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Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
Quantum computing (QC) holds the promise of revolutionizing problem-solving by exploiting quantum phenomena like superposition and entanglement. It offers exponential speed-ups across various domains, from machine learning and security to…
As a general framework, Matrix Exponential Dimensionality Reduction (MEDR) deals with the small-sample-size problem that appears in linear Dimensionality Reduction (DR) algorithms. High complexity is the bottleneck in this type of DR…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…