothresholds and present classical and quantum fault-tolerant circuits exhibiting pseudothresholds that differ by a factor of $4$ from fault-tolerance thresholds for typical relationships between component failure rates. We develop tools for visualizing how reliability is influenced by recursive simulation in order to determine the asymptotic threshold. Finally, we conjecture that refinements of these methods may establish upper bounds on the fault-tolerance threshold for particular codes and noise models.

scholarly journals Upper bounds on the noise threshold for fault-tolerant quantum computing

2010 ◽  
Vol 10 (5&6) ◽  
pp. 361-376
Author(s):  
J. Kempe ◽  
O. Regev ◽  
F. Unger ◽  
R. de Wolf
Keyword(s):  
Fault Tolerant ◽  
Quantum Circuit ◽  
Upper Bounds ◽  
Final State ◽  
Important Special Case ◽  
Main Technique ◽  
Noise Threshold ◽  
Special Case ◽  
Tolerable Level ◽  
Better Than

We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary $k$-qubit gates each of whose input wires is subject to depolarizing noise of strength $p$, as well as arbitrary one-qubit gates that are essentially noise-free. We assume that the output of the circuit is the result of measuring some designated qubit in the final state. Our main result is that for $p>1-\Theta(1/\sqrt{k})$, the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. For the important special case of $k=2$, our bound is $p>35.7\%$. Moreover, if the only allowed gate on more than one qubit is the two-qubit CNOT gate, then our bound becomes $29.3\%$. These bounds on $p$ are numerically better than previous bounds, yet are incomparable because of the somewhat different circuit model that we are using. Our main technique is the use of a Pauli basis decomposition, in which the effects of depolarizing noise are very easy to describe.

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

scholarly journals A silicon-based surface code quantum computer

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Device Fabrication ◽  
Impurity Atoms ◽  
Dipole Interactions ◽  
Total Phase ◽  
Surface Code ◽  
Silicon Based

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

Graph Models for Backbone Sets and Limited Packings in Networks

2021 ◽  
pp. 213-274
Author(s):  
Vadim Zverovich
Keyword(s):  
Fault Tolerant ◽  
Dominating Set ◽  
Facility Location Problem ◽  
Upper Bounds ◽  
Sensor Nodes ◽  
Theoretic Approach ◽  
Dominating Sets ◽  
Packing Number ◽  
Graph Theoretic ◽  
Threshold Functions

Here, a graph-theoretic approach is applied to some problems in networks, for example in wireless sensor networks (WSNs) where some sensor nodes should be selected to behave as a backbone/dominating set to support routing communications in an efficient and fault-tolerant way. Four different types of multiple domination (k-, k-tuple, α‎- and α‎-rate domination) are considered and recent upper bounds for cardinality of these types of dominating sets are discussed. Randomized algorithms are presented for finding multiple dominating sets whose expected size satisfies the upper bounds. Limited packings in networks are studied, in particular the k-limited packing number. One possible application of limited packings is a secure facility location problem when there is a need to place as many resources as possible in a given network subject to some security constraints. The last section is devoted to two general frameworks for multiple domination: <r,s>-domination and parametric domination. Finally, different threshold functions for multiple domination are considered.

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