Quantum State Engineering Using One-dimensional Discrete-time Quantum Walks

Abstract

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin, and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

Dynamical learning of a photonics quantum-state engineering process

“…This confirms that the adopted algorithm can reach performances compatible or even superior with respect to the one obtained with the direct method presented in Ref. 24 that consider ideal experimental platforms. In this sense, the algorithm can take into account and compensate for the experimental imperfections.…”

“…). Following the engineering protocol presented in, 11,24 we project the coin degree of freedom at the end of the evolution, so that our target state is some |φ target ∈ H W .…”

“…In fig. 3-b we report, for each engineered state, the ratio between the fidelities found by the RBFOpt algorithm, and those found using the method presented in 24 to find the optimal values of the parameters. Indeed, as demonstrated in Ref.…”

“…[16][17][18][19][20][21][22][23] In particular, engineering of arbitrary qudit states has been experimentally demonstrated with QWs in the Orbital Angular Momentum (OAM) and polarization degrees of freedom of light. 11,24,25 In the paraxial approximation, the angular momentum of light can be decomposed in spin angular momentum, also referred to as polarization in this context, and OAM, which is related to the spatial transverse structure of the electromagnetic field. [26][27][28] In the classical regime, OAM finds application in particle trapping, 29 microscopy, 30,31 metrology, 32 imaging [33][34][35] and communication.…”

“…This platform was shown to be able to engineer arbitrary target quantum states. 11,24 Such approach, however, requires full knowledge of the inner workings of the underlying experimental apparatus. This feature makes it harder to flexibly adapt a protocol to the perturbations arising in realistic noisy conditions.…”