Vol.20 No.15&16, December 1, 2020

Research Articles:

Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement (pp1261-1280)
          Francisco Delgado and Carlos Cardoso-Isidoro
Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in  the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

Localization and discrete probability function of Szegedy’s quantum search one-dimensional cycle with self-loops (pp1281-1303)
          Mengke Xu, Zhihao Liu, Hanwu Chen, and Sihao Zheng
We study the localization and  the discrete probability function of a quantum search on the one-dimensional (1D) cycle with self-loops for $n$ vertices and  $m$ marked vertices. First, unmarked vertices have no localization since the quantum search on unmarked vertices behaves like the 1D three-state quantum walk (3QW) and localization does not occur with nonlocal initial states on a 3QW, according to residue calculations and the Riemann-Lebesgue theorem. Second, we show that localization does occur on the marked vertices and derive an analytic expression for localization by the degenerate 1-eigenvalues contributing to marked vertices. Therefore localization can contribute to a quantum search. Furthermore, we emphasize that localization comes from the self-loops. Third, using the localization of a quantum search, the asymptotic average probability distribution (AAPD)  and the discrete probability function (DPF) of a quantum search are obtained. The DPF shows that Szegedy’s quantum search on the 1D cycle with self-loops spreads ballistically.

Testing the context-independence of quantum gates (pp1304-1352)
          Andrzej Veitia and Steven J. van Enk
The actual gate performed on, say, a qubit in a quantum computer may depend, not just on the actual laser pulses and voltages we programmed to implement the gate, but on its {\em context} as well. For example, it may depend on what gate has just been applied to the same qubit, or on how much a long series of previous laser pulses has been heating up the qubit's environment. This paper analyzes several tests to detect such context-dependent errors (which include various types of non-Markovian errors). A key feature of these tests is that they are robust against both state preparation and measurement (SPAM) errors and gate-dependent errors. Since context-dependent errors are expected to be small in practice, it becomes important to carefully analyze the effects of statistical fluctuations and so we investigate the power and precision of our tests as functions of the number of repetitions and the length of the sequences of gates. From our tests an important quantity emerges: the logarithm of the determinant (log-det) of a probability (relative frequency) matrix $\mP.$ For this reason, we derive the probability distribution of the log-det estimates which we then use to examine the performance of our tests for various single- and two-qubit sets of measurements and initial states. Finally, we emphasize the connection between the log-det and the degree of reversibility (the unitarity) of a context-independent operation.
 

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