Qubit Measurements

Simon Perdrix

Since quantum measurement is universal for quantum computation (Nielsen [3]), the minimization of the resources required for measurement‐based quantum computation is a crucial point ([3, 1, 4, 5, 6]). We have shown in [6] that a set of observables composed of one two‐qubit measurement and three one‐qubit measurements form a universal set for quantum computation if one ancillary qubit is available as an additional resource. This set is minimal in terms of two‐qubit measurements, because at least one multi‐qubit operation is needed to create entanglement, and is also minimal in terms of ancillary qubits, because at least one ancillary qubit is required to simulate reversible transformations with projective measurements only. We discuss in this paper the required number of one‐qubit measurements for a set of observables to be universal. A set composed of one two‐qubit measurement and only two one‐qubit measurements is proved universal, at the cost of a second ancillary qubit. Thus an additional ancillary qubit seems to be required to obtain a smaller universal set of measurements. One may conclude to a trade off between ancillary qubits and observables in measurement‐based quantum computation.

Graham P. Collins

Luca Chirolli, Guido Burkard

We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum nondemolition (QND) character. The qubit is coupled to a harmonic oscillator, which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred from the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the oscillator, and (ii) quantum tunneling between the qubit states $|0⟩$ and $|1⟩$ during measurements. Our theory can be applied to QND measurements performed on superconducting qubits coupled to a circuit oscillator.

Shengjun Wu, Klaus Mølmer

Subarna Adhikari, Kimmo Halunen

Crosstalk is one of the major issues for scalability of superconducting quantum processors. But it can also be used by threat actors to intentionally sabotage computations and steal information. This paper analyzes data leakage due to crosstalk during qubit measurement. Prior research yielded an accuracy of 96% in classifying measurement of one qubit in IBM quantum computers. When evaluated on superconducting hardware from VTT, we achieved an accuracy of 71.68% with similar framework. Our extended framework with additional labels yields an accuracy of 76.30% for classifying measurement of one qubit and 53.37% for measurement of two qubits using Support Vector Machine (SVM). Experimental results indicate that measurement operation on a qubit can affect the probability of measuring adjacent qubits. The impact on the target qubit is dependent on the number of neighboring qubits measured and also the measurement outcome.