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 Do you have any questions? 17.