The search for information in a system has been a continuous problem for a computer. This has resulted in the construction of a set of classical algorithms that can search for a set of data. This is why search systems can be divided into the type of information being searched, the number of solutions to find, and even the terms used for searching. With the emergence of quantum computing, new algorithms have been generated for this type of process. An example is the Grover algorithm, which performs theoretically better than traditional algorithms. This is why there has been research on optimizing it, applying it to new fields, and making it more accessible to industry users. Even if the algorithm is a promising alternative, one of the disadvantages of Grover’s algorithm is the use of an oracle function that must be generated for every set of search data. This review describes three sets of methodologies for generating quantum circuits that can be applied to constructing this oracle quantum circuit.
The search for information in a system has been a continuous problem for a computer. This has resulted in the construction of a set of classical algorithms that can search for a set of data. This is why search systems can be divided into the type of information being searched, the number of solutions to find, and even the terms used for searching. With the emergence of quantum computing, new algorithms have been generated for this type of process. An example is the Grover algorithm, which performs theoretically better than traditional algorithms. This is why there has been research on optimizing it, applying it to new fields, and making it more accessible to industry users. Even if the algorithm is a promising alternative, one of the disadvantages of Grover’s algorithm is the use of an oracle function that must be generated for every set of search data. This review describes three sets of methodologies for generating quantum circuits that can be applied to constructing this oracle quantum circuit.
We observe an enormous increase in the computational power of digital computers. This was due to the revolution in manufacturing processes and controlling semiconductor structures on submicron scale, ultimately leading to the control of individual atoms. Eventually, the classical electric circuits encountered the barrier of quantum mechanics and its effects. However, the laws of quantum mechanics can be also used to produce computational devices that lead to extraordinary speed increases over classical computers. Thus quantum computing becomes a very promising and attractive research area. The Computer Aided Design for Quantum circuits becomes an essential ingredient for such emerging research which may lead to these powerful computers to be realized—an era of Quantum computing. This thesis presents an integrated theoretical study of software algorithms to design circuits of quantum oracles as well as methods for designing quantum oracles for Grover algorithm to solve combinatorial problems. An implementation of quantum algorithm involves the initialization of the input state and its manipulation with quantum gates followed by the measurements. In Grover algorithm the problem to be solved is specified by a permutative logic oracle – the fundamental problem is then how to build this oracle from quantum logic circuits and how to optimize these circuits. These problems are NP-hard and require search algorithms. In future, the search will be also done in quantum and this thesis leads to quantum algorithms to design quantum circuits more efficiently.
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.
Several prominent quantum computing algorithms—including Grover’s search algorithm and Shor’s algorithm for finding the prime factorization of an integer—employ subcircuits termed ‘oracles’ that embed a specific instance of a mathematical function into a corresponding bijective function that is then realized as a quantum circuit representation. Designing oracles, and particularly, designing them to be optimized for a particular use case, can be a non-trivial task. For example, the challenge of implementing quantum circuits in the current era of NISQ-based quantum computers generally dictates that they should be designed with a minimal number of qubits, as larger qubit counts increase the likelihood that computations will fail due to one or more of the qubits decohering. However, some quantum circuits require that function domain values be preserved, which can preclude using the minimal number of qubits in the oracle circuit. Thus, quantum oracles must be designed with a particular application in mind. In this work, we present two methods for automatic quantum oracle synthesis. One of these methods uses a minimal number of qubits, while the other preserves the function domain values while also minimizing the overall required number of qubits. For each method, we describe known quantum circuit use cases, and illustrate implementation using an automated quantum compilation and optimization tool to synthesize oracles for a set of benchmark functions; we can then compare the methods with metrics including required qubit count and quantum circuit complexity.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.
Many applications such as Graph coloring, Triangle finding, Boolean satisfiability, Traveling salesman problem can be solved by Grover's search algorithm, which is one of the remarkable quantum computing algorithm. To design a quantum circuit for a given quantum algorithm, which involves Grover's search, we need to define an oracle circuit specific to the given algorithm and the diffusion operator for amplification of the desired quantum state. In this paper, we propose a quantum circuit implementation for the oracle of the vertex coloring problem based on Grover's algorithmic approach. To the best of our knowledge, this is a first of its kind approach in regards to the quantum circuit synthesis of the vertex coloring oracle in binary quantum domain. We have performed the synthesis of the proposed oracle circuit for the six commonly available Physical Machine Description (PMD) gate libraries using the Fault Tolerant Quantum Logic Synthesis (FTQLS) tool. The synthesis results have been presented to understand the cost estimation of the oracle circuit for the various PMDs in terms of number of quantum operations and number of cycles.