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Digital Switching in Quantum Domain I. –Ming Tsai and Sy-Yen Kuo

Digital Switching in Quantum Domain I. –Ming Tsai and Sy-Yen Kuo. Presented by Chin-Yi Tsai. Outline. Introduction Notation and Preliminaries Digital Switching Networks Digital Quantum Switching Conclusions. Introduction.

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Digital Switching in Quantum Domain I. –Ming Tsai and Sy-Yen Kuo

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  1. Digital Switching in Quantum DomainI. –Ming Tsai and Sy-Yen Kuo Presented by Chin-Yi Tsai

  2. Outline • Introduction • Notation and Preliminaries • Digital Switching Networks • Digital Quantum Switching • Conclusions

  3. Introduction • A switching architecture such that digital data can be switched in the quantum domain. • The proposed mechanism supports unicasting and multicasting. • (interface conversion) The quantum switch can be used to build classical and quantum information networks. • To define the connection digraph which can be used to describe the behavior of a switch at a given time. • The connection digraph can be implemented using elementary quantum gates.

  4. Introduction (cont’d) • Compared with a traditional space or time domain switch, the proposed switching mechanism is much more scalable.

  5. control target Notations and Preliminaries

  6. Qubit Permutation and Replication • A typical permutation P is represented using the symbol • A cycle is basically an ordered list, which is represented as C=(e1, e2, …, en-1, en). • The number of elements in a cycle is called length. • Length 1：trivial cycle • Length 2：transposition • P = (a, d )(c )(b, e, f )=(a, d )(b, e, f )

  7. Qubit Permutation and Replication (cont’d) (transposition circuit)

  8. Qubit Permutation and Replication (cont’d) • For a general n-qubit cycle C=(q0, q1, q2, …, qn-1), it can be done by six layers of CN gates with ancillary qubits. • For an even n (n=2m, m=2, 3, …), we define the following nonoverlapping qubit transpositions as: • The cycle can be implemented using

  9. For the odd n(n=2m+1, m=1, 2, 3, …) n=6 X=(2, 4)(1, 5) Y=(3, 4)(2, 5)(1, 2) n=5 X=(2, 3)(1, 4) Y=(2, 4)(1, 0)

  10. Qubit Replication (FANOUT) • Qubit replication takes one bit as input and gives two copies of the same bit value as output.

  11. Digital Switching Networks • In classical digital communication, switching is needed in order to avoid a fully meshed transmission network. • Digital switching technologies fall under two broad categories: • Circuit switching • Packet switching • In both circuit switching and packet switching, the control subsystem needs to specify the switching configuration

  12. Digital Switching Networks (cont’d) • The switching configuration can be described using a connection digraph. • Definition 1: Given an n x n switch, the connection digraph at time t, Gt={V, Et }, is a digraph such that: • Each represents an I/O port • if and only if a connection exists from the input port vm to the output port vn at time t. • A digraph Gtdescribes the connection status of a switch at a specific time, and is called the connection digraph at time t

  13. Elementary Topologies • The connection digraph can be built from a set of elementary topologies • null point, loopback, queue, cycle, tree, forest

  14. Connection with null points and loopbacks Connection Connection digraph

  15. Queue connection and its connection digraph

  16. Cycle connection and its connection digraph

  17. Tree connection and its connection digraph

  18. Forest connection and its connection digraph

  19. Digital Quantum Switching • The proposed architecture for building a digital quantum switching 0 -> |0> 1 -> |1> |0> -> 0 |1> -> 1

  20. Connection Digraph Implementation • A connection digraph can be implemented using CN gates. • Transformation guideline can be used to implement a connection digraph.

  21. Transformation Guideline • Unicasting and multicasting have different types of connection digraphs • The digraph of a unicast connection has a connection of disjointed null points, loopbacks, queues, and/or cycles as subdigraphs. • However, in the digraph of a multicast connection, subdigraph such as trees and forests are possible.

  22. tree forest Interrelated Connection Topologies Cycle U=YX

  23. forest Cycle Extraction • The process of cycle extraction detaches all the null points, queues • This procedure transforms a forest into one cycle and a collection of null point, queues, and/or trees. • null point and queues  loopback and cycles • Tree  forest

  24. Link Recovery • After each cycle has been implemented, the links that had been cut must be recovered.

  25. Unicast Quantum Switching GC=(q3, q4, q6, q7, q5) GQ=[q0, q1, q2] GC’=(q0, q1, q2)

  26. GC=(q3, q4, q6, q7, q5) X=(q6, q7)(q4, q5) Y=(q6, q5)(q4, q3) (q4, q5)=CN(q4, q5).CN(q5, q4).CN(q4, q5) GC’=(q0, q1, q2) X=(q1, q2) Y=(q1, q0)

  27. Multicast Quantum Switching tree GT=[q0, q1][q1, q4][q1, q3][q3, q5, q2][q3, q6, q7]

  28. Multicast Quantum Switching tree forest

  29. Conclusions • An architecture of digital quantum switching. • The proposed mechanism allows digital data to be switched using a series of quantum operations. • Connection digraph • Null point, queue, cycle, tree, forest

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