Related papers: Quantum Branching Programs and Space-Bounded Nonun…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational…
Different platforms for quantum computation are currently being developed with a steadily increasing number of physical qubits. To make today's devices practical for quantum software engineers, novel programming tools with maximal…
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…
We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
The parameters of a quantum system grow exponentially with the number of involved quantum particles. Hence, the associated memory requirement goes well beyond the limit of best classic computers for quantum systems composed of a few dozen…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
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…
Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their…
In the future, quantum computers will become widespread and a network of quantum repeaters will provide them with end-to-end entanglement of remote quantum bits. As a result, a pervasive quantum computation infrastructure will emerge, which…