CN110120799A - A kind of insulation shortcut method of high-fidelity population inversion in two-level energy system - Google Patents
A kind of insulation shortcut method of high-fidelity population inversion in two-level energy system Download PDFInfo
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- CN110120799A CN110120799A CN201910306592.2A CN201910306592A CN110120799A CN 110120799 A CN110120799 A CN 110120799A CN 201910306592 A CN201910306592 A CN 201910306592A CN 110120799 A CN110120799 A CN 110120799A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03K—PULSE TECHNIQUE
- H03K5/00—Manipulating of pulses not covered by one of the other main groups of this subclass
- H03K5/22—Circuits having more than one input and one output for comparing pulses or pulse trains with each other according to input signal characteristics, e.g. slope, integral
- H03K5/26—Circuits having more than one input and one output for comparing pulses or pulse trains with each other according to input signal characteristics, e.g. slope, integral the characteristic being duration, interval, position, frequency, or sequence
Abstract
The invention discloses a kind of insulation shortcut methods of high-fidelity population inversion in two-level energy system, using the revertive control method based on Lewis-Riesenfeld quantum invariant, the time-dependent Schrodinger equation of Converse solved two-level energy system, building is able to achieve the set of pulses signal of two-level energy system population inversion, using Arbitrary Waveform Generator generate pulse signal, thus within shorter action time high-fidelity realization population inversion.The pulse signal that the present invention generates can realize the reversion of two-level energy system i on population under the premise of Rabi frequency is no more than 15GHz within the action time of 1ns, fidelity under the influence of phase noise and decoherence not less than 92%, toFrequency detuning within the scope of, fidelity be not less than 99.85%.
Description
Technical field
The invention belongs to quantum calculation fields, and in particular to the insulation of high-fidelity population inversion in a kind of two-level energy system
Shortcut method.
Background technique
Under applied field containing when, the main target that quantum state is always people's research is effectively manipulated and prepares, and
And has and be extremely widely applied.Such as the diffraction of nuclear magnetic resonance and relevant frequency spectrum technical aspect, interference and at present rapidly
In terms of the quantum information of development and quantum calculation, very important application and researching value are suffered from.
In these above-mentioned fields, two-level energy system model is generally existing basic model, is to constitute that other are more complex
Multilevel system basic structural unit, manipulation to two-level energy system quantum state namely realize that its population inversion is one
Very important quantum state manipulation.This manipulation request speed is fast, and fidelity is high, and to stablize, not vulnerable to outside noise and
The influence of system perturbation, and to have feasibility in practice.
Currently, many scholars propose many methods for realizing population inversion, and such as: Adiabatic Fast Passage technology, π
Impulse method, composite pulse method, optimized control method, excited Raman are insulated passage technology and its deriving method etc..However, these
Method have the shortcomings that it is respective, such as: π impulse method speed quickly, but the poor robustness when considering systematic error.Quickly absolutely
Passage of heat technology is a kind of effective and simple and easy control method, and phylogeny is slowly to guarantee not occur to appoint during being somebody's turn to do
What quantum leap, but the evolution time for needing to grow very much, this will lead to the generation of quantum decoherence, to influence fidelity.Most
Optimal control method can obtain optimization scheme according to different physical limits, but it often solution is complicated, and as one
Black box allows people to be unable to control parameter, while it is also possible to cannot get analytic solutions.Therefore it is desirable to obtain being easy manipulation and Shandong
The high nonadiabatic quantum of stick manipulates scheme.
Summary of the invention
It is an object of the invention to solve evolution overlong time, poor robustness, a kind of two energy level systems are provided
The insulation shortcut method of high-fidelity population inversion in system.This method generates set of pulses signal, and the group pulse signal is by two
Duration is equal, and the two is applied on quantum dot Two-level system by the different pulse composition of amplitude, phase and frequency simultaneously, can
Population inversion is completed to manipulate the Two-level system.
Pulse signal generated have the following characteristics that 1) the pulse signal effect time it is short, pulse signal Rabi frequency not
Under the premise of 15GHz, action time is no more than 1ns；2) realize that the fidelity of population inversion is not less than 99.85%；3)
Consider the fidelity when having phase noise and decoherence influences not less than 92%.
In order to achieve the purpose that foregoing invention, The technical solution adopted by the invention is as follows:
A kind of insulation shortcut method of high-fidelity population inversion in two-level energy system, comprising the following steps:
A. in a two-level energy system, using the revertive control method based on Lewis-Riesenfeld quantum invariant,
Converse solved Schrodinger equation:
Two-level energy system Hamiltonian are as follows:
Wherein Δ and Ω are the detuning and Rabi frequency containing when respectively；Hamiltonian eigenstate meets H (t) | ψ±(t) >=ε±
(t)|ψ±(t) >, define the lower one group of orthogonal basic vector of the systemThe then instantaneous eigenvector of Hamiltonian
It indicates are as follows:
The following differential equation is obtained according to dynamics invariant condition for such two-level energy system:
Wherein, θ and β is respectively polar angle and azimuth on Bloch ball.In order to make the instantaneous eigenstate of Hamiltonian from first
When state t=0 | 1 > it is inverted to final states t=tfWhen | 2 >, go out to meet boundary condition using multinomial or other Function Fittings
θ and β, to solve Δ and Ω according to Hamiltonian system differential equation is counter；
B. Δ obtained in step a and Ω are input in Arbitrary Waveform Generator, generating has obtained in above-mentioned steps
The pulse signal of phase and amplitude；
C. the pulse signal generated in step b is applied on GaAs/Aluminum gallium arsenide's hetero-junctions wafer electrode, pulse
The reversion of i on population is realized in signal and semiconductor-quantum-point interaction.
In the step a, in order to be in Hamiltonian initial state | 1 >, reversion is completed when final states to be in | 2 >, it is necessary to it is full
Sufficient boundary condition: θ (0)=0, θ (tf)=π.In order to enable Hamiltonian to be smoothly inverted to final states by initial state, and obtain steady
Fixed eigenstate, also needs to meet boundary condition:
Compared with prior art, advantages of the present invention is mainly reflected in:
As long as the present invention theoretically Rabi frequency is sufficiently large, the duration of the pulse signal of generation theoretically can be any
It is short.The present invention realizes that the fidelity of population inversion is higher, and the phylogeny time is short, and to the robustness of noise and decoherence
It is good.Different Evolution Paths can be chosen by different Function Fitting θ and β in the present invention, namely can according to need life
At the pulse signal of different performance.
Detailed description of the invention
Fig. 1 is the image that the pulse signal Δ and Ω of the reversion of two ionic fractional abundances are realized in the embodiment of the present invention one.
Fig. 2 is that pulse signal is drilled at any time with i on population in quantum two-level system mechanism in the embodiment of the present invention one
The image of change.
Fig. 3 is system in pulse signal in the embodiment of the present invention one and quantum two-level system mechanism in Bloch ball
On evolutional path.
Fig. 4 is the image that the pulse signal Δ and Ω of the reversion of two ionic fractional abundances are realized in the embodiment of the present invention two.
Fig. 5 is that pulse signal is drilled at any time with i on population in quantum two-level system mechanism in the embodiment of the present invention two
The image of change.
Fig. 6 is system in pulse signal in the embodiment of the present invention two and quantum two-level system mechanism in Bloch ball
On evolutional path.
Fig. 7 is decoherence rate γ=7 × 10 in the embodiment of the present invention three6s-1When, pulse signal and quantum two-level system
Evolutional path of the system on Bloch ball in mechanism.
Fig. 8 is fidelity F in pulse signal in the embodiment of the present invention three and quantum two-level system mechanism with dephasign
The variation relation figure of dry rate γ.
Fig. 9 is pulse signal in the embodiment of the present invention four and there are the interactions of the quantum two-level system of frequency detuning
When, realize the objective quantum state that population inversion generates | ψ (tf) > fidelity F with frequency detuning δ variation relation figure.
Specific embodiment
Above scheme is described further with reference to the accompanying drawings and embodiments, the preferred embodiment of the present invention is described in detail such as
Under:
Embodiment one:
A kind of insulation shortcut method of high-fidelity population inversion in two-level energy system, according to the initial state of system
And final statesUsing multinomialIt is fitted θ and β:
θ (t)=a0+a1t+a2t2+a3t3,
β (t)=b0+b1t+b2t2+b3t3,
Wherein θ is in [0, π] range, β value in [0,2 π] range.Using based on Lewis-Riesenfeld quantum not
The time-dependent Schrodinger equation of the Converse solved two-level energy system of insulation shortcut technology of variable theory obtains pulse signal.By what is obtained
Pulse signal is input to Arbitrary Waveform Generator generation pulse and is applied on GaAs/Aluminum gallium arsenide's hetero-junctions wafer electrode.
It is the image of pulse signal Δ and Ω that the technical solution generates as shown in Figure 1.It can be seen that curve from image
It is smooth readily available in an experiment enough.Pulse operating time only 1ns short enough.
It is the image of i on population Temporal Evolution as shown in Figure 2.It can see this method by the Evolution maps of i on population
Make the i on population of two-level energy system from initial stateDevelop to final statesSuccessfully realize the anti-of i on population
Turn.
It is evolutional path of the system on Bloch ball as shown in Figure 3, completes system from initial state to last State evolution, correspond to
Evolutional path on to Bloch ball is to develop from the arctic of Bloch ball to the South Pole.
Fidelity F=| < -1 | ψ (tf) > |, wherein | ψ (tfThe quantum state that two energy level coupled differential of) > be to solve for obtains |
ψ (t) > in t=tfThe state function at moment.The fidelity F=1 of generation objective quantum state in the present embodiment, but the pulse signal
It is only applicable to the quantized system there is no frequency detuning and phase noise.
Embodiment two:
The present embodiment is basically the same as the first embodiment, and is particular in that in the present embodiment using trigonometric function and is fitted θ
And β:
β (t)=ArcCot (0.1tfθ'(t))
Referring to fig. 4, Fig. 4 can be seen that curve is smooth readily available in an experiment enough to the pulse signal of generation.Pulse is made
It is still 1ns with the time.
It is the image of i on population Temporal Evolution as shown in Figure 5.It can see this method by the Evolution maps of i on population
Make the i on population of two-level energy system from initial stateDevelop to final statesSuccessfully realize the anti-of i on population
Turn.
It is evolutional path of the system on Bloch ball as shown in Figure 6.By comparison diagram 3, we are it can be found that by making
It is fitted θ and β with different functions, we have obtained realization can be with the different phylogeny tracks of population inversion.
Embodiment three:
The present embodiment is on the basis of example 1, it is contemplated that the influence of two energy level phase noises and decoherence.System
Master equation utilize Lindblad equation form indicate are as follows:
Wherein γ is decoherence rate, ρ and σiRespectively density matrix and Pauli matrices.
Just as referring to Fig. 1 in the pulse signal and embodiment one used in the present embodiment.
Fidelity F=| < -1 | ψ (tf)>|.In decoherence rate γ=7 × 106s-1When, fidelity F=94.56%.System
Evolutional path on Bloch ball is referring to Fig. 7, it will be seen that system is still drilled from the arctic of Bloch ball from Fig. 7
Change to the South Pole, namely realize the reversion of i on population, but due to the influence of phase noise and decoherence, there is no drill completely
Change at the Geophysical South Pole (0,0, -1) on Bloch ball.
It is to generate objective quantum state as shown in Figure 8 | ψ (tf) > fidelity F with decoherence rate γ variation relation figure, protect
True degree reduces with the increase of decoherence rate, but in γ > 107s-1When, fidelity F > 92%.
Example IV:
The present embodiment is that on the basis of example 1, detection realizes the fidelity of population inversion with frequency detuning
Variation relation.The pulse signal that the present embodiment uses is identical with embodiment one, and referring to Fig. 1, pulse operating time is still
1ns。
It is that the pulse signal generated in the present embodiment and the quantum two-level system there are frequency detuning are mutual as shown in Figure 9
When effect, the objective quantum state that population inversion generates is realized | ψ (tf) > fidelity F with frequency detuning δ variation relation
Figure.When there is no frequency detuning, i.e. δ=0, fidelity 1；Within the scope of Rabi frequency immediate vicinity ± 300MHz, fidelity F
> 99.85% shows stronger robustness to existing frequency detuning, and this point is there are the quantum systems of frequency detuning
The key element of quantum calculation is realized in system.
Claims (3)
1. a kind of insulation shortcut method of high-fidelity population inversion in two-level energy system, which comprises the following steps:
A. in a two-level energy system, using the revertive control method based on Lewis-Riesenfeld quantum invariant, inversely
Solve Schrodinger equation:
Two-level energy system Hamiltonian are as follows:
Wherein Δ and Ω are the detuning and Rabi frequency containing when respectively；Hamiltonian eigenstate meets H (t) | ψ±(t) >=ε±(t)|
ψ±(t) >, define the lower one group of orthogonal basic vector of the systemThen the instantaneous eigenvector of Hamiltonian indicates
Are as follows:
The following differential equation is obtained according to dynamics invariant condition for such two-level energy system:
Wherein, θ and β is respectively polar angle and azimuth on Bloch ball；In order to make the instantaneous eigenstate of Hamiltonian from initial state t=
When 0 | 1 > it is inverted to final states t=tfWhen | 2 >, using multinomial or other Function Fittings go out to meet boundary condition θ and
β, to solve Δ and Ω according to Hamiltonian system differential equation is counter；
B. Δ obtained in step a and Ω are input in Arbitrary Waveform Generator, generating has phase obtained in above-mentioned steps
With the pulse signal of amplitude；
C. the pulse signal generated in step b is applied on GaAs/Aluminum gallium arsenide's hetero-junctions wafer electrode, pulse signal
It interacts with semiconductor-quantum-point and realizes the reversion of i on population.
2. the insulation shortcut method of high-fidelity population inversion, feature exist in two-level energy system according to claim 1
In in the step a, in order to be in Hamiltonian initial state | 1 >, reversion is completed when final states to be in | 2 >, it is necessary to meet boundary
Condition: θ (0)=0, θ (tf)=π.
3. the insulation shortcut method of high-fidelity population inversion, feature exist in two-level energy system according to claim 1
In in order to enable Hamiltonian to be smoothly inverted to final states by initial state, and obtaining stable eigenstate, also need to meet perimeter strip
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111120236A (en) * | 2019-12-18 | 2020-05-08 | 上海大学 | Quantum thermal insulation shortcut heat engine with coupling harmonic oscillator as working medium and design method of thermal insulation shortcut process of quantum thermal insulation shortcut heat engine |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105358999A (en) * | 2013-05-03 | 2016-02-24 | 量子谷投资基金有限合伙公司 | Using a cavity to polarize a spin ensemble |
| CN105553569A (en) * | 2015-12-28 | 2016-05-04 | 上海电机学院 | Method for converting path entangled state from atom system to photon system |
| CN105960650A (en) * | 2014-01-06 | 2016-09-21 | 谷歌公司 | Constructing and programming quantum hardware for robust quantum annealing processes |
| CN108415206A (en) * | 2018-03-21 | 2018-08-17 | 苏州大学 | The light pulse generation method of the arbitrary superposition state of three-lever system quantum bit can be created |
-
2019
- 2019-04-17 CN CN201910306592.2A patent/CN110120799A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105358999A (en) * | 2013-05-03 | 2016-02-24 | 量子谷投资基金有限合伙公司 | Using a cavity to polarize a spin ensemble |
| CN105960650A (en) * | 2014-01-06 | 2016-09-21 | 谷歌公司 | Constructing and programming quantum hardware for robust quantum annealing processes |
| CN105553569A (en) * | 2015-12-28 | 2016-05-04 | 上海电机学院 | Method for converting path entangled state from atom system to photon system |
| CN108415206A (en) * | 2018-03-21 | 2018-08-17 | 苏州大学 | The light pulse generation method of the arbitrary superposition state of three-lever system quantum bit can be created |
Non-Patent Citations (1)
| Title |
|---|
| 路晓静: "量子系统中快速非绝热操控及其最优化设计", 《中国博士学位论文全文数据库 基础科学辑》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111120236A (en) * | 2019-12-18 | 2020-05-08 | 上海大学 | Quantum thermal insulation shortcut heat engine with coupling harmonic oscillator as working medium and design method of thermal insulation shortcut process of quantum thermal insulation shortcut heat engine |
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