Related papers: Classical Complexity of Unitary Transformations
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
We present conditions for the efficient simulation of a broad class of optical quantum circuits on a classical machine: this class includes unitary transformations, amplification, noise, and measurements. Various proposed schemes for…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Model-independent semantic requirements for user specification and interpretation of data before and after quantum computations are characterized. Classical computational costs of assigning classical data values to quantum registers and to…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
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…
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…
The classical approximation may be applied to a number of problems in non-equilibrium field theory. The principles and limits of classical real-time lattice simulations are presented, with particular emphasis on the definition of particle…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.