Related papers: Experimental Realization of an Order-Finding Algor…
Quantum query complexity is typically characterized in terms of XOR queries |x,y> to |x,y+f(x)> or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is…
We present an efficient exact quantum algorithm for order finding problem when a multiple $m$ of the order $r$ is known. The algorithm consists of two main ingredients. The first ingredient is the exact quantum Fourier transform proposed by…
Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We report the experimental implementation of Grover's quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled spin-1/2…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit…
Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
We propose and experimentally realize an algorithmic benchmark that demonstrates coherent control with a sequence of quantum operations that first generates and then decodes the cat state (|000...>+|111...>)/sqrt(2) to the standard initial…
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure…
We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN).…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…
Theoretical Quantum Information Processing (QIP) has matured from the use of qubits to the use of qudits (systems having states> 2). Where as most of the experimental implementations have been performed using qubits, little experimental…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…