Related papers: Quantum Mechanics of Stochastic Systems
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
The paper investigates the non-local property of quantum mechanics in the quantum hydrodynamic analogy (QHA) given by Madelung. The role of the quantum potential in generating the non-local dynamics of quantum mechanics is analyzed. The…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
Quantum theory is based on a mathematical structure totally different from conventional arithmetic. Due to the symmetric nature of bosonic particles, annihilation or creation of single particles translates a quantum state depending on how…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…