The transmission of quantum information between different parts of a quantum computer is of fundamental importance. Spin chains have been proposed as quantum channels for transferring information. Different configurations for the spin couplings were proposed in order to optimize the transfer. As imperfections in the creation of these specific spin-coupling distributions can never be completely avoided, it is important to find out which systems are optimally suited for information transfer by assessing their robustness against imperfections or disturbances. We analyze different spin coupling distributions of spin chain channels designed for perfect quantum state transfer. In particular, we study the transfer of an initial state from one end of the chain to the other end. We quantify the robustness of different coupling distributions against perturbations and we relate it to the properties of the energy eigenstates and eigenvalues. We find that the localization properties of the systems play an important role for robust quantum state transfer.

Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.

We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic bath spectra, the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.

One spin excitation states are involved in the transmission of quantum states and entanglement through a quantum spin chain, the localization properties of these states are crucial to achieve the transfer of information from one extreme of the chain to the other. We investigate the bipartite entanglement and localization of the one excitation states in a quantum XX chain with one impurity. The bipartite entanglement is obtained using the Concurrence and the localization is analyzed using the inverse participation ratio. Changing the strength of the exchange coupling of the impurity allows us to control the number of localized or extended states. The analysis of the inverse participation ratio allows us to identify scenarios where the transmission of quantum states or entanglement can be achieved with a high degree of fidelity. In particular we identify a regime where the transmission of quantum states between the extremes of the chain is executed in a short transmission time ∼ N/2, where N is the number of spins in the chain, and with a large fidelity.

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin-spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.Keywords: quantum state transfer, quantum control, spin dynamics, decoherence One dimensional (1D) chains of spin-1 2 systems with nearest-neighbor couplings, nicknamed spin chains, constitute a paradigmatic quantum many-body system of the Ising type [1]. As such, spin chains are well suited for studying the transition from quantum to classical transport and from mobility to localization of excitations as a function of disorder and temperature [2]. In the context of quantum information (QI), spin chains are envisioned to form reliable quantum channels for QI transmission between nodes (or blocks) [3,4]. Contenders for the realization of high-fidelity QI transmission are spin chains comprised of superconducting qubits [5,6], cold atoms [7-10], nuclear spins in liquid-or solid-state NMR [11][12][13][14][15][16][17][18], quantum dots [19], ion traps [20,21] and nitrogen-vacancy centers in diamond [22][23][24][25].

We consider a thermometer modelled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe enables us to dramatically increase the accuracy of temperature estimation at low temperatures, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error at low temperatures obtained in conventional thermometers, periodic modulation of the probe enables high-precision thermometry close to the absolute zero, with a constant (temperature-independent) relative error bound. Alternatively, such control may allow for high-precision measurement of a broad range of temperatures. The proposed approach may find diverse applications related to precise probing of the temperatures of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.

The transmission of quantum states through spin chains is an important element in the implementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all disorder models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.

This is a shortened and slightly edited version of a chapter [1] in the collection Quantum State Transfer and Network Engineering, edited by G.M. Nikolopoulos and I. Jex [2], where we review our own research about the robustness of spin-chain state-transfer schemes along with other approaches to the topic. Since our own research is documented elsewhere to a large extent we here restrict ourselves to a review of other approaches which might be useful to other researchers in the field.