Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.

arXiv:quant-ph/0703146Mar 16, 20071 citation

Special section on frontier of quantum computing

Mary Inaba, Takeshi Koshiba, Tomohiro Ogawa +2 more

IEICE Transactions on Fundamentals of Electronics Communications and Computer SciencesJan 1, 20090 citations

Computation in finitary stochastic and quantum processes

Karoline Wiesner, James P. Crutchfield

arXiv:quant-ph/0608206Physica D Nonlinear PhenomenaFeb 5, 200827 citations

Optimal lower bound for lossless quantum block encoding

George Androulakis, Rabins Wosti

Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two positive integers $m$ and $l$ . We encode any tensor product of $m$ many states emitted by the quantum stochastic source by breaking the tensor product into $m$ many blocks where each block has length $l$ , and considering sequences of $m$ many isometries so that each isometry encodes one of these blocks into the Fock space, followed by the concatenation of their images. We only consider certain sequences of such isometries that we call \lq\lq special block codes\rq\rq\ in order to ensure that the string of encoded states is uniquely decodable. We compute the minimum average codeword length of these encodings which depends on the quantum source and the integers $m$ , $l$ , among all possible special block codes. Our result extends the result of [Bellomo, Bosyk, Holik and Zozor, Scientific Reports 7.1 (2017): 14765] where the minimum was computed for one block, i.e.\ for $m=1$ . Lastly, we give a simplified non-adaptive compression technique based on constrained special block codes for general quantum stochastic sources. For quantum stationary sources in particular, we show that the minimum average codeword length per symbol computed over all constrained special block codes is equal to the von-Neumann entropy rate of the source for an asymptotically long block size.Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two positive integers $m$ and $l$. We encode any tensor product of $m$ many states emitted by the quantum stochastic source by breaking the tensor product into $m$ many blocks where each block has length $l$, and considering sequences of $m$ many isometries so that each isometry encodes one of these blocks into the Fock space, followed by the concatenation of their images. We only consider certain sequences of such isometries that we call \lq\lq special block codes\rq\rq\ in order to ensure that the string of encoded states is uniquely decodable. We compute the minimum average codeword length of these encodings which depends on the quantum source and the integers $m$, $l$, among all possible special block codes. Our result extends the result of [Bellomo, Bosyk, Holik and Zozor, Scientific Reports 7.1 (2017): 14765] where the minimum was computed for one block, i.e.\ for $m=1$. Lastly, we give a simplified non-adaptive compression technique based on constrained special block codes for general quantum stochastic sources. For quantum stationary sources in particular, we show that the minimum average codeword length per symbol computed over all constrained special block codes is equal to the von-Neumann entropy rate of the source for an asymptotically long block size.

arXiv:2305.18748Quantum Information and ComputationNov 1, 20240 citations

On the Study of Quantum Computing

Myo Myo Aung

Oct 30, 20190 citations

Symplectic structure of quantum phase and stochastic simulation of qubits

Yu. P. Rybakov, T. F. Kamalov

Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.

Physics of Particles and Nuclei LettersNov 19, 20090 citations

m

and

l

. We encode any tensor product of

m

many states emitted by the quantum stochastic source by breaking the tensor product into

m

many blocks where each block has length

l

, and considering sequences of

m

many isometries so that each isometry encodes one of these blocks into the Fock space, followed by the concatenation of their images. We only consider certain sequences of such isometries that we call \lq\lq special block codes\rq\rq\ in order to ensure that the string of encoded states is uniquely decodable. We compute the minimum average codeword length of these encodings which depends on the quantum source and the integers

m

l

, among all possible special block codes. Our result extends the result of [Bellomo, Bosyk, Holik and Zozor, Scientific Reports 7.1 (2017): 14765] where the minimum was computed for one block, i.e.\ for

m=1

. Lastly, we give a simplified non-adaptive compression technique based on constrained special block codes for general quantum stochastic sources. For quantum stationary sources in particular, we show that the minimum average codeword length per symbol computed over all constrained special block codes is equal to the von-Neumann entropy rate of the source for an asymptotically long block size.