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arXiv:1911.12211 · New Journal of Physics

Perturbative many-body transfer

Wayne Jordan Chetcuti, Claudio Sanavio, Salvatore Lorenzo, Tony J. G. Apollaro

Published Feb 28, 2020• 24 citations
arXivHTMLPDF

Abstract

Abstract The transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum information processing. We address the transfer of n > 1 bosonic and fermionic excitations between the edges of a one-dimensional chain modelled by a quadratic hopping Hamiltonian, where the block edges, embodying the sender and the receiver sites, are weakly coupled to the quantum wire. We find that perturbative high-quality transfer is attainable in the weak-coupling limit, for both bosons and fermions, only for certain modular arithmetic equivalence classes of the wire’s length. Finally we apply our findings to the transport of spins and the charging of a many-body quantum battery.

DOI
10.1088/1367-2630/ab7a33

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Abstract The transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum information processing. We address the transfer of n > 1 bosonic and fermionic excitations between the edges of a one-dimensional chain modelled by a quadratic hopping Hamiltonian, where the block edges, embodying the sender and the receiver sites, are weakly coupled to the quantum wire. We find that perturbative high-quality transfer is attainable in the weak-coupling limit, for both bosons and fermions, only for certain modular arithmetic equivalence classes of the wire’s length. Finally we apply our findings to the transport of spins and the charging of a many-body quantum battery.
Abstract The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of three and four interacting qubits.
The transfer of an unknown quantum state, from a sender to a receiver, is one of the main requirements to perform quantum information processing (QIP) tasks. In this respect, the state transfer of a single qubit by means of spin chains has been widely discussed, and many protocols aiming at performing this task have been proposed. Nevertheless, the state transfer of more than one qubit has not been properly addressed so far. In this paper, we present a modified version of a recently proposed quantum state transfer (QST) protocol (Lorenzo S, Apollaro T J G, Sindona A and Plastina F 2013 Phys. Rev. A 87 042313 ) to obtain a quantum channel for the transfer of two qubits. This goal is achieved by exploiting Rabi-like oscillations due to excitations induced by means of strong and localized magnetic fields. We derive exact analytical formulae for the fidelity of the QST and obtain a high-quality transfer for general quantum states as well as for specific classes of states relevant for QIP.
The quantum information science (QIS) is relatively young, but quite broad and emerging field of modern physics. This is an interdisciplinary field where quantum mechanics, computer science, mathematics and computing technologies meet together. Using the laws of quantum mechanics to deal with information opens many new opportunities. However, these opportunities can only be used if one can construct a quantum logic device to implement QIS methods. In the last decade many researchers proposed the variety of physical systems, that can be used as building blocks of the so called quantum computer. But the question of building an effective connection between different blocks remains open. Recently, the idea to build a ’quantum wire’ using chains of permanently coupled spins was studied by a number of authors. The purpose of this thesis is to investigate and develop advanced schemes for using quantum chains as wires. The first part of the thesis shortly describes the concepts of quantum computing and quantum state transfer. We then briefly introduce different schemes to couple two superconducting qubits and analyze more closely one of them. Then we analyze the process of the state transfer for the chain of flux qubits. Next, we propose a new method of improved quantum state transfer which was created as a part of this thesis. Finally, we study the effects and the role of interference in quantum state transfer via spin chains.
We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.
We study the information transferring ability of a spin-1∕2 XXZ Hamiltonian for two different proposals of state transfer, namely, the well-studied attaching scenario and the recently proposed measurement induced transport. The latter one has been inspired by recent achievements in optical lattice experiments for local addressability of individual atoms and their time evolution when only local rotations and measurements are available and local control of the Hamiltonian is very limited. We show that while the both scenarios performs with almost similar quality in the case of non-interacting free fermionic XX phase, the difference become more pronounced around the isotropic Heisenberg point. Our study shows that the presence of spin-flip symmetry plays a key point in the quality of state transfer and each scenario which benefits from this symmetry transfers the quantum states with higher fidelity. In fact, for even chains this symmetry exists only for the measurement induced dynamics which then gives higher transport quality and for odd chains the spin-flip symmetry is only valid for the attaching scenarios which become more superior. We also study the effect of thermal fluctuations and environmental interactions on both scenarios.
In the present thesis we perform a step towards understanding the effec- tiveness of Hamiltonian perturbation theory in quantum dynamics, which is made possible by the Hamiltonian framing of quantum mechanics. To such a purpose, we focus our attention on quantum spin chains, namely on the isotropic Heisenberg ferromagnet, which is well known to be equivalent, via the Jordan-Wigner transformation, to a system of interacting fermions, and is also known to be exactly integrable through the Bethe ansatz. The interaction term of the Hamiltonian, of order four in fermionic creation and annihilation operators, is treated as a perturbation in the regime of small excitations: small number of reversed spins or, equivalently, small number of fermions per site. The calculation of the first order normal form Hamiltonian amounts to erasing all the nonresonant interaction terms, and allows to draw interesting conclusions on the dynamics of the system, e.g. to determine ap- proximately conserved quantities. Moreover, we get a good correspondence between our perturbative energy spectrum and the exact one computed via the Bethe ansatz, the approximation being of course the more accurate the smaller is the number of fermions per site. The present method, here tested in an exactly solvable case, can be applied to any nonintegrable system of weakly interacting fermions (and/or bosons).