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IEEE International Symposium on Multiple-Valued Logic (ISMVL)

Test Generation and Fault Localization for Quantum Circuits

Marek A. Perkowski, Jacob Biamonte, M. Lukac

Published May 24, 2005• 44 citations
Publisher

Abstract

It is believed that quantum computing will begin to have a practical impact in industry around year 2010. We propose an approach to test generation and fault localization for a wide category of fault models. While in general we follow the methods used in test of standard circuits, there are two significant differences: (2) we use both deterministic and probabilistic tests to detect faults, (2) we use special measurement gates to determine the internal states. A fault table is created that includes probabilistic information. "Probabilistic set covering" and "probabilistic adaptive trees" that generalize those known in standard circuits, are next used.

DOI
10.1109/ismvl.2005.46

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It is believed that quantum computing will begin to have a practical impact in industry around year 2010. We propose an approach to test generation and fault localization for a wide category of fault models. While in general we follow the methods used in test of standard circuits, there are two significant differences: (2) we use both deterministic and probabilistic tests to detect faults, (2) we use special measurement gates to determine the internal states. A fault table is created that includes probabilistic information. "Probabilistic set covering" and "probabilistic adaptive trees" that generalize those known in standard circuits, are next used.
It is believed that quantum computing will begin to have an impact around year 2010. Much work is done on physical realization and synthesis of quantum circuits, but nothing so far on the problem of generating tests and localization of faults for such circuits. Even fault models for quantum circuits have been not formulated yet. We propose an approach to test generation for a wide category of fault models of single and multiple faults. It uses deterministic and probabilistic tests to detect faults. A Fault Table is created that includes probabilistic information. If possible, deterministic tests are first selected, while covering faults with tests, in order to shorten the total length of the test sequence. The method is applicable to both binary and ternary quantum circuits. The system generates test sequences and adaptive trees for fault localization for small binary and ternary quantum circuits.
This work extends a general method used to test classical circuits to quantum circuits. Gate internal errors are address using a discrete fault model. Fault models to represent unwanted nearest neighbor entanglement as well as unwanted qubit rotation are presented. When witnessed, the faults we model are probabilistic, but there is a set of tests with the highest probability of detecting a discrete repetitive fault. A method of probabilistic set covering to identify the minimal set of tests is introduced. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies for quantum networks. Faculty Mentor: Marek A. Perkowski
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
Detection and isolation of faults is a crucial step in the physical realization of quantum circuits. Even though quantum gates and circuits compute reversible functions, the standard techniques of automatic test pattern generation (ATPG) for classical reversible circuits are not directly applicable to quantum circuits. For faulty quantum circuits under the widely accepted single fault assumption, we show that their behavior can be fully characterized by the (single) faulty gate and the corresponding fault model. This allows us to efficiently determine test input states as well as measurement strategy for fault detection and diagnosis. Building on top of these, we design randomized algorithms which are able to detect every nontrivial single-gate fault with minimal probability of error. We also describe similar algorithms for fault diagnosis. We evaluate our algorithms by the number of output samples that needs to be collected and the probability of error. Both of these can be related to the eigenvalues of the operators corresponding to the circuit gates. We experimentally compare all our strategies with the state-of-the-art ATPG techniques for quantum circuits under the “single missing faulty gate” model and demonstrate that significant improvement is possible if we can exploit the quantum nature of circuits.
This paper introduces the problem of test generation and test minimization for quantum circuits using a discrete fault model. QuFault, our software package generates test sequences for arbitrary quantum circuits using the very efficient simulator QuIDDPro [1]. The quantum fault table and the test set minimization algorithm is presented, along with some tricks to make quantum testing as deterministic as possible. As our fault model we use the single qubit rotation operators about the x, y and z axis. The angle of the rotation is based on the expected accuracy of the mechanism performing the unitary operations, or the largest impact of expected noise from the environment. We consider superposition inputs as well as interference in order to detect phase faults, such as possible errors traveling backwards through controlled gates.
We first introduce a method called quantum path verification, where we search for a break in a quantum network. After explaining these capabilities, we address gate internal faults. We present new fault models to represent crosstalk and unwanted nearest neighbor entanglement. When witnessed, these errors are probabilistic, but there is a set of tests that has the highest probability of detecting a fault. We introduce a method of probabilistic set covering to identify this set of tests. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies.