RU2483357C2 - Method of processing quantum information - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: in the method, parameters of the working medium and type of dopant rare-earth element are selected. Photons acquire relative nonlinear phase shift in the medium. The value of the shift is controlled by varying settings of two additional optical pumping fields. Given quantum logic operations take place through nonlinear phase progression of pulses in said medium.

EFFECT: efficient information processing using an optical technique.

2 dwg

Description

The invention relates to the field of optical quantum computing, and in particular to methods for processing quantum information, and can be used to process quantum information.

A known method of implementing quantum logical operations using the polarizing states of single photons [application 2005128554/09, 02.17.2004 for the grant of a patent for the invention "Method and programmable device for quantum computing", http://wwwl.fips.ru/fips_servl/fips_servlet] . The method is based on the use of two polarization beam splitters, the first of which mixes the first single-photon pulse with the idle mode, followed by feeding one of the obtained polarization modes to the second beam splitter. Such a logical operation can be used to perform quantum computing. There is also a method of quantum computing ["Techniques for performing logic operations using quantum states of single photons", US patent 6741374, The Johns Hopkins University http://www.freepatentsonline.com/6741374.html], in which there is a program for finding functions describing the procedures for calculating the value. Continuate the encoded program and express it as a differential operator. Next, a differential operator is implemented in a physical environment and a solution for a continualized encoded program is extracted from it.

The disadvantages of these methods are that they relate mainly to the design of individual logic elements and do not combine the individual processing units of quantum information to implement distributed information processing and create a quantum processor.

Closest to the proposed method is a method of quantum computing using non-linear effects. The interaction of a pair of photons with multiple pairs of atoms of the medium gives a strong nonlinear phase shift ["Optical method for quantum computing", US patent 6678450, The Johns Hopkins University, http://www.freepatentsonline.com/6678450.html]. This shift can be controlled by changing the interaction parameters using numerous laser pulses and a buffer gas. At a certain phase shift, conditions are fulfilled under which a change in the polarization of photons occurs, corresponding to the quantum XOR operation.

The disadvantage of this method is the use of gas media to achieve phase shifts, which does not allow the use of these media for mass production.

The problem solved by the invention is the ability to efficiently process quantum information through the use of optical materials doped with atoms of rare-earth elements, which can be effectively used in serial production of the element base of quantum computing.

The proposed problem is solved by the fact that in the method of processing quantum information, including the interaction of the atomic medium with optical single-photon probe pulses of light, which obtain a relative nonlinear phase shift ϕ _i , the magnitude of the shift is controlled by changing the settings of two additional optical pump fields when using the M-scheme of atomic optical interaction in an optical medium doped with atoms of rare-earth elements and is determined by the formula

и левой

циркулярных поляризаций пробных фотонов а и b на входе среды и принимает значения i=1 для

, i=2 для

, i=3 для

, i=4 для

; показатели преломления среды имеют вид

,

,

,

,

,

,

; L - длина среды, n₀=1.45 - коэффициент преломления оптического кристалла, по которому распространяются фотоны,where i corresponds to various combinations of the right

and left

circular polarizations of the test photons a and b at the input of the medium and takes values i = 1 for

, i = 2 for

, i = 3 for

, i = 4 for

; the refractive indices of the medium are

,

,

,

,

,

,

; L is the length of the medium, n ₀ = 1.45 is the refractive index of the optical crystal along which the photons propagate,

- эффективная добавка к показателю преломления среды за счет наличия резонансных атомов,

- то же самое, но в случае, когда поляризация одного из пробных импульсов не соответствует правилу отбора на соответствующем атомном переходе и М-схема редуцирует к Λ-схеме, χ_p1(p2) - восприимчивости ансамбля допированных атомов, g_p1(p2) - частоты Раби пробных импульсов, N - концентрация атомов.

- an effective addition to the refractive index of the medium due to the presence of resonant atoms,

is the same, but in the case when the polarization of one of the probe pulses does not correspond to the selection rule at the corresponding atomic transition and the M-scheme reduces to the Λ-scheme, χ _{p1 (p2)} is the susceptibility of the ensemble of doped atoms, g _{p1 (p2)} - Rabi frequencies of test pulses, N is the concentration of atoms.

. В допированной среде реализуется М-схема атомно-оптического взаимодействия (см. Фиг.1) с участием двух дополнительных полей оптической накачки определенных поляризаций

и

и с малыми частотами отстройки δ₁₍₂₎. При прохождении сквозь дотированную среду пробных фотонов, ими приобретается различный относительный набег фазы ϕ_i, определяемый комбинацией поляризаций пробных фотонов на входе - в формуле (1). В качестве рабочего используется перепутанное состояние пробных фотонов а и b на входе среды в форме:Technically, the problem is realized by the fact that two single-photon test light pulses with arbitrary circular polarizations are fed into the optical working medium doped with atoms of rare-earth elements

. In a doped medium, an M-scheme of atomic-optical interaction is implemented (see Figure 1) with the participation of two additional optical pump fields of certain polarizations

and

and with low detuning frequencies δ _{1 (2)} . When test photons pass through a subsidized medium, they acquire a different relative phase incursion ϕ _i , determined by the combination of polarizations of the test photons at the input — in formula (1). As a worker, the entangled state of test photons a and b at the input of the medium is used in the form:

- комплексные амплитуды, определяющие вероятности соответствующих базисных состояний,

,

- начальные фазы.Where

- complex amplitudes that determine the probabilities of the corresponding basis states,

,

- initial phases.

The phase difference of the probe photons is measured using polarizing photodetectors. When choosing the system parameters, changes in the frequency detunings δ _{1 (2)} make it possible to change the phase incursions ϕ _i for the possibility of implementing various quantum logical operations performed on state (2).

An example implementation of the method

As the working medium, a crystal doped with ⁵⁹ Pr atoms was used, the working level diagram of which is shown in FIG. 1, and with the following interaction parameters: medium length L = 1 mm; parameters of doped atoms: γ _opt = 43.5 kHz, γ _mag = 4 kHz, γ _s - 0.25 kHz. The durations of the test pulses were chosen equal to τ _{p1, p2} = 258 ps, the durations of the pump pulses τ _{s1, c2} = 939.1 ps, the intensity of the test pulses I _{p1, p2} = 44.84 kW / m ² .

при выборе начальной фазы перепутанного состояния

, равной нулю - Фиг.2, и осуществлении фазового сдвига

. На втором этапе, при изменении частот отстроек полей накачки δ₁₍₂₎ и достижении фазовых набегов

, реализована квантовая логическая операция XOR в соответствии с таблицей истинности.For example, the logical XOR command was implemented in two stages. At the initial stage, phase encoding of the entangled state was carried out to achieve the necessary parameters

when choosing the initial phase of a confused state

equal to zero - Figure 2, and the implementation of the phase shift

. At the second stage, with a change in the frequencies of the detunings of the pump fields δ _{1 (2)} and the achievement of phase incursions

, implemented a quantum logical operation XOR in accordance with the truth table.

Effect: in comparison with prototypes, the implementation of this information processing method does not occur in a gas but in a solid medium, which is preferable for serial production and long-term use of samples. The possibility of external optical control allows the implementation of several quantum logical operations in one doped medium.

Truth table for XOR conversion condition

0 0

π / 2 π / 2

π 3π / 2

3π / 2 π

Claims (1)

A method of processing quantum information, including the interaction of an atomic medium with optical single-photon probe light pulses that obtain a relative nonlinear phase shift ϕ _i , characterized in that its value is controlled by changing the settings of two additional optical pump fields when using the M-scheme of atomic-optical interaction in optical medium doped with rare-earth atoms and is determined by the formula:

,
where i corresponds to various combinations of the right | σ ⁺ > and left | σ ^- > circular polarizations of the test photons a and b at the input of the medium and takes the values i = 1 for

, i = 2 for

, i = 3 for

i = 4 for

the refractive indices of the medium are

,

,

,

,

,

,

; L is the length of the medium, n ₀ = 1.45 is the refractive index of the optical crystal,

- an effective addition to the refractive index of the crystal due to the presence of resonant atoms,

is the same, but in the case when the polarization of one of the probe pulses does not correspond to the selection rule at the corresponding atomic transition and the M-scheme reduces to the Λ-scheme, χ _{p1 (p2)} is the susceptibility of the ensemble of doped atoms.

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