Quantum Router Research Articles

A Systematic Literature Review of Quantum Computing for Routing Problems

Quantum Computing is drawing a significant attention from the current scientific community. The potential advantages offered by this revolutionary paradigm has led to an upsurge of scientific production in different fields such as economics, industry, or logistics. The main purpose of this paper is to collect, organize and systematically examine the literature published so far on the application of Quantum Computing to routing problems. To do this, we embrace the well-established procedure named as Systematic Literature Review. Specifically, we provide a unified, self-contained, and end-to-end review of 18 years of research (from 2004 to 2021) in the intersection of Quantum Computing and routing problems through the analysis of 53 different papers. Several interesting conclusions have been drawn from this analysis, which has been formulated to give a comprehensive summary of the current state of the art by providing answers related to the most recurrent type of study (practical or theoretical), preferred solving approaches (dedicated or hybrid), detected open challenges or most used Quantum Computing device, among others.

Quantum router: Storing and redirecting light at the photon level

We propose a method for spatially rerouting single photons or light in a coherent state with a small average photon number by purely electronic means, i.e., without using mechanical devices such as micromirror arrays. The method is based on mapping the quantum state of the incoming light onto a spin-wave in an atomic ensemble, as is done in quantum memories of light. Then the wave vector of the spin-wave is modified in a controlled way by an applied magnetic field gradient. Finally, by reapplying the same control beam as for storing, the signal pulse is released in a new direction that depends on the deflected wave vector of the spin-wave. We show by numerical simulation that efficiencies can be achieved for arbitrary deflection angles in the plane that are comparable with simple photon storage and reemission in the forward direction, and we propose a method for eliminating the stored momentum as a source of decoherence in the quantum memory. In a reasonable parameter regime, the rerouting should be achievable on a timescale on the order of a few to $\ensuremath{\sim}100$ microseconds, depending on the deflection angle. The shifts in the wave vector that can be achieved using the Zeeman effect, with otherwise minimal changes to the spin-wave, can also be used to complement existing ac-Stark spin-wave manipulation methods.

Optimisation of the routing protocol for quantum wireless Ad Hoc network

This study addresses the optimisation of on-demand routing protocols for quantum wireless Ad Hoc network. The study improves the route discovery protocol by proposing a ‘reverse synchronisation method’, which means after the route request is completed, the quantum channel establishment process can be carried out simultaneously with the route reply process. This method is better than the general method which builds quantum channels after the forward path establishment, reduces the time and the number of messages for quantum channel establishment, thus improving the efficiency. Accordingly, this study elaborates the specific methods, procedures and related upgrading message formats involved in quantum route discovery, quantum channel establishment and qubit information transmission of on-demand routing protocol for quantum wireless Ad Hoc network.

Quantum frequency conversion from ultraviolet to visible band through waveguides in a period-poled MgO:LiTaO3 crystal.

In research on hybrid quantum networks, visible or near-infrared frequency conversion has been realized. However, technical limitations mean that there have been few studies involving the ultraviolet band, and unfortunately the wavelengths of the rare-earth or alkaline-earth metal atoms or ions that are used widely in research on quantum information are often in the UV band. Therefore, frequency conversion of the ultraviolet band is very important. In this paper, we demonstrate a quantum frequency conversion between ultraviolet and visible wavelengths by fabricating waveguides in a period-poled MgO:LiTaO3 crystal with a laser writing system, which will be used to connect the wavelength of the dipole transition of 171Yb+ at 369.5 nm and the absorption wavelength of Eu3+ at 580 nm in a solid-state quantum memory system. An external conversion efficiency of 0.85% and a signal-to-noise ratio of greater than 500 are realized with a pumping power of 3.28 W at 1018 nm. Furthermore, we complete frequency conversion of the classical polarization state by means of a symmetric optical setup based on the fabricated waveguide, and the process fidelity of the conversion is (96.13 ± 0.021)%. This converter paves the way for constructing a hybrid quantum network and realizing a quantum router in the ultraviolet band in the future.

Probing quantum nonlinearity of cavity-QED systems with quantum light

Giant optical circular birefringence (GCB) induced by a single quantum-dot-confined spin in an optical microcavity finds wide applications in quantum and optical technologies, such as quantum gates, quantum transistors, quantum repeaters, quantum routers, etc. If the system is probed with a classical light, such as the laser light where the photons are uncorrelated with each other, then the single-photon GCB is detected. In this work we develop a general approach to investigate the many-body dynamics of $n$ photons bound to one quantum emitter and apply this method to calculate the $n$-photon GCB probed with quantum light in Fock states. With suppressed atomic saturation, quantum light loads photons into dressed states more efficiently than classical light such that the whole Jaynes-Cummings energy ladder and the quantum nonlinearity related to the multiphoton transitions can be observed. The $n$-photon GCB lying at the cavity mode resonance allows the spin-cavity quantum gates and quantum transistors to extend from single-photon to $n$-photon operations and generate entangled photonic Fock states, i.e., the NOON states which are useful for quantum metrology and lithography.

Quantum routing with fast reversals.

We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length , we show that there exists a constant such that the quantum routing time is at most , whereas any SWAP-based protocol needs at least time . This represents the first known quantum advantage over swAP-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of in expectation for uniformly random permutations, whereas SWAP-based protocols require time asymptotically. Additionally, we consider sparse permutations that route qubits and give algorithms with quantum routing time at most on paths and at most on general graphs with radius .

Nonreciprocal single-photon router in quantum networks

High-efficiency single-photon routing of photon signals between different quantum channels is of great importance for the quantum networks with the ability to coherently transfer quantum states between the desired sender and receiver nodes. We proposed an efficient scheme for realizing quantum routers via multiple semi-infinite coupled-resonator waveguides (CRWs) coupled to cavities nonreciprocally. Numerical results show that with the change of the phase difference value, the quantum routing function of multiple output ports can be realized, in the meantime, the information conversion rate can almost reach 100%. The optimal conditions for these phenomena are obtained by the time-reversal symmetry breaking the nonreciprocal of the single-photon transport. Moreover, we have also described a scalable scheme that can extend the router to an arbitrary number of outputs. Our results pave the way to design high-quality quantum devices based on breaking time-reversal symmetry waveguide-cavity systems.

Entanglement distribution in multi-platform buffered-router-assisted frequency-multiplexed automated repeater chains

Realization of a globe-spanning quantum network is a current worldwide goal, where near and long term implementations will benefit from connectivity between platforms optimized for specific tasks. Towards this goal, a quantum network architecture is herewith proposed whereby quantum processing devices based on NV− colour centers act as quantum routers (QR) and, between which, long-distance entanglement distribution is enabled by spectrally-multiplexed quantum repeaters based on absorptive quantum memories in rare-earth ion-doped crystals and imperfect entangled photon-pair sources. The inclusion of a quantum buffer structure between repeaters and routers is shown to, albeit the increased complexity, improve the achievable entanglement distribution rates in the network. Although the expected rate and fidelity results are presented for a simple linear network (point-to-point), complex topologies are compatible with the proposed architecture through the inclusion of an extra layer of temporal multiplexing in the QR’s operation. Figures of merit are extracted based on parameters found in the literature for near-term scenarios and attest the availability of the proposed buffered-router-assisted frequency-multiplexed automated repeater chain network.

Quantum signatures of chaos in a cavity-QED-based stimulated Raman adiabatic passage

Nonlinear stimulated Raman adiabatic passage (STIRAP) is a fascinating physical process that dynamically explores chaotic and nonchaotic phases. In a recent paper [A. Dey and M. Kulkarni, Phys. Rev. Res. 2, 042004(R) (2020)], such a phenomenon is realized in a cavity-QED platform. There, the emergence of chaos and its impact on STIRAP efficiency are mainly demonstrated in the semiclassical limit. In the present paper we treat the problem in a fully quantum many-body framework. With the aim of extracting quantum signatures of a classically chaotic system, it is shown that an out-of-time-ordered correlator (OTOC) measure precisely captures chaotic and nonchaotic features of the system. The prediction by OTOC is in precise matching with classical chaos quantified by Lyapunov exponent analysis. Furthermore, it is shown that the quantum route corresponding to the semiclassical followed state encounters a dip in single-particle purity within the chaotic phase, depicting a consequence of chaos. A dynamics through the chaotic phase is associated with spreading of the many-body quantum state and an irreversible increase in the number of participating adiabatic eigenstates.

A quantum route to the classical Lagrangian formalism

Using the recently developed groupoidal description of Schwinger’s picture of Quantum Mechanics, a new approach to Dirac’s fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function [Formula: see text] on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call q-Lagrangian, can be described in terms of a new function [Formula: see text] on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold M, the quadratic expansion of [Formula: see text] will reproduce the standard Lagrangians on TM used to describe the classical dynamics of particles.

Fragmentation-Aware Entanglement Routing for Quantum Networks

New capabilities enabled by quantum networks, e.g. quantum key distribution, rely on the concurrent quantum entanglements via multiple untrusted repeaters between the source-destination pairs, which is known as quantum routing. Existing quantum routing algorithms pre-assign the free qubits to specific paths, in order to avoid resource contention in the process of entanglement swapping. Since not all pre-assigned qubits can be utilized, the resource fragmentation problem caused can limit the network throughout. In this paper, a new fragmentation-aware entanglement routing (FER) algorithm is proposed. With FER, the entangled qubits are shared by all the paths, and the resource contention problem is solved by a priority connection mechanism. Simulation results show that FER consistently outperforms existing algorithms under different network settings.

Realization of single-photon transport in one-dimensional coupled-resonator waveguides via phase control

We study theoretically the influence of the phase difference of the coupling strength changes on the transport of a single-photon in coupled-resonator waveguides (CRWs). Two cases are considered: single-photon transport in a one-dimensional CRW with nonlocal coupling to a cavity, and a single-photon in a waveguide consisting of two coupled semi-infinite CRWs, which are coupled to a cavity and two cavities. The results show that the phase difference of the coupling strength can not only improve the conversion efficiency of single-photon transport in CRWs but also can adjust the irregular energy band spectrum to become regular. This will provide an important physical parameter for the experimental realization of quantum solid-state devices such as quantum switches and quantum routers.

Quantum router modulated by two Rydberg atoms in a X-shaped coupled cavity array

We theoretically investigate the single-photon router using two Rydberg atoms embedded in a multi-channel coupled cavity arrays(CCAs) driven by a classical field. It is shown that when the Rydberg interaction is in the proper range, three kinds of photons with different frequencies are absorbed and the quantum routing can be achieved due to the spontaneous emission of the formed dressed states. The Rydberg interaction can also cause photons that are not originally in the energy range to be routed. Furthermore, the total reflection of the single photon is obtained because of the coherent resonance and the existence of the photonic bound states. Based on these characteristics, it is a feasible scheme to generate a multi-frequency photons router and it could be useful for designing the single-photon devices.

Experimental Realization of a Deterministic Quantum Router with Superconducting Quantum Circuits

A quantum router is an elementary building block for quantum-information processing. It directs the incoming quantum signal to different routes with phase coherence. To realize scalable quantum routing, a single particle needs to deterministically and coherently route the paths of a flying qubit, which requires nonlinear interaction at the single quantum level and complicated path-data qubit control so far beyond the experimental reach. Here we demonstrate a deterministic quantum router working at microwave frequencies based on superconducting circuits, which can naturally integrate with a leading platform for quantum computing. We encode the quantum signal into a weak coherent pulse and use an entanglement witness to rigorously verify the generated entanglement between the control qubit and the path of the data qubit, thus proving quantum coherence of the routing operation. Our experiment lays the foundation for useful applications of quantum routers in quantum networks and quantum random-access memories.

Single plasmon router with two quantum dots side coupled to two plasmonic waveguides with a junction

We proposed a new multichannel scheme of quantum routing for single plasmons with two quantum dots (QDs) side coupled to two plasmonic waveguides, one of which is infinite and the other is semi-infinite, with a junction. We investigated theoretically the routing properties of the proposed system for the incident single plasmons, such as the transmission, reflection, and transfer rates via the real-space approach. Our results show that in such a coupled system, the incident single plasmons can be routed by controlling the parameters, such as the detuning, the atomic transition frequencies, the coupling strengths, and the spacing between QDs. In particular, we showed that the transfer rate of single plasmons could be greatly changed according to the position of the junction. Our multichannel scheme for routing of single plasmons could be utilized for realizing quantum devices, such as quantum switches, directional couplers, and quantum routers.

Implementation of a single-photon fully quantum router with cavity QED and linear optics

Both cavity quantum electrodynamics and linear optics are promising platforms for the implementation of coherent manipulations of quantum information, and have potential applications in the development of practical quantum devices. In this paper, we propose a simple and deterministic scheme for implementing a single-photon fully quantum router by a combination of both platforms. With this router, a polarization encoded signal photonic qubit can be coherently routed to one of two distinct spatial output ports or their coherent superposition according to the state of a control photonic qubit, while keeping the signal information stored in the signal qubit unaltered under the quantum routing operation. Our scheme has several advantages in contrast to previously published ones, and on top of that, this device meets all the requirements imposed on a fully featured quantum router and is easily scalable for multiqubit quantum routing. Moreover, it exhibits high experimental feasibility with current or near-future technologies. Therefore, this router can be integrated with protocols for the realization of quantum information processing and future complex quantum networks.

Bidirectional highly-efficient quantum routing in a T-bulge-shaped waveguide* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFC0110403) and the Scientific Research Foundation of the Jiangxi Provincial Education Department, China (Grant No. GJJ180424).

Quantum routing in a T-bulge-shaped waveguide system coupled with a driven cyclic three-level atom and a two-level atom is investigated theoretically. By employing the discrete-coordinate scattering method, exact expressions of the transport coefficients along three ports of the waveguide channels are derived. Our results show that bidirectional high transfer-rate single-photon routing between two channels can be effectively implemented, with the help of the effective potential generated by two atoms and the external driving. Moreover, multiple band zero-transmission emerges in the scattering spectra, arising from the quantum interferences among photons scattered by the boundary and the bulged resonators. The proposed system may suggest an efficient duplex router with filtering functions.

Tunable quantum switcher and router of single atoms using localized artificial magnetic fields

We propose to generate localized artificial magnetic fields using two thin Raman laser beams intersected at a narrow region of a two-leg ladder, where the frequency difference must approximately match the energy offset between the two legs. Based on this method, we investigate the single-atom transport in a two-leg ladder with only two rungs, which, together with the legs, enclose a localized artificial magnetic flux. Here, the atoms on the two legs (channels) possess different onsite energies that produce another energy offset. We find that the atom incoming from the left channel can experience from blockade to transparency via modifying the onsite energy, tunneling strength, or magnetic flux, which can be potentially used for a quantum switcher. Furthermore, the atom incoming from the left channel can also be perfectly routed into the right leg, when, intriguingly, the outgoing atom in the right channel possesses a quasimomentum that can be modulated by the magnetic flux. The result may be potentially used for the interface that controls the communication between two individual quantum devices of cold atoms. The method can also be generalized to other artificial quantum systems, such as superconducting quantum circuit systems, optical systems, etc.2 MoreReceived 10 April 2020Accepted 19 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033484Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoherent controlScattering theoryAtomic, Molecular & OpticalQuantum Information

Driven spin chains as high-quality quantum routers

We propose a setup, based on a periodically driven spin chain, that can realize a high-quality quantum router. We present two protocols, which utilize this setup, that can either generate highly entangled two-qubit states over an arbitrary distance or transfer single-qubit states with high fidelity to any desired location on the chain. In addition, we can execute several protocols at the same time and also store quantum states on the spin chain. Our protocols exploit the effect of coherent destruction of tunneling to control, which spins on the chain couple to each other. This control is acquired by suitably shaping the external driving field. The success of our protocols does not depend on the values of the couplings between the spins as long as they are finite and much smaller than the driving frequency. Our setup is scalable, robust against errors, and may be of practical use for future quantum information technologies.

Efficient single-photon routing in a double-waveguide system with a mirror

High-efficiency routing of photon signals between different quantum channels is of great importance for a quantum network. We investigate theoretically the quantum routing of single photons in a double-waveguide system with an infinite waveguide channel and a semi-infinite waveguide channel terminated by a perfect mirror. Numerical results show that high transfer-rate routing between two channels can be effectively performed in a wide frequency range, arising from the interferences among photons scattered by the boundary mirror and the qubits coupled to the waveguide system. This may suggest a potential scattering setup to effectively control the single-photon quantum routing.