Implementation of quantum permutation algorithm with classical light

Abstract

We report the experimental implementation of quantum permutation algorithm using polarization and orbital angular momentum of the classical optical beam. The easy-handling optical setup to realize all eight cyclic permutation transformations for an input four-dimensional system has been constructed. The two-to-one speed-up ratio to determine the parity of each permutation has been demonstrated. Moreover, we have theoretically discussed the extension to the case with eight elements, and the limitations on the generalization of our proposal to higher-dimensional cases. Our scheme exhibits outstanding stability and demonstrates that optical quantum computation is possible using classical states of light.

Analog Programmable‐Photonic Computation

“…However, in contrast to quantum computing, in APC we will not be able to perform instantaneous non‐local operations (i.e., the entanglement of multiple anbits) because the underlying physical laws are deterministic, [ 53 ] a computational limitation that is also shared by any classical emulation of quantum computing. [ 32–40 ]…”

“…However, in contrast to quantum computing, in APC we will not be able to perform instantaneous non-local operations (i.e., the entanglement of multiple anbits) because the underlying physical laws are deterministic, [53] a computational limitation that is also shared by any classical emulation of quantum computing. [32][33][34][35][36][37][38][39][40] Furthermore, taking into account the vector formalism required to describe an anbit and its mathematical similitude with a qubit, let us introduce at this point the use of Dirac's notation [43,54,55] in order to: (i) simplify the mathematical calculations when designing complex APC computing architectures and (ii) extrapolate diverse analysis and design strategies from quantum computing, preserving the same notation between both computation theories. Therefore, from now on, let us express the anbit as |𝜓⟩ = 𝜓 0 |0⟩ + 𝜓 1 |1⟩, with 𝝍 ≡ |𝜓⟩, ‚ e 0 ≡ |0⟩, and ‚ e 1 ≡ |1⟩.…”

“…[4,6,11,[28][29][30] Being PIP a hardware technology that naturally performs matrix transformations on optical signals, and whose building block may be designed by using a mathematical framework similar to quantum computing [31] (based on matrix transformations of the quantum bits or qubits, which are respectively the gates and the units of information in quantum computation), one could ask whether a classical version of quantum computing might be proposed within the realm of classical wave-optics. Different attempts have been reported revolving around this idea in order to: [32][33][34][35][36][37][38][39][40] (i) simulate a quantum computer with a classical computer and (ii) dig into the fundamental differences between quantum and classical systems. However, to our knowledge, the quantum computing formalism has never been extrapolated to a classical scenario to construct an analog computing landscape based on deterministic physical laws.…”

Optical Realization of Wave-Based Analog Computing with Metamaterials

“…In addition, the quantum optical system do not need extremely cold temperatures to function. The central idea of quantum optical computing is that quantum information can be encoded by different degrees of freedom of photons (e.g., polarization, orbital angular momentum, spatial and temporal modes), by utilizing the common properties shared by both classical optics and quantum mechanics, such as superposition and interference, it is possible to simulate certain quantum behaviors with classical light [37,39,40,42,43,45,[48][49][50][51][52][53][55][56][57][58][59]62,67,153].…”

State transfer with separable optical beams and variational quantum algorithms with classical light

“…The proposed experimental setups accomplish the same task without the need for a single photon source, which is hard to prepare [33]. There are many more quantum phenomena and algorithms that have been simulated with classical light, but not necessarily with OAM modes [34][35][36][37][38][39][40][41][42]. For a detailed review of classical entanglement, one may refer to [29] and references therein.…”