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Deterministic Preparation of Dicke States

  • Andreas BärtschiEmail author
  • Stephan Eidenbenz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11651)

Abstract

The Dicke state Open image in new window 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 \(\mathcal {O}(kn)\) gates, has depth \(\mathcal {O}(n)\) 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.

Notes

Acknowledgments

We thank Yiğit Subaşı for helpful discussions.

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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.National Security Education CenterLos Alamos National LaboratoryLos AlamosUSA

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