Quantum Packet Switching

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

2. 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

3. 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.

4. 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?

5. 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 arereversible:

6. 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 2nn-bit binary strings.

7. 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.

8. qubit-1 qubit-2 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.

9. Blocking 000 000 001 000 0 => up 1 => down 000: up, up, up 001: up, up, down 001 001 010 010 011 011 100 100 101 101 110 110 111 111 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 => Blocking possible even for permutation assignments

10. 000 000 001 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Can quantum parallelism help switching? • Question: Can we use quantum parallelism to achieve better switch designs if packets are represented using quantum bits (qubits)?

11. Quantum switch Prob. = |a|2 c=1 Quantum Switch Prob. = |b|2 c=0 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

12. = invalid Prob=1/4 Quantum Baseline Network Binary output address: used to set control qubit • All feasible permutations are present in parallel in output superposition • Observation collapses the state: classical result • How to increase probability of favorable outcome? 11 10 00 01

13. Routing stage Randomization stage 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

14. Probability filter Routing stage 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. > 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

15. 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

16. 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.

17. Applying quantum search for changing permutation probabilities: an example • 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. Desired output • tag qubit = 0 else tag qubit = 1 Routing Stage 11 00 00 11 00 10 01 10 01 11 01 10 10 10 01 00 10 00 11 01 11 01 00 11 Co-eff = 1/√2 Co-eff = 1/(2√2) =>Prob. = 1/2 Self-route =>Prob. = 1/8 each Randomize 7/5√2 -1/10√2

18. 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.