CN114528999A - Optical pulse generation method for carrying out high-fidelity control on ensemble qubits - Google Patents

Abstract

The invention belongs to the field of quantum computation, and discloses an optical pulse generation method for high-fidelity manipulation of ensemble qubits in order to improve the robustness and the fidelity of quantum manipulation.A time-contained Schrodinger equation of a three-level system is reversely solved in an ensemble nitrogen vacancy center system on the basis of a transition-free quantum drive theory so as to eliminate a microwave field between two ground state levels as a target, and an expression form of a time evolution operator is designed by introducing a degree of freedom parameter; designing the amplitude and the phase of the two light pulses by a time evolution operator in a reverse direction; the light is input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the light pulse, and the radio signal is used for driving an acousto-optic modulator in a continuous laser light path to obtain +1 level or-1 level deflection output light to generate a group of bicolor light pulses; and vertically injecting the generated bicolor light pulse into a three-energy-level quantum system medium, and generating any superposition state of the qubits by the interaction of the bicolor light pulse and the quantum system medium.

Description

Optical pulse generation method for carrying out high-fidelity control on ensemble qubits

Technical Field

The invention belongs to the field of quantum manipulation and quantum computation, and particularly relates to an optical pulse design theory capable of quickly creating a quantum bit superposition state with high robustness.

Background

At the end of the nineteenth century, the increasing maturity of the classical physical development brought the change of the people's life. With the development of informatics, the continuous and deep research on big data, artificial intelligence and the like in recent years means that the requirement on the speed of information processing is higher and higher, and phenomena which cannot be explained by classical physics appear, so that the information processing by a classical computer is more and more difficult, and the search for a new solution becomes a current urgent matter to be solved. At this point the advent of quantum mechanics in the twentieth century was able to describe areas where physics cannot describe the micro world. At present, with the gradual improvement and development of the field of quantum mechanics, the superiority of quantum computation is being embodied step by step. Instead of using conventional bits consisting of 1's and 0's, they use qubits that represent different values of the quantum, i.e., two quantum states |0> and |1> to encode information. The processing of this information is realized by other methods such as microwave pulses or light pulses. Thus, quantum computation stores an enormous amount of information, and the computation speed rises exponentially. Furthermore, due to the complexity of quantum computers, they are made faster in performing certain tasks, enabling them to solve problems that modern machines are almost impossible to solve. Therefore, the method is widely applied to the aspects of quantum neural network simulation, artificial intelligence, large-scale factorization, disordered database retrieval and the like. And the wide application in the fields of materials science, biology, informatics and the like also promotes the emergence of emerging interdisciplines. However, in the implementation process of quantum computing, the quantum computing is often influenced by ambient noise, and the quantum state is fragile and sensitive, so that the quantum state is often difficult to control. It would be a great challenge to find a physical system that has excellent coherence properties, is easy to manipulate, and has a high enough manipulation fidelity.

At present, there are many physical systems for carrying qubits, such as trapping ion systems, superconducting qubit systems, rare earth ion systems, diamond nitrogen vacancy center systems, etc. Different systems have different characteristics, so that proper light pulses are designed according to the characteristics of the system where different carriers are located to realize high-fidelity quantum state control, which has important significance for the research and development of quantum computation.

Among these systems, diamond nitrogen vacancy centres have attracted much research interest because of their simple stable spin-level structure, efficient and convenient optical transitions, and their ultra-long spin quantum state coherence times at room temperature. The maximum characteristics of the method are that the spin quantum bit has extremely long coherence time at room temperature, the extremely long spin state coherence time brings extremely high magnetic field detection sensitivity, and in addition, the nitrogen vacancy center is of a sub-nanometer scale structure, stably exists in diamond single crystals and nanoparticles, is convenient to couple with other systems (such as an optical cavity and a microwave cavity), and extremely high-efficiency quantum manipulation is realized by using an optical method and radio frequency microwave pulses. In a nitrogen vacancy center experimental system, energy levels are generally split through the zeeman effect of an external magnetic field, and a two-energy-level or three-energy-level system can be obtained. The spin state of the nitrogen vacancy center is regulated by using a spin magnetic resonance technology, namely, the evolution of the spin state is regulated by utilizing the interaction of a microwave field and spin. The base electron spin state is initialized and read out of the quantum state through optical transition, and the quantum state is controlled by microwave to form any superposed state. In an ensemble nitrogen vacancy centre system, spin ensemble occurs, non-uniform broadening of spin transitions in the ensemble may occur due to random distribution of spins in the diamond, and the degree of non-uniform broadening in the ensemble nitrogen vacancy centre is strongly dependent on the concentration of nitrogen vacancy centres, which need to be highly robust if manipulated as a quantum unit. Therefore, when quantum state manipulation is performed, the main limiting factor is the decoherence effect caused by natural frequency detuning in a certain range. That is, in such a system, quantum steering needs to be robust to frequency detuning that exists in ensemble qubits when creating arbitrary superposition states of the qubits.

First, take the ensemble nitrogen vacancy center as an example, in this system, the ground state is due to being at | m_s＝0>And | m_s＝±1>In between

Zero field splitting produces a spin triplet state. Then at | m_s＝±1>By applying an external magnetic field along the crystallographic axis at the center of the nitrogen vacancy, an additional zeeman splitting is produced, resulting in a three-level system. Typically, one nitrogen vacancy center is generally considered one spin, and one ensemble nitrogen vacancy center is considered one ensemble spin. In experiments, the quantum state is usually initialized and read out by the spin state of the base electron³A ground state |0>_jRespectively with the first excited state |1>_jAnd a second excited state |2>_jOptical transitions are performed. The random distribution of spins in diamond may lead to non-uniform broadening of spin transitions in the ensemble (about 300MHz), and the extent of non-uniform broadening is strongly dependent on the concentration of nitrogen vacancy centres (here, the number of nitrogen vacancy centres is 10)¹²Illustratively), if these ensemble nitrogen vacancy centers are used as a quantum unit to manipulate the ensemble qubits therein, quantum manipulation is required to be highly robust to frequency detuning. At this time, microwave and optical pulse are reasonably designed to realize high fidelity control for the non-uniform broadening in the system.

Then the rare earth ion system Pr with the doping concentration of 0.05 percent³⁺:Y₂SiO₅For example, during the process of forming doped crystals by substituting yttrium ions in matrix crystals with trace praseodymium ions, matrix lattices are distorted, nonuniform broadening can reach GHz level, and a narrow transition line of each praseodymium ion is completely buried in the matrix lattices. In the system, optical hole burning technology is firstly adopted to carry out non-uniform developmentCreating a zero absorption region with a width of about 18MHz in the wide line; a small fraction of ions with similar optical transition frequencies (about 170kHz linewidth) are then selectively pumped back into this region by optical pumping as a qubit. It is characterized by billions of randomly distributed rare earth ions and is therefore called an ensemble qubit. Wherein two qubit energy levels |0>And |1>Coupled between them by respective excited states | e>Optical transition between. In such a system, to create arbitrary superposition states of qubits with high fidelity, quantum steering should not only be robust to frequency detuning due to non-uniform broadening present in ensemble qubits, but also be highly inhibitory to non-resonant excitation of other ions near the qubit ion addressing frequency.

Therefore, in a three-level system like this, in order to create an arbitrary qubit stacking state quickly and with high robustness, it is necessary to satisfy: (1) in an ensemble nitrogen vacancy-centered system: the optical pulse can equally control multiple quantum bits within a detuning range of 300MHz within a short time of 4ns, namely high fidelity is required to be generated within a range of +/-300 MHz. (2) In the rare earth ion system: the optical pulse can perform equal control on the ensemble qubit in the frequency detuning range of +/-170 kHz within a short time of 4 mu s, namely the control fidelity in the interval is as close to 1 as possible; the off-resonance excitation of ions other than about 3.5MHz from the ensemble qubit ion is sufficiently small.

The methods currently used to design their light pulses fall broadly into three categories: (1) simple resonance pulse; (2) quantum adiabatic channel technology; (3) quantum adiabatic shortcut techniques. Although the simple resonance pulse speed is high, the simple resonance pulse speed is easily influenced by system parameter change, and the robustness is poor; the quantum adiabatic channel technology has better robustness for parameter change, but needs to meet adiabatic conditions, so the operation time is longer and the influence of decoherence is easy to be caused; in order to simultaneously meet the requirements of rapidness and high robustness, a quantum adiabatic shortcut technology is proposed. The common quantum adiabatic shortcut technology has two types, one is a reverse engineering method based on Lewis-Riesenfeld invariant, and the other is a transition-free quantum driving theory. Both of these methods have been demonstrated to perform the qubit initialization operation quickly and with high robustness.

At present, for high-fidelity control of a three-energy-level system, some work solves the problem of phase decoupling effect caused by frequency detuning. For example, in the optical pulse design method (application number: 201810234933.5) capable of creating any superposition state of quantum bit of the three-level system, Yanying et al propose an optical pulse design method for creating any superposition state of quantum bit in the three-level system in the rare earth ion system, and a group of bichromatic optical pulses capable of generating any superposition state of quantum bit is constructed by reversely solving the time-dependent Schrodinger equation of the three-level system by adopting the invariant theory. However, in the invariant theory, it is necessary to find the invariant of the hamilton amount first during the use, and in most systems, the invariant is unknown, so this method is limited by the configuration invariant in some cases. The transition-free quantum drive theory provides an efficient method because it does not require the construction of invariant amounts of the hamiltonian, and is not limited by most systems, i.e., the quantum states are still evolving exactly along the instantaneous eigenstates of the initial hamiltonian by adding an anti-adiabatic coupling term to the initial hamiltonian. However, in the traditional quantum drive without transition, a microwave coupling term between two ground state energy levels appears, and a concise expression analytical formula of the microwave coupling term is difficult to directly construct and difficult to implement in experiments. Therefore, the invention is inspired by the theory of the quantum drive without transition, in a nitrogen vacancy center system, the microwave coupling terms between ground state energy levels are cancelled by reasonably designing a time evolution operator and combining reverse engineering, the experimental operation is simplified, the quantum bit is controlled, and the high robustness of the frequency detuning quantity occurring in the experiment can be realized.

Disclosure of Invention

The optical pulse designed in the invention has the following characteristics:

(1) aiming at the center of the nitrogen vacancy of the ensemble, the pulse action time is not more than 4 ns;

(2) for the ensemble nitrogen vacancy center, there is high fidelity to at least 300MHz of frequency detuning in the system;

(3) aiming at the rare earth ion system, under the action time of pulse of 4 mus, the method has robustness on frequency detuning in the range of at least +/-170 kHz in the quantum system; the method is suitable for a quantum system needing to select the quantum bit depending on the frequency band;

the technical problem solved by the invention is as follows: in an ensemble nitrogen vacancy center system and a rare earth ion system, the robustness to frequency detuning quantity in the pulse action process is poor, and the non-resonant excitation to other ions near a qubit is high. Therefore, in order to improve robustness and inhibit non-resonant excitation, the invention seeks a design method of a bicolor optical pulse, the bicolor optical pulse consists of two pulses with equal duration and different amplitudes, frequencies and phases, the two pulses simultaneously act on a three-energy-level quantum system consisting of two quantum bit energy levels and one excited state energy level, and the three-energy-level quantum system can be controlled from an initial state |0 and a target state under the premise of knowing an initial state and a target state of the system>Evolution into arbitrary superposition states of qubits

Wherein α, β and

is three angles, alpha, beta being [0, 2 pi ]]Within the range, the number of characterization placements is |0>，|e>And |1>Distribution over three energy levels;

at [0, 2 π]Value in the range representing the qubit energy state |0>And |1>Relative phase therebetween.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

an optical pulse generation method for high fidelity control of an ensemble qubit is characterized in that in an ensemble nitrogen vacancy center system, a time-dependent Schrodinger equation of a three-level system is reversely solved based on a transition-free quantum drive theory, when the time-dependent Schrodinger equation of the three-level system is solved, a microwave field between two ground level levels is eliminated as a target on the premise that an initial state and a target state of the system are known, and an expression form of a time evolution operator is designed by introducing a degree of freedom parameter; then designing the amplitude and phase of two light pulses in an ensemble nitrogen vacancy center system through the time evolution operator in a reverse direction; inputting the amplitude and the phase into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the optical pulse, and driving an acousto-optic modulator in a continuous laser light path by using the radio signal to obtain +1 level or-1 level deflection output light to generate a group of bicolor optical pulses; and vertically injecting the generated bicolor light pulse into a three-energy-level quantum system medium, and enabling the bicolor light pulse and the quantum system medium to interact to generate any superposition state of the qubits.

The design of the time evolution operator involves the introduction of a degree of freedom parameter, and combines reverse engineering to eliminate a microwave coupling term between two ground state energy levels, thereby simplifying experimental operation; in the pulse action process, the method has high robustness on the nonuniform broadening appearing in the ensemble system, and realizes the high-fidelity control on the quantum bit.

Description of principle and effect: in the implementation process of the scheme, based on a group of orthonormal and complete auxiliary state basis vectors, a direct coupling microwave field between two ground state energy levels is eliminated by combining reverse engineering, so that the experiment difficulty is reduced; meanwhile, in the pulse action process, the initialization operation of the quantum bit can be realized with high robustness.

Compared with the prior art, the invention has the following remarkable characteristics:

and vertically injecting the generated bicolor light pulse into a three-energy-level quantum system medium, and enabling the bicolor light pulse and the quantum system medium to interact to generate any superposition state of the qubits.

The generated bicolor optical pulse is suitable for a three-energy-level quantum system and comprises two optical pulses which act simultaneously but have different frequencies, amplitudes and phases, and the parameters of the optical pulses can be completely controlled by any wave generator and an acousto-optic modulator.

The bicolor light pulse can generate any superposition state of one qubit in a three-level system, including any layout number distribution and any relative phase regulation between two qubit levels.

The starting value and the ending value of the bicolor light pulse are zero, so that the interference on a target quantum state is avoided, and an arbitrary superposition state of the quantum bit is generated.

The amplitude of the bi-color light pulse varies with time, but the frequency and phase do not vary with time.

In the center of the nitrogen vacancy of the ensemble, the action length of the light pulse does not exceed 4ns, so that decoherence is avoided.

In the rare earth ion system, the action length of the light pulse is not more than 4 mus, so that decoherence is avoided.

In the process of the action of the bicolor light pulse and the qubit, direct microwave coupling between two ground state energy levels of the qubit is avoided, and experimental operation can be simplified in an ensemble nitrogen vacancy center system and a rare earth ion system.

The bicolor optical pulse is suitable for a quantum system needing to select quantum bits depending on frequency bands, and non-resonance excitation is inhibited.

Drawings

FIG. 1 is a schematic diagram of the relative energy level structure of nitrogen-vacancy centres with frequency detuning;

wherein, Ω is shown in the figure_pIs energy level |0>To excited state energy level |2>The optical transition of (a); omega_sIs energy level |1>To excited state energy level |2>The optical transition of (a);

is |1>To excited state level |2>The phase of the optical transition of (1); t is the pulse action time; p_mIs ion at time t in m>Probability of a state; m is 0,1, e; f is the fidelity at which the target state is generated; Δ is the difference in transition frequency between energy levels, the amount of frequency detuning; a is₄Is one of the degree of freedom parameters contained in the design of the optical pulses; in FIG. 1, |2>The state being an excited state energy level | e>。

FIG. 2 is the draw ratio frequency Ω of the optical pulse_p,sAn evolution plot over time;

FIG. 3 is a time evolution diagram of the number of the layouts of the energy levels of the system when optical pulses are applied to a quantum system without detuning;

FIG. 4 is the draw ratio frequency Ω of the optical pulse_p,sAn evolution plot over time;

FIG. 5 is a plot of the number of energy levels of the system as a function of time during which optical pulses are applied to a quantum system without detuning;

FIG. 6 is a graph of the dependence of the fidelity of the system evolution to a given target state on the amount of frequency detuning under the effect of light pulses;

FIG. 7 is a graph of the fidelity and frequency detuning and the degree of freedom parameter a of the system evolving to a given target state under the action of light pulses₄A dependency graph of (2);

FIG. 8 is a graph of random doping at Y₂SiO₅Pr ion in crystal³H₄-¹D₂Schematic diagram of energy level structure;

FIG. 9 is the ratio frequency Ω of the optical pulse_p,sAn evolution plot over time;

FIG. 10 is a plot of the number of energy levels of the system as a function of time during which optical pulses are applied to a quantum system without detuning;

FIG. 11 is a graph showing the dependence of the fidelity of the system evolution to a given target state on frequency detuning under the action of light pulses in a rare earth ion system;

FIG. 12 is a graph showing the dependence of the number of arrangements of the energy levels of a three-level system on the amount of frequency detuning in a rare earth ion system,

wherein, Ω is shown in the figure_pIs energy level |1>To energy level | e>The optical transition of (a); omega_sIs energy level |0>To energy level | e>The optical transition of (a);

is |0>To energy level | e>The phase of the optical transition of (1); t is the pulse action time; p_mIs that the ion is at | m at time t>Probability of a state; m is 0,1, e; f is the fidelity at which the target state is generated; Δ is the non-resonant frequency detuning quantity; a is₄Is the light pulseOne degree of freedom parameter in the stroke.

Detailed Description

The invention is further described with reference to the following figures and examples.

The first embodiment is as follows:

an optical pulse generation method for high fidelity control of ensemble qubits according to the initial state |0 of the system>And target state

Wherein, α, β and

is three angles, alpha, beta being [0, 2 pi ]]Within the range, the number of characterization placements is |0>，|e>And |1>Distribution over three energy levels; i is an imaginary unit;

at [0, 2 π]Value in the range representing the qubit energy state |0>And |1>Relative phase therebetween;

the method is mainly used for solving the time-dependent Schrodinger equation of the three-level system reversely on the basis of the transition-free quantum drive theory, is different from the transition-free quantum drive theory, mainly aims at the microwave field between two ground state energy levels, utilizes the ingenious design of a time evolution operator, eliminates the microwave coupling term between the two ground state energy levels on the basis of a group of orthonormal and complete auxiliary state basis vectors and combines reverse engineering, simplifies experimental operation, realizes the initialization operation of quantum bits, and obtains the Hamilton quantity of the system; the key point is that a time-containing parameter is additionally introduced into a time evolution operator, and the parameter provides an additional degree of freedom for regulating and controlling the interaction between light and a substance; in the experimental system, an arbitrary waveform generator directly generates microwave pulses. The first order deflected beam of the acousto-optic modulator produces optical pulses, with typical rise times of the first order deflected beam of tens of nanoseconds when the focusing diameter is 100 μm. The acousto-optic modulator is driven by two radio frequency signals generated by an arbitrary waveform generator; specifically, under the premise of the known initial state and the known target state of the system, the amplitude and the phase of two optical pulses are designed, the amplitude and the phase are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the optical pulses, and the radio signal is used for driving an acousto-optic modulator in a continuous laser light path to obtain +1 level or-1 level deflection output light to generate a group of bicolor optical pulses;

wherein: the driving frequency of the acousto-optic modulator is f_aomThe laser frequency in the continuous laser beam path is f_laserThe qubit consists of two energy levels |0>And |1>Characterized by a frequency difference f between them_0-1Electron from energy level |1>To energy level | e>Has an optical transition frequency of v_pElectron from energy level |0>To energy level | e>Has an optical transition frequency of v_sThe acousto-optic modulator is driven to generate an action |1>-|e>The frequency of the radio signal of the optical pulses of the transition being f_pDriving an acousto-optic modulator to produce an effect of |0>-|e>The frequency of the radio signal of the optical pulses of the transition being f_sBoth satisfy f_p＝f_aom，f_s＝f_aom+f_0-1；f_laser+f_p＝ν_p；f_laser+f_s＝ν_s(ii) a The phases of the two radio signals are represented as:

and

the amplitude is expressed as: e_pAnd E_s；

Then:

E_pand E_sBoth vary with time and are determined by the following relationship:

in the formula of_p,sIs |1>-|e>And |0>-|e>Transition dipole of optical transitionMoment; omega_p,sIs the ratio frequency of the two light pulses; c is the draw ratio frequency omega of the slave light pulse_p,sTo the amplitude E of the radio signal_p,sThe conversion coefficient of (2) is determined by an experimental system; the ratio frequency omega_p,sThe time dependence t is shown by the following equation:

where α (t) and β (t) are time dependent

And

is the differential of the functions α (t) and β (t) with respect to time;

in addition, in consideration of the limiting conditions of the light pulse in the experiment and the manipulation target of any quantum state, the following alpha (t) and beta (t) are proposed:

in the formula a_kIs the coefficient of each Fourier component, C is a constant, and the value is selected under the boundary condition of alpha (t); consider the simplest case where the Hamiltonian drives the system along | φ₁(t)>From an initial state |0>Evolution to target stack state

Then according to | phi₁(t)>Alpha (t) and beta (t) have defined boundary stripsLet C be 0 here, depending on the constraints of the boundary conditions for α (t).

In the invention, in order to solve the problem that the microwave field between two ground state energy levels is difficult to operate in some experiments, a quantum state is evolved from an initial time to a termination time by introducing a time evolution operator; one approach involved therein is to introduce a time-dependent parameter into the design of the time-evolution operator, thus enlarging the operable space for the interaction of light and matter; before designing a time evolution operator, a set of orthonormal and complete auxiliary state basis vectors needs to be constructed:

the design of the time evolution operator is then as follows:

U(t)＝|φ₁(t)><φ₁(0)|+∑_m,n＝2,3γ_mn(t)|φ_m(t)><φ_n(0)| (4)，

wherein, | phi₁(t)>Is an evolving state, γ_mn(t) is an included time parameter introduced; m, n are time independent constants; due to the normalising properties of the time evolution operator

Then gamma is_mn(t) satisfies the following relationship:

∑_j＝1γ_mj(t)γ_nj(t)＝δ_mn,(m,n＝2,3) (5)，

within the constraints of the above formula, gamma is converted by means of a further time-dependent variable l (t)_mn(t)Expressed, the time evolution operator is then expressed in another form:

U(t)＝|φ₁(t)><φ₁(0)|+cosl(t)|φ₂(t)><φ₂(0)|+sinl(t)|φ₂(t)><φ₃(0)|-

sinl(t)|φ₃(t)><φ₂(0)|+cosl(t)|φ₃(t)><φ₃(0)| (6)，

then, in conjunction with reverse engineering, the hamiltonian is expressed as:

will be phi_n(t)>Substituting the formula (7) to obtain a new expression form of Hamilton quantity under the basis vector, and eliminating microwave coupling terms in two ground state energy levels by using the freedom degree parameters quoted in the formula (3); then comparing the Hamiltonian with the initial Hamiltonian to obtain an expression form of the light pulse; the light pulse obtained in the above way is used for initialization operation in a quantum system; in the center of the ensemble nitrogen vacancy, an arbitrary waveform generator directly generates microwave pulses; the first-order deflected light beam of the acousto-optic modulator generates light pulse, and when the focusing diameter is 100 mu m, the typical rising time of the first-order deflected light beam is tens of nanoseconds; the acousto-optic modulator is driven by two radio frequency signals generated by an arbitrary waveform generator; wherein: the driving frequency of the acousto-optic modulator is f_aomThe laser frequency in the continuous laser beam path is f_laserThe qubit consists of two energy levels |0>And |1>Characterized by a frequency difference f between them_0-1Electron from energy level |1>To energy level | e>Has an optical transition frequency of v_pElectron from energy level |0>To energy level | e>Has an optical transition frequency of v_sThe acousto-optic modulator is driven to generate an action |1>-|e>The frequency of the radio signal of the optical pulses of the transitions being f_pThe acousto-optic modulator is driven to generate action |0>-|e>The frequency of the radio signal of the optical pulses of the transition being f_sBoth satisfy f_p＝f_aom，f_s＝f_aom+f_0-1；f_laser+f_p＝ν_p；f_laser+f_s＝ν_s(ii) a The phases of the two radio signals are represented as:

and

the amplitude is expressed as: e_pAnd E_s；

Then:

E_pand E_sBoth vary with time and are determined by the following relationship:

in the formula of_p,sIs |1>-|e>And |0>-|e>Transition dipole moment of optical transition; omega_p,sIs the ratio frequency of the two light pulses; c is the draw ratio frequency omega of the slave light pulse_p,sTo the amplitude E of the radio signal_p,sThe conversion coefficient of (2); the ratio frequency omega_p,sThe time dependence t is shown by the following equation:

where α (t) and β (t) are time dependent

And

is the differential of the functions α (t) and β (t) with respect to time;

in addition, in consideration of the limiting conditions of the light pulse in the experiment and the manipulation target of any quantum state, the following alpha (t) and beta (t) are proposed:

in the formula a_kIs the coefficient of each Fourier component, C is a constant, and the value is selected under the boundary condition of alpha (t); consider the simplest case where the Hamiltonian drives the system along | φ₁(t)>From an initial state |0>Evolution to target stack state

Then α (t) and β (t) have defined boundary conditions, i.e. C is taken to be 0, depending on the boundary conditions of α (t).

The amplitude of the two-color light pulse generated by the above-described technical means includes a plurality of degrees of freedom (a)_k K 1,2,3 … ∞), taking the maximum value of k 4 as an example to illustrate the feasibility of the solution, adjusting a in the real number range_kDesigning light pulses with different performances;

the attached figure 1 is: there is a frequency detuned representation of the relative energy level structure of the nitrogen-vacancy centres. The nitrogen vacancy defect center of the diamond consists of substituted nitrogen atoms and vacancies of adjacent lattice sites; its ground state is also a spin triplet, consisting of between ground state sub-levels

Is split at | m_s＝±1>By applying an external magnetic field along the crystallographic axis of the nitrogen vacancy centre, an additional zeeman splitting is produced; the initialization and readout of the quantum states is here achieved by optical transitions between energy levels.

In the embodiment with a lineState of sexual superimposition

For example, the shape, the working performance and the quantum manipulation robustness of the optical pulse are explained; at the end of the optical pulse interaction with the quantum system, the quantum state of the qubit at the end of the pulse is in [ phi ] (t)_f)>Is shown at |0>State, | e>Sum of states |1>Probability of state by P_mCharacterized in that the expression is as follows:

P_m＝|<m|φ(t_f)>|²

wherein m is 0, e, 1.

Parameter a included in amplitude of optical pulse₁,a₂,a₃,a₄In [0,1 ]]Reasonable values are taken in the range, frequency detuning quantity is introduced by using a coupling differential equation describing the action of light and a three-energy-level quantum system, and the shape, the working performance and the robustness of light pulses are simulated in software; how to measure the robustness of an optical pulse is generally measured in terms of the fidelity F of the target state of the qubit. This definition is as follows:

F＝|<φ_target|φ(t_f)>|²

where | φ (t)_f)>Is a quantum state | phi (t) obtained by solving a three-level coupled differential equation>At t ═ t_fState function of time, | phi_target>Is the target quantum state.

Example two:

optical pulse generation method for high fidelity manipulation of ensemble qubits based on embodiment (11) for all a_kTake the value of k as 4, respectively for a₁，a₂，a₃，a₄Assigning a value, wherein C in formula (12) is 0; at this time:

a₁+2a₂+3a₃+4a₄＝0， (13),

a diamond material is selected in the ensemble nitrogen vacancy center system to construct a spinning environment of the ensemble nitrogen vacancy center; by scanning a_kDetecting the termination time of the action of the optical pulse and the quantum system, and influencing the fidelity condition of a target state in the ensemble due to the nonuniform broadening of spin transition in the ensemble caused by the random distribution of spins in the diamond in the nitrogen vacancy center of the ensemble to obtain a in formula (11)_kThe optimum value of (c).

The values of the bicolor pulses at the beginning and end are constantly equal to 0, i.e. omega_p,s(t＝0,t_f)＝0；a_kIn the real number range [0,1 ]]Optionally selecting the target state, constructing light pulse under the constraint of the conditions, and quickly and high-fidelity controlling the quantum system to create the set target state | phi_target>(ii) a In the simplest case, a_1,2＝0，a₃＝-0.8，a₄The shape and the handling behavior of the light pulse are explained for example 0.6.

FIG. 2 is a graph showing the evolution of the ratio frequency of the generated bicolor pulse with time; the pulse duration is 4ns, and at the initial and final moments, the values of the ratio frequency are all 0, so that the interference of a plurality of redundant frequency components caused by sharp pulse edges in a frequency domain on quantum state control is avoided.

FIG. 3 is a graph of the evolution of the number of the placement of the various energy levels of the system over time under the action of the pulse, without frequency detuning; all the layout numbers of the quantum system start from the ground state |0> and are finally distributed evenly over the energy levels |0> and |1>, which is consistent with the expected initial and target states.

The light pulse generated in this embodiment can create a quantum superposition state | φ_target>The optical pulse is only suitable for quantum systems where no frequency detuning is present.

The advantage of the optical pulse in this embodiment is that when the optical pulse acts on the quantum system, the values of the specific-pull frequency at the initial and final times are all 0. Because if the amplitude of the optical pulse varies rapidly in the time domain, it will necessarily bring a number of redundant components in the frequency domain, possibly disturbing the target quantum state. The method has the disadvantages that under the ideal condition, the method does not introduce interference of factors such as frequency detuning and the like, and the application range is limited.

Example three:

an optical pulse generation method for high fidelity manipulation of ensemble spins at center of ensemble nitrogen vacancies based on the first embodiment, wherein a is expressed in formula (11) for all a_kTake the value of k as 4, respectively for a₁，a₂，a₃，a₄And carrying out assignment again. At this time:

a₁+2a₂+3a₃+4a₄＝0，

wherein a is_kThe value of (2) ensures that the value of the bicolor pulse at the initial and final time is constantly equal to 0, i.e. omega_p,s(t＝0,t_f) Under the condition of 0, a_kIn [0,1 ] of an additional degree of freedom]Randomly selecting within the range, and constructing light pulses under the constraint of the conditions, so that the quantum system can be rapidly controlled with high fidelity, and a set target state is created; herein, with a₁＝-0.4357,a₂＝0.8439,a₃＝0,a₄The shape and the handling behavior of the light pulse are explained for example by-0.313.

Fig. 4 is a graph showing the evolution of the ratio frequency of the generated bicolor pulse with time according to the embodiment. The pulse duration is 4ns, and at the initial and final moments, the values of the ratio frequency are all 0, so that the interference of a plurality of redundant frequency components brought by sharp edges in a frequency domain on quantum state control is avoided.

FIG. 5 is a diagram showing the evolution of the number of the arrangement of the energy levels of the system with time when optical pulses are applied to a quantum system without detuning. The layout numbers are all distributed at energy level |0> at the initial time and are approximately equally distributed at energy levels |0> and |1> at the final time.

Fig. 6 is a graph showing the dependence of the fidelity between the final state of the system evolution and the given target state on the frequency mismatch existing in the ensemble at the termination time of the optical pulse. At a frequency detuning of 300MHz, the fidelity has reached 99.39%, and in an ensemble nitrogen vacancy-centered system, high fidelity is guaranteed for the non-uniform broadening that occurs in the spin ensemble.

FIG. 7 shows the fidelity of the optical pulse at the termination time, between the final state of the system evolution and the predetermined target state, and the frequency mismatch existing in the ensemble, and the pair a₄A scan of the effective range dependence. In the figure, let a₃＝0，a₄At [ -0.488,0.488]Within the effective range of (A), the important observation is₄The effect on fidelity in the frequency detuning range of ± 300 MHz. It is found from the figure that when Δ is 0, the fidelity is not affected. With more precise control, the robustness is significantly reduced, which means to some extent that the arbitrary waveform generator provides more precise control. Therefore, in a system that takes into account a frequency mismatch, the parameter a for this detuning range_kAnd further optimizing.

The light pulse generated in the embodiment has the advantages that the values of the ratio frequency at the initial and final moments are all 0, so that the requirement on the response speed of the acousto-optic modulator is reduced; and when quantum state control is carried out in a system with nonuniform broadening of about 300MHz, high fidelity (99.39%) is ensured; and the degree of freedom parameters contained in the light pulse have a large space for optimization, so that the light pulse has a larger application space.

The optical pulse generation method for performing high-fidelity control on the ensemble qubits based on the application can also be applied to quantum state control based on an ensemble nitrogen vacancy center system.

Example four:

an optical pulse generation method for performing high fidelity manipulation on ensemble qubits based on embodiment one, for a in equation (11)_kThe value is reasonably assigned to design the optical pulse to be applied to a quantum bit system depending on frequency band screening, such as a rare earth ion system. The degree of freedom parameter in the optical pulse at this time satisfies (for example, k ═ 4):

a₁+2a₂+3a₃+4a₄＝0，

wherein a is_kThe value of (A) ensures that the value of the bicolor pulse at the initial and final time is constantly equal to 0, i.e. omega_p,s(t＝0,t_f) Under the condition of 0, a_kIn the real number range [0,1 ]]Randomly selecting, constructing light pulse under the constraint of the upper member, and quickly and high-fidelity controlling the quantum system to establish a set target state | phi_target>. In the following cases

a_3,4The shape and the handling behavior of the light pulse are explained with 0 as an example.

FIG. 8 is a randomly doped dopant in Y₂SiO₅Pr ion in crystal³H₄-¹D₂The energy level structure diagram is a typical three-energy level system with non-uniform broadening, and the technical scheme is illustrated by taking the three-energy level system as an example; the ground state and the excited state in the figure both comprise 3 hyperfine energy levels, and the spacing between the three energy levels is between 4.6 and 17.3 MHz. The quantum bit energy level is from |0>Sum of states |1>Configuration, | e>Is an excited state. Coupling between qubit energy levels via optical transitions |0>-|e>And |1>-|e>To be implemented.

Fig. 9 is a graph showing the evolution of the ratio frequency of the two-tone pulses generated in this embodiment. The pulse duration is 4 mus, and at the initial and final moments, the values of the ratio frequency are all 0, so that the interference of a plurality of redundant frequency components caused by sharp pulse edges in a frequency domain on quantum state control is avoided.

FIG. 10 is a diagram showing the evolution of the number of the arrangement of the energy levels of the system with time when optical pulses are applied to a quantum system without detuning. The layout numbers are all distributed at energy level |0> at the initial time and are approximately equally distributed at energy levels |0> and |1> at the final time.

Fig. 11 is a diagram showing the dependence of the fidelity between the final state of the system evolution and the given target state on the frequency mismatch existing in the ensemble at the termination time of the optical pulse. Wherein the frequency detuning is the difference between the optical pulse center frequency and the actual optical transition frequency of the qubit ion. Within the range of +/-140 kHz, the fidelity is always kept above 99.1 percent, namely, the method has better robustness to frequency detuning in the range. Between hundreds of kHz and 3.5MHz, there are no ions, so the fidelity of this interval is not critical; when the frequency is detuned beyond 3.5MHz, the fidelity is between 50% -50.27%, which deviates from the ideal value by 50%, indicating that the bicolor pulse has some off-resonance excitation for this range of ions.

FIG. 12 is a graph showing the dependence of the number of placements on levels |0>, | e >, and |1> on the amount of frequency detuning when a light pulse is applied to a three-level system, which better illustrates the non-resonant excitation of background ions by the light pulse. For rare earth ion systems, outside a range of ± 3.5MHz from the center frequency, |1> states are about 1.13% and less than 3%, which means that off-resonance excitation is suppressed very effectively, which is within an acceptable range for rare earth ion ensemble qubits.

The optical pulse generated in the embodiment has the advantages that the optical pulse has better robustness to frequency detuning existing in the ensemble quantum system, is low enough to perform non-resonant excitation on background ions, and is suitable for a qubit system depending on frequency band screening. Therefore, the light pulse in the embodiment has the characteristics of high robustness and low resonance excitation, and the realization of high-fidelity quantum manipulation is ensured.

The optical pulse generation method for performing high-fidelity control on the ensemble qubits based on the application can also be applied to the control of quantum states in a rare earth ion system. In the rare earth ion system, there are two features: the optical transition of the ensemble qubit ions has a certain frequency width due to the non-uniform broadening; the target ensemble qubit is not clean in the environment in the frequency domain, and other qubits exist nearby, and their off-resonance excitation can cause interference to the target qubit. In solving for a_kShould satisfy the optimum value ofThe robustness in the preset small frequency domain meets the requirement and ensures that interference excitation is not caused in the preset large frequency domain. The preset small frequency domain and the preset large frequency domain are two frequency range values set according to an actual experimental device.

On the basis of solving the problem of decoherence caused by frequency detuning, the invention further solves the problem of the microwave field between two ground state energy levels, simplifies the experimental operation and carries out fast and high-robustness quantum state initialization control. The light pulse which solves the two problems simultaneously has better application prospect. The method can be used for an ensemble nitrogen vacancy center system, even a rare earth ion system, a superconducting quantum bit system and the like. In addition, although the technical scheme is developed for a three-level system, under a specific condition, the three-level system is collapsed into a two-level system by controlling the light pulse, so that the light pulse for performing layout number transfer and creating a superposition state on the two-level system is constructed; furthermore, the method herein is mainly directed to the design of time evolution operators, and then arbitrary single-qubit logic gates are implemented by reasonable changes to their form (such as the degree of freedom parameters involved therein). These minor variations or modifications in the technology are still within the scope of the present invention.

The technical solution is not described in detail and belongs to the technology known to the skilled person.

Claims (10)

1. An optical pulse generation method for high fidelity control of ensemble qubits, characterized in that: in an ensemble nitrogen vacancy center system, a time-dependent Schrodinger equation of a three-level system is reversely solved based on a transition-free quantum drive theory, when the time-dependent Schrodinger equation of the three-level system is solved, on the premise that an initial state and a target state of the system are known, a microwave field between two ground state levels is eliminated as a target, and an expression form of a time evolution operator is designed by introducing a degree of freedom parameter; then reversely designing the amplitude and phase of the two light pulses in the ensemble nitrogen vacancy center system through a time evolution operator; inputting the amplitude and the phase into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the optical pulse, and driving an acousto-optic modulator in a continuous laser light path by using the radio signal to obtain +1 level or-1 level deflection output light to generate a group of bicolor optical pulses; and vertically injecting the generated bicolor light pulse into a three-energy-level quantum system medium, and enabling the bicolor light pulse and the quantum system medium to interact to generate any superposition state of the qubits.

2. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 1, characterized in that: according to the initial state |0 of the system>And target state

Wherein, α, β and

is three angles, alpha, beta being [0, 2 pi ]]Within the range, the number of characterization placements is |0>，|e>And |1>Distribution over three energy levels; i is a unit of an imaginary number,

at [0, 2 π]Value in the range representing the qubit energy state |0>And |1>Relative phase therebetween;

first, assuming that a time variable is expressed by t, two time-containing variables α (t) and β (t), a set of orthonormal and complete auxiliary state basis vectors is constructed:

suppose the time evolution operator of the system is:

U(t)＝|φ₁(t)><φ₁(0)|+∑_m,n＝2,3γ_mn(t)|φ_m(t)><φ_n(0)| (4)，

where m, n are time independent constants, i.e., the system will be along the initial state | φ of the qubit₁(t)>Evolution is carried out, the parameter gamma being due to the normalization of the time evolution operator_mn(t) it is necessary to satisfy:

∑_j≠1γ_mj(t)γ_nj(t)＝δ_mn(m,n＝2,3) (5)，

wherein, delta_mnIs a function of Kronecker Delta, gamma is converted by means of another time-dependent variable l (t) under the constraint of equation (5)_mn(t) is expressed such that equation (4) is expressed in another form:

U(t)＝|φ₁(t)><φ₁(0)|+cosl(t)|φ₂(t)><φ₂(0)|+sinl(t)|φ₂(t)><φ₃(0)|-sinl(t)|φ₃(t)><φ₂(0)|+cosl(t)|φ₃(t)><φ₃(0)| (6)，

then, in conjunction with reverse engineering, the hamiltonian is expressed as:

will be phi_n(t)>Substituting the formula (7) to obtain a new expression form of the Hamiltonian under the basis vector; then comparing the Hamiltonian with the initial Hamiltonian to obtain an expression form of the light pulse;

the light pulse obtained in the above way is used for initialization operation in a quantum system; in the center of the nitrogen vacancy of the ensemble, an arbitrary waveform generator directly generates microwave pulses; the first-order deflected light beam of the acousto-optic modulator generates light pulse, and when the focusing diameter is 100 mu m, the typical rising time of the first-order deflected light beam is tens of nanoseconds; the acousto-optic modulator is driven by two radio frequency signals generated by an arbitrary waveform generator; it is composed ofThe method comprises the following steps: the driving frequency of the acousto-optic modulator is f_aomThe laser frequency in the continuous laser beam path is f_laserThe qubit consists of two energy levels |0>And |1>Characterized by a frequency difference f between them_0-1Electron from energy level |1>To energy level | e>Has an optical transition frequency of v_pElectron slave energy level |0>To energy level | e>Has an optical transition frequency of v_sThe acousto-optic modulator is driven to generate an action |1>-|e>The frequency of the radio signal of the optical pulses of the transition being f_pDriving an acousto-optic modulator to produce an effect of |0>-|e>The frequency of the radio signal of the optical pulses of the transition being f_sBoth satisfy f_p＝f_aom，f_s＝f_aom+f_0-1；f_laser+f_p＝ν_p；f_laser+f_s＝ν_s(ii) a The phases of the two radio signals are represented as:

and

the amplitude is expressed as: e_pAnd E_s；

Then:

E_pand E_sBoth vary with time and are determined by the following relationship:

in the formula of_p,sIs |1>-|e>And |0>-|e>Transition dipole moment of optical transition; omega_p,sIs the ratio frequency of the two light pulses; c is the draw ratio frequency omega of the slave light pulse_p,sTo the amplitude E of the radio signal_p,sThe conversion coefficient of (2); the ratio frequency omega_p,sThe time dependence t is shown by the following equation:

where alpha (t) and beta (t) are time-dependent,

and

is the differential of the functions α (t) and β (t) with respect to time.

3. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 2, characterized in that:

in the formula a_kIs the coefficient of each fourier component, C is a constant, and its value is selected under the boundary condition that satisfies α (t).

4. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 3, wherein: hamiltonian driving system along | phi₁(t)>From an initial state |0>Evolution to target stack state

According to equation (1), the boundary conditions of α (t) and β (t) are determined, where C is 0.

5. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 2, characterized in that: when k is 4 in formula (11), a_kThe value of (A) is required to satisfy the following conditions

a₁+2a₂+3a₃+4a₄＝0 (13)，

6. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 2, characterized in that: a diamond material is selected in the ensemble nitrogen vacancy center system to construct a spinning environment of the ensemble nitrogen vacancy center; by scanning a_kDetecting the termination moment of the action of the optical pulse and the quantum system, and influencing the fidelity condition of a target state in the ensemble due to the nonuniform broadening of spin transition in the ensemble caused by the random distribution of spins in diamond in the nitrogen vacancy center of the ensemble to obtain a value of a in equation (11)_kThe optimum value of (c).

7. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to claim 5, wherein: a is_kThe optimal values of (a) are: a is₁＝-0.4357,a₂＝0.8439,a₃＝0,a₄＝-0.313。

8. An optical pulse generation method for high fidelity manipulation of ensemble qubits according to one of claims 1 to 6 for producing an optical pulse system for high fidelity manipulation of qubits.

9. Rare earth ion systems made using the optical pulse generation method for high fidelity manipulation of ensemble qubits of one of claims 1 to 7.

10. The rare earth ion system according to claim 9, wherein: in solving for a_kThe optimal value of (2) should meet the requirement of robustness meeting in a preset small frequency domain range and ensure that no interference excitation is caused in a preset large frequency domain.

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