Knitting distributed cluster-state ladders with spin chains

Abstract

Recently there has been much study on the application of spin chains to quantum state transfer and communication. Here we discuss the utilization of spin chains (set up for perfect quantum state transfer) for the knitting of distributed cluster-state structures, between spin qubits repeatedly injected and extracted at the ends of the chain. The cluster states emerge from the natural evolution of the system across different excitation number sectors. We discuss the decohering effects of errors in the injection and extraction process as well as the effects of fabrication and random errors.

Anderson localisation in spin chains for perfect state transfer

“…The transfer maintains high fidelity in this parameter region, which is why PST spin chains are considered to be useful elements for short range quantum communication. Nevertheless, for larger N values there is seen to be exponential damping of the transfer fidelity with N , along with Gaussian dependence on the relevant noise amplitude [21,22,31] 1 . These previous studies have looked at the transfer fidelity at some chosen time, which for example would be t = t M if the objective is perfect quantum communication along a chain.…”

“…Our systems of interest without any disorder are by design 'perfect wires', that is chains that transport an excitation from one end to the other with perfect fidelity in a time t M . Furthermore, modest length N chains with low levels of decoherence (including disorder) exhibit potentially useful robustness against decoherence [21,22]. The transfer maintains high fidelity in this parameter region, which is why PST spin chains are considered to be useful elements for short range quantum communication.…”

“…The PST type of chain we analyse in this paper, when unperturbed, ensures perfect state transfer (PST) not only between its end spins, but also between any pair of spins at opposite but equal distance with respect to the chain centre due to the 'mirroring' property introduced in the previous section. Within quantum information processing, this property can be exploited in various devices/scenarios, for example to construct inputoutput registers such as the one described in Figure 15 of reference [22]. Because of the 'mirroring' property, it is then important to assess the effect of disorder-driven localisation on injection also in sites distant from the chain ends, and in this respect the study of injection at the chain end and centre sites allows us to assess the effect of disorder-driven localisation in the 'worst' and 'best' case injection scenarios.…”

“…b e-mail: mpee500@york.ac.uk c e-mail: irene.damico@york.ac.uk d e-mail: timothy.spiller@york.ac.uk it can be conjectured that long chains would be the most affected by random fabrication defects [20][21][22][23][24][25][26] or by slowly varying external fields. Within this context, we have investigated the question of if and how random defects would affect the relevant transmission properties of PST spin chains, through the appearance of weak localisation or Anderson localisation.…”

Robust quantum entanglement generation and generation-plus-storage protocols with spin chains

“…Hardware in which the chain defects can be engineered to generate localised protected states are the edges of graphene ribbons [33], the edges of honeycomb arrays of microcavity pillars [34], or BoseEinstein condensates of Rb 87 atoms in suitable optical lattice potentials [35,36], as well as optical silicon waveguides [37]. Previous works have shown spin chains engineered for 'PST' to be good candidates for entanglement formation [15] and the knitting of distributed cluster states [38][39][40][41]. Nonetheless, in these proposals to achieve such behaviour requires all the couplings of the chain to be individually tuned, potentially introducing difficulties in experimentally engineering such systems, and high sensitivity to fabrication errors.…”