Hybrid scheme for magnetic-based quantum devices

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