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Register a new userThe role of controllability in optimizing quantum dynamics
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This paper discusses the important role of controllability played on the complexity of optimizing quantum mechanical control systems. The study is based on a topology analysis of the corresponding quantum control landscape, which is referred to as the optimization objective as a functional of control fields. We find that the degree of controllability is closely relevant with the ruggedness of the landscape, which determines the search efficiency for global optima. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dynamic symmetry group. We show that multiple local false traps (i.e., non-global suboptima) exist even if the target gate is realizable and that the number of these traps is increased by the loss of controllability, while the controllable systems are always devoid of false traps.
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$ $In its usual form, Grovers quantum search algorithm uses $O(sqrt{N})$ queries and $O(sqrt{N} log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to $O(sqrt{N}loglog N)$ for the special case where the database has a unique solution, without significantly increasing the number of queries. We show how to reduce this further to $O(sqrt{N}log^{(r)} N)$ gates for any constant $r$, and sufficiently large $N$. This means that, on average, the gates between two queries barely touch more than a constant number of the $log N$ qubits on which the algorithm acts. For a very large $N$ that is a power of 2, we can choose $r$ such that the algorithm uses essentially the minimal number $frac{pi}{4}sqrt{N}$ of queries, and only $O(sqrt{N}log(log^{star} N))$ other gates.
Complete controllability of degenerate quantum system using quantum accessor modeled as a qubit chain with nearest neighborhood coupling is investigated. Sufficient conditions on the length of accessor and the way of coupling between controlled system and accessor are obtained. General approach to arbitrary finite system is presented and two and three level degenerate systems are investigated in detail.
We investigate the controllability of the Jaynes-Cummings dynamics in the resonant and nearly resonant regime. We analyze two different types of control operators acting on the bosonic part, corresponding - in the application to cavity QED - to an external electric and magnetic field, respectively. We prove approximate controllability for these models, for all values of the coupling constant g except those in a countable set S which is explicitly characterized in the statement. The proof relies on a spectral analysis which yields the non-resonance of the spectrum for every real g which is not in S.
In the theory of open quantum systems interaction is a fundamental concepts in the review of the dynamics of open quantum systems. Correlation, both classical and quantum one, is generated due to interaction between system and environment. Here, we recall the quantity which well known as total entropy production. Appearance of total entropy production is due to the entanglement production between system an environment. In this work, we discuss about the role of the total entropy production for detecting non-Markovianity. By utilizing the relation between total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity.
We devise a protocol to build 1D time-dependent quantum walks in 1D maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e. the angle $theta$, such that for $theta=0$ we have the $hatsigma_z$, while for $theta=pi/4$ we obtain the Hadamard gate. The optimal $theta$ sequences present non-trivial patterns, with mostly $thetaapprox 0$ alternated with $thetaapprox pi/4$ values after increasingly long periods. We provide an analysis of the entanglement properties, quasi-energy spectrum and survival probability, providing a full physical picture.
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