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Cross-platform certification of the qubit space with a minimal number of parameters

Tomasz Rybotycki, Tomasz Białecki, Josep Batle, Jakub Tworzydło, Adam Bednorz

TL;DR

A determinant dimension witness of a qubit space is demonstrated, which is robust against common imperfections and shows that numerous qubits, especially from the newest IBM Heron family devices, fail the test by more than ten standard deviations.

Abstract

We demonstrate a determinant dimension witness of a qubit space. Our test has a minimal number of independent parameters. We achieve it by mapping the Bloch sphere $π/2$-rotation axis angle on the non-planar so-called Viviani curve. We ran our test on different platforms: IBM Quantum, IQM Resonance, and IonQ. Our investigations show that numerous qubits, especially from the newest IBM Heron family devices, fail the test by more than ten standard deviations. The nature of those deviations has no simple explanation as the test is robust against common imperfections.

Cross-platform certification of the qubit space with a minimal number of parameters

TL;DR

A determinant dimension witness of a qubit space is demonstrated, which is robust against common imperfections and shows that numerous qubits, especially from the newest IBM Heron family devices, fail the test by more than ten standard deviations.

Abstract

We demonstrate a determinant dimension witness of a qubit space. Our test has a minimal number of independent parameters. We achieve it by mapping the Bloch sphere -rotation axis angle on the non-planar so-called Viviani curve. We ran our test on different platforms: IBM Quantum, IQM Resonance, and IonQ. Our investigations show that numerous qubits, especially from the newest IBM Heron family devices, fail the test by more than ten standard deviations. The nature of those deviations has no simple explanation as the test is robust against common imperfections.
Paper Structure (12 sections, 4 equations, 10 figures, 5 tables)

This paper contains 12 sections, 4 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Description of the test
  3. Experiments
  4. Conclusions
  5. Acknowledgements
  6. Data Availability
  7. Author contributions statement

Figures (10)

  • Figure 1: The quantum circuit for the dimension test with two parameters, angles $\beta$ and $\phi$. The protocol starts from the initial state $\ket{0}$, followed by preparation phase, gates $S$ and $S_{\beta}$ and the measurement phase, $S_{\phi}$ and $S$, with the final readout in the computational basis.
  • Figure 2: The Bloch vectors for the preparations $\boldsymbol p$ (red and blue arrows) and measurements $\boldsymbol m$ (red arrows) corresponding to the angles used in the test, positioned on the Viviani curve (blue curve).
  • Figure 3: The topology of ibm_brisbane device. We highlighted the most faulty qubits tested in February -- yellow, and in March 2024 -- red. The rest of the qubits, highlighted green, have passed the test. Two-qubit Echoed Cross Resonance gates, unused in the test, connect the qubits.
  • Figure 4: The probabilities $F_{kj}$ for the test using selected quantum states and measurement represented by Bloch vectors on the Viviani curve. From the top-left: ideal, ibm_nairobi qubit 0, ibm_brisbane qubits 18, 24 (Feb 2024), and 67, 81 (Mar 2024).
  • Figure 5: The values of the witness for individual jobs: ibm_nairobi qubit 0, ibm_brisbane qubits 18, 24 (Feb 2024) and 67, 81 (Mar 2024). We use symbols $n\#$ and $b\#$ for ibm_nairobi and ibm_brisbane qubits respectively.
  • ...and 5 more figures