Related papers: Checking Equivalence of Quantum Circuits and State…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and…
The magnificence grandeur of quantum computing lies in the inherent nature of quantum particles to exhibit true parallelism, which can be realized by indubitably fascinating theories of quantum physics. The possibilities opened by quantum…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
Driven by potential exponential speedups in business, security, and scientific scenarios, interest in quantum computing is surging. This interest feeds the development of quantum computing hardware, but several challenges arise in…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We introduce a local concept of speed-up applicable to intermediate stages of a quantum algorithm. We use it to analyse the complementary roles played by quantum parallel computation and quantum measurement in yielding the speed-up. A…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Software under test can be analyzed dynamically, while it is being executed, to find defects. However, as the number and possible values of input parameters increase, the cost of dynamic testing rises. This paper examines whether quantum…
Quantum computers facing chaos. Quantum parallelism allows to perform computation in a radically new manner. A quantum computer based on these new principles may resolve certain problems exponentially faster than a classical computer. We…
Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the…