Magic of Random Matrix Product States
POSTER
Abstract
Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing.
In this paper, we study the magic of the 1-dimensional Random Matrix Product States (RMPSs) using the L1-norm measure. We firstly relate the L1-norm to the L4-norm. We then employ a unitary 4-design to map the L4-norm to a 24-component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the L1-norm. This bound grows exponentially with respect to the qudit number n, indicating that the 1D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case.
In this paper, we study the magic of the 1-dimensional Random Matrix Product States (RMPSs) using the L1-norm measure. We firstly relate the L1-norm to the L4-norm. We then employ a unitary 4-design to map the L4-norm to a 24-component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the L1-norm. This bound grows exponentially with respect to the qudit number n, indicating that the 1D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case.
* This work was supported in part by ARO Grant W911NF-19-1-0302, ARO MURI Grant W911NF-20-1-0082, and NSF Eager Grant 2037687.
Publication: https://arxiv.org/abs/2211.10350
Presenters
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Liyuan Chen
Harvard University
Authors
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Liyuan Chen
Harvard University
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Arthur M Jaffe
Harvard University
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Roy Garcia
Harvard University
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Kaifeng Bu
Harvard University