Hybrid scheme for magnetic-based quantum devices
Davide Nuzzi
The realization of a quantum computer, after being considered only a wishful thinking for many years, \nlooks now more solid, with the major issues about its realization looking like “engineering problems”, whose \nsolution is not far to be found. \nThe most considerable open problems concerning the realization of a quantum computer concern: the \nsensitivity to external disturbances, the addressability of any single qubit, and the scalability of the proposed \narchitectures. These problems may have opposite solutions, since a good scalability would require high \ndensity of qubits embedded in solid state matrices, making it more difficult to address and protect each of \nthem. Conversely, well separated qubits realized by atoms or ions are easily addressed and protected, but \nmake it more difficult to achieve scalability. \nAnother aspect related to the realization of generic quantum devices (i.e. devices which exploit the \nquantum features of their constituents to realize some operations) is connected to the way one interfaces \nwith them: we live in a “classical world”, and any quantum device will have to interface with it at some \nstage, e.g. to be controlled or measured. The problem, in this case, is keeping our classical disturbances as \nfar as possible from the action taking place at the heart of the quantum device. \nHowever, the problem of being able to find the proper “interface” can be turned into an advantage, \nsince macroscopic systems may posses robustness features which can be exploited for the realization of novel \nquantum devices where the sensitivity problem is much alleviated. A good interface can be thus provided by \nsemi-classical systems, i.e. objects whose nature is intimately quantum, but whose features and behaviour is \nwell framed within a classical description. Any scheme, application or device, where a semi-classical system \ninteracts with some pure quantum object (e.g. a qubit) for realizing a quantum operation, will be referred \nto as hybrid. \nIn this thesis, we have developed the idea of exploiting the robustness features of some non-linear classical \nsystems in order to realize quantum devices where the sensitivity problem is alleviated. Hence, we have \nproposed a hybrid scheme for accomplishing the most basic actions related with the realization of a magnetic- \nbased quantum device, i.e. the control of a qubit state and entanglement generation. In particular, we have \ndeveloped it focusing on magnetic one-dimensional systems, i.e. spin chains, as channels connecting one or \nmore qubits to some external control apparatus. \nThis choice follows from the observation that classical spin chains are non-linear systems which enumerate \nsolitons among their dynamical configurations which are solutions of their equations of motion. In fact, \nsolitons are those particular solutions of non-linear systems which show space-time localization and shape- \ninvariant evolution and are celebrated for their impressive properties of robustness against scattering and \nexternal disturbances. These properties make them suitable candidates for practical purposes. \nWe have considered systems made by one-dimensional discrete lattices hosting, at each lattice site, one \nclassical spin (classical spin chain) or a large-S spin, i.e. a quantum spin characterized by a S-value large \nenough for the spin to be well described by a semi-classical behaviour (large-S spin chain). \nA classical, or a large-S, spin chain (with its solitons) can play the role of the robust partner while \nthe role of the fragile quantum system is played by the qubit, which is the agent of the relevant quantum \noperations in our hybrid quantum device.We have first introduced a method for generating solitons on discrete, classical Heisenberg chains by \napplying a time-dependent magnetic field to one of the chain extremities. The method has been numerically \nchecked, revealing the actual possibility of producing soliton-like dynamical configurations running on the \nspin chain, which resemble the known analytical solitons of the continuous chain if their typical width is \nlarge with respect to the chain spacing. The robustness of the generated solitons has been also tested with \nrespect to thermal noise present in the system. \nWe have then proposed a set-up where the generated soliton acts as a magnetic signal that travels along \nthe chain and eventually reaches a qubit and changes its quantum state. Since any unitary action on a single \nqubit can be represented in terms of a Zeeman interaction lasting for a precise time interval, qubit state \ncontrol is usually assumed to be obtained by applying suitable sequences of external magnetic fields. Indeed, \nfor this particular application, the spin chain needs not to be quantum and the suitable magnetic field is \nprovided by the moving deformation of the uniform chain represented by the magnetic soliton travelling \nalong the chain. Numerical results confirm that solitons are suitable for this task, giving the possibility to \nremotely control the qubit state by an appropriate choice of soliton shape and qubit-chain coupling. \nWe have finally addressed the problem of generating entanglement between distant qubits by introducing \na model where two qubits, distant and non-interacting, are locally coupled with a large-S Heisenberg chain, \nwhose dynamics is assumed to be characterized by the presence of solitons. The aim of this study was to \nverify if, by properly choosing the state of the spin chain, the evolution of such a robust semi-classical system \ncan bring the two qubits from a separable initial state to a non-separable state after a certain amount of \ntime, i.e., if a semi-classical channel could generate entanglement between the two qubits. \nAt variance with the previous application, the spin chain must here be considered, and consequently \ntreated, as a quantum system in order to allow for entanglement generation/transfer, but a suitable approximation \nis needed to solve the chain dynamics, as accounting for the exact evolution of large-S spin chain \nis out of reach, even numerically. This leads us to introduce a particular set of chain states built as product \nof single-spin coherent states which are in one-to-one correspondence with the configurations of the classical \nspin chain and are thus referred to as the semi-classical states of the chain. Being able to solve the evolution \nof the coherent state products, allow us to complete the hybrid scheme for entanglement generation: in \nfact, it is shown that, choosing the chain initial state as a semi-classical state corresponding to a soliton \nconfiguration, the correlations, generated between one qubit and the corresponding spin-S, are efficiently \ntransferred along the chain up to the other qubit, finally leaving the two qubits in an entangled state. \nThe results about the proposed hybrid schemes, showing their effectiveness for remotely controlling qubit \nstates and generating entanglement between distant qubits, encourage further studies opening also new \nperspectives for the realization of novel quantum devices based on the exploitation of the robustness features \nof semi-classical systems.
•Jan 1, 2017•0 citations