Lower bounding the description complexity of quantum states
IQC Math and CS Seminar featuring Chinmay Nirkhe - IBM ZOOM watch party in QNC 1201
Quantum states wear many hats in quantum information: they simultaneously generalize distributions from classical complexity theory, describe quantum mechanical phenomena, and capture the complexity of quantum computation. This myriad of roles makes understanding the complexity of quantum states a central question in quantum complexity theory. In this talk, we will explore the complexity of classically describing physically relevant quantum states. In particular, we will discuss the complexity of ground states and low-energy states of local Hamiltonians. This talk is based on recent progress on the NLTS problem [1], QCMA vs QMA [2], and search-to-decision for QMA [3].
[1] NLTS Hamiltonians from good quantum codes. A. Anshu, N. Breuckmann, and C. Nirkhe.
[2] A classical oracle separation between QMA and QCMA. A. Natarajan and C. Nirkhe.
[3] Quantum search-to-decision and the state synthesis problem. S. Irani, A. Natarajan, C. Nirkhe, S. Rao, and H. Yuen.
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