Related papers: Composing Quantum Algorithms
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…
Quantum applications are most often hybrid, i.e. they are not only made of implementations of pure quantum algorithms but also of classical programs as well as workflows and topologies as key artifacts, and data they process. Since…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
A generic approach for compiling any classical block compression algorithm into a quantum block compression algorithm is presented. Using this technique, compression asymptoticaly approaching the von Neumann entropy of a qubit source can be…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
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…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
To implement quantum algorithms on a quantum computer, we must overcome the twin problems of fault-tolerance -- how can we realize a relatively noiseless computation by cleverly combining noisy components? -- and compilation -- how can we…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…