TY - JOUR
T1 - Tomography and generative training with quantum Boltzmann machines
AU - Kieferová, Mária
AU - Wiebe, Nathan
PY - 2017/12/22
Y1 - 2017/12/22
N2 - The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP, provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.
AB - The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP, provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.
UR - http://www.scopus.com/inward/record.url?scp=85039840831&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.96.062327
DO - 10.1103/PhysRevA.96.062327
M3 - Article
VL - 96
SP - 1
EP - 13
JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information
JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information
SN - 2469-9926
IS - 6
M1 - 062327
ER -