EXPLOITING QUANTUM TELEPORTATION IN QUANTUM CIRCUIT MAPPING

Stefan Hillmich, Alwin Zulehner, and Robert Wille Johannes Kepler University Linz, Austria [email protected], [email protected] http://iic.jku.at/eda/research/quantum_dd QUANTUM COMPUTING

 Basic unit is the qubit with basis states 0 and 1  Utilize quantum mechanical effects  Superposition: 휑 = 훼 ⋅ 0 + 훽 ⋅ |1〉, where |훼|2 + |훽|2 = 1  Entanglement: operation on one qubit may affect other qubits  Measurement: Collapse wavefunction and read result

 Allows for exponential speedup in the best case  Integer factorization  Database search  Quantum chemistry  …

2 QUANTUM COMPILATION

Conceptional algorithm

Limited Gate Set

Synthesis

Limited Connectivity

Mapping

Limited Fidelity and Coherence

Optimizations

3 EFFICIENT MAPPING SATISFYING THE COUPLING CONSTRAINT

Target Device  IBM QX4  Different approaches for mapping  Trade-off runtime vs quality of result

Naïve Approach Heuristics Approach Minimal Approach

4 SWAP-BASED MAPPING WITH LAYERS

 General idea: partition into layers  Find locally optimal permutations 휋푖  Map layers successively (푙0휋1푙1휋2푙2)  Use A* search to cope with complexity  Fix mapping at beginning

logical qubits physical qubits

5 QUANTUM TELEPORTATION

 Transport the state of a qubit over arbitrary distances  Requires some setup and a channel for 2 conventional bit

 Can be exploited for quantum circuit mapping  Create Bell-Pair  Bell-Pair is moved during regular SWAP operations  Teleport qubit via Bell-Measurement when beneficial  Re-create Bell-Pair

6 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)

7 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

8 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume 푄12 and 푄17 are prepared

9 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume 푄12 and 푄17 are prepared  and moving during mapping

10 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume 푄12 and 푄17 are prepared  and moving during mapping

11 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume Bell-Pair (푄2, 푄17)  Virtual edges

12 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume Bell-Pair (푄2, 푄17)  Virtual edges

13 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs

 Assume Bell-Pair (푄2, 푄17)  Virtual edges

14 MAPPING WITH QUANTUM TELEPORTATION

 Example IBM Q Tokyo 20 qubits

 Operation CNOT(푄3, 푄16)  Baseline: 2 SWAPs Quantum Teleportation may be used as a  Assume Bell-Pair (푄2, 푄17)complementary technique to existing  Virtual edges mapping approaches

 Larger search space for potentially cheaper mappings

15 RESULTS

 Teleportation allows to move qubits over arbitrary distances with constant costs* (requires suitable positioned Bell-Pairs)

 Experiments showed by up to around 20% improved costs for IBM Q Tokyo

 We predict larger improvements with larger architectures

16 CONCLUSIONS

 Mappings should be as effective as possible to avoid unnecessary operations

 Quantum teleportation provides a complementary approach to augment existing methods, enlarging the search space

 Quantum teleportation will have a bigger impact on architectures with larger distances

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