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Automatic Test Pattern Generation for Robust Quantum Circuit Testing

Kean Chen, Mingsheng Ying

TL;DR

This article introduces the stabilizer projector decomposition (SPD) for representing the quantum test pattern and construct the test application using Clifford-only circuits, which are rather robust and efficient as evidenced in the fault-tolerant quantum computation.

Abstract

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 paper 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 which can exploit both locality and sparsity in generating SPDs. The effectiveness of our algorithms are validated by 1) theoretical guarantees under reasonable conditions, 2) experimental results on commonly used benchmark circuits, such as Quantum Fourier Transform (QFT), Quantum Volume (QV) and Bernstein-Vazirani (BV) in IBM Qiskit.

Automatic Test Pattern Generation for Robust Quantum Circuit Testing

TL;DR

This article introduces the stabilizer projector decomposition (SPD) for representing the quantum test pattern and construct the test application using Clifford-only circuits, which are rather robust and efficient as evidenced in the fault-tolerant quantum computation.

Abstract

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 paper 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 which can exploit both locality and sparsity in generating SPDs. The effectiveness of our algorithms are validated by 1) theoretical guarantees under reasonable conditions, 2) experimental results on commonly used benchmark circuits, such as Quantum Fourier Transform (QFT), Quantum Volume (QV) and Bernstein-Vazirani (BV) in IBM Qiskit.
Paper Structure (34 sections, 15 theorems, 36 equations, 8 figures, 4 tables, 3 algorithms)

This paper contains 34 sections, 15 theorems, 36 equations, 8 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Challenges in Quantum ATPG
  3. Related Works
  4. Main Idea
  5. Organization
  6. Preliminaries
  7. Quantum Circuits
  8. Fault Models
  9. Discrimination of Quantum Gates
  10. Test Patterns for Single-Fault Quantum Circuits
  11. Stabilizer Formalism and Clifford Circuits
  12. Pauli Operators
  13. Stabilizer Formalism
  14. Clifford Operation
  15. SPD-Based Sampling Algorithm for Test Application
  16. ...and 19 more sections

Key Result

Proposition 1

If quantum state $\rho$ and measurement $\{M,I-M\}$ satisfy the following conditions: where $\sqsubseteq$ is the Loewner order and $Q$ is some projection on the state space of the qubits that are not in gates $U_i$ and $U'_i$, then $\rho$ and $\{M,I-M\}$ are optimal state and measurement at the primary input and output for distinguishing between faulty and fault-free circuits, i.e.,

Figures (8)

  • Figure 1: Components of quantum ATPG.
  • Figure 2: An example of the quantum analogue of classical $D$-value, where $\vert \omega\rangle/\vert \omega'\rangle$ corresponds to the Helstrom measurement for distinguishing quantum states $T\vert +\rangle$ and $\vert +\rangle$
  • Figure 3: (a) Non-robust testing: the test pattern $(\rho,M)$ is directly implemented, which is susceptible to SPAM errors (see the challenge (\ref{['item-5261712']})). (b) Robust testing: the test pattern is decomposed into simpler ones (i.e., $(\rho_i,M_i)$), which are implemented using Clifford-only circuits, and are then combined through classical randomness.
  • Figure 4: Our quantum ATPG framework. Linked to Fig. \ref{['fig-fw']}, the quantum state and POVM are represented by SPDs, and the state preparation and measurement are implemented using Clifford circuits. The test application and test generation are conducted by the SPD-based sampling algorithm (see Section \ref{['sec-testapp']}) and the SPD generation algorithm (see Section \ref{['sec-spdgen']}), respectively.
  • Figure 5: Examples of single and multi-qubit quantum gates.
  • ...and 3 more figures

Theorems & Definitions (24)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Proposition 1
  • Example 5
  • Lemma 1
  • Corollary 1
  • Definition 1: Stabilizer Projector Decomposition, SPD
  • Definition 2: Norms of SPD
  • ...and 14 more