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fQuantum : A Quantum Computing Fault Simulator

Suresh k Devanathan, M.L. Bushnell

Published Mar 1, 2013• 0 citations
OpenAlex

Abstract

Abstract—We like to introduce fQuantum, a Quantum Computing Fault Simulator and new quantum computing fault model based on Hadamard, PauliX, PauliY and PauliZ gates, and the traditional stuck-at-1 SA1 and stuck-at-0 SA0 faults. We had close to 100 % fault coverage on most circuits. The problem with lower coverage comes from function gates, which we will deal with, in future versions of this paper. Keywords—fQuantum,Fault Simulator, Quantum Computing I.

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Abstract—We like to introduce fQuantum, a Quantum Computing Fault Simulator and new quantum computing fault model based on Hadamard, PauliX, PauliY and PauliZ gates, and the traditional stuck-at-1 SA1 and stuck-at-0 SA0 faults. We had close to 100 % fault coverage on most circuits. The problem with lower coverage comes from function gates, which we will deal with, in future versions of this paper. Keywords—fQuantum,Fault Simulator, Quantum Computing I.
Matrix method for quantum diagnosing functional failures and stuck-at faults in software or hardware units is proposed. It is based on qubit data structures comprising diagnostic information, which allows significantly reducing the computational complexity of the simulation and diagnosis due to the introduction of parallel logical operations on the matrix data. The quantum method for fault-free simulating digital units with the possibility of online repair of digital system components is presented. It is characterized by significantly improved performance due to addressed processing procedure of the functional primitives, defined by Q-coverages.
It is shown that the fault testing for quantum circuits does not follow conventional classical techniques. If probabilistic gate like Hadamard gate is included in a circuit then the classical notion of test vector is shown to fail. We have reported several new and distinguishing features of quantum fault and also presented a general methodology for detection of functional faults in a quantum circuit. The technique can generate test vectors for detection of di erent kinds of fault. Speci c examples are given and time complexity of the proposed quantum fault detection algorithm is reported. 1
Quantum data structures, methods, algorithms and software applications for parallel solution of combinatorial problems, including design and test, on classical computers by using extra memory are proposed. Quantum models and methods for design and test of specific logic functionalities are developed based on the use of vector qubit data structures and memory-driven architectures for parallel computing algorithms, in order to significantly improve the performance of testing and deductive simulation of digital systems-on-chips. A new quantum method of test generation for single stuck-at faults of logic functions through taking Boolean derivatives with respect to their qubit coverages is proposed. The quantum method of deductive simulation of stuck-at faults of logical functions through the synthesis of matrices of Boolean derivatives with respect to their qubit coverage has been developed. The performance of methods for test synthesis and their analysis has no analogues in algorithmic performance.
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and σz1/4{σ_z}^{1/4}σz​1/4), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of πππ) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev.
Testing for quantum circuits (QC) is a challenging task because QC is intrinsically probabilistic. Existing fault models for QC, such as missing gate faults, are not suitable for quantum dot QC. This paper proposes realistic fault models and fault simulation for quantum dot QC. Our fault models are based on real physical phenomenon of quantum dot devices so that they represent real defect behavior or control errors. Our fault simulation does not need to fully expand gate matrices to 2nx 2n, where n is the number of qubits. Using sparse matrix multiplication, our fault simulation saves a lot of memory and CPU time. We also calculate the test repetition of each test pattern so that we can estimate our test time. Based on fault simulation of a full adder QC, we can select a small test set of six test patterns, totally 526 repetitions, to detect all faults with 99% confidence level.
We show that quantum circuits cannot be made fault-tolerant against a depolarizing noise level of thetas = (6 - 2radic2)/7 ap 45%, thereby improving on a previous bound of 50% (due to Razborov, 2004). More precisely, the circuit model for which we prove this bound contains perfect gates from the Clifford group (CNOT, Hadamard, S, X, Y, Z) and arbitrary additional one-qubit gates that are subject to depolarizing noise thetas. We prove that this set of gates cannot be universal for arbitrary (even classical) computation, from which the upper bound on the noise threshold for fault-tolerant quantum computation follows