A linear Solution of the Four Dimensionality Problem

The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.

Physical Review AMay 1, 19890 citations

The quest for higher dimensionality

Stanislav S. Straupe, S. P. Kulik

Nature PhotonicsAug 31, 201026 citations

Experimental realization of quantum algorithms for a linear system inspired by adiabatic quantum computing

Jingwei Wen, Xiangyu Kong, Shijie Wei +3 more

Adiabatic quantum computation is of fundamental importance in the field of quantum computation as it offers an alternative approach to the gate-based model for the manipulation of quantum systems. Recently, an interesting work [arXiv:1805.10549] indicated that we can solve a linear equation system via an algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm in a four-qubit nuclear magnetic resonance system by determining the solution of an eight-dimensional linear equation $A\mathbf{x}=\mathbf{b}$ . The result is by far the maximum-dimensional linear equation solution with a limited number of qubits in experiments, which include some ingenious simplifications. Our experiment provides the possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.Adiabatic quantum computation is of fundamental importance in the field of quantum computation as it offers an alternative approach to the gate-based model for the manipulation of quantum systems. Recently, an interesting work [arXiv:1805.10549] indicated that we can solve a linear equation system via an algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm in a four-qubit nuclear magnetic resonance system by determining the solution of an eight-dimensional linear equation $A\mathbf{x}=\mathbf{b}$. The result is by far the maximum-dimensional linear equation solution with a limited number of qubits in experiments, which include some ingenious simplifications. Our experiment provides the possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.

arXiv:1806.03295Physical Review AJan 14, 201953 citations

Spin-measurement retrodiction

Shahar Ben‐Menahem

We address the problem of choosing an initial state and final measurement that enable maximal retrodiction of the result of an unknown intermediate spin measurement of a spin-(1/2 particle, along any one of a given set of directions. Details are given of the derivation of the most general possible solution of the problem, which we reported recently. The maximal retrodiction is shown to be the determination of the result of the intermediate spin measurement, along any of four different directions that span three-dimensional space and satisfy a specific linear relation.We address the problem of choosing an initial state and final measurement that enable maximal retrodiction of the result of an unknown intermediate spin measurement of a spin-(1/2 particle, along any one of a given set of directions. Details are given of the derivation of the most general possible solution of the problem, which we reported recently. The maximal retrodiction is shown to be the determination of the result of the intermediate spin measurement, along any of four different directions that span three-dimensional space and satisfy a specific linear relation.

Physical Review AFeb 1, 198917 citations

One-Dimensional Problems

Franz Schwabl

Springer eBooksJan 1, 19921 citation

A\mathbf{x}=\mathbf{b}

. The result is by far the maximum-dimensional linear equation solution with a limited number of qubits in experiments, which include some ingenious simplifications. Our experiment provides the possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.