Preparing Dicke States on a Quantum Computer
Chandra Sekhar Mukherjee, Subhamoy Maitra, Vineet Gaurav, Dibyendu Roy
Abstract
Exact requirement of controlled NOT (CNOT) and single-qubit gates to implement a quantum algorithm in a given architecture is one of the central problems in this computational paradigm. In this article, we take a tutorial approach in explaining the preparation of Dicke states (|D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> 〉) using concise realizations of partially defined unitary transformations. We show how to efficiently implement the state-of-the-art deterministic Dicke state preparation circuits and in turn optimize them in terms of CNOT and single-qubit gate counts. We explain theoretical ideas in reducing the gate counts and observe how these improvements are reflected in actual implementation of the circuits. To emphasize the advantages, we describe the circuit for preparing |D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> 〉 on the “ibmqx2” machine of the IBM quantum experience (QX) service. Our approach shows that the error induced due to noise in the system is lesser in comparison to the existing works. We conclude by describing the CNOT map of the generic |D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> 〉 preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its effect on the induced error in the Noisy Intermediate Scale Quantum environment.