Related papers: Quantum Algorithmic Gate-Based Computing: Grover Q…
The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the…
Quantum architecture search (QAS) is desired to construct a powerful and general QAS platform which can significantly accelerate quantum advantages in error-prone and depth limited quantum circuits in today Noisy Intermediate-Scale Quantum…
This study proposes a GPA for designing optimal Quantum Sensor Circuits (QSCs) to address complex quantum physics problems. The GPA consists of two parts: the Quantum Policy Evaluation (QPE) and the Quantum Policy Improvement (QPI). The QPE…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
We present QCAM, a quantum analogue of Content-Addressable Memory (CAM), useful for finding matches in two sequences of bit-strings. Our QCAM implementation takes advantage of Grover's search algorithm and proposes a highly-optimized…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum…
The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of…
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…
Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
Quantum Machine Learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources…