Supersymmetry and Quantum Computation

• URL: http://arxiv.org/abs/2011.01239v2
• Date: Tue, 25 May 2021 13:09:10 GMT
• Title: Supersymmetry and Quantum Computation
• Authors: P. Marcos Crichigno
• Abstract summary: The interplay between supersymmetry and classical and quantum computation is discussed. Concrete examples, including the supersymmetric SYK model and fermion hard-core models are discussed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore intractable. Then, the notions of supersymmetry in the space of qubits and supersymmetric quantum circuits are introduced and some of their properties discussed. In particular, it is shown that these define a nontrivial subclass of quantum algorithms with robustness properties typical of supersymmetric systems. Concrete examples, including the supersymmetric SYK model and fermion hard-core models are discussed. Some applications and open questions are suggested.

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