Related papers: Discrimination of unitary transformations in the D…
A new approach to the implementation of a quantum computer by high-resolution nuclear magnetic resonance (NMR) is described. The key feature is that two or more line-selective radio-frequency pulses are applied simultaneously. A three-qubit…
The well-known Deutsch Algorithm (DA) and Deutsch-Jozsha Algorithm (DJA) both are used as an evidence to the power of quantum computers over classical computation mediums. In these theoretical experiments, it has been shown that a quantum…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
A scheme to execute an n-bit Deutsch-Jozsa (D-J) algorithm using n qubits has been implemented for up to three qubits on an NMR quantum computer. For the one and two bit Deutsch problem, the qubits do not get entangled, hence the NMR…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate…
The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to…
We show that one can implement the Deutsch-Josza algorithm, one of the first and simplest quantum algorithms, in a fault-tolerant manner using the smallest quantum error-detecting code -- the $[[4,2,2]]$ code -- without any ancillae. We…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or…
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…
We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there are no standard ways to…
A hybrid model of the Deutsch-Jozsa algorithm is presented, inspired by the proposals of hybrid computation by S. Lloyd and P. van Loock et. al. The model is based on two observations made about both the discrete and continuous algorithms…
Using the Deutsch-Jozsa algorithm, we will develop a method for solving a class of problems in which we need to determine parts of an array and then apply a specified function to each independent part. Since present quantum computers are…
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then…
Quantum information processing has been one of the pillars of the new information age. In this sense, the control and processing of quantum information plays a fundamental role, and computers capable of manipulating such information have…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
In 1985, David Deutsch challenged the Church-Turing thesis by stating that his quantum model of computation "could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine". While this is…