The quantum brachistochrone problem for an arbitrary spin in a magnetic field

Kuzmak, A. R.; Tkachuk, V. M.

doi:10.1016/j.physleta.2015.03.003

Cited by 24 publications

(27 citation statements)

References 35 publications

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“…As in the previous case, the best coincidence of the results with theoretical prediction we obtain for θ = π/2. Finally, substituting Hamiltonian (25) with initial state (23) into expression (10) we obtain…”

Section: Ising Modelmentioning

confidence: 99%

“…The concept of a distance between quantum states in Hilbert space [1][2][3] has found its application in different fields of quantum mechanics related to the evolution of quantum systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], quantum entanglement [8,[20][21][22][23][24][25][26][27][28][29][30], quantum computations [31][32][33][34][35], etc. It was shown that the distance, which the quantum system passes during the evolution in the Hilbert space, is related to the integral of the uncertainty of energy that in turn defines the speed of evolution [4].…”

Section: Introductionmentioning

confidence: 99%

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Measuring distance between quantum states on a quantum computer

Kuzmak¹

2021

Preprint

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We propose protocols for determining the distances in Hilbert space between pure and mixed quantum states prepared on a quantum computer. In the case of pure quantum states the protocol is based on measuring the square of modulus of scalar product between certain states. Determination of the distance between mixed quantum states is reduced to measuring the squares of modules of scalar products between all pure states included in the mixed states. In addition, we develop a protocol which allows one to determine the speed of evolution of the spin system simulated by quantum computer. These protocols we apply to measure distances and speeds of evolution of different quantum systems implemented on the ibmq-santiago quantum computer.

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Section: Ising Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Measuring distance between quantum states on a quantum computer

Kuzmak¹

2021

Preprint

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“…If the parameter χ is fixed then we have the manifold which contains all possible initials states. It has the geometry of a sphere with radius γ Ns/2 (for instance, see, [22,71,72]). Also it is easy to see that the manifolds with different certain φ have the same geometry.…”

Section: The Long-range Ising-type Modelmentioning

confidence: 99%

Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction

Krynytskyi

Kuzmak

2019

Annals of Physics

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We study the evolution of a spin-s system described by the long-range zz-type Ising interaction. The Fubini-Study metric of the quantum state manifold defined by this evolution is obtained. We explore the topology of this manifold and show that it corresponds to a sphere. Exploration of the Riemannian curvature allows us to determine the manifold geometry. Also we calculate the speed of evolution of the system and represent the curvature by means of this speed. This is important for an experimental measurement of the curvature. The conditions for achieving the minimal and maximal values of the speed of evolution are obtained. Also we examine the geometry of state manifold and speed of evolution of spin system in the thermodynamic limit. We propose the physical system of methane molecule for application of our considerations. Finally, we study the influence of an external magnetic field on the metric of state manifold and on the speed of evolution. In this case we obtain the conditions for achieving the minimal possible speed of evolution. For some predefined initial states the orientations of magnetic fields to reach the minimal and maximal values of the speed are found.

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“…In our previous paper [4], we use the geometric characteristics such as curvature and torsion to study the quantum evolution. The geometry of quantum states in the evolution of a spin system was studied in [5,6]. In [7], the distance between quantum states was used for quantifying the entanglement of pure and mixed states.…”

Section: Introductionmentioning

confidence: 99%

Geometric measure of mixing of quantum state

Laba¹,

Tkachuk²

2018

Condens. Matter Phys.

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We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated.

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The quantum brachistochrone problem for an arbitrary spin in a magnetic field

Cited by 24 publications

References 35 publications

Measuring distance between quantum states on a quantum computer

Measuring distance between quantum states on a quantum computer

Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction

Geometric measure of mixing of quantum state

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