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

Introduction The goal of our research is to use the unique properties of quantum systems to explore the design of efficient and novel switching systems 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 What: Why:

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.

Quantum Computing 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. What if bits were “superposed” together?

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:

Multi-qubit system State of multi-qubit system obtained by taking tensor product of individual qubit vectors Same applies for multiple qubits, i.e., an n-qubit quantum system can be a superposition of 2 n n-bit binary strings. equivalently,

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.

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. qubit-1qubit-2

Classical Networks Blocking => up 1 => down 000: up, up, up 001: up, up, down “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 => Blocking possible even for permutation assignments

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

Quantum switch Works as a classical switch when c is “0” or “1” Quantum Switch Has a “combined” state in addition to classical switch states Classical Switch Works in either “through” or “cross” states Works in a superposition of “through” and “cross” states when control qubit c is in a superposition of “0” and “1” Prob. = |a| 2 Prob. = |b| 2 c=1 c=0

Quantum Baseline Network Prob=1/4 Binary output address: used to set control qubit = invalid All feasible permutations are present in parallel in output superposition Observation collapses the state: classical result How to increase probability of favorable outcome?

Challenges Randomization stage Routing stage 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 Two stage model (First approach):

Challenges… Routing stage Probability filter 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. > 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 Two stage model (Second approach):

Probability Filter Stage: Grover-like search One Grover iteration consists of two blocks: U a followed by U s U a flips the sign of the desired component and U s inverts the coefficients about the average, i.e., Flip sign of a invert about avg.

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.

Applying quantum search for changing permutation probabilities: an example  tag qubit = 0 else tag qubit = 1 Co-eff = 1/(2√2 )Co-eff = 1/√2 Desired output =>Prob. = 1/2 =>Prob. = 1/8 each Randomize Self-route Routing Stage 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. 7/5√2-1/10√2

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.