Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks

Abstract

The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call "directionally-biased". Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated. Keywords: quantum walks; linear optics; quantum information processing 2 of 32The increase in dimensionality enables employing and manipulating more information, and this needs to be achieved in a coherent way. Optical networks are constructed to perform this task by constructing higher dimensional unitary matrices. It is known that higher dimensional unitary matrices can be decomposed using lower dimensional unitary matrices. By repeating this procedure, any complex unitary matrix can be eventually decomposed using only two-dimensional ones. The Reck decomposition model has been introduced to describe this procedure [11]. A symmetric version of the Reck model is often called the Clements model [12]. For instance, these two models have been used by researchers in designing and building experimental linear-optical networks for boson sampling purposes [13][14][15][16]. During the boson sampling process, photons propagate from one side of a complex nodal structure to the other side of the optical network, thus performing a computational task. Direct implementation of multimode optical device has been experimentally verified in integrated platforms [17][18][19][20]. Quantum walks over the network of quantum nodes represent another form of quantum information processing, as an alternative to the quantum gate model. QW can also perform certain computations more efficiently than classical algorithms [6,[21][22][23][24][25][26][27][28]. Quantum walks in 1D and 2D systems have been experimentally demonstrated in optical systems [29][30][31][32][33][34][35][36][37][38][39][40].The traditional quantum walk approach uses a coin operator and a shift operator to execute each elementary step. An alternative description of a quantum walk can be impl...

Implementation of a 3 x 3 directionally-unbiased linear optical multiport

“…Let us consider a 3×3 linear optical multiport as shown in Fig. 1(a) and (b) where a tritter is a 3 × 3 BS based on a fused optical fiber [22]. These multiports form an interferometer to control an amplitude distribution among input and output modes using phase shifters.…”

Higher-dimensional Hong-Ou-Mandel effect and state redistribution with linear-optical multiports

“…A photon can enter any of the four ports, and exit at any of the four ports (labeled as a, b, c, and d). With a specific choice of phase settings, a Grover matrix can be realized by coherently summing all possible paths to each output [31]. A schematic symbol for this device is shown on the right.…”

“…Theoretical analysis of the reversible Grover matrix has been performed by linear-optical directionally-unbiased four-ports [31,38,39], which consist of four beam splitters, four phase shifters, and four mirrors as indicated in Fig. 2(a).…”

Interferometry and higher-dimensional phase measurements using directionally unbiased linear optics

“…But beam splitters are essentially one-way devices: the photons can never reverse direction to exit at the same port from which they entered. Recently, optical multiports have been studied [8][9][10][11] that do not share this directional bias: light entering a given port can exit at any port, including the one through which it entered. The three-port versions of these unbiased multiports have been implemented in bulk devices in two different manners in [9] and [11], while plans are currently…”