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Deterministic and Probabilistic Test Generation for Binary and Ternary Quantum Circuits

Sowmya Aligala, Sreecharani Ratakonda, Kiran Narayan, Kanagalakshmi Nagarajan, Martin Lukáč, Jacob Biamonte, Marek A. Perkowski

Published Jan 1, 2004• 6 citations
OpenAlex

Abstract

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.

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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.
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.
A new approach to detecting and diagnosing faults in quantum circuits is introduced. In order to account for the probabilistic nature of quantum circuits, collections of test experiments, called binary tomographic tests (BTTs), are generated. A BTT can identify a fault with respect to some user-defined confidence threshold τ. We present an algorithm to generate BTTs that either detect, or ensure the absence of, all modeled faults in a given circuit. We also present an adaptive diagnostic method to locate quantum faults. While classical circuits, even probabilistic ones, only handle ordinary probabilities, quantum circuits deal with quantum states, which have phase as an extra probabilistic parameter. The tomographic testing methods introduced previously for probabilistic circuits are unable to detect differences in phase, and therefore leave many quantum faults undetected. In contrast, we develop a design-for-test method which is specifically intended to detect faults that only affect the phase of a quantum state. We give experimental results for benchmark and random circuits which show high coverage of quantum faults by BTTs, and good resolution in the case of the adaptive diagnosis method.
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.
Abstract This work justifies several quantum gate level fault models and discusses the causal error mechanisms thwarting correct function. A quantum adaptation of the classical test set generation technique known as constructing a fault table is given. This classical technique optimizes test plans to detect all the most common error types. This work therefore considers the set of predominate errors modeled by unwanted qubit rotations. In classical test, a fault table is constructed allowing the comparison between a circuit’s nominal response and a response perturbed by each separately considered error. It was found that isolating a correct circuit from a circuit containing any of the Pauli Fault rotations, requires applications of just two independent test vectors. This is related to the proven fact that a reversible system preserves the probability that additional information may be present. Thus, the probability of detection for an observable fault is related only to the probability of presence. A theorem that better connects classical ideas to quantum test set generation is presented. This leads directly to a relationship between the deterministic presence of a fault in the state vector observed with some probability and the probabilistic presence of a fault observed deterministically (Relating Time and Space Error Models). 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 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