Imperial College London
Portrait Picture

Professor Myungshik Kim

Faculty of Natural Sciences, Department of Physics

Chair in Theoretical Quantum Information Sciences
 
 
 
//

Contact

 

+44 (0)20 7594 7754m.kim

 
 
//

Location

 

1202Electrical EngineeringSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Haug:2021:10.1103/PRXQuantum.2.040309,
author = {Haug, T and Bharti, K and Kim, MS},
doi = {10.1103/PRXQuantum.2.040309},
journal = {PRX Quantum},
pages = {1--14},
title = {Capacity and quantum geometry of parametrized quantum circuits},
url = {http://dx.doi.org/10.1103/PRXQuantum.2.040309},
volume = {2},
year = {2021}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of particular initialization strategies. We assess the expressive power of various popular circuit types and find striking differences depending on the type of entangling gates used. Particular circuits are characterized by scaling laws in their expressiveness. We identify a transition in the quantum geometry of the parameter space, which leads to a decay of the quantum natural gradient for deep circuits. For shallow circuits, the quantum natural gradient can be orders of magnitude larger in value compared to the regular gradient; however, both of them can suffer from vanishing gradients. By tuning a fixed set of circuit parameters to randomized ones, we find a region where the circuit is expressive but does not suffer from barren plateaus, hinting at a good way to initialize circuits. We show an algorithm that prunes redundant parameters of a circuit without affecting its effective dimension. Our results enhance the understanding of parametrized quantum circuits and can be immediately applied to improve variational quantum algorithms.
AU  - Haug,T
AU  - Bharti,K
AU  - Kim,MS
DO  - 10.1103/PRXQuantum.2.040309
EP  - 14
PY  - 2021///
SN  - 2691-3399
SP  - 1
TI  - Capacity and quantum geometry of parametrized quantum circuits
T2  - PRX Quantum
UR  - http://dx.doi.org/10.1103/PRXQuantum.2.040309
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000707518900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.040309
UR  - http://hdl.handle.net/10044/1/92426
VL  - 2
ER  -
Download