This paper describes a method for using Grovers algorithm to create a quantum vector database, the database stores embeddings based on Controlled-S gates, which represent a binary numerical value. This value represents the embeddings value. The process of creating meaningful embeddings is handled by a classical computer and the search process is handled by the quantum computer. This search approach might be beneficial for a large enough database, or it could be seen as a very qubit-efficient (super dense) way for storing data on a quantum computer, since the proposed circuit stores many embeddings inside one quantum register simultaneously.
This paper describes a method for using Grovers algorithm to create a quantum vector database, the database stores embeddings based on Controlled-S gates, which represent a binary numerical value. This value represents the embeddings value. The process of creating meaningful embeddings is handled by a classical computer and the search process is handled by the quantum computer. This search approach might be beneficial for a large enough database, or it could be seen as a very qubit-efficient (super dense) way for storing data on a quantum computer, since the proposed circuit stores many embeddings inside one quantum register simultaneously.
Abstract The steadily growing research interest in quantum computing—together with the accompanying technological advances in the realization of quantum hardware—fuels the development of meaningful real-world applications, as well as implementations for well-known quantum algorithms. One of the most prominent examples till today is Grover’s algorithm, which can be used for efficient search in unstructured databases. Quantum oracles that are frequently masked as black boxes play an important role in Grover’s algorithm. Hence, the automatic generation of oracles is of paramount importance. Moreover, the automatic generation of the corresponding circuits for a Grover quantum oracle is deeply linked to the synthesis of reversible quantum logic, which—despite numerous advances in the field—still remains a challenge till today in terms of synthesizing efficient and scalable circuits for complex Boolean functions. In this paper, we present a flexible method for automatically encoding unstructured databases into oracles, which can then be efficiently searched with Grover’s algorithm. Furthermore, we develop a tailor-made method for quantum logic synthesis, which vastly improves circuit complexity over other current approaches. Finally, we present another logic synthesis method that considers the requirements of scaling onto real world backends. We compare our method with other approaches through evaluating the oracle generation for random databases and analyzing the resulting circuit complexities using various metrics.
The steadily growing research interest in quantum computing - together with the accompanying technological advances in the realization of quantum hardware - fuels the development of meaningful real-world applications, as well as implementations for well-known quantum algorithms. One of the most prominent examples till today is Grover's algorithm, which can be used for efficient search in unstructured databases. Quantum oracles that are frequently masked as black boxes play an important role in Grover's algorithm. Hence, the automatic generation of oracles is of paramount importance. Moreover, the automatic generation of the corresponding circuits for a Grover quantum oracle is deeply linked to the synthesis of reversible quantum logic, which - despite numerous advances in the field - still remains a challenge till today in terms of synthesizing efficient and scalable circuits for complex boolean functions. In this paper, we present a flexible method for automatically encoding unstructured databases into oracles, which can then be efficiently searched with Grover's algorithm. Furthermore, we develop a tailor-made method for quantum logic synthesis, which vastly improves circuit complexity over other current approaches. Finally, we present another logic synthesis method that considers the requirements of scaling onto real world backends. We compare our method with other approaches through evaluating the oracle generation for random databases and analyzing the resulting circuit complexities using various metrics.
Grover’s algorithm harnesses the power of quantum computing to swiftly locate specific elements in an unstructured database, outperforming classical computers in tasks like database searching. This algorithm capitalizes on the unique ability of qubits to be in both 0 and 1 states simultaneously (superposition), allowing it to scan the entire search space at once. It then boosts the probability of the target element, making it more prominent. While the foundational concepts of Grover’s algorithm are well-documented, practical implementation using quantum operators, especially for large search spaces, remains less explored beyond basic examples with a small number of qubits. Existing general synthesis techniques often involve numerous operators or are time-consuming. Our proposed methods specifically address the amplitude-amplification component of Grover’s algorithm for any size of search space. These methods detail the required types and quantities of qubits and operators, emphasizing minimal usage and efficient assembly. Developed and evaluated in Python, our methods consistently identified target elements with over 95% accuracy and achieved configurations comparably compact as those in the existing literature but at a faster pace. We anticipate that these methods facilitate practical implementations of Grover’s algorithm across various domains.
Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.
In the classical model of a computer, the most fundamental building block, the bit, can only exist in one of two distinct states, a 0 or a 1. Computations are carried out by logic gates that act on these bits to produce other bits. Unless there is duplicate (parallel) hardware, only one problem instance (i.e. input data set) can be handled at a time. In this classical computing, increasing the number of bits increases the complexity of the problem and the time necessary to arrive at a solution. A quantum algorithm consists of a sequence of operations on a register, to transform it into a state which, when measured, yields the desired result with high probability. An n-bit quantum register can store an exponential amount of information. This paper aims at taking advantage of the superiority of quantum computing over classical computing to solve the problem of searching unstructured databases for a particular item or more than one item in good time. The general aim of this work is to establish the correctness and optimality of Grover’s quantum database search algorithm compared against classical database search methods in order to investigate the superiority or otherwise of quantum computing over classical computing. This is followed by a simulation of the algorithm using a classical computer, namely through functions that are present in MATLAB, referred to as “Quantum Computing Functions”. Povzetek: Clanek predstavlja implementacijo kvantnega iskanja v nestrukturiranih bazah.
A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.