Flexible distribution of data in the form of quantum bits (qubits) amongst spatially separated entities is an essential component of envisioned scalable quantum computing architectures. Since qubits cannot be copied, this operation of moving qubits can be relatively costly in terms of resources. Moreover, implementation of quantum gates requires precise and extensive classical control and computation too. Accordingly, we consider the problem of dynamically permuting groups of qubits, i.e., qubit packets using reconfigurable quantum switches in which routing information is calculated classically as a possible way to reduce this cost. We design a 2 x 2 switch based on the controlled-swap quantum gate and show that if switch settings are determined using efficient classical algorithms, then quantum switches can be mapped onto classical non-blocking interconnection switch topologies with low cost by using this switch. Specific quantum switch designs for the optimal Benes network and the planar Spanke-Bcnes network are given.
Flexible distribution of data in the form of quantum bits (qubits) amongst spatially separated entities is an essential component of envisioned scalable quantum computing architectures. Since qubits cannot be copied, this operation of moving qubits can be relatively costly in terms of resources. Moreover, implementation of quantum gates requires precise and extensive classical control and computation too. Accordingly, we consider the problem of dynamically permuting groups of qubits, i.e., qubit packets using reconfigurable quantum switches in which routing information is calculated classically as a possible way to reduce this cost. We design a 2 x 2 switch based on the controlled-swap quantum gate and show that if switch settings are determined using efficient classical algorithms, then quantum switches can be mapped onto classical non-blocking interconnection switch topologies with low cost by using this switch. Specific quantum switch designs for the optimal Benes network and the planar Spanke-Bcnes network are given.
Flexible distribution of data in the form of quantum bits or qubits among spatially separated entities is an essential component of envisioned scalable quantum computing architectures. Accordingly, we consider the problem of dynamically permuting groups of quantum bits, i.e., qubit packets, using networks of reconfigurable quantum switches. We demonstrate and then explore the equivalence between the quantum process of creation of packet superpositions and the process of randomly routing packets in the corresponding classical network. In particular, we consider an n × n Baseline network for which we explicitly relate the pairwise input-output routing probabilities in the classical random routing scenario to the probability amplitudes of the individual packet patterns superposed in the quantum output state. We then analyze the effect of using quantum random routing on a classically non-blocking configuration like the Benes network. We prove that for an n × n quantum Benes network, any input packet assignment with no output contention is probabilistically self-routable. In particular, we prove that with random routing on the first (log n-1) stages and bit controlled self-routing on the last log n stages of a quantum Benes network, the output packet pattern corresponding to routing with no blocking is always present in the output quantum state with a non-zero probability. We give a lower bound on the probability of observing such patterns on measurement at the output and identify a class of 2 n-1 permutation patterns for which this bound is equal to 1, i.e., for all the permutation patterns in this class the following is true: in every pattern in the quantum output assignment all the valid input packets are present at their correct output addresses. In the second part of this thesis we give the complete design of quantum sparse crossbar concentrators. Sparse crossbar concentrators are rectangular grids of simple 2 × 2 switches or crosspoints, with the switches arranged such that any k inputs can be connected to some k outputs. We give the design of the quantum crosspoints for such concentrators and devise a self-routing method to concentrate quantum packets. Our main result is a rigorous proof that certain crossbar structures, namely, the fat-slim and banded quantum crossbars allow, without blocking, the realization of all concentration patterns with self-routing. In the last part we consider the scenario in which quantum packets are queued at the inputs to an n × n quantum non-blocking switch. We assume that each packet is a superposition of m classical packets. Under the assumption of uniform traffic, i.e., any output is equally likely to be accessed by a packet at an input we find the minimum value of m such that the output quantum state contains at least one packet pattern in which no two packets contend for the same output. Our calculations show that for m=9 the probability of a non-contending output pattern occurring in the quantum output is greater than 0.99 for all n up to 64.
Quantum networks have the potential to enhance the utility of quantum protocols (for, e.g., cryptography, communication, computation, etc.) by enabling the interoperation of multiple quantum systems. In this paper, we address the distribution of entanglement to the neighbors of a central entanglement source node equipped with a number of sources of entangled photon pairs. A switching network can be an effective component connecting the central node to its neighbors, thus enabling the reconfigurable routing of generated photons. We consider optimal (in terms of insertion loss and the number of component switches) photonic switching networks designed to satisfy the particular requirements of entanglement distribution. We begin by developing a rigorous framework for the study of such entanglement-distribution switching networks. Next, we devise and apply search strategies to design optimal switching networks applicable to entanglement source nodes with 10 or fewer neighbors. Scalable switching networks are then considered for an arbitrarily large number of neighbors, resulting in asymptotically optimal switching fabrics. For all designs, we address efficient routing algorithms for determining a switching-network state that provides the entanglement distribution desired of the switching network at a given time. The combination of optimal switching-network structures and associated efficient routing algorithms addresses a key component of entanglement distribution, thus advancing the state of the art of quantum networks toward practical implementation.
Quantum switching networks are analogs of classical switching networks in which classical switches are replaced by quantum switches. These networks are used to switch quantum data among a set of quantum sources and receivers. They can also be used to efficiently switch classical data, and help overcome some limitations of classical switching networks by utilizing the unique properties of quantum information systems, such as superposition and parallelism. In this thesis, we design several such networks which can be broadly put in the following three categories: 1. Quantum unicast networks: We give the design of quantum Baseline network (QBN) which is a self-routing and unicast quantum packet switch that uses the Baseline topology. The classical version of the network blocks packets internally even when there are no output contentions and each input packet is addressed to a different output. The QBN uses the principles of quantum superposition and parallelism to overcome such blocking. Also, for assignments that have multiple input packets addressed to an output, this network creates a quantum superposition of all these packets on that output, ensuring that all packets have non-zero probabilities of being observed on that output. 2. Quantum concentrators: We introduce a new network called quantum concentrator, which is a key component of our quantum multicasting network design. This concentrator is also an n × n quantum switching network, to be denoted by n-QC, and which, for any m, 1 ≤ m ≤ n, routes arbitrary quantum states on any m of its inputs to its top m outputs. This network uses O(n log n) quantum gates, and has a gate level depth of O(log 2 n). We also give several variations of this network, the main ones being order-preserving and priority quantum concentrators. 3. Quantum multicast networks: We first design a quantum multicasting network, called a generalized quantum connector (GQC) which can be used to multicast quantum information from n input sources to n outputs. Since general quantum states cannot be copied due to the no-cloning theorem, this network actually multicasts superposed classical information packets, contained in a finite number of qubits at each input. Copying needed for such multicasting is obtained by Wootters and Zurek's quantum copying machines or controlled-not gates. This n-input and n-output (n × n) network, to be denoted by n-GQC, is recursively constructed using n/2-GQCs and uses O(n log 2 n) quantum gates. The time complexity of this network in terms of gate level depth is O(log 3 n). We also give two variations of this network which improve its behavior when routing multicast assignments that have multiple input packets contending for same outputs.
We present the design of a self-routing quantum packet switch which improves on a previous design given by the authors [1]. Like the earlier design, this switch too routes packets represented by quantum bits (qubits) but it reduces the routing overhead per packet from O(log N) qubits to O(1) qubits by eliminating the need for an extra "dummy" inputoutput pair and their associated "dummy" packets at each 2 2 internal switch. The quantum self-routing switch creates a superposition of all the maximum size non-blocking subsets of input packets at its outputs, which cannot be achieved by any classical self-routing switching network that is internally blocking. In addition to the network design, we give a method to characterize the output quantum state of the switch using the concepts of frames and balanced matrices.
A switching device is required to build a realistic network which can handle the explosive growth of network traffic. However, the drawback of the switching device is mainly focused on the blocking problem. Previous studies have presented the solutions in the quantum context to avoid blocking at the expense of increasing packet loss and the exponential size of quantum gates. In this paper, we design a fully non-blocking quantum switch using the linear number O(N2) of quantum SWAP gates. Comparisons with a previously proposed quantum self-routing packet switch is also presented in terms of the hardware complexity, the propagation delay and packet loss probability
We present a framework for analyzing random routing on multistage interconnection networks and show its relation to routing on quantum interconnects proposed earlier by the authors. Quantum interconnects operate on quantum bits (qubits) and have the potential to form non-blocking networks with simple routing schemes by exploiting properties like superposition. Broadly speaking, quantum circuits operate probabilistically, and our random routing model on classical networks is a step in the direction of characterizing the design of such quantum networks. Specifically, we use the probability settings for individual switches to obtain the rate matrix for the network and show how this information is automatically encoded by the quantum network in its output state. Also, the inverse problem of finding the switch probability parameters given a rate matrix is shown to have direct relation to quantum interconnect design.