Short-path optical pulse based on three-energy-level system, generation method and application

Abstract

The invention discloses a short-path optical pulse based on a three-energy-level system, a generation method and application. Specific forms of Hamiltonian and Rabian frequency parameters thereof are constructed in a three-level quantum system, and the parameters are optimized to obtain a light pulse which enables an evolution path of a quantum state on a Bloch sphere to be shortest and is high in fidelity. According to the optical pulse obtained by the technical scheme, the quantum state can be changed into a target state from any initial state through a circular evolution path, and logic gate operation is executed. The evolution time of the gate can be effectively shortened through the circular evolution trajectory, and the quantum gate reduces the influence of environmental noise while keeping the robustness of the control error. According to the quantum logic gate, multi-parameter optimization is carried out on the optical pulse waveform, the quantum logic gate is suitable for a rare earth ion Pr < 3 + >: Y2SiO5 quantum bit system device and an inverted-V-shaped three-energy-level system, and the high-fidelity quantum logic gate is obtained.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing, and specifically relates to various systems that can realize single-bit quantum logic gates, such as superconducting quantum computing systems, nuclear magnetic resonance quantum systems, ion trap systems, and rare earth ion quantum systems. Background Art

[0002] Quantum computing is based on the basic properties of quantum mechanics and has a natural and powerful exponential parallel computing capability. It can be used to deal with difficult problems in scientific research and engineering technology that classical computers cannot solve, such as large number decomposition and molecular simulation. At present, quantum computers can be divided into two categories based on different algorithms. One is quantum simulation computers, including quantum simulation, quantum annealing and adiabatic quantum computing; the other is quantum digital circuit computers, which mainly use a combination of multiple quantum logic gates (qubitgates) to perform quantum computing. At present, the latter is generally considered to be the mainstream direction of future quantum computing.

[0003] The most basic unit of quantum digital circuits is a single-bit quantum logic gate, which converts an arbitrary quantum state into another arbitrary quantum state. It is generally believed that if a usable small- to medium-scale fault-tolerant quantum computing scheme is to be realized, the fidelity of the single-bit quantum logic gate must reach at least 99.9%. Single-bit quantum logic gates are an indispensable component of quantum computers. The fidelity and path length of quantum logic gates determine the accuracy and speed of quantum computing. High-fidelity and short-path single-bit quantum logic gates are the research goals we hope to achieve, which can lay the foundation for more complex quantum computing.

[0004] The design of optical pulses for implementing quantum logic gates is often based on three-level quantum systems. There are many experimental systems, such as ensemble rare earth ion systems, superconducting systems, trapped ions, nitrogen-vacancy color centers, etc. Chinese invention patent CN108415206A provides a method for designing optical pulses that can create arbitrary superposition states of quantum bits in a three-level system, and realizes the initialization of quantum bits in an ensemble rare earth ion system; on this basis, Chinese invention patent CN114580646A proposes a method for constructing arbitrary geometric quantum logic gates of imperfect systems in an ensemble rare earth ion system, and realizes arbitrary geometric quantum logic gates in an ensemble rare earth ion quantum bit system by designing and optimizing optical pulses containing multiple degree of freedom parameters. The evolution trajectory of the optical pulse designed by the above method on the Bloch sphere is in the shape of an orange segment, that is, the optical pulse controls the quantum state to start from the North Pole and follow the meridian of the Bloch sphere to the South Pole, and then returns from the South Pole to the North Pole after rotating a certain angle. The disadvantage is that for different quantum logic gates, their evolutionary trajectories on the Bloch sphere are the same, and this evolutionary path is not the shortest path to realize quantum logic gates. In the method described in the literature that can construct arbitrary geometric quantum logic gates in imperfect systems, the evolutionary trajectories of all quantum logic gates are the same, resulting in the same evolutionary time for all logic gates; and the entire evolutionary path is in the shape of an orange segment, and the evolutionary time is relatively long, resulting in low fidelity of arbitrary quantum logic gates in a three-level system. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a short-path optical pulse based on a three-level system, a generation method and an application thereof, which can realize a high-fidelity quantum logic gate in a three-level quantum system while minimizing the evolution path of the quantum state, thereby shortening the operation time of the logic gate and further improving the control fidelity of the quantum logic gate.

[0006] The technical solution to achieve the purpose of the present invention is to provide a short-path optical pulse generation method based on a three-level system, wherein a three-level quantum system is formed between the energy levels |0, |1 and |e, including: constructing a Hamiltonian in the three-level quantum system Among them, Ω p (t) = Ω(t)sin(θ / 2), Among them, Ω p (t) and Ω s (t) is the Rabi frequency of the two-color light pulse, θ is the parameter that controls the amplitude of the light pulse, are the parameters for controlling the phase of the optical pulse, θ and are all constants in the range of [0,2π], which are related to the selection of logic gates. Ω(t) is the Rabi frequency Ω p,s (t), α(t) and β(t) are the polar angle and azimuthal angle on the Bloch sphere of the equivalent two-level system b and e, respectively. The ranges of α(t) and β(t) are [0, α m (γ)] and [0,π], and is their differential with respect to time, and Δ(t) is the frequency detuning amount.

[0007] Set the parameters of the time-dependent component Ω(t) of the Rabi frequency, where the polar angle α(t) on the Bloch sphere satisfies the condition: in, Among them, α m (γ) is the maximum value reached by α(t) during its evolution, γ is the geometric phase, ranging from [0,π], and τ is the pulse action time. is a parabolic function, n and k are positive integers greater than 0, and the degree of freedom parameter c is n is a real number greater than 0; β(t) is given by the torus equation Sure.

[0008] Scanning degree of freedom parameter c n At the end of the action of the pulse on the three-level quantum system, the fidelity of the target state and the relationship between the non-resonant excitation of the ion and the frequency detuning amount are detected to obtain the degree of freedom parameter c n The optimal value of is used to obtain the short-path optical pulse waveform that drives any quantum state to transition to the target quantum state.

[0009] The technical solution of the present invention also includes a short-path optical pulse based on a three-level system obtained according to the above optical pulse generation method.

[0010] The short-path optical pulse based on the three-level system described in the present invention is applied to rare earth ion Pr 3+ :Y2SiO5 quantum bit system device and Λ-type three-level system to obtain high-fidelity quantum logic gates.

[0011] The present invention aims to construct the specific form of Hamiltonian and its Rabi frequency parameters in a three-level quantum system, and optimize the parameters to provide a light pulse that can make the evolution path of the quantum state on the Bloch sphere shortest and with high fidelity. This light pulse can make the quantum state from any initial state |ψ0=cosξ|1+sinξe iη|0, where ξ and η both take values ​​in the range [0,2π], and after a circular evolution path, they become the target state |ψ target , performing logic gate operations. The circular evolution trajectory can effectively shorten the evolution time of the gate, so that the quantum gate can maintain robustness to control errors while reducing the impact of environmental noise.

[0012] In order to solve the deficiencies in the prior art, the present invention seeks a short-path optical pulse based on a three-level system, a generation method and an application. The method designs a two-color optical pulse that can make any initial state evolve along a circular path to the target state determined by the logic gate. That is, for a given logic gate, the geometric phase accumulated by the quantum state during the evolution process is determined. Under the premise of satisfying this geometric phase, the technical solution of the present invention adopts the shortest circular path to achieve it. The evolution trajectory of the quantum state on the Bloch sphere with {|b>,|e>} as the basis vector is a great circle, see the attached Figure 2 , is a schematic diagram of the evolution trajectory of the quantum state on the Bloch sphere with {|b>,|e>} as the basis vector, and its evolution trajectory is a large circle; Figure 2 It can be seen that for different logic gates, the radius of the circle is different, that is, the length of the evolution path is determined by the geometric phase of the logic gate. The larger the geometric phase, the larger the radius of the circle. The pulse is vertically incident on the three-level quantum system medium, and after interacting with the medium, a high-fidelity arbitrary geometric quantum logic gate is generated.

[0013] The technical solution provided by the present invention is for any initial state of the system |ψ0=cosξ|1+sinξe iη |0, where ξ and η are both in the range of [0,2π]. First, based on the optical pulse design method that can create an arbitrary superposition state of the three-level system quantum bit, the quantum state is initialized on the three-level quantum system medium. Then, a laser optical path that can realize geometric quantum computing is built. For the specific experimental device, see the attached Figure 7 According to the theory of non-adiabatic geometric quantum computing, the Rabi frequency Ω in the Hamiltonian of the interaction between the light pulse and the three-level quantum system p,s The time component of (t) is where α(t) and β(t) are the polar angle and azimuthal angle on the Bloch sphere of the equivalent two-level system b and e, and the ranges of α(t) and β(t) are [0, α m (γ)] and [0,π], and is their differential with respect to time. By designing the specific forms of α(t) and β(t), the evolution trajectory of the light pulse on the Bloch sphere is made into a large circle. The von Neumann equation is then used to obtain the constraints of the amplitude and phase of the two light pulses that perform logic gate manipulation, and the amplitude and phase of the light pulse can be obtained. This amplitude and phase are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the light pulse. The radio signal drives the acousto-optic modulator in the continuous laser optical path to obtain a +1-level deflected output light, generating a set of two-color light pulses; the generated two-color light pulses are vertically incident into the three-level quantum system medium, and the two-color light pulses interact with the quantum system medium to drive an arbitrary state to transition to the target quantum state. The pulse signal after the interaction with the medium is detected by a photodetector and output to an oscilloscope and an operation circuit respectively. The oscilloscope can be used to display the transmission signal of the scanning light pulse detected by the photodetector. Deconvolution operation can be performed in the operation circuit to obtain the absorption spectrum in the quantum bit frequency window, and then obtain the final state information of the quantum bit after the two-color light pulse interacts with the rare earth ion.

[0014] Compared with the prior art, the present invention has the following significant features:

[0015] 1. The two-color light pulse generated according to the technical solution of the present invention is suitable for a three-level quantum system, and includes two light pulses that act simultaneously but have different frequencies, amplitudes and phases. The above parameters of the light pulses can be fully controlled by an arbitrary wave generator and an acousto-optic modulator.

[0016] 2. Two-color light pulses can manipulate the quantum state of a quantum bit in a three-level system, causing it to evolve into the target quantum state determined by the quantum logic gate, including arbitrary layout number distribution and arbitrary relative phase control.

[0017] 3. The starting and ending values ​​of the Rabi frequency of the dual-color light pulse are zero to avoid exciting unnecessary energy level transitions of adjacent ions.

[0018] 4. The amplitude, frequency and phase of the two-color light pulses all vary with time.

[0019] 5. The duration of the light pulse can be arbitrarily short in theory as long as the light field intensity is large enough. For a light field with a maximum Rabi frequency of 10 MHz, the length of the light pulse does not exceed 80 ns.

[0020] 6. For a given quantum logic gate, among all possible evolution paths, the evolution path in this scheme is the shortest (circular).

[0021] 7. For different geometric quantum logic gates, the smaller the geometric phase, the smaller the solid angle of the spherical cap enclosed by the closed evolution path, and the shorter the required evolution time. This has obvious advantages over traditional evolution schemes, because in traditional evolution schemes, the evolution time of all quantum logic gates is the same. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of the three-level structure of the rare earth ion system. (a) is a three-level system with 0, 1, and e as basis vectors, and (b) is a three-level system with d, b, and e as basis vectors, which is equivalent to a two-level system with b and e as basis vectors.

[0023] Figure 2 It is a schematic diagram of the evolution trajectory of the quantum state on the Bloch sphere with {|b>,|e>} as the basis vector, and its evolution trajectory is a great circle.

[0024] Figure 3 is the evolution of the time-dependent component Ω(t) and the frequency detuning Δ(t) of the Rabi frequency of the S gate over time.

[0025] Figure 4 It is the distribution of the number of layouts of quantum states in |0, |1, |e states during the execution of the S gate, as well as the evolution of the fidelity F over time.

[0026] Figure 5 is the evolution of the time-dependent component Ω(t) and the frequency detuning Δ(t) of the Rabi frequency of the T gate over time.

[0027] Figure 6 It is the distribution of the number of layouts of quantum states in |0, |1, |e states during the execution of the T gate, as well as the evolution of the fidelity F over time.

[0028] In each figure, Ω s is the Rabi frequency of the optical transition from energy level |1 to energy level |e; Ω p is the Rabi frequency of the optical transition from energy level |0 to energy level |e; τ is the pulse action time; P m is the probability of the ion being in the |m state at time t, m = 0, 1, e; F is the fidelity of producing the target state; Δ(t) is the frequency detuning amount.

[0029] Figure 7 Schematic diagram of an experimental device for applying the optical pulse provided by the present invention to a rare earth ion quantum bit system, wherein 1 is a laser, 2 is an acousto-optic modulator, 3 is an arbitrary wave generator, 4 is a plane reflector, and 5 is a crystal doped with rare earth ions (Pr 3+ :Y2SiO5), 6 is a photodetector, 7 is an oscilloscope, 8 is an operation circuit, 9 is a light block, 10 is a lens, and 11 is a liquid helium cryostat. DETAILED DESCRIPTION

[0030] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0031] Embodiment 1:

[0032] This embodiment provides a short-path optical pulse generation method based on a three-level system, and a two-color optical pulse can be designed. When the optical pulse acts on the three-level quantum system, any initial state on the Bloch sphere can be made |ψ0=cosξ|1+sinξe iη |0, where ξ and η both take values ​​in the range [0,2π], and evolve to the target state along the shortest evolution path.

[0033] See attached Figure 1 , is a schematic diagram of the three-level structure of the rare earth ion system. (a) is a three-level system with 0, 1, and e as basis vectors, and (b) is a three-level system with d, b, and e as basis vectors, which is equivalent to a two-level system with b and e as basis vectors.

[0034] As attached Figure 1 As shown in Figure (a), |e is an excited state, |0 and |1 are two ground state energy levels, which are used to characterize the two energy levels of the quantum bit. The energy level spacing between the two is within the radio frequency range, and the specific value varies depending on the specific rare earth ion. p,s (t) represents the Rabi frequency between |0-|e and |1-|e.

[0035] The specific design method of the shortest path optical pulse is as follows:

[0036] The Hamiltonian of the interaction between the light pulse and the three-level quantum system is shown in equation (1):

[0037] Wherein, the time-varying detuning value Δ(t) = 2π[f p (t)-ν e-0 (t)]=2π[f s (t)-ν e-1 (t)]. p (t), f s (t), ν e-1 (t) and v e-0 (t) are all time-dependent frequencies, where f p (t) is the frequency of the radio signal driving the AOM to generate the optical pulse acting on the |0>-|e> transition; f s (t) is the frequency of the radio signal driving the AOM to generate the optical pulse acting on the |1>-|e> transition; ν e-1 (t) is the transition frequency of |e>-|1>; ν e-0(t) is the transition frequency of |e>-|0>. The quantum bit is encoded in the computational subspace of {|0>, |1>}, and the number of layouts on |e> is zero at the beginning and end of the pulse evolution. The Rabi frequency Ω p，s The dependence of (t) on time t is given by equations (2) and (3) as follows:

[0038] Where θ is the parameter that controls the amplitude of the light pulse, are the parameters for controlling the phase of the optical pulse, θ and are all constants in the range of [0, 2π] and are related to the selection of logic gates. Different logic gates correspond to different θ and Ω(t) is the Rabi frequency Ω p，s The time-dependent component of (t).

[0039] Using the bright state and dark state The definition of , the energy level structure of {|b>, |d>, |e>} can be found in the appendix Figure 1 As shown in Figure (b) in the figure, the Hamiltonian can be rewritten as formula (4): H(t)=Δ(t)|e> <e|+Ω(t)|b><e|+Ω * (t)|e> <b| (4)

[0040] Among them, the dark state |d> has been decoupled. When the parallel movement condition is satisfied, the dynamic phase is always kept at zero. At this time, the frequency detuning amount Δ(t) is in constant proportion to the time-dependent component Ω(t) of the Rabi frequency. The time-dependent component Ω(t) of the Rabi frequency is given by equation (5):

[0041] In formula (5), α(t) and β(t) are the polar angle and azimuthal angle on the Bloch sphere of the equivalent two-level system {|b>, |e>}. The ranges of α(t) and β(t) are [0, αm(γ)] and [0, π], respectively. and is their differential with respect to time. α(t) is composed of some polynomials, as shown in equations (6) and (7):

[0042] n, k are positive integers greater than 0, c n is a degree of freedom parameter not less than zero, α m (γ) is the maximum value that α(t) can reach during the evolution, which depends on the size of the geometric phase γ in equation (9). is a parabolic function. Equation (6) satisfies α(0) = α(τ) = 0, which naturally satisfies the cyclic evolution condition. Therefore, at the end of the evolution, the quantum state returns to the computational subspace {|0>, |1>}.

[0043] The single-bit quantum logic gate can be expressed as formula (8):

[0044] in is a unit vector, σ = (σx, σy, σz) is a Pauli matrix, γ is the geometric phase, and its value range is [0, π], as shown in the following equation (9):

[0045] In order to make the path shortest, the trajectory of the unit vector determined by α(t) and β(t) is set to be a circle. That is, for a given α(t), as shown in equation (6), β(t) is determined by the following equation (10):

[0046] This is the equation of a ring on the sphere passing through the North Pole. The solid angle of the spherical cap formed by the ring is 2γ. The ratio of the time component Ω(t) of the Rabi frequency and the frequency detuning Δ(t) is a constant, as shown in equation (11):

[0047] The amplitude of the two-color light pulse generated by the above technical solution contains n degrees of freedom, and the degree of freedom parameter c is adjusted within the range of positive real numbers. n By taking the value of , two-color light pulses with different performances can be generated.

[0048] In order to consider the decoherence effect of the environment, the aforementioned two-color light pulse can be substituted into the Lindblad master equation describing the interaction between light and a three-level quantum system, and the working performance of the light pulse can be simulated in MATLAB. The Lindblad master equation is shown in equation (12):

[0049] where ρ(t) = |ψ(t)><ψ(t)| is the density matrix of the system evolution, Γ1 and Γ2 are the decay coefficient and decoherence coefficient, and is the Lindblad operator, where A is σ1 or σ2. For the rare earth ion system (Pr 3+ :Y2SiO5), Γ1=1 / 164μs -1 , Γ2=1 / 132μs -1,σ1=|0><e|+|1><e|,σ2=|e><e|-|0> <0|-|1><1|; For a Λ-type three-level system, Γ1=2ππ×3kHz, Γ2=2ππ×3kHz, σ2=|e>Me|+2|1><1|+3|h><h|,|h> is another excited state, used to characterize the effect of the environment. The fidelity F of the target state of the generated quantum bit is defined as follows: F=<ψ target |ρ(τ)|ψ target > (13)

[0050] Due to the limitation of computing power, the value of n cannot be too large when optimizing, otherwise the optimization process may fail to converge to a local maximum. If the value of k is small, it cannot guarantee that the optimization pulse has enough scanning range. Therefore, α(t) takes the form of the following formula (14):

[0051] Based on equations (2), (3), (6), (7), (10) and (14), the Rabi frequencies of the two optical pulses can be obtained. n (n=4) must be a real number greater than 0 to satisfy α(0)=α(τ)=0 and α(t)∈[0,α m γ] and other boundary conditions.

[0052] Embodiment 2:

[0053] Based on the short-path optical pulse generation method based on a three-level system provided in Example 1, this embodiment applies optical pulses to a rare earth ion quantum bit system (Pr 3+ :Y2SiO5), the experimental device is shown in the attached Figure 7 shown.

[0054] Figure 7 In the figure, 1 is a laser, 2 is an acousto-optic modulator, 3 is an arbitrary wave generator, 4 is a plane reflector, and 5 is a crystal doped with rare earth ions (Pr 3+ :Y2SiO5), 6 is a photodetector, 7 is an oscilloscope, 8 is an operation circuit, 9 is a light block, 10 is a lens, and 11 is a liquid helium cryostat.

[0055] The specific implementation plan is as follows:

[0056] The amplitude and phase of the two-color light pulse obtained based on equations (2), (3), (6), (7), (10) and (14) in Example 1 are input into an arbitrary wave generator 3 to generate a radio signal with the same amplitude and phase as the light pulse, which can drive the acousto-optic modulator 2 in the continuous laser optical path.

[0057] The two radio signals driving the AOM 2 have the same duration, but different amplitudes, frequencies, and phases. The amplitudes change with time, and the specific shape depends on the target quantum state to be achieved; the frequencies are within the driving frequency bandwidth of the AOM 2, and the frequency difference between the two radio signals is f 0-1 , but its value varies with time and depends on the target quantum state; the phases of the two are constants, and their values ​​depend on the target quantum state.

[0058] The laser 1 outputs a continuous laser, which is incident on the acousto-optic modulator 2 driven by the arbitrary wave generator 3. The wavelength of the laser is near the optical transition frequency of the quantum bit ion. 3+ Ionic 3 H4- 1 D2 transition line, the output wavelength of laser 1 should be 605.977nm, and the line width of continuous laser should not exceed 100kHz.

[0059] The two radio signals cause the refractive index of the crystal built into the AOM 2 to change periodically. Therefore, when the continuous laser propagates in the AOM 2, the zero-order light still travels in the original direction and is intercepted by the light block 9; while the propagation direction of the +1-order or -1-order light is deflected, and the amplitude, phase and frequency of the +1-order or -1-order light are modulated by the two radio signals. The +1-order or -1-order light has the same amplitude, phase and duration as the two radio signals.

[0060] Where, the driving frequency of the acousto-optic modulator (AOM) is f aom , the laser frequency in the continuous laser light path is ν laser , the qubit is characterized by two energy levels |0 and |1, the frequency difference between them is f 0-1 , the frequency of the optical transition of electrons from energy level |0 to energy level |e is ν p , the frequency of the optical transition of electrons from energy level |1 to energy level |e is ν s The frequency of the radio signal driving the AOM 2 to generate the optical pulse acting on the |0-|e transition is f p (t), the frequency of the radio signal driving the AOM to generate the optical pulse acting on the |1-|e transition is f s (t), both satisfy f p (t) = f aom (t), f s(t) = f aom (t)-f 0-1 ; ν laser (t)+f p (t) = ν p (t), ν laser (t)+f s (t) = ν s (t); The phase of the two radio signals is expressed as: and The amplitude is represented by E p and E s ; then it satisfies: E p and E s Both of them vary with time and are determined by the following relationship (15):

[0061] Where μ p,s is the transition dipole moment of the |0-|e and |1-|e optical transitions; Ω p,s (t) is the Rabi frequency of the two optical pulses; C is the Rabi frequency Ω of the optical pulses p,s To the radio signal amplitude E p,s The conversion factor is determined by the experimental system.

[0062] The generated two-color light pulse passes through the optical path formed by the plane reflector 4 and the lens 10, and then vertically enters the rare earth ion doped crystal 5. The rare earth ion doped crystal 5 is placed in a liquid helium cryostat 11, which can ensure that the crystal 5 is in a low temperature environment of 2K. The two-color light pulse interacts with the quantum system medium to drive an arbitrary quantum superposition state to transition to another arbitrary target quantum superposition state, and perform quantum logic gate manipulation.

[0063] In order to detect the manipulation result of the light pulse on the rare earth ions, after the light pulse and the rare earth ions are finished, the arbitrary wave generator 3 generates a square wave signal whose frequency changes linearly with time, and the continuous laser generates a frequency scanning light pulse under the modulation of this square wave signal. When the light pulse is incident on the crystal 5, the quantum bit will selectively absorb some frequency components according to its own quantum state, so that the information of the quantum bit quantum state is modulated on the scanning light pulse, and the scanning light pulse transmitted from the crystal 5 is collected by the photodetector 6. The oscilloscope 7 is used to display the transmission signal of the scanning light pulse detected by the photodetector 6; at the same time, the transmission signal is transmitted to the operation circuit 8 for deconvolution operation, and the absorption spectrum in the quantum bit frequency window is obtained, and then the final state information of the quantum bit after the two-color light pulse and the rare earth ion are obtained.

[0064] Embodiment 3:

[0065] Based on the short-path optical pulse generation method based on a three-level system provided in Example 1, it is applied to a Λ-type three-level system, and optical pulses that can realize S gate and T gate are designed respectively. For a Λ-type three-level system, in the Linblad equation, Γ1=2π×3kHz, Γ2=2π×3kHz, σ2=ee+211+3hh, which is different from the rare earth ion system (Pr 3+ :Y2SiO5).

[0066] See attached Figure 3 , is to realize the S gate The time-dependent component Ω(t) of the Rabi frequency of the optical pulse and the evolution of the detuning amount Δ(t) over time. m =10MHz, indicating the maximum instantaneous Rabi frequency, and the pulse action time τ = 54.2ns. The time-dependent component of the Rabi frequency is zero at the initial and final moments, which avoids the multiple Fourier frequency components generated in the frequency domain due to the rapid change of the field strength at the endpoints, which excites the background ions near the quantum bit and further affects the quantum state of the target quantum bit.

[0067] See attached Figure 4 , when the degree of freedom parameters c1 = 8.0574, c2 = 5.7639, c3 = 1.8294, c4 = 2.4237, under the action of the S gate, the initial quantum state And the evolution of fidelity over time. During the evolution, the number of layouts on |0 remains constant, and although the number of layouts on |1 changes during the evolution, at the end of the pulse, the probability of the quantum state being in |0 and |1 is 50%, and the fidelity of the generated quantum state to the target quantum state of the S gate is 99.85%.

[0068] See attached Figure 5 , is to realize T gate The time-dependent component Ω(t) and detuning Δ(t) of the Rabi frequency of the optical pulse and their evolution over time. m =10MHz, indicating the maximum instantaneous Rabi frequency, and the pulse action time τ = 39.8ns. The time-dependent component of the Rabi frequency of the optical pulse has a value of zero at the initial and final moments.

[0069] See attached Figure 6 , is the evolution of the initial quantum state |ψ0=|0 and the fidelity over time under the action of the T gate when the degree of freedom parameters c1=6.9500, c2=3.1800, c3=9.5100, c4=0.3500. During the evolution period, the number of configurations on the |0 state slowly decreases, while the number of configurations on |1 continues to increase. At the end of the pulse, the probability of the quantum state being in |0 and |1 is 50%, and the fidelity of reaching the target state is 99.92%.

[0070] The advantages of the optical pulses generated by the above technical solution are: 1. The evolution path of the light pulses that realize the quantum logic gate is the shortest, and the fidelity of the target state is high, at about 99.9%; 2. The starting and ending values ​​of the light pulse are zero to avoid exciting unnecessary energy level transitions of adjacent ions; 3. Light pulses can drive any initial state to evolve into any target quantum state, and have a wide range of applications.

[0071] It is worth pointing out that although the technical solution is developed for a three-level system, under certain conditions, on the one hand, the three-level system can collapse into a two-level system, thereby constructing a light pulse that can perform layout number transfer on the two-level system and create a superposition state, and on the other hand, the technical solution is also applicable to other rare earth ion systems or any system that can be equivalent to a three-level system, such as superconducting systems, trapped ions, nitrogen-vacancy color centers, etc. These minor technical variations or modifications still fall within the scope of the present invention.

[0072] The parts of this technical solution that are not described in detail belong to the common knowledge of those skilled in the art.

Claims

1. A method for generating short-path optical pulses based on a three-level system, wherein a three-level quantum system is formed between the energy levels |0>, |1> and |e>, characterized in that: Constructing the Hamiltonian in a three-level quantum system: Among them, Oh p (t)=Ω(t)sin(θ / 2), Among them, Ω p (t) and Ω s (t) is the Rabi frequency of the two-color light pulse, θ is the parameter that controls the amplitude of the light pulse, are the parameters for controlling the phase of the optical pulse, θ and are all constants in the range of [0,2π], which are related to the selection of logic gates. Ω(t) is the Rabi frequency Ω p,s (t), α(t) and β(t) are the polar angle and azimuthal angle on the Bloch sphere of the equivalent two-level system {|b>,|e>}, respectively. The ranges of α(t) and β(t) are [0,α m (γ)] and [0,π], and is their differential with respect to time, Δ(t) is the frequency detuning; Set the parameters of the time-dependent component Ω(t) of the Rabi frequency, where the polar angle α(t) on the Bloch sphere satisfies the condition: in, Among them, α m (γ) is the maximum value that α(t) reaches in the evolution, γ is the geometric phase, ranging from [0,π], τ is the pulse action time, is a parabolic function, n and k are positive integers greater than 0, and the degree of freedom parameter c is n is a real number greater than 0; β(t) is given by the torus equation Sure; Scanning degree of freedom parameter c n At the end of the action of the pulse on the three-level quantum system, the fidelity of the target state and the relationship between the non-resonant excitation of the ion and the frequency detuning amount are detected to obtain the degree of freedom parameter c n The optimal value of is used to obtain the short-path optical pulse waveform that drives any quantum state to transition to the target quantum state.

2. A short-path optical pulse based on a three-level system obtained by the optical pulse generation method according to claim 1.

3. The application of a short-path optical pulse based on a three-level system as claimed in claim 2, characterized in that: For rare earth ions Pr 3+ :Y2SiO5 quantum bit system device and Λ-type three-level system to obtain high-fidelity quantum logic gates.

Images