Related papers: Several natural BQP-Complete problems
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
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 computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum…
We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of time-independent, constant-norm, 2-local…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
We demonstrate the superior capabilities of the recently proposed Lorentz quantum computer (LQC) compared to conventional quantum computers. We introduce an associated computational complexity class termed bounded-error Lorentz quantum…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
It is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various…
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…