Related papers: Polarization Requirements for Ensemble Implementat…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear…
We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…
We propose a passively self-error-rejecting single-qubit transmission scheme for an arbitrary polarization state of a single qubit over a collective-noise channel, without resorting to additional qubits and entanglement. By splitting a…
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…
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for…
A probabilistic version of the Bernstein-Vazirani problem (which is a generalization of the original Bernstein-Vazirani problem) and a quantum algorithm to solve it are proposed. The problem involves finding one or more secret keys from a…
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
The query model has generated considerable interest in both classical and quantum computing communities. Typically, quantum advantages are demonstrated by showcasing a quantum algorithm with a better query complexity compared to its…