RU2538296C2 - Method of determining qubit state - Google Patents

Abstract

FIELD: measurement technology.

SUBSTANCE: method based on reading of a qubit in several different measurement bases, comprising the impact on the qubit with electromagnetic radiation on transitions between levels of the qubit and some auxiliary level. To read the qubit in the necessary measurement basis, the qubit is affected with bichromatic radiation, the spectral components of which are resonant to transitions from the levels of the qubit to the auxiliary level, the intensity and phases of the spectral components of the bichromatic radiation are set so that to highlight the measurement basis necessary for reading the qubit. The result of reading is determined by recording the excitation of the qubit to the auxiliary level.

EFFECT: increase in measurement accuracy, reduction of measurement time.

4 cl, 5 dwg

Description

The invention relates to computer systems based on specific computational models, in particular to quantum computers and optical logic elements, and can be used to fully determine the state of a qubit.

As the basic elements of a quantum computer, it is currently proposed to use qubits - quantum systems with two basis states | 0> and | 1>. Unlike a conventional digital computer, in which the smallest unit of information is a bit, it can take only two values, “0” and “1”, the qubit can be both in the states | 0> and | 1>, and in an arbitrary superposition state:

$$|\psi 〉=\alpha |0〉+\beta |\mathrm{one}〉,\left(\mathrm{one}\right)$$

where α and β are complex numbers related by the condition:

$${\left|\alpha \right|}^2+{\left|\beta \right|}^2=\mathrm{one}\left(2\right)$$

(see, for example, M. Nielsen, I. Chang, “Quantum computing and quantum information.” M: Mir, 2009, 33-37).

Expression (1) is called the expansion of the state | ψ〉 in terms of the states | 0> and | 1>, and the numbers α and β are the projections of the state | ψ〉 on the states | 0> and | 1>, respectively. As a basis, one can choose a pair of states | 0 ′> and | 1 ′> that are different from | 0> and | 1> (each of which represents a superposition of states | 0> and | 1>) and, similarly to (1), expand the state into a basis of states | 0 ′> and | 1 ′>:

$$|\psi 〉=\alpha \text{'}\text{'}|0\text{'}\text{'}〉+\beta \text{'}\text{'}|\mathrm{one}\text{'}\text{'}〉,\left(3\right)$$

$$$$

where α ′ and β ′ are complex numbers related, like α and β, by the condition:

$${\left|\alpha \text{'}\text{'}\right|}^2+{\left|\beta \text{'}\text{'}\right|}^2=\mathrm{one}.\left(\mathrm{four}\right)$$

To implement quantum computing, it is necessary to provide: initialization of the initial state of the qubit (data loading), unitary transformations over qubits (implementation of the calculation algorithm) and reading of the final state of the qubit (reading the results of calculations) (see, for example, M. Nielsen, I. Chang “Quantum computing and quantum information. ”M.: Mir, 2009, 347-349).

Qubit reading is a quantum measurement. A widespread class of quantum measurements are projective measurements. In this case, a quantum measurement is described by a set of certain orthonormal states (in the case of a qubit, by a set of two orthonormal states), called a measuring basis. If we imagine the qubit state | ψ〉 as an expansion in the measuring basis | m> and | n>:

$$|\psi 〉=c_m|m〉+c_n|n〉,\left(5\right)$$

then, as a result of the quantum measurement procedure, a qubit with probability | with _m | ² will be detected in the state | m〉 and with probability | with _n | ² in the state | n〉. In this case, we speak of quantum measurement in the measuring basis | m〉, | n〉 and, accordingly, reading the qubit in the measuring basis | m>, | n> (see, for example, M. Nielsen, I. Chang “Quantum calculations and quantum information. ”M: Mir, 2009, 120-126).

(см., например, К.Блум «Теория матрицы плотности и ее приложения». М.: Мир, 1983), которая для кубита (квантовой системы с двумя базисными состояниями) представляет собой квадратную эрмитову матрицу 2×2.The density matrix is widely used to describe the state of quantum systems. $$\hat{\rho }$$

(see, for example, K. Bloom, “The Theory of the Density Matrix and its Applications.” M .: Mir, 1983), which for a qubit (a quantum system with two basis states) is a 2 × 2 square Hermitian matrix.

$$\hat{\rho }=\left(\begin{array}{cc}{\rho }_{00}& {\rho }_{01}\\ {\mathrm{<figure-callout\; id="10"\; label="\rho "\; filenames="00000032.png,00000033.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_{10}& {\rho }_{\mathrm{eleven}}\end{array}\right),\left(6\right)$$

where ρ ₀₀ and ρ ₁₁ are real numbers satisfying the condition:

$${\rho }_{00}+{\rho }_{\mathrm{eleven}}=\mathrm{one},\left(7\right)$$

and ρ ₀₁ and ρ ₁₀ are complex numbers satisfying the condition:

$${\rho }_{01}={\mathrm{<figure-callout\; id="10"\; label="\rho "\; filenames="00000032.png,00000033.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_{10}^{*}.\left(8\right)$$

Elements of the density matrix depend on the choice of basis. Let the density matrix

written in the basis of states | 0> and | 1>. In this case, the diagonal elements of the density matrix ρ ₀₀ and ρ ₁₁ are called the populations of the states | 0> and | 1> respectively, and the off-diagonal elements ρ ₀₁ and ρ ₁₀ are called the quantum coherences at the transition between the states | 0> and | 1>. Taking into account conditions (7) and (8), the assignment of one diagonal element of the density matrix, i.e., population, and one off-diagonal element of the density matrix - quantum coherence make it possible to completely determine the state of the qubit. The populations ρ ₀₀ and ρ ₁₁ determine the probability of detecting a qubit in the states | 0> and | 1>, respectively, that is, in a quantum measurement of the state of a qubit described by the density matrix ρ in the measuring basis | 0> and | 1>, the qubit with probability ρ ₀₀ will be detected in the state | 0>, and with probability ρ ₁₁ - in the state | 1>.

The procedure of quantum measurement in the general case changes the state of the measured quantum system, therefore, repeated measurements on the same quantum system in the general case does not lead to correct results. However, the repeated carrying out of the measurement procedure over identical quantum systems (that is, systems in the same state) makes it possible to determine the populations of the measuring basis.

As qubits, it is proposed to use both single quantum systems and ensembles of such systems in the same state. In the first case, the qubit reading procedure in some measuring basis leads to the detection of the qubit in one of the states of the measuring basis with probabilities determined by the populations of the measuring basis. Repeated reading of identical qubits allows measuring the population of the measuring basis. In the second case, the reading of a qubit in some measuring basis is a simultaneous quantum measurement over a large number of quantum systems in the same state, and allows you to directly measure the population of the measuring basis.

Reading a qubit in any given measuring basis, even if it is carried out repeatedly, allows measuring only the populations of the measuring basis. This is not enough to fully determine the state of the qubit. To completely determine the state of a qubit, it is also necessary to measure quantum coherence at the transition between the states of the measuring basis. However, it turns out that when taking measurements in several different measuring bases (in this case, it is assumed that the measurements are carried out on identical qubits), the state of the qubit can be completely determined (see, for example, M. Nielsen, I. Chang “Quantum calculations and quantum information ". M.: Mir, 2009, 483-484).

Currently, active searches are underway for quantum systems capable of playing the role of qubits. One of the promising approaches to the physical realization of qubits is the use of active centers (atoms, ions, etc.) with long-lived energy levels, from which transitions under the influence of electromagnetic radiation to a certain auxiliary energy level (or several energy levels) are possible. In this case, two of the long-lived energy levels are used to implement the qubit, and transitions to the auxiliary energy level (or several energy levels) are used to perform unitary transformations over the qubit, initialize the initial state, and read the final state of the qubit. It is also promising to use ensembles of such active centers as qubits, in particular, ensembles of ions of rare-earth elements in crystals.

To read the qubit, you can directly use electromagnetic radiation that is resonant to the transition between the energy levels of the qubit. However, such transitions are often prohibited. In addition, the spatial resolution of such a measurement is usually limited by the wavelength of the transition between the energy levels of the qubit. This circumstance, in the case of qubits with close level energies, limits the possibility of selective reading of qubits.

More convenient for reading the qubit is the use of electromagnetic radiation, the resonance transition from one of the energy levels of the qubit | 0> or | 1> to the auxiliary energy level. To perform the operation of reading the qubit, the qubit is subjected to monochromatic electromagnetic radiation, a resonant transition from one of the energy levels of the qubit, for example | 0>, to the auxiliary energy level. Thus, registering the excitation of a qubit (or lack of excitation) at an auxiliary energy level, the qubit is read. To register the excitation, the absorption of resonant electromagnetic radiation or the population of the auxiliary energy level is measured, for example, by a fluorescence signal from it. In the case of qubits based on single active centers, if a qubit was excited to an auxiliary energy level, then the read result corresponds to the detection of a qubit in the state | 0>, if a qubit was not excited to the auxiliary energy level, then the read result corresponds to the detection of a qubit in the state | 1 >. In the case of qubits, based on ensembles of active centers, the population of the upper energy level as a result of excitation and, accordingly, the absorption of resonant electromagnetic radiation and the fluorescence signal from the auxiliary energy level are proportional to the population of the state | 0> of the read qubit. The described method for reading qubits is proposed to be used to read the states of a qubit in the method of processing quantum information, known from US patent (US 6800837 "Method for quantum information processing and quantum information processor)), IPC7 G02F 3/00, publ. 10/05/2004).

There are also known methods for reading a qubit by adiabatic transfer of one of the energy levels of a qubit to a certain auxiliary level with subsequent registration of the population of the auxiliary level in various ways (see, for example, US patent No. US 7667853 "Quantum bit reading device and method", current CPC class G06N 99/002, publ. 23.02.2010 and US patent No. US 7791052 "Single-photon generation apparatus and quantum bit reading apparatus and method", current CPC class G06N 99/002, publ. 09/07/2010).

The disadvantage of all these methods is that they allow the qubit to be read in only one measuring basis — the basis of the energy levels of the qubit. This is not enough to fully determine the state of the qubit. For a complete determination of the state of a qubit, the ability to read the state of a qubit in several different measuring bases is necessary.

The closest analogue in technical essence to the proposed method is a method for determining the state of a qubit based on reading a qubit in several different measuring bases, which is selected as a prototype (see L. Rippe, Julsgaard, A. Walther, Yan Ying, and S. Kroll, “Experimental quantum-state tomography of a solid-state qubit”, Physical Review A, V.77, 022307 (2008)). The prototype method allows the qubit to be read in an arbitrary required measuring basis and based on the read results in several measuring bases, a complete determination of the qubit state can be made.

The reading of the qubit in an arbitrary, predetermined measuring basis in the prototype method takes place in two stages. At the first stage, a qubit is converted, which translates a given measuring basis into a basis of energy levels. The stage includes the following steps. At the first step, the qubit is affected by the first π-pulse of electromagnetic radiation. The first π-pulse transfers the population of the selected superpositional state of the qubit to the auxiliary level | e>. At the second step, the qubit is affected by a second π-pulse, which is out of phase with respect to the first. The second π-pulse produces a reverse transfer of the population of the auxiliary level | e> to the selected superposition state of the qubit. As a result, the selected superposition state acquires a phase shift determined by the phase shift between the first and second π pulses. This procedure allows you to translate an arbitrary, predefined measurement basis in the basis of energy levels. At the second stage, a qubit is read in the basis of energy levels. To do this, the qubit is affected by monochromatic radiation, a resonant transition between one of the qubit levels and the auxiliary level. In this case, the absorption of resonant monochromatic radiation is measured. The result of reading a qubit is determined by the absorption of resonant monochromatic radiation.

For qubits, based on ensembles of active centers, the population of states of the measuring basis is calculated from the qubit reading. If the measurement procedure is not calibrated, that is, the coupling coefficient between the absorption of monochromatic resonant radiation and the population of the qubit level interacting with it is not known, an additional measurement is used in the prototype method at the stage of reading the qubit in the basis of energy levels. First, the qubit is affected by monochromatic radiation, a resonant transition between one of the qubit levels and the auxiliary level. In this case, the absorption of resonant monochromatic radiation is measured. After that, the qubit is affected by monochromatic radiation, a resonant transition between the second level of the qubit and the auxiliary level. In this case, the absorption of resonant monochromatic radiation is measured. Based on the measurement results, the measurement procedure is calibrated and the population of the states of the measuring basis is calculated.

To fully determine the state of the qubit in the prototype method, the populations of the measuring basis are measured in several different measuring bases, the state of the qubit is completely determined on the basis of the measurement results.

The disadvantages of the prototype method are: firstly, the need for a complex qubit conversion procedure that requires precise control of the parameters of the used π-pulses and the phase difference between them; secondly, the time required for conversion is limited by the duration of the used l-pulses; thirdly, to carry out the transformation procedure, it is necessary that the lifetime of the population of the auxiliary level | e> and the lifetime of the quantum coherence at the transitions between the qubit levels and the auxiliary level be longer than the conversion duration.

The problem solved by the present invention is the development of a method for determining the state of a qubit, based on reading the qubit in several different measuring bases, which allows to read the qubit in the required measuring basis without performing conversion on the qubit.

The technical result in the developed method for determining the state of the qubit, as well as in the prototype method based on reading the qubit in several different measuring bases, is achieved due to the fact that the qubit is exposed to electromagnetic radiation at the transitions between the levels of the qubit and some auxiliary level.

A new one in the developed method for determining the state of a qubit is that for reading the qubit in the required measuring basis, the qubit is exposed to bichromatic radiation, the spectral components of which are resonant to the transitions from the qubit levels to the auxiliary level, the intensities and phases of the spectral components of the bichromatic radiation are set so as to select the required read qubit measuring basis, while registering the excitation of the qubit to the auxiliary level.

In the first particular case of the implementation of the developed method, it is advisable to register the qubit excitation to an auxiliary level by the absorption of bichromatic radiation.

In the second particular case, the excitation of the qubit to the auxiliary level is advisable to register by fluorescence from it.

In the third particular case, it is advisable to use a qubit as a qubit based on ensembles of rare-earth ions doped into a crystal.

In the case of qubits on the basis of ensembles of active centers or upon repeated reading of states of identical qubits on the basis of single active centers, the populations of states of the measuring basis are calculated on the basis of the readings.

Based on several such measurements, the state of the qubit is completely determined in several different measuring bases.

The developed method does not require qubit conversion. This simplifies the technical implementation of the method and improves the accuracy of measurements, since it is free from errors associated with the qubit conversion procedure. The developed method allows to reduce the measurement time, since it does not require time to transform the qubit. The time t necessary for reading the qubit in each of several measuring bases required for determining the qubit state is limited only by the spectral width of the components of the bichromatic radiation pulse, which should not exceed the transition frequency between the qubit levels. That is, the time t must be less than 1 / ω, where ω is the transition frequency between the qubit levels. For the developed method, the lifetime of the auxiliary level and the lifetime of quantum coherence at the transitions between the qubit levels and the auxiliary level are not important.

The developed method is illustrated by the following figures:

Figure 1 presents a diagram of a possible technical implementation of the developed method in accordance with claim 1 or claim 2 of the formula.

Figure 2 presents a diagram of a possible technical implementation of the developed method in accordance with paragraph 3 of the formula.

через вспомогательный уровень, |0> и |1> - уровни кубита, |е> - вспомогательный уровень, используемый для реализации способа.Figure 3 presents a qubit resonantly interacting with bichromatic radiation $$\overrightarrow{E}=\overrightarrow{E_0}{e}^{-i{\omega }_{0}t}+\overrightarrow{E_{\mathrm{one}}}{e}^{-i{\omega }_{\mathrm{one}}t}$$

through the auxiliary level, | 0> and | 1> are the qubit levels, | e> is the auxiliary level used to implement the method.

через вспомогательный уровень.Figure 4 presents the qubit in the basis of light | C> and dark | T> states, resonantly interacting with bichromatic radiation $$\overrightarrow{E}=\overrightarrow{E_0}{e}^{-i{\omega }_{0}t}+\overrightarrow{E_{\mathrm{one}}}{e}^{-i{\omega }_{\mathrm{one}}t}$$

through the auxiliary level.

Figure 5 presents a diagram of the working levels of the Pr ³⁺ ion in the LaF ₃ crystal, used to implement qubit based on the spectrally separated groups of Pr ³⁺ ions in the LaF ₃ crystal and to implement the developed method for determining the state of the qubit.

Various technical implementations of the developed method are possible. A diagram of one of the possible technical implementations of the developed method is presented in figure 1. It contains a laser 1, beam dividers 2 and 4, acousto-optical modulators 3 and 8, mirrors 7 and 9, qubit 5 and photodetector 6.

The method for determining the state of a qubit in accordance with claim 1 of the formula using the circuit shown in figure 1, is as follows.

The radiation frequency of laser 1 is chosen close to the frequency of transitions from the qubit levels | 0> and | 1> to the auxiliary level | e>. Laser radiation 1 is divided into two beams in beam splitter 2, each of the beams passes through a separate acousto-optic modulator 3 or 8. Using acousto-optical modulators 3 and 8, the radiation frequencies of the laser beams passing through them are shifted so that they coincide with the transition frequencies from the qubit levels | 0> and | 1> to the auxiliary level | e>, respectively, and thus form the components of the resonant bichromatic radiation E ₀ and E ₁ (see figure 3). The components of the resonant bichromatic radiation E ₀ and E ₁ combine on the beam splitter 4, and thus form a resonant bichromatic radiation E of the form:

$$\overrightarrow{E}=\overrightarrow{E_0}{e}^{-i{\omega }_{0}t}+\overrightarrow{E_{\mathrm{one}}}{e}^{-i{\omega }_{\mathrm{one}}t}.\left(9\right)$$

Resonant dichromatic radiation E acts on qubit 5. It is known (see, for example, B.D. Agapiev, M. B. Gorny, B. G. Matisov, Yu. V. Rozhdestvensky “Coherent population trapping in quantum systems” Successes in Physical Sciences , T. 163, No. 9, pp. 1-36 (1993)), that in this case resonant bichromatic radiation interacts only with the superposition state of the levels | 0> and | 1>, the so-called light state | C>, and orthogonal to the light - also a superpositional, dark state | T> does not interact with the bichromatic field (see figure 4). In this case, the light and dark states as follows depend on the components of the resonant bichromatic radiation:

$$|T〉=\frac{{\Omega }_{\mathrm{one}}}{\Omega }|0〉-\frac{{\Omega }_0}{\Omega }|\mathrm{one}〉,\left(10\right)$$

$$|C〉=\frac{{\Omega }_{{}_{\mathrm{one}}}^{*}}{\Omega }|0〉+\frac{{\Omega }_{{}_0}^{-}}{\Omega }|\mathrm{one}〉,\left(\mathrm{eleven}\right)$$

, $${\Omega }_1=\overrightarrow{E_1},{\overrightarrow{d}}_1/\hslash$$

, - частоты Раби компонент бихроматического излучения, $${\overrightarrow{\text{d}}}_{\text{0}}\text{, }{\overrightarrow{\text{d}}}_{\text{1}}$$

- дипольные моменты переходов |0>→|е> и |1>→|е> соответственно $$\Omega =\sqrt{\text{|}{\Omega }_{\text{0}}{\text{|}}^{\text{2}}+\text{|}{\Omega }_{\text{1}}{\text{|}}^{\text{2}}}$$

.Where $${\Omega }_0=\overrightarrow{E_0},{\overrightarrow{d}}_0/\hslash$$

, $${\Omega }_{\mathrm{one}}=\overrightarrow{E_{\mathrm{one}}},{\overrightarrow{d}}_{\mathrm{one}}/\hslash$$

, are the Rabi frequencies of the bichromatic radiation component, $${\overrightarrow{\text{d}}}_{\text{0}}\text{,}{\overrightarrow{\text{d}}}_{\text{one}}$$

are the dipole moments of transitions | 0> → | e> and | 1> → | e>, respectively $$\Omega =\sqrt{\text{|}{\Omega }_{\text{0}}{\text{|}}^{\text{2}}+\text{|}{\Omega }_{\text{one}}{\text{|}}^{\text{2}}}$$

.

The authors propose to use this effect to read the qubit in the required measuring basis and, based on reading the qubit in several different measuring bases, to completely determine the state of the qubit. Using acousto-optical modulators 3 and 8, the intensities and phases of the bichromatic radiation spectral components E ₀ and E _{1 are} set so as to select the measuring basis required for reading qubit 5, that is, so that the light | C> described by expressions (10) and (11) and the dark states | T> coincided with the states of the measuring basis required for reading the qubit. If necessary, to limit the measurement time, the acousto-optical modulators 3 and 8 are also used to form a pulse of resonant bichromatic radiation. In this case, the excitation of qubit 5 to the auxiliary level is recorded. Why, for example, measure the absorption of resonant bichromatic radiation E when interacting with qubit 5 using a photodetector 6.

In the case of qubits, based on ensembles of active centers, the population of the auxiliary level as a result of excitation is proportional to the population of the state | C> of the read qubit 5.

In the case of qubits based on single active centers, if qubit 5 was excited to an auxiliary level, then the reading result corresponds to the detection of qubit 5 in the state | C>. If qubit 5 is not excited to the auxiliary level, then the read result corresponds to the detection of qubit 5 in the state | T>.

In the case of qubits, based on ensembles of active centers, the population of states of the measuring basis is calculated on the basis of the result of reading the qubit. In the case of qubits, based on single active centers, the reading procedure is carried out repeatedly over qubits in the same state, and the population of states of the measuring basis is calculated based on the results of reading qubits.

In the manner described above, the population of the measuring basis is measured for several (not less than three) different measuring bases. To do this, several (not less than three) different measurements are carried out, in each of which different measurement bases are set by choosing the intensities and phases of the spectral components of the bichromatic radiation. In each of the measurements, the population of the state of the measuring basis | C>, described by expression (11), is measured. Elements of the density matrix depend on the choice of basis. The population of the state | C> described by expression (11) is as follows related to the elements of the density matrix in the basis of the energy levels of the qubit | 0> and | 1>

$${\rho }_{\mathrm{from}\mathrm{from}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{${\Omega }^2$}\right.\left({\left|{\Omega }_0\right|}^2{\rho }_{00}+{\rho }_{\mathrm{eleven}}+2\mathrm{Re}\left({\Omega }_0{\Omega }_{\mathrm{one}}^{*}{\rho }_{01}\right)\right).\left(12\right)$$

As a result of several measurements, several different population values of the state | C> corresponding to different states | C> are obtained. Based on the measurement results, the state of the qubit is completely determined.

The following three dimensions can be suggested as an example. In the first measurement using acousto-optic modulators 3 and 8, the intensities and phases of the spectral components of the bichromatic radiation are set so that the corresponding Rabi frequencies satisfy the following condition:

$${\Omega }_{\mathrm{one}}=0,{\Omega }_0-ne\mathrm{to}\mathrm{about}t\mathrm{about}R\mathrm{but}\mathrm{I\; am}PR\mathrm{about}\mathrm{and}s\mathrm{at}\mathrm{about}lbn\mathrm{but}\mathrm{I\; am}\mathrm{at}el\mathrm{and}h\mathrm{and}n\mathrm{but},\left(13\right)$$

while measuring the population of the measuring basis. In this case, the measured population of the state of the measuring basis | C> according to expression (12) is written as:

$${\rho }_{\mathrm{from}\mathrm{from},\mathrm{one}}={\rho }_{00}.\left(\mathrm{fourteen}\right)$$

In the second measurement, using the acousto-optical modulators 3 and 8, the intensities and phases of the spectral components of the bichromatic radiation are set so that the corresponding Rabi frequencies satisfy the following condition:

$${\Omega }_0={\Omega }_{\mathrm{one}},\left(\mathrm{fifteen}\right)$$

while measuring the population of the measuring basis. In this case, the measured population of the state of the measuring basis | C> according to expression (12) and condition (7) is written as

$${\rho }_{\text{c}c,\text{2}}=\text{l / 2}+\text{Re (}{\rho }_{\text{01}}\text{)}\text{.}\text{(16)}$$

In the third measurement, using the acousto-optical modulators 3 and 8, the intensities and phases of the spectral components of the bichromatic radiation are set so that the corresponding Rabi frequencies satisfy the following condition:

$${\Omega }_{\mathrm{one}}=i{\Omega }_0,\left(17\right)$$

while measuring the population of the measuring basis. In this case, the measured population of the state of the measuring basis | C> according to expression (12) and condition (7) is written as

$${\rho }_{\text{c}c,\text{3}}=\text{l / 2}+\mathrm{Im}\text{(}{\rho }_{\text{01}}\text{)}\text{.}\text{(eighteen)}$$

Based on the results of these three measurements, the populations of the energy levels of the qubit and the real and imaginary parts of quantum coherence at the transition between the energy levels of the qubit are calculated:

$${\rho }_{00}={\rho }_{cc,\mathrm{one}},\left(19\right)$$

$${\rho }_{\mathrm{eleven}}=\mathrm{one}-{\rho }_{cc,\mathrm{one}},\left(\mathrm{twenty}\right)$$

$$\mathrm{Re}({\rho }_{01})={\rho }_{cc,2}-\mathrm{one}/2,\left(21\right)$$

$$\mathrm{Im}({\rho }_{01})={\rho }_{cc,3}-\mathrm{one}/2.\left(22\right)$$

These characteristics fully determine the state of qubit 5.

Thus, the developed method allows determining the state of the qubit on the basis of reading the qubit in several different measuring bases, while it allows you to read the qubit in the required measuring basis without performing conversion on the qubit, that is, it allows you to solve the problem.

As an example, consider reading a qubit based on spectrally separated groups of Pr ³⁺ ions in a LaF ₃ crystal. Figure 5 shows a diagram of the working levels of the Pr ³⁺ ion in the LaF ₃ crystal used to implement the qubit, and the developed method for determining the state of the qubit. Two ultrathin sublevels of the ³ H ₄ (1) state are used as levels | 0> and | 1> qubits, and one of the ultrathin sublevels of the ¹ D ₂ (1) state is used as an auxiliary level | e> (for a more detailed description of the implementation of qubits on based on spectrally separated groups of Pr ³⁺ ions in a LaF ₃ crystal _, see, for example, Akhmedzhanov R.A., Bondartsev A.A., Gushchin L.A., Zelensky I.V., Litvak A.G. basis of spectrally separated groups of Pr ³⁺ ions in a LaF ₃ crystal. ”Letters in JETP, vol. 94, N12, pp. 945-950 (2011)). As laser 1, a single-mode stabilized dye laser with a wavelength of 592.52 nm can be used, and acousto-optical modulators 3 and 8 can be used with acousto-optical modulators at a wavelength of 592 nm, which provide tuning of the wavelength in the range of at least 40 MHz.

Claims (4)

1. A method for determining the state of a qubit, based on reading the qubit in several different measuring bases, including the effect on the qubit of electromagnetic radiation at the transitions between the levels of the qubit and some auxiliary level, characterized in that for reading the qubit in the required measuring basis, the qubit is subjected to bichromatic radiation, the spectral components of which are resonant to transitions from the qubit levels to the auxiliary level, intensities and phases of the spectral components of the bichromate The radiation frequency is set so as to distinguish the measuring basis required for reading the qubit, while the excitation of the qubit to the auxiliary level is recorded. 2. The method according to claim 1, characterized in that the excitation of the qubit to an auxiliary level is recorded by the absorption of bichromatic radiation. 3. The method according to claim 1, characterized in that the excitation of the qubit to an auxiliary level is recorded by fluorescence from it. 4. The method according to any one of paragraphs. 1, 2 or 3, characterized in that qubits are used as qubits based on ensembles of rare-earth ions doped into crystals.

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