Digital Switching in Quantum DomainDigital Switching in Quantum DomainI. –Ming Tsai and Sy-Yen KuoI. –Ming Tsai and Sy-Yen Kuo

Presented by Chin-Yi Tsai Presented by Chin-Yi Tsai

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OutlineOutline IntroductionIntroduction

Notation and PreliminariesNotation and Preliminaries

Digital Switching NetworksDigital Switching Networks

Digital Quantum SwitchingDigital Quantum Switching

ConclusionsConclusions

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IntroductionIntroduction A switching architecture such that digital data can A switching architecture such that digital data can

be switched in the quantum domain.be switched in the quantum domain.

The proposed mechanism supports The proposed mechanism supports unicastingunicasting and and multicastingmulticasting..

(interface conversion)(interface conversion) The quantum switch can The quantum switch can be used to build classical and quantum information be used to build classical and quantum information networks.networks.

To define the To define the connection digraphconnection digraph which can be used which can be used to describe the behavior of a switch at a given time.to describe the behavior of a switch at a given time.

The connection digraph can be implemented using The connection digraph can be implemented using elementary quantum gateselementary quantum gates..

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Introduction (cont’d)Introduction (cont’d) Compared with a traditional space or time domain Compared with a traditional space or time domain

switch, the proposed switching mechanism is much switch, the proposed switching mechanism is much more scalable.more scalable.

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Notations and PreliminariesNotations and Preliminaries

1

0

21

20

10

|

1||||

1|0||

c

c

cc

cc

2

3

1

0

3

2

1

0

3

2

1

0

0100

1000

0010

0001

c

c

c

c

c

c

c

c

c

c

c

c

CN

control

target

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Qubit Permutation and ReplicationQubit Permutation and Replication A typical permutation A typical permutation PP is represented using the is represented using the

symbolsymbol

A A cyclecycle is basically an ordered list, which is is basically an ordered list, which is represented as represented as CC=(e=(e11, e, e22, …, e, …, en-1n-1, e, enn).).

The number of elements in a cycle is called The number of elements in a cycle is called lengthlength.. Length 1Length 1 ：： trivial cycletrivial cycle Length 2Length 2 ：： transpositiontransposition

P P = (= (aa, , d d )()(c c )()(bb, , ee, , f f )=()=(aa, , d d )()(bb, , ee, , f f ))

.

b

f

f

e

a

d

c

c

e

b

d

aP

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Qubit Permutation and Replication Qubit Permutation and Replication (cont’d)(cont’d)

11|10|01|00|,| 11100100 cccc

))(,)((

11|11|

01|10|

10|01|

00|00|

11100100 ccccP

(transposition circuit)

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Qubit Permutation and Replication Qubit Permutation and Replication (cont’d)(cont’d)

For a general For a general n-qubit cyclen-qubit cycle C=( C=(qq00, , qq11, , qq22, …, , …, qqn-1n-1), it ), it can be done by six layers of CN gates with ancillary can be done by six layers of CN gates with ancillary qubits.qubits.

For an For an eveneven n (n=2m, m=2, 3, …), we define the n (n=2m, m=2, 3, …), we define the following nonoverlapping following nonoverlapping qubit transpositionsqubit transpositions as: as:

The cycle can be implemented usingThe cycle can be implemented using

),)(,(),(

),)(,(),(

01121

112211

qqqqqqY

qqqqqqX

nmm

nnmm

YXU

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For the odd n(n=2m+1, m=1, 2, 3, …)For the odd n(n=2m+1, m=1, 2, 3, …)

),)(,(),(

),)(,(),(

01122

11221

qqqqqqY

qqqqqqX

nmm

nnmm

n=6X=(2, 4)(1, 5)Y=(3, 4)(2, 5)(1, 2)

n=5X=(2, 3)(1, 4)Y=(2, 4)(1, 0)

1010

Qubit Replication (FANOUT)Qubit Replication (FANOUT) Qubit replication takes one bit as input and Qubit replication takes one bit as input and

gives two copies of the same bit value as gives two copies of the same bit value as output.output.

1111

Digital Switching NetworksDigital Switching Networks In classical digital communication, switching is In classical digital communication, switching is

needed in order to avoid a fully meshed needed in order to avoid a fully meshed transmission network.transmission network.

Digital switching technologies fall under two Digital switching technologies fall under two broad categories:broad categories: Circuit switchingCircuit switching Packet switchingPacket switching

In both circuit switching and packet switching, In both circuit switching and packet switching, the control subsystemthe control subsystem needs to specify the needs to specify the switching configurationswitching configuration

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Digital Switching Networks (cont’d)Digital Switching Networks (cont’d) The switching configuration can be The switching configuration can be

described using a connection digraph.described using a connection digraph.

Definition 1Definition 1: Given an : Given an n n x x n n switch, the switch, the connection digraph at time connection digraph at time tt, , GGtt ={={VV, , EEt t }, is }, is a digraph such that:a digraph such that: Each represents an I/O port Each represents an I/O port

if and only if a connection exists from if and only if a connection exists from the input port vthe input port vmm to the output port v to the output port vnn at time at time t.t.

A digraph A digraph GGtt describes the connection status describes the connection status of a switch at a specific time, and is called of a switch at a specific time, and is called the connection digraph at time tthe connection digraph at time t

)1,1,0( niVvi

tnm Evv

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Elementary TopologiesElementary Topologies The connection digraph can be built from a The connection digraph can be built from a

set of elementary topologiesset of elementary topologies null point, loopback, queue, cycle, tree, forestnull point, loopback, queue, cycle, tree, forest

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Connection with null points and Connection with null points and loopbacksloopbacks

Connection digraphConnection

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Queue connection and its connection Queue connection and its connection digraphdigraph

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Cycle connection and its connection Cycle connection and its connection digraphdigraph

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Tree connection and its connection Tree connection and its connection digraphdigraph

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Forest connection and its connection Forest connection and its connection digraphdigraph

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Digital Quantum SwitchingDigital Quantum Switching The proposed architecture for building a digital The proposed architecture for building a digital

quantum switchingquantum switching

0 -> |0>1 -> |1>

|0> -> 0 |1> -> 1

2020

Connection Digraph ImplementationConnection Digraph Implementation A connection digraph can be implemented A connection digraph can be implemented

using CN gates.using CN gates.

Transformation guideline can be used to Transformation guideline can be used to implement a connection digraph.implement a connection digraph.

2121

Transformation GuidelineTransformation Guideline Unicasting and multicasting have different Unicasting and multicasting have different

types of connection digraphstypes of connection digraphs

The digraph of a The digraph of a unicastunicast connection has a connection has a connection of disjointed connection of disjointed null pointsnull points, , loopbacksloopbacks, , queuesqueues, and/or , and/or cyclescycles as as subdigraphs.subdigraphs.

However, in the digraph of a However, in the digraph of a multicastmulticast connection, subdigraph such as connection, subdigraph such as treestrees and and forestsforests are possible. are possible.

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Interrelated Connection TopologiesInterrelated Connection Topologies

forest

tree

CycleU=YX

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Cycle ExtractionCycle Extraction The process of cycle extraction detaches all the The process of cycle extraction detaches all the

null points, queuesnull points, queues

This procedure transforms a forest into one cycle This procedure transforms a forest into one cycle and a collection of null point, queues, and/or and a collection of null point, queues, and/or trees.trees.

null point and queues null point and queues loopback and cycles loopback and cycles Tree Tree forest forest

forest

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Link RecoveryLink Recovery After each cycle has been implemented, the After each cycle has been implemented, the

links that had been cut must be recovered.links that had been cut must be recovered.

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Unicast Quantum SwitchingUnicast Quantum SwitchingGC=(q3, q4, q6, q7, q5)GQ=[q0, q1, q2]

GC’=(q0, q1, q2)

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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)

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Multicast Quantum SwitchingMulticast Quantum Switching

treeGT=[q0, q1][q1, q4][q1, q3][q3, q5, q2][q3, q6, q7]

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Multicast Quantum SwitchingMulticast Quantum Switching

tree forest

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ConclusionsConclusions An architecture of digital quantum switching.An architecture of digital quantum switching.

The proposed mechanism allows digital data The proposed mechanism allows digital data to be switched using a series of quantum to be switched using a series of quantum operations.operations.

Connection digraphConnection digraph Null point, queue, cycle, tree, forestNull point, queue, cycle, tree, forest