Authors:
Shintaro Narisada
;
Shohei Beppu
;
Kazuhide Fukushima
and
Shinsaku Kiyomoto
Affiliation:
KDDI Research, Inc., Fujimino, Japan
Keyword(s):
Dicke State, Hamming Weight, Noisy Computation, Quantum Circuit, Quantum Computing, Generalization.
Abstract:
A Dicke state is a superposition of n-qubit with Hamming weight k, denoted by D^n_k. Dicke states are frequently employed to prepare input superpositions for quantum search algorithms (e.g., Grover search and quantum walks) that solve combinatorial problems with a certain number (n k) of candidate solutions. Bärtschi and Eidenbenz propose a concrete quantum circuit to construct the Dicke state D^n_k with polynomial quantum gates, and they generalize the circuit in terms of Hamming weight k to prepare a superposition of Dicke states. Subsequently, Esser et al. present another quantum circuit to generate the Dicke state D^n_k with polynomial gates and a few auxiliary quantum bits. In this paper, we generalize Esser’s state preparation circuit to construct a superposition of Dicke states. We conduct a concrete comparison with two generalized Dicke state preparation circuits. We perform noisy simulations and experiments using real quantum machines from the IBM quantum experience service
(IBMQ). Both circuits successfully construct the generalized Dicke state superposition using a noisy intermediate-scale quantum (NISQ) device, albeit somewhat affected by noise.
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