Deterministic Preparation of Dicke States

2019/04/15 by Andreas Bärtschi, Stephan Eidenbenz · 2 citations
Physics and Astronomy · Computer Science · #quant-ph #cs.DS

paper · pdf · doi:10.1007/978-3-030-25027-0_9

published as 22nd International Symposium on Fundamentals of Computation Theory, FCT'19, 126-139, 2019

arxiv created 2019/04/15 · arxiv updated 2020/08/27

Abstract

The Dicke state |D_kⁿ⟩ is an equal-weight superposition of all n-qubit states with Hamming Weight k (i.e. all strings of length n with exactly k ones over a binary alphabet). Dicke states are an important class of entangled quantum states that among other things serve as starting states for combinatorial optimization quantum algorithms. We present a deterministic quantum algorithm for the preparation of Dicke states. Implemented as a quantum circuit, our scheme uses O(kn) gates, has depth O(n) and needs no ancilla qubits. The inductive nature of our approach allows for linear-depth preparation of arbitrary symmetric pure states and -- used in reverse -- yields a quasilinear-depth circuit for efficient compression of quantum information in the form of symmetric pure states, improving on existing work requiring quadratic depth. All of these properties even hold for Linear Nearest Neighbor architectures.

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