Discovering pragmatic and efficient approaches to construct ε-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior ε-approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the ε-approximate processes and the exact symmetries in a semicoherent context—where measurements occur at each logical clock cycle. We draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.
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September 2024
Research Article|
September 26 2024
Semicoherent symmetric quantum processes: Theory and applications
Yan Wang
;
Yan Wang
a)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing)
Computational Sciences and Engineering Division, Oak Ridge National Laboratory
, Oak Ridge, Tennessee 37831, USA
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Sarah Chehade
;
Sarah Chehade
b)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Writing – original draft, Writing – review & editing)
Computational Sciences and Engineering Division, Oak Ridge National Laboratory
, Oak Ridge, Tennessee 37831, USA
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Eugene Dumitrescu
Eugene Dumitrescu
c)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing)
Computational Sciences and Engineering Division, Oak Ridge National Laboratory
, Oak Ridge, Tennessee 37831, USA
Search for other works by this author on:
a)
Electronic mail: wangy2@ornl.gov
b)
Electronic mail: chehades@ornl.gov
c)
Electronic mail: dumitrescuef@ornl.gov
AVS Quantum Sci. 6, 033805 (2024)
Article history
Received:
April 26 2024
Accepted:
July 30 2024
Citation
Yan Wang, Sarah Chehade, Eugene Dumitrescu; Semicoherent symmetric quantum processes: Theory and applications. AVS Quantum Sci. 1 September 2024; 6 (3): 033805. https://doi.org/10.1116/5.0215919
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