Robust Quantum State Transfer in Random Unpolarized Spin Chains

Abstract

We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed.PACS numbers: 03.67. Lx, 03.67.Hk, 05.50.+q, 75.10.Dg In addition to diverse applications ranging from quantum key distribution to quantum teleportation [1, 2], reliable quantum state transfer between distant qubits forms an essential ingredient of any scalable quantum information processor [3]. However, most direct qubit interactions are short-range and the corresponding interaction strength decays rapidly with physical separation. For this reason, most of the feasible approaches that have been proposed for quantum computation rely upon the use of quantum channels which serve to connect remote qubits; such channels include: electrons in semiconductors [4], optical photons [5][6][7][8], and the physical transport of trapped ions [9]. Coupled quantum spin chains have also been extensively studied [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. A key advantage of such spin chain quantum channels is the ability to manipulate, transfer, and process quantum information utilizing the same fundamental hardware [25]; indeed, both quantum memory and quantum state transfer can be achieved in coupled spin chain arrays [26], eliminating the requirement for an external interface between the quantum channel and the quantum register. Prior work on spin chain quantum channels has focused on three distinct regimes, in which the spin chain is either initialized [10][11][12][13]24], engineered [15,27,29] or dynamically controlled [19,28,[30][31][32]].An important application of spin-chain mediated coherent coupling is in the context of realizing a room temperature quantum information processor based upon localized spins in the solid-state [33]. In this case, it is difficult to envision mechanical qubit transport, while other coupling mechanisms are often not available or impose additional prohibitive requirements such as cryogenic cooling [8]. At the same time, long spin chains are generally difficult to polarize, impossible to control with single-spin resolution, and suffer from imperfect spin-positioning [21,22]; such imperfections can cause both on-site and coupling disorder, resulting in localization [34]. For these reasons, a detailed understanding of quantum coherence and state transfer in rando...

Smooth optimal control with Floquet theory

“…if dipole-dipole interaction is suppressed because of a large spatial separation of the spins [36]. Nevertheless, an interaction can still be possible by using the indirect coupling via neighboring spins, as proposed for nitrogen-vacancy centers [37,38]. With our method we can create entanglement between the end spins of a spin chain, even if the coupling strengths between the spins are only known up to a certain extent.…”

Perfect quantum transport in arbitrary spin networks

“…Note that for the simplest case of spin chains, the symmetry of the modes ensures the network is already balanced 7,8,37 . However, to drive transport in arbitrary networks, one does need an active control scheme for balancing.…”

“…Engineering the coupling between spins can improve the transport fidelity 4 , even allowing for perfect quantum state transport (QST), but it is difficult to achieve in experimental systems. Remarkable work 5,6 found relaxed coupling engineering requirements -however, even these proposals still required linear chains with nearest-neighbor couplings 7,8 or networks will all equal couplings 9 . These requirements remain too restrictive to allow an experimental implementation, since manufacturing highly regular networks is challenging with current technology [10][11][12][13] .…”

“…in crystals) with almost no fabrication requirements. In large networks, the end-spins are intrinsincally weakly coupled to the bulk network, allowing the use of a perturbative approach to describe the transport dynamics in this weak-coupling regime [5][6][7][8][9]14 . We identify two different scenarios for engineering perfect transport: the endspins could be set far off-resonance from the rest of the network -transport is then driven by a second-order process and hence is slow, but it requires no active control.…”

Noise effects in perfect transmission of quantum states

“…This idea was first introduced in [1], where it was shown that the natural dynamics of a Heisenberg ferromagnetic spin chain can achieve high-fidelity transfer of qubits over distances as long as 80 lattice units.In contrast to this traditional "passive" protocol, different approaches soon emerged. One idea was to engineer the couplings between the various spins in the chain in such a way that states are transferred with perfect [2]- [9] or with arbitrary high fidelity [10]- [16]; in addition, some minimal external control on the chain dynamics was also introduced in order to achieve similar results [18]- [26].…”