Download A Quantum self-Routing Packet Switching

A Quantum selfRouting Packet
Switching
Manish Kumar Shukla, Rahul Ratan and A. Yavuz Oruc,
Department of Electrical and Computer Engineering,
University of Maryland, College Park.
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Abstract
• Use quantum superposition and
entanglement to obtain non-blocking
switches with efficient routing schemes
and low crosspoint complexity
• Design a self-routing network using
quantum circuits/gates based on Banyan
network
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Outline
•
•
•
•
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Introduction
Preliminary
Quantum Switch
Quantum Banyan Network
Concluding Remarks And Future Work
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Introduction
• non-blocking: An interconnection network is can route all
possible one-to-one input-output mappings
• Many non-blocking interconnection networks exist but
either their crosspoint complexity is high
• An N×N Banyan network is composed of log(N) stage ,
each having N/2 switches and is self-routing
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• Self-routing: The routing decision for a packet at any
stage in the network is made solely on the basis of the
output address in the packet’s haeader
N
2
• Banyan network: (N/2)log(N) switches and N states
• As a result , a Banyan network cannot route N!  N
permutation maps
N
2
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• Contention occur
1.Classical network: random packet drops
2.Quantum network: Using quantum superposition
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Preliminary
• Qubits and Superposition
• Quantum gates
• Self-routing interconnection networks
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Qubits and Superposition
• A qubits state is a vector in a two dimensional complex
Hilbert space
• A qubit can also exist in a superposition of the ‘0’ and ‘1’
states
• Qubit: qubit ‘s state can be written as x  a 0  b 1 , a, b  C
where a  b 1 and
2
2
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Quantum Gates
• The Hadamard gate’s transformation matrix
H
1 1 1 


2 1 - 1
• The CCN gate’s operation and figure
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Self-routing interconnection networks
• A network has self-routing property if a packet can be
routed by only knowing its input and output address ,
and nothing about other packets’ output address
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• A packet is routed to the lower output of a switch , at the
th
th
i stage if the i most significant address bit is ‘1’ and
to the upper output if the bit is ‘0’
I
0
 O5 addressbit : 101
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Quantum Switch
• The switch gate
• A 2×2 Quantum switch
• Quantum switch with Dummy input
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A switch gate
• The basic building block of the quantum switch is a
quantum gate , which we call a switch gate(Fig)
n
1
n
Cin  0 : through  state
If n=2
Cin  1 : cross  state
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• For n=1 , matrix representation of this gate in the
computational basis control1, t arg et 1, t arg et  2 is
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• We use the switch gate to superpose the packets that
contend for one output of a 2×2 switch and to route the
superposition on the output
• For example n=1 , if the control qubit of the gate is set in
1
( 0  1 ) then the action of the gate is
2
1
1
(0 1)x y 
(0 x y 1 y x )
2
2
• Also , if we observe packet x at one of the outputs then
packet y will be observed with certainty at the other
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A 2×2 Quantum switch
th
• The input packets of a 2×2 switch at the i stage are in
th
contention for an output link if the i most significant
bits of their address are same
• The purpose of our quantum switch is to remove this
blocking in the network so that the two contending
packets can be routed in parallel on the same link using
quantum superposition
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• A simple design for such a 2×2 switch is in below
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• Even though this design creates a superposition of the
contending packets at desired output , a complementary
superposition is created on the other output also which is
undesirable
• Even if we go ahead and make a Banyan network using
this switch , the outputs of the network might receive
packets that are not addressed to them
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• Also , it will not be possible to verify whether the
received packet was intended for that output or not
because the output address bits are removed by the
nodes of the network
• We can overcome the problem of verifying the received
packets by keeping a copy of the output address in the
data portion of the packet
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Quantum switch with Dummy input
• Redesign the switch by introduction a dummy inputoutput pair
• The undesirable superposition mentioned in pre-section
is dumped on the dummy output
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• The switch is show in below
I 3 is always fed with dummy packets which are distinguishable from data packet
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• To keep the dummy packets distinguishable from data
packets , the following scheme is used
(1) The address bits of the data-packets are replicated
(2) The address part of the dummy packets is formed by
repeating ‘01’ (P/2)-1 times , where the P is the number
of bits in the address part of packets at I 1 and I 2
(3) The first bit of the data part is also used for
distinguishing between data and dummy packets .
This bit is set to ‘0’ in the dummy packets and to ‘1’ in
data packets
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• The quantum circuit for this switch is show in below
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• (a) When A1,A2= (00,11) or (00,01) or (01,11) or (01,01) ,
all the switch gates act in through state , the function of
the circuit is (Di is a dummy packet on Ii , i=1,2)
switch  state :
A , A ,P ,P ,D
1
2
1
2
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• (b) When A1,A2 = (11,00) or (11,01) or (01,00) ,thus
S1 ,S2 and S3 act in through state and S4 is cross state ,
the function of circuit is
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• (c) When A1,A2 = (00,00)
• The function of circuit is
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• (d) When A1,A2 = (11,11)
• The function of the circuit is
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• When contention occurs ,a superposition of the input
packets is sent to their intended output and a dummy
packet is sent on the other output
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Quantum Banyan network
• A 4×4 quantum Banyan network is show in below
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• Suppose inputs 0,1,2,3 have packets for outputs 3,2,0,1
• The packets are represented by the tuple (A,P)
P: data part
A: address part (represent address bits ‘00’ , ‘11’ and ‘01’
by ‘0’ , ‘1’ and ‘d’ )
• Thus the packets at the four inputs are (11,P3) , (10,P2)
(00,P0) and (01,P1)
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• The input state A is
• The state at location B is
• The output state is
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• If we do a measurement at the outputs of the switch , we
will observe one of the tuple in the above expression
with probability 1/4 each
• The probability of observing packet Pi , i=0,1,2,3 at
output i is 1/2
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Concluding remarks and future work
• A simple measurement destroys this superposition and
gives only one such output sub-permutation , which is
equivalent to classical routing through a Banyan network
with random packet drops in case of contention
• Another direction would be to extend our result to more
powerful switching structure such as the Benes and Clos
networks
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