Related papers: The Halting Problem for Quantum Computers
Although the current information revolution is still unfolding, the next industrial revolution is already rearing its head. A second quantum revolution based on quantum technology will power this new industrial revolution with quantum…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
Quantum computing relies on processing information within a quantum system with many continuous degrees of freedom. The practical implementation of this idea requires complete control over all of the 2^n independent amplitudes of a…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
In this survey, we aim to explore the fundamental question of whether the next generation of artificial intelligence requires quantum computing. Artificial intelligence is increasingly playing a crucial role in many aspects of our daily…
Two of the major obstacles to achieve quantum computing (QC) are (i) scalability to many qubits and (ii) controlled connectivity between any selected qubits. Using Josephson charge qubits, here we propose an experimentally realizable method…
Quantum computers promise massive computational speedup for problems in many critical domains, such as physics, chemistry, cryptanalysis, healthcare, etc. However, despite decades of research, they remain far from entering an era of…
We study design challenges associated with realizing a ground state quantum computer. In such a computer, the energy gap between the ground state and first excited state must be sufficiently large to prevent disruptive excitations. Here, an…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
We address the problem of checking query containment, a foundational problem in database research. Although extensively studied in theory research, optimization opportunities arising from query containment are not fully leveraged in…
Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…
Quantum computers are becoming real, and they have the inherent potential to significantly impact many application domains. We sketch the basics about programming quantum computers, showing that quantum programs are typically hybrid…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…