Abstract
In a Quantum Walk (QW) the “walker” follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the searching of problem solution spaces faster than with classical random walks, and holds promise for advances in dynamical quantum simulation, biological process modelling and quantum computation. Here we employ a versatile and scalable resonator configuration to realise quantum walks with bright classical light. We experimentally demonstrate the versatility of our approach by implementing a variety of QWs, all with the same experimental platform, while the use of a resonator allows for an arbitrary number of steps without scaling the number of optics. This paves the way for future QW implementations with spatial modes of light in free-space that are both versatile and scalable.
Highlights
Quantum walks (QWs) may arguably be dated back to Feynman and even Dirac [1], but certainly have become topical since the seminal paper by Aharonov et al [2], offering a probability distribution that spreads quadratically faster than that of a classical random walk
Like in a classical random walk, each step of a quantum walk consist of a change of the coin state and a shift of the position of a walker according to the coin state
This was achieved by placing the quarter-wave plates (QWP) with the fast axis at 45 ̊ after the QP while adjusting the fast axis of the half-wave plates (HWP) before the resonator
Summary
Quantum walks (QWs) may arguably be dated back to Feynman and even Dirac [1], but certainly have become topical since the seminal paper by Aharonov et al [2], offering a probability distribution that spreads quadratically faster than that of a classical random walk. Such set-ups have included optical cavities [29], photonic crystal chips [30], and optical fiber time loops [31, 32] In these approaches the walker is directed through physical paths involving multiple interferometers to achieve the interference effect, without the use of a coin degree of freedom, akin to a Galton board. Entanglement (non-separable correlation) between the coin and position degrees-offreedom (DoF) is a necessary requirement In this sense, coined QWs may be considered to act as entanglement generators [36], and the use of classical light to achieve this has been outlined theoretically [37]. Our resonator-type configuration, which is implemented by means of a ring cavity, overcomes scalability and flexibility issues associated with many cascaded step schemes, where the resources scale linearly with the number of steps
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