Learning Adaptive Quantum State Tomography with Neural Networks & Differentiable Programming Stanislav Fort Stanford University (prev. Google Research) [email protected] stanford.edu/~sfort1/ @stanislavfort Primarily based on arXiv 1812.06693 Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Primarily based on arXiv 1812.06693, in review Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Primarily based on arXiv 1812.06693, in review Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA AI, ML, DL & differentiable programming ● Artificial intelligence: The science of making machines smart ● Machine learning: Machines getting smart from data ● Deep learning: Machines getting smart from data using deep neural networks as functional approximators ● Differentiable programming: Taking partial derivatives through programs, not restricted to deep neural networks as functions Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA AI, ML, DL & differentiable programming ● Artificial intelligence: The science of making machines smart ● Machine learning: Machines getting smart from data ● Deep learning: Machines getting smart from data using deep neural networks as functional approximators ● Differentiable programming: Taking partial derivatives through programs, not restricted to deep neural networks as functions Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA AI, ML, DL & differentiable programming ● Artificial intelligence: The science of making machines smart ● Machine learning: Machines getting smart from data ● Deep learning: Machines getting smart from data using deep neural networks as functional approximators ● Differentiable programming: Taking partial derivatives through programs, not restricted to deep neural networks as functions Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA AI, ML, DL & differentiable programming ● Artificial intelligence: The science of making machines smart ● Machine learning: Machines getting smart from data ● Deep learning: Machines getting smart from data using deep neural networks as functional approximators ● Differentiable programming: Taking partial derivatives through programs, not restricted to deep neural networks as functions Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Differentiable programming Heat equation example ∂ Bridging ML & scientific computing ∂ temperature field Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Differentiable programming Quantum games example ∂ ∂ quantum game strategy Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Writing down a solution vs learning a solution Bubble sort (explicit) Image classification (learned) f( )= “tortoise” Translation (much better when learned) Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Writing down a solution vs learning a solution Even solving symbolic math Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Machine learning Learning to get faster (& better) heuristics Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Machine learning Learning to get faster (& better) heuristics Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Network & data structure How to induce the correct learning prior? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ? ? ? (Adaptivity) Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ? ?? ?? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first ? ? ?? ?? ? ?? ??? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first N ? ? ?? ? ?? ??? ? ?? ???? ? ? ? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first N ?? ? ??? ?? ????? ? ? ?? ??? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography Pure states first N ?? ? ??? ?? ????? ? ? ?? ??? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Quantum state tomography What is difficult? N ?? ? ??? ?? ????? ? ? ?? ??? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Pure states → density matrices Pure states Density matrices Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA What do we care about? 1) How precisely can you reconstruct the unknown state, given N copies of the unknown state? 2) How much compute does it take? Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Regular Quantum State Tomography Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Regular Quantum State Stage 1: Take measurementsTomography Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Regular Quantum State TomographyStage 2: Process them Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Regular Quantum State Tomography Problem: Measurements expensive Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Adaptive Quantum State Tomography Ferenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895 Stage 1: Take measurements up to t Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Adaptive Quantum State Tomography Ferenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895 Stage 2: Determine the next POVM Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Adaptive Quantum State Tomography Particle bank maintaining and update Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Adaptive Quantum State Tomography Particle bank maintaining and update Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA Adaptive Quantum State Tomography Particle bank resampling Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming