Magic of Random Matrix Product States

Abstract

Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the $1$-dimensional Random Matrix Product States (RMPSs) using the $L_1$-norm measure. We firstly relate the $L_1$-norm to the $L_4$-norm. We then employ a unitary $4$-design to map the $L_4$-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 $L_1$-norm. This bound grows exponentially with respect to the qudit number $n$, indicating that the $1$D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case.

arXiv comment7 pages, 1 figure + 7 pages, 1 figure + 10 pages

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Cited by in corpus (12)

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• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Clifford Dressed Time-Dependent Variational Principle
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Disentangling magic states with classically simulable quantum circuits
• Maximal Magic for Two-qubit States
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• Nonstabilizerness generation in a multiparticle quantum walk
• On the Hardness of Measuring Magic
• On the stabilizer complexity of Hawking radiation
• High-expressibility Quantum Neural Networks using only classical resources