Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Journal Article · Mon Nov 08 00:00:00 EST 2021 · PRX Quantum

DOI:https://doi.org/10.1103/PRXQuantum.2.040327· OSTI ID:1829532

Volkoff, Tyler ; Holmes, Zoë; Sornborger, Andrew

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1829532
• Alternate ID(s): OSTI ID: 1841941
• Report Number(s): LA-UR-21-24060; PQRUAG; 040327
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Vol. 2 Journal Issue: 4; ISSN 2691-3399
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
quantum algorithms
quantum machine learning
continuous variables