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Asia and South Pacific Design Automation Conference (ASP-DAC)

Detection and diagnosis of faulty quantum circuits

Alexandru Paler, Ilia Polian, John P. Hayes

Published Jan 1, 2012• 16 citations
Publisher

Abstract

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.

DOI
10.1109/aspdac.2012.6164942

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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.
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.
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.
Currently, noisy intermediate-scale quantum (NISQ) circuits may not always generate correct outputs due to noise and faults. In this work, we propose a diagnosis technique for NISQ circuits. The proposed technique contains static diagnosis and dynamic diagnosis. Static diagnosis uses a fault dictionary that contains output probability distribution for each fault. Dynamic diagnosis uses binary search to find the accurate fault locations of faulty quantum circuits. We demonstrate our technique using the Qiskit simulator with realistic noise models. We evaluate 15 benchmarks with unitary and non-unitary faults injected. Simulation results show that the average accuracy and resolution are 97.70% and 1.81. Experiments on the IBM Q devices have also been performed, and results show that our technique is feasible on real quantum circuit devices.
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.