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arXiv:2301.03296 · EPJ Quantum Technology

Precise certification of a qubit space

Tomasz Białecki, Tomasz Rybotycki, Josep Amengual i Batle, J. Tworzydło, Adam Bednorz

Published Mar 19, 2024• 3 citations
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Abstract

Abstract We demonstrate an implementation of the precise test of dimension on the qubit, using the public IBM quantum computer,using the determinant dimension witness.The accuracy is below 10-3 comparing to maximal possible value of the witness in higher dimension.The test involving minimal independent sets of preparation and measurement operations (gates) is applied both for specific configurations andparametric ones. The test is be robust against nonidealities such as incoherent leakage and erroneous gate execution.Two of the IBM devices failed the test by more than 5 standard deviations, which has no simple explanation.

DOI
10.1140/epjqt/s40507-024-00230-4

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Abstract We demonstrate an implementation of the precise test of dimension on the qubit, using the public IBM quantum computer,using the determinant dimension witness.The accuracy is below 10-3 comparing to maximal possible value of the witness in higher dimension.The test involving minimal independent sets of preparation and measurement operations (gates) is applied both for specific configurations andparametric ones. The test is be robust against nonidealities such as incoherent leakage and erroneous gate execution.Two of the IBM devices failed the test by more than 5 standard deviations, which has no simple explanation.
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We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to ddd states, optionally reduced to the real subspace. As a dimension certificate, we use the linear independence tested by a determinant. We find the sets of preparations and measurements that maximize the chance to detect larger space if the extra contribution is very small. We discuss the practical application of the test to certify the space logical operations on a quantum computer.
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