Quantum Packet Switching

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Quantum Packet Switching
A. Yavuz Oruç Department of Electrical and
Computer Engineering University of Maryland,
College Park
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Introduction
What

• The goal of our research is to use the unique
  properties of quantum systems to explore the
  design of efficient and novel switching systems

Why

• Quantum computing is an emerging and exciting
  field of research and its application to
  designing switching networks presents a
  challenging and interesting research problem
• This investigation could lead to new insights
  into switch design because of the utilization of
  quantum properties like superposition and
  entanglement

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How is quantum switching different?

• Quantum systems can operate simultaneously on a
  superposition of multiple states, giving inherent
  parallelism.
• They also provide inherent randomization which
  has been an important tool in many classical
  networks
• Can manipulate probability amplitudes via quantum
  circuits
• Phenomenon of entanglement can be used to create
  correlation between random states this has no
  classical analogue.

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Quantum Computing

• What if bits were superposed together?

• Classical bit 0 or 1 only
• Qubit can be in a superposition of both
  where and
• Measurement (w.r.t.) basis ( , ) affects
  the state or collapses it and we get 0 or 1 where
  
• Superposition implies both 0 and 1 states are
  encoded in qubit. In other words, 0 and 1 coexist
  within a qubit until it is collapsed to one of
  the two values.

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Quantum Gates

• A qubit is a vector in , i.e.,
• Operations on qubits done by quantum gates all
  gates are unitary transformations.
• Gates represented by unitary matrices, e.g.,
  Hadamard
• Unitary evolution of qubits implies that all
  quantum computations are reversible

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Multi-qubit system

• State of multi-qubit system obtained by taking
  tensor product of individual qubit vectors

equivalently,

• Same applies for multiple qubits, i.e., an
  n-qubit quantum system can be a superposition of
  2n n-bit binary strings.

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Why superpose bits?

• Superposition provides a natural process for
  parallel computations by way of unitary
  transformations on qubits.
• What happens is that the operations which we
  would perform on a string of binary bits in
  classical computing can be applied to all such
  strings all at once.
• These strings can represent numbers in a
  spreadsheet, vertices in a graph, instructions in
  computer programs, etc., and if processing such
  lists of strings or objects all at once can be
  useful then superposing bits makes sense.
• In our case, we superpose permutations/sets of
  qubit packets.

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Entanglement of qubits

• If a state with two or more qubits cannot be
  expressed as a tensor product of these qubits
  then qubits are entangled , e.g

We can describe the state of both qubits
together but not one qubit individually they are
correlated or entangled

• Can be thought of as a communication setup
  between the two qubits.
• A very important application of entanglement is
  quantum teleportation.

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Classical Networks

• Classical sparse switches (with log N stages)
  have low cost but block routes
• Easier routing on such switches, can use
  oblivious (self-routing) routing

Paths are unique gt Blocking possible even for
permutation assignments
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Can quantum parallelism help switching?

• Question Can we use quantum parallelism to
  achieve better switch designs if packets are
  represented using quantum bits (qubits)?

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Quantum switch
Prob. a2
c1
Quantum Switch
Prob. b2
c0
Has a combined state in addition to classical
switch states
Works as a classical switch when c is 0 or 1
Classical Switch
Works in a superposition of through and cross
states when control qubit c is in a superposition
of 0 and 1
Works in either through or cross states
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Quantum Baseline Network
Binary output address used to set control qubit
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10
00
01

• All feasible permutations are present in parallel
  in output superposition
• Observation collapses the state classical result
• How to increase probability of favorable outcome?

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Challenges
Two stage model (First approach)

• Create a quantum superposition of packet
  permutations and drive it to a state in which
  the probability of permutations which can be
  easily/self routed in the next stage is maximized
• Use entanglement to achieve above

• Self-route the packet superposition at the output
  of the first stage.
• All the permutations at the output of
  randomization stage gets routed in parallel.
• With high probability desired permutation is
  observed

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Challenges
Two stage model (Second approach)

• Create a quantum superposition of packet
  permutations and route them.
• Output state has desired output permutation with
  non-zero probability.
• This is a randomized non-blocking network any
  input permutation always gives desired
  permutation in output superposition state w/
  prob. gt 0

• Use Grover search like approach on output state
  of previous stage to boost the probability of the
  desired output permutation.
• With high probability desired permutation is
  observed

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Probability Filter Stage Grover-like search

• One Grover iteration consists of two blocks Ua
  followed by Us
• Ua flips the sign of the desired component and Us
  inverts the coefficients about the average, i.e.,

invert about avg.
Flip sign of a
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Applying quantum search for filtering permutation
probabilities

• We apply quantum search on tag qubits.
• There is one tag qubit per packet in a
  permutation. Each packet permutation in the
  superposition has a corresponding tag state of N
  qubits.
• A tag qubit is reset by the routing stage when
  the corresponding packet is routed incorrectly.
• We do a quantum search for tag state
  , which corresponds to correct routing.

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Applying quantum search for changing permutation
probabilities an example

• tag qubit 0
• else tag qubit 1

Desired output
Routing Stage
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00
00
11
00
10
01
10
01
11
01
10
10
10
01
00
10
00
11
01
11
01
00
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Co-eff 1/(2v2 )
Co-eff 1/v2
gtProb. 1/2
gtProb. 1/8 each
Self-route
Randomize

• 1 iteration of Grover search for the tag state
  1111 (corres. to desired output) on the output
  state of routing stage
• Coefficients become and ,
  i.e., Prob. 49/50 and 1/200 respectively.

7/5v2
-1/10v2
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Concluding Remarks

• Quantum mechanics provides an exciting research
  frontier for creating systems that can operate on
  large collections of data all at once. This, so
  called quantum parallelism, has the prospect to
  revolutionize packet switching leading to
  contention free packet switching.
• Our research has just scratched the surface, and
  further exploration of quantum packet switching
  is likely to form the basis for quantum packet
  switching and routing systems.