scholarly journals Accuracy threshold for postselected quantum computation

2008 ◽  
Vol 8 (3&4) ◽  
pp. 181-244 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Stochastic Noise ◽  
Strongly Correlated ◽  
Error Detecting ◽  
Error Detecting Code

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, $1.04\times 10^{-3}$, is well below Knill's numerical estimates.

scholarly journals Magic-state distillation with the four-qubit code

2013 ◽  
Vol 13 (3&4) ◽  
pp. 195-209
Author(s):  
Adam M. Meier ◽  
Bryan Eastin ◽  
Emanuel Knill
Keyword(s):  
Quantum Computing ◽  
Error Probability ◽  
Practical Interest ◽  
Universal Quantum ◽  
Special Subset ◽  
Error Detecting ◽  
Hadamard Gate ◽  
Error Detecting Code

The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the $+1$ eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Use of this routine in combination with the $15$-to-$1$ distillation routine described by Bravyi and Kitaev allows for further improvements in overhead.

Error detecting code for long haul network

2018 ◽  
Author(s):  
Amrindra Pal ◽  
Santosh Kumar ◽  
Sandeep Sharma ◽  
Vivek K. Srivastava
Keyword(s):  
Error Detecting ◽  
Error Detecting Code

scholarly journals Self-Checking Combinational Circuits with Unidirectionally Independent Outputs

VLSI Design ◽  
1998 ◽  
Vol 5 (4) ◽  
pp. 333-345 ◽  
Author(s):  
A. Morosow ◽  
V. V. Saposhnikov ◽  
Vl. V. Saposhnikov ◽  
M. Goessel
Keyword(s):  
Fault Model ◽  
Systematic Design ◽  
Combinational Circuits ◽  
Heuristic Solution ◽  
Unidirectional Error ◽  
Berger Code ◽  
Free Case ◽  
Error Detecting ◽  
Error Detecting Code ◽  
Circuit Graph

In this paper we propose a structure dependent method for the systematic design of a self-checking circuit which is well adapted to the fault model of single gate faults and which can be used in test mode.According to the fault model considered, maximal groups of independent and unidirectionally independent outputs of an arbitrarily given combinational circuit are determined. A parity bit is added to every group of independent outputs. A few additional outputs are added to every group of unidirectionally independent outputs. In the error free case, these groups of unidirectional independent outputs together with their corresponding additional outputs are elements of a unidirectional error detecting code; for example, a Berger code or an r-out-of-s code.It is demonstrated how the pairs of (unidirectionally) independent outputs of a given circuit can be determined. A simple heuristic solution for this problem based on a modified circuit graph is also given.The maximal classes of (unidirectionally) independent outputs can be computed as cliques of a dependency graph where the nodes of the graph are the outputs of the circuit. The applicability of the proposed method is demonstrated for the MCNC benchmarks circuits.

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