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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Detection and Diagnosis of Single Faults in Quantum Circuits

Debajyoti Bera

Published Jun 22, 2017• 16 citations
Publisher

Abstract

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.

DOI
10.1109/tcad.2017.2717783

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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.
Detecting and isolating faults is crucial for synthesis of quantum circuits. Under the single fault assumption that is now routinely accepted in circuit fault analysis, we show that the behaviour of faulty quantum circuits 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 that can be used to detect every single-gate fault using very few test cases and with minimal probability of error; in fact we demonstrate that most commonly used quantum gates can be isolated without any error under the single missing gate fault (SMGF) model. We crucially exploit the quantum nature of circuits to show vast improvement upon the existing works of automatic test pattern generation (ATPG) for quantum circuits.
Test pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found that quantum mechanics allows one to execute multiple test vectors concurrently, making each gate realized in the process act on a complete set of characteristic states in space/time complexity that breaks classical testability lower bounds.
Quantum circuit testing is essential for detecting potential faults in realistic quantum devices, while the testing process itself also suffers from the inexactness and unreliability of quantum operations. This article alleviates the issue by proposing a novel framework of automatic test pattern generation (ATPG) for robust testing of logical quantum circuits. We introduce the stabilizer projector decomposition (SPD) for representing the quantum test pattern and construct the test application (i.e., state preparation and measurement) using Clifford-only circuits, which are rather robust and efficient as evidenced in the fault-tolerant quantum computation. However, it is generally hard to generate SPDs due to the exponentially growing number of the stabilizer projectors. To circumvent this difficulty, we develop an SPD generation algorithm, as well as several acceleration techniques that can exploit both locality and sparsity in generating SPDs. The effectiveness of our algorithms are validated by (1) theoretical guarantees under reasonable conditions and (2) experimental results on commonly used benchmark circuits, such as Quantum Fourier Transform (QFT), Quantum Volume (QV), and Bernstein-Vazirani (BV) in IBM Qiskit.
Quantum circuits have recently been developed thanks to the global companies like IBM, Google, Microsoft and Intel. The physical realization of quantum circuits motivates to explore new areas of research. Testing of quantum circuits is one such area which needs significant attention in order to detect faulty gate operations in the circuits. To this end, first we need to identify the different types of faults that can result due to some unwanted physical failures during the implementation of the gate operations. This paper investigates those possibilities of physical failures in realizing the quantum operations and introduces a new family of fault models for quantum circuits. Experimental results include the actual number of newly proposed faults that can occur at the physical level of any quantum circuit.
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
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.