Quantum Router Research Articles

Advantages and Limitations of Quantum Routing

The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected $n$-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an $\Omega(n)$ speedup if we also allow fast local interactions.

Quantum wavelength-division-multiplexing and multiple-access communication systems and networks: Global and unified approach

The march towards successful global quantum internet requires introducing all-quantum networks and signal processing techniques. In this paper, we develop and discuss methods for various wavelength-division-multiplexing and multiple-access (WDM) communication systems and networks in fully quantum mechanical terms to obtain all-quantum WDM (QWDM) systems and networks. We begin the paper with a detailed discussion on various possible narrow-band and wideband sources of light signals used in typical WDM systems, such as coherent, number, and Poissonian mixed states. After introducing a generic and fully quantum mechanical WDM network, we develop methodologies for obtaining the necessary mathematical evolutions through wavelength distributors such as arrayed-waveguide-grating multiplexers and demultiplexers, and wavelength-sensitive and -insensitive broadcasting star couplers. In particular, using the methodologies introduced, one can use the results to obtain a complete and exact expression for any evolved pure quantum light signal through a typical WDM network using the aforementioned optical components. To test the validity and robustness of our mathematical expression for the evolved QWDM light signals, we use two opposing and extreme signals, namely, coherent state and number state, as inputs to various WDM communication and network systems and architecture. The methodologies and the required mathematical QWDM models introduced here can be extended to any fully quantum network architecture deemed necessary in a future global quantum internet, e.g., fiber to the home, Lambdanet-based broadcast WDM networks, and quantum routers based on a waveguide grating router.

Tunable single-photon routing between two single-mode waveguides by a giant [formula omitted]-type three-level atom

We explore the influence of a giant Λ-type three-level atom on the modulation of single photon quantum routing in two channels composed of two linear waveguides. The results show that the single photon scattering behavior is strongly dependent on the phase difference between the two atom-waveguide coupling points, and the coupling strengths between the giant atom and the waveguides. To improve the efficiency of the quantum routing, another configuration with a terminated waveguide is proposed. We find the single-photon routing probability can reach 100% through adjusting the phase shifts induced by the giant atom and the terminated waveguide. The effects of the driving field on the quantum routing are also investigated. Our work may provide a feasible approach to control the single-photon quantum routing using the giant-atom setup.

Entanglement of Signal Paths via Noisy Superconducting Quantum Devices.

Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement-the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible.

Multiport quantum routing with four quantum dots placed at the junctions of ladder-type plasmonic waveguide

Multiport quantum routing with four quantum dots placed at the junctions of ladder-type plasmonic waveguide

Multichannel Adjustable Single-Photon Router Based on Large Detuning

Quantum router as a key device in quantum information processing always attracts researchers' attention. This work suggests a single-photon (SP) router based on one bus-waveguide side coupled to numerous Jaynes-Cummings emitters (JCEs). Each JCE connects with a semi-infinite branch waveguide as an output channel. Different from the commonly used scheme that the JCEs are set in the tuning regime, we here let them work in the large-detuning regime. This change brings about the following amazing benefits for the SP router. Firstly, the number of channels can reach more than a thousand. Secondly, the router is adjustable, that is, the SP can be routed into any output channel on demand. Thirdly, the router has a remarkable monochromaticity. Fourthly, such a SP router can also depress the influence of cavity losses and interferential levels in atoms. Finally, the routing probability can reach approximately $100\mathrm{%}$ for each channel by adding a mirror and a phase shifter to the end of the bus waveguide. This work takes the Rydberg atoms ${}^{87}\mathrm{Rb}$ whose levels can be adjusted by an external electrostatic field as an example to demonstrate the feasibility of the router, which can be applied to quantum informatics.

A Heuristic Remote Entanglement Distribution Algorithm on Memory-Limited Quantum Paths

Remote entanglement distribution plays a crucial role in large-scale quantum networks, and the key enabler for entanglement distribution is quantum routers (or repeaters) that can extend the entanglement transmission distance. However, the performance of quantum routers is far from perfect yet. Amongst the causes, the limited quantum memories in quantum routers largely affect the rate and efficiency of entanglement distribution. To overcome this challenge, this paper presents a new modeling for the maximization of entanglement distribution rate (EDR) on a memory-limited path, which is then transformed into entanglement generation and swapping sub-problems. We propose a greedy algorithm for short-distance entanglement generation so that the quantum memories can be efficiently used. As for the entanglement swapping sub-problem, we model it using an Entanglement Graph (EG), whose solution is yet found to be at least NP-complete. In light of it, we propose a heuristic algorithm by dividing the original EG into several sub-problems, each of which can be solved using dynamic programming (DP) in polynomial time. By conducting simulations, the results show that our proposed scheme can achieve a high EDR, and the developed algorithm has a polynomial-time upper bound and reasonable average runtime complexity.

Controllable single-photon routing between two waveguides by two giant two-level atoms

We investigate the single-photon quantum routing composed of two infinite waveguides coupled to two giant two-level atoms. The exact expressions of the single-photon transmission and reflection amplitudes are derived with the real-space approach. It is found that the single photon scattering behavior is strongly dependent on the phase difference between the two adjacent atom-waveguide coupling points, the frequency detuning, the coupling strength between the two giant atoms, and the interaction strengths between the giant atoms and the waveguides. Our studies show that an ideal single photon router with unit efficiency can be realised by designing the size of the giant atom, and the frequency detuning or adjusting the interaction strengths between the atoms and the waveguides. The results suggest the potential to effectively control the single-photon quantum routing based on the giant-atom setup.

Wavelength Division Multiplexing-Like Quantum Routing for Single Plasmons in the Quantum Dots–Waveguides Hybrid System

Wavelength Division Multiplexing-Like Quantum Routing for Single Plasmons in the Quantum Dots–Waveguides Hybrid System

Performance analysis of all optical-based quantum internet circuits

A Quantum dot implanted within a double-sided optical microcavity is considered and investigated as a critical component for all optical-based quantum internets. Due to the duality as the photonic quantum transistor and gate, the QD cavity system repsents a sturdy base for the future photonic quantum network. With the help of the analytical investigation and review presented in this paper, a quantum dot cavity unit can be developed for implementing deterministic quantum gates and transistors. The maximum fidelity observed for quantum diode, router, and storage is 95.24, 62.06, and 90.42%without considering a noisy environment, respectively, and 62.12, 60.36, and 43.66% under a noisy environment, respectively. Fidelity is also calculated with varying coupling conditions (strong and weak coupling), and optimized cavity parameters are calculated.

Quantum routing of few photons using a nonlinear cavity coupled to two chiral waveguides

We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.

A quantum router architecture for high-fidelity entanglement flows in quantum networks

The past decade has seen tremendous progress in experimentally realizing the building blocks of quantum repeaters. Repeater architectures with multiplexed quantum memories have been proposed to increase entanglement distribution rates, but an open challenge is to maintain entanglement fidelity over long-distance links. Here, we address this with a quantum router architecture comprising many quantum memories connected in a photonic switchboard to broker entanglement flows across quantum networks. We compute the rate and fidelity of entanglement distribution under this architecture using an event-based simulator, finding that the router improves the entanglement fidelity as multiplexing depth increases without a significant drop in the entanglement distribution rate. Specifically, the router permits channel-loss-invariant fidelity, i.e. the same fidelity achievable with lossless links. Furthermore, this scheme automatically prioritizes entanglement flows across the full network without requiring global network information. The proposed architecture uses present-day photonic technology, opening a path to near-term deployable multi-node quantum networks.

Nonreciprocal Phonon Blockade in a Spinning Acoustic Ring Cavity Coupled to a Two-Level System

Quantum nonreciprocal devices have received extensive attention in recent years because they can be used to realize unidirectional quantum routing and noise isolation. In this work, we show that the shift of resonance frequencies of propagating phonons induced by spin-orbit interactions (SOI) of phonons in a rotating acoustic ring cavity can be used to realize nonreciprocal phonon blockade. When driving the cavity from different directions, nonreciprocal single-, two-phonon blockade and phonon-induced tunneling can take place by varying the parameters of the system to an appropriate value. To realize phonon blockade, the sublevels of the lower orbit branch of the ground state of silicon-vacancy (SiV) color centers in the diamond membrane are employed to induce self-interactions of phonons in the cavity. This work provides a way to achieve acoustic nonreciprocal devices, such as directional acoustic switches and quantum noise isolation, which may help acoustic information network processing.

Multi-outlet single photon quantum router between optics and microwave based on a hybrid optomechanical system

A Multi-outlet single photon quantum router between microwave and optical frequency domain is investigated in a system consisting of a superconducting microwave cavity and an optical nanomechanical cavity coupled to a commom nanomechanical resonator (NAMR). It is demonstration that the single-photon of optical frequency can be routed into three different output ports by adjusting microwave power. More importantly, the two output signals can be selected according to microwave power. Meanwhile, we also show that thermal noise will be insignificant for the optical performance of the single-photon router at temperature of the order of 20 mK. Our proposal may have paved a new avenue towards multi-channel router and quantum network.

Realization of Tunable Highly-Efficient Quantum Routing in Chiral Waveguides

The chiral interaction between single photons in waveguides and quantum emitters has gained considerable attention. Here, we proposed a tunable quantum routing scheme with a chiral quantum system by coupling an emitter to two chiral waveguides. Conventional quantum routers can only be achieved with each port output probability no larger than 25%. But our scheme can transfer quantum information arbitrarily from an input port to another, and each port’s output probability is 100%. Besides, we investigated the influence of the Purcell factor in quantum routing properties. No matter how to change the size of the directionalities Sj or set a specific value to the dissipation of the emitter, we always found that the quantum routing has very high efficiency. Moreover, we also used a superconducting qubit coupled to two resonators to show the present scheme is pretty feasible for experimental implementation.

Quantum Routing for Single Plasmons Modulated by the Dipole–Dipole Interaction in a π-Shaped Channel

Quantum Routing for Single Plasmons Modulated by the Dipole–Dipole Interaction in a π-Shaped Channel

Few-photon routing via chiral light-matter couplings

A quantum router is one of the essential elements in the quantum network. Conventional routers only direct a single photon from one quantum channel into another. Here, we propose a few-photon router. The active element of the router is a single qubit chirally coupled to two independent waveguides simultaneously, where each waveguide mode provides a quantum channel. By introducing the operators of the scatter-free space and the controllable space, the output state of the one-photon and two-photon scattering are derived analytically. It is found that the qubit can direct one and two photons from one port of the incident waveguide to an arbitrarily selected port of the other waveguide with unity, respectively. However, two photons cannot be simultaneously routed to the same port due to the anti-bunch effect.

Nonreciprocal single-photon quantum router

The quantum router is an elementary building block in quantum information processing and quantum communication. This work constitutes a step forward in this direction, i.e., an efficient scheme is proposed for the implementation of a nonreciprocal single-photon quantum router, allowing the routing of a single photon from one side but blocking it from the other side. Our model consists of two directly coupled coplanar-waveguide resonators and a superconducting ring resonator, which are connected together through a transmission line. The nonreciprocity is realized by unidirectionally interacting the rotating microwave modes of the ring resonator with a dissipative magnon mode in an yttrium iron garnet disk. We find that a single-photon signal can be delivered from a given input port to either of the two output ports, but is fully absorbed from the opposite one. The proposed scheme not only enriches the family of nonreciprocal quantum devices, but also finds useful applications in chiral quantum technologies.

DQRA: Deep Quantum Routing Agent for Entanglement Routing in Quantum Networks

Quantum routing plays a key role in the development of the next-generation network system. In particular, an entangled routing path can be constructed with the help of quantum entanglement and swapping among particles (e.g., photons) associated with nodes in the network. From another side of computing, machine learning has achieved numerous breakthrough successes in various application domains, including networking. Despite its advantages and capabilities, machine learning is not as much utilized in quantum networking as in other areas. To bridge this gap, in this article, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a novel quantum routing model</i> for quantum networks that employs machine learning architectures to construct the routing path for the maximum number of demands (source–destination pairs) within a time window. Specifically, we present a deep reinforcement routing scheme that is called Deep Quantum Routing Agent (DQRA). In short, DQRA utilizes an empirically designed deep neural network that observes the current network states to accommodate the network’s demands, which are then connected by a qubit-preserved shortest path algorithm. The training process of DQRA is guided by a reward function that aims toward maximizing the number of accommodated requests in each routing window. Our experiment study shows that, on average, DQRA is able to maintain a rate of successfully routed requests at above 80% in a qubit-limited grid network and approximately 60% in extreme conditions, i.e., each node can be repeater exactly once in a window. Furthermore, we show that the model complexity and the computational time of DQRA are polynomial in terms of the sizes of the quantum networks.

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.