We present an experimental realization of the first iteration in Grover's quantum algorithm using classical light and linear optical elements. The algorithm serves to find an entry marked by an oracle in an unstructured database. In our scheme, the quantum states encoding the database are represented by helical modes generated by means of a Spatial Light Modulator, while the marking corresponds to a π phase shift of the hidden mode. The optical implementation of Grover's algorithm then selectively amplifies the intensity of the marked mode such that it can be revealed by a modal decomposition. The core of the algorithm – a geometrical reflection of the point representing all database entries – is implemented in a single step independent of the size of the database. Moreover, we demonstrate experimentally that one iteration of the algorithm is enough to identify the marked entry, as a consequence of using classical states of light.
We present an experimental realization of the first iteration in Grover's quantum algorithm using classical light and linear optical elements. The algorithm serves to find an entry marked by an oracle in an unstructured database. In our scheme, the quantum states encoding the database are represented by helical modes generated by means of a Spatial Light Modulator, while the marking corresponds to a π phase shift of the hidden mode. The optical implementation of Grover's algorithm then selectively amplifies the intensity of the marked mode such that it can be revealed by a modal decomposition. The core of the algorithm – a geometrical reflection of the point representing all database entries – is implemented in a single step independent of the size of the database. Moreover, we demonstrate experimentally that one iteration of the algorithm is enough to identify the marked entry, as a consequence of using classical states of light.
Standard quantum computation proceeds via the unitary evolution of physical qubits (twolevel systems) that carry the information.A remarkably different model is one-way quantum computing where a quantum algorithm is implemented by a set of irreversible measurements on a large array of entangled qubits, known as the cluster state.The order and sequence of these measurements allow for different algorithms to be implemented.With a large enough cluster state and a method in which to perform single-qubit measurements the desired computation can be realised.We propose a potential implementation of one-way quantum computing using qubits encoded in the orbital angular momentum degree of freedom of single photons.Photons are good carriers of quantum information because of their weak interaction with the environment and the orbital angular momentum of single photons offers access to an infinite-dimensional Hilbert space for encoding information.Spontaneous parametric down-conversion is combined with a series of optical elements to generate a four-photon orbital angular momentum entangled cluster state and single-qubit measurements are carried out by means of digital holography.The proposed set-up, which is based on an experiment that utilised polarised photons, can be used to realise Grover's search algorithm which performs a search through an unstructured database of four elements.Our application is restricted to a two-dimensional subspace of a multi-dimensional system, but this research facilitates the use of orbital angular momentum qubits for quantum information processing and points towards the usage of photonic qudits (multi-level systems).We also review the application of Dirac notation to paraxial light beams on a classical and quantum level.This formalism is generally employed in quantum mechanics but the analogy with paraxial optics allows us to represent the classical states of light by means of Dirac kets.An analysis of the analogy between the classical and quantum states of light using this formalism, is presented.i Declaration 1 -Plagiarism I, Humairah Bassa declare that 1.The research reported in this dissertation, except where otherwise indicated, is my original research.2. This dissertation has not been submitted for any degree or examination at any other university.3. This dissertation does not contain other persons' data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons.4. This dissertation does not contain other persons' writing, unless specifically acknowledged as being sourced from other researchers.Where other written sources have been quoted, then: a. Their words have been rewritten but the general information attributed to them has been referenced.
The essential operations of a quantum computer can all be accomplished using only standard linear optical elements (e.g., beamsplitters, waveplates, polarizers, etc.), with the individual bits represented by different spatial orpolarization degrees of freedom. The difference from a genuine quantum computer with distinct entangleable registers is that the optical implementation requires a number of elements which grows exponentially with the number of bits. However, by “compiling” the code, and making multiple use of redundant components, the required number of elements can be substantially reduced, allowing the realization of quantum algorithms involving several bits. Here we present a simple optical implementation of Grover’s algorithm for efficiently searching a database. In our example a database of four elements is searched with a single query, in contrast to the classical expected value of 2.25 queries. It is seen that the “quantum” computer in this case is no more than an interferometer, albeit a complicated one. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Photonic quantum technologies have become pivotal in the implementation of communication, imaging, and computing modalities. Among these applications, quantum ghost imaging (GI) exploits photon correlations to surpass classical limits, with recent advances in spatial-mode encoding and phase imaging. In parallel, all-optical computing offers powerful, passive-light processing capabilities. Here, we explore the intersection of these domains, revealing a conceptual and operational link between GI and Grover’s quantum search algorithm, which is designed to search for elements in an unstructured database. Here, the elements are encoded as phases in the position basis states of photons. To show this, we use entangled photon pairs, with one photon encoding the oracle features, while the other photon is used to find the marked element.
Grover's search algorithm is a well-known quantum algorithm that has been extensively studied and improved to increase its success rate and enhance its flexibility. However, most improved search algorithms require an adjustment of the oracle, which may not be feasible in practical problem-solving scenarios. In this work, we report an experimental demonstration of a deterministic quantum search for multiple marked states without adjusting the oracle. A linear optical setup is designed to search for two marked states, one in a 16-state database with an initial equal-superposition state and the other in an 8-state database with different initial nonequal-superposition states. The evolution of the probability of finding each state in the database is also measured and displayed. Our experimental results agree well with the theoretical predictions, thereby proving the feasibility of the search protocol and the implementation scheme. This work is a pioneering experimental demonstration of deterministic quantum search for multiple marked states without adjusting the oracle.
Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The original formulation of Grover's algorithm is non-deterministic, finding the answer with a probability that varies with the size of the search space and the number of marked elements. A recent reformulation introduced a deterministic form of Grover's algorithm that - in principle - finds the answer with certainty. Here we realise the deterministic Grover's algorithm on a programmable photonic integrated circuit, finding that it not only outperforms the original Grover's algorithm as predicted, but is also markedly more robust against technological imperfections. We explore databases of 4 to 10 elements, with every choice of a single marked element, achieving an average success probability of 99.77±0.05%.
Orbital angular momentum (OAM) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires O(N) number of optical elements for 2N OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.