Related papers: Efficient state preparation for a register of quan…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
Quantum protocols often require the generation of specific quantum states. We describe a quantum algorithm for generating any prescribed quantum state. For an important subclass of states, including pure symmetric states, this algorithm is…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…