CN111464154A - Control pulse calculation method and device - Google Patents
Control pulse calculation method and device Download PDFInfo
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- CN111464154A CN111464154A CN201910060283.1A CN201910060283A CN111464154A CN 111464154 A CN111464154 A CN 111464154A CN 201910060283 A CN201910060283 A CN 201910060283A CN 111464154 A CN111464154 A CN 111464154A
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Abstract
In the existing non-adiabatic and harmonic quantum computation, it is common to find the analytic form of controlling the hamiltonian amount and the strength of the control pulse by manual analysis and guess for a specific type of quantum system, which may result in non-adiabatic and harmonic quantum computation not having good portability and being unable to be combined with an optimization method to reduce errors. In order to solve the above problems, the present application provides a method for calculating the parameters of non-adiabatic and harmonic quantum control pulses in any quantum system, which combines the non-adiabatic and harmonic conditions with the quantum optimization method, and combines the methods of gradient optimization and loop iteration to select the optimal control pulse for the quantum system, thereby having good portability in practice and being capable of increasing robustness against quasi-static noise and system errors by combining with the optimization method.
Description
Technical Field
The application relates to the technical field of quantum computation, in particular to a computation method of control pulses.
Background
Quantum computing was a concept proposed in the last 80 th century. For a conventional computer, the input state and the output state are conventional signals, for example, binary values are represented by the high and low of potentials. Whereas for quantum computers, the input and output states may be considered to be eigenstates of some mechanical quantity. If the input binary number 0(1) is represented by a quantum symbol, i.e., |0> (|1 >). Quantum computers can input a superposition state, such as a |0> + b |1>, which conventional computers cannot achieve.
In particular, quantum computers have improved the limitations of not being able to prepare, manipulate, and measure quantum superposition states, and the input to a quantum computer is described by a quantum system with finite energy levels, such as a two-level system, also known as a qubit (qubit). The input state and the output state of the quantum computer are general superposition states which are not orthogonal with each other; the transforms in a quantum computer are all possible unitary transforms. After the output state is obtained, the quantum computer performs certain measurement on the output state to give a calculation result. For example, a qubit can be represented by the spin states of controlled particles. Fig. 1 is a schematic diagram of a quantum computer representing eigenstates and stacking states using states of particles. As shown in FIG. 1, the state where the particle spin is directed upward is defined as |0>The state where the particle spin is directed downward is set to |1>Then the pointing of the arrow of the particle to either angle will form a state, since the device capturing the particle can switch the particle from one state to another, and the particle does not only have two states, arrow up and arrow down. Therefore, as shown in FIG. 1, a quantum computer can represent more than just |0>And |1>Such eigenstates may also represent
Such a superimposed state.
Due to the superposition nature of quantum world material states and the resulting multi-distributed entanglement nature, quantum computers, driven by suitable algorithms, may exhibit superior characteristics at the computational complexity level to traditional computers for certain specific problems. The computational superiority of quantum computers needs to be based on a suitable algorithm and an ideal controllable quantum system. Since quantum operation can be regarded as continuous evolution of Hilbert space, the continuity makes quantum computation have higher requirements on the accuracy of evolution operation, which is difficult to meet under common experimental conditions. Errors caused by such inaccurate operations accumulate and amplify with the increase of the calculation depth (i.e., the number of quantum wire layers), which may cause problems such as calculation interruption and output of erroneous results.
In order to reduce the error that may occur in the operation, various countermeasures have been subsequently proposed in the academic and industrial circles. Among them, professor Zanardi proposed adiabatic and le quantum calculations in 1999. Adiabatic means that the evolution process is very slow and no level crossing can occur. He-le (Holonomy) is a non-Abel geometric phase that is related only to the evolution path. The term "Geometric Phase" means that, after the hamiltonian is allowed to evolve in the parameter space for one cycle along the loop, the hilbert space undergoes a twist only with respect to the loop. Non-Abelian (Non-Abelian) means that the elements in it do not all satisfy the commutative law, i.e. there are at least two elements a and b, satisfying the condition a b ≠ a.
Under the condition of adopting adiabatic and harmonic quantum computation, an operation result only depends on an evolution path of a quantum system, is irrelevant to a specific evolution form and local jitter, has inherent fault tolerance for reducing operation errors, is an important scheme for solving bottleneck difficulties such as inaccurate operation and the like, and brings wide attention to people.
In practice, however, adiabatic and harmonic quantum computation still has certain difficulties, because of the requirement of satisfying adiabatic conditions, the change of system Hamilton quantity with time is slow enough, however, the coherent retention time of a general quantum system is always limited, and the influence of environmental noise is accumulated due to the excessively long computation time, which brings larger error, thereby reducing the practical significance of using non-Abel geometric phase for precise operation of the quantum system.
However, existing solutions for non-adiabatic and harmonic quanta are based only on a specific type of quantum system and require finding an analytic form in a manual analysis that controls the hamiltonian of the system. When the controlled quantum system changes, the optimal control method needs to be searched again. This results in a special application scenario, which does not have good portability, and because the technical scheme strictly specifies the expression of the hamilton quantity, which does not have an optimizable degree of freedom, it is difficult to combine with an optimization control method to further eliminate other low-frequency errors such as system errors, quasi-wonderful noise, etc. through optimization.
Disclosure of Invention
The application provides a control pulse calculation method, which can calculate the parameters of the control pulse required by the operation of a quantum gate in any quantum system and can be combined with an optimization method, so that the control pulse has robustness against noise and system errors.
In a first aspect, an embodiment of the present invention provides a method for calculating a control pulse, where the method is used in a computer device, and the control pulse is used to control a quantum computer to complete a quantum gate operation, and the method includes: receiving operation information, wherein the operation information comprises Hamiltonian of quantum system of quantum computer, type U of quantum gatewantAnd operating time; determining an objective function O ═ O according to the operation information1-aO2A is a coefficient; obtaining a current candidate parameter value; calculating a function value according to the current candidate parameter value and the objective function, and calculating the gradient of the objective function relative to the candidate parameter value; and when the output condition is met, outputting the current candidate parameter value as the parameter value of the control pulse, wherein the output condition comprises that the difference value between the calculated gradient and 0 is less than or equal to a first preset value and the difference value between the calculated function value and 1 is less than or equal to a second preset value, the output parameter value is used for representing the strength of the control pulse in N channels in the operation time, the N channels are mutually independent, and N is a positive integer.
By adopting the method, the fidelity of quantum gate operation and the non-adiabatic and harmonic conditions are combined, and the optimal parameter value is found out by adopting a gradient ascending algorithm, so that the strength of the control pulse can be calculated in different types of quantum systems, and the method has feasibility and universality.
With reference to the first aspect of the present invention, in a possible implementation manner, the method further includes: when the output condition is not met, updating the candidate parameter values, recalculating the function values according to the updated current candidate parameter values and the target function, recalculating the gradient of the target function relative to the updated candidate parameter values, and repeating the steps until the output condition is met; and outputting the current candidate parameter value adopted when the output condition is met as the parameter value of the control pulse.
By adopting the method, the candidate parameter values can be updated under the condition that the output condition is not met, so that the optimal candidate parameter values can be found out through iteration and output as the parameter values of the control pulse.
With reference to the first aspect of the present application, another possible implementation manner is that, when the output condition is not satisfied, updating the candidate parameter value includes: when the difference value between the gradient calculated at the previous time and 0 is greater than a first preset value and the difference value between the function value calculated at the previous time and 1 is greater than a second preset value, multiplying the gradient calculated at the previous time by a preset coefficient to obtain a gradient adjustment value, and taking the sum value of the gradient adjustment value and the candidate parameter value before updating as the updated candidate parameter value; or when the difference between the previously calculated gradient and 0 is less than or equal to a first preset value and the difference between the previously calculated function value and 1 is greater than a second preset value, randomly acquiring updated candidate parameter values.
By adopting the method, two conditions which do not meet the output condition are distinguished, and different methods for updating the candidate parameter values are respectively adopted, so that the calculation efficiency of the control pulse is increased.
With reference to the first aspect of the present application, another possible implementation manner is that, calculating a function value according to a current candidate parameter value and the target function, and calculating a gradient of the target function with respect to the candidate parameter value, including: setting of auxiliary quantities
Wherein the operating time is divided into n time segments, HiAs the Hami of the quantum system in the ith time periodPause amount, Ti-1In the (i-1) th time period, n is a positive integer, and i is a positive integer not greater than n; calculating an objective function
Wherein U is the actual evolution function of the quantum gate, ISThe computation subspace for the quantum system is shown at L as the dimension of the computation subspace.
With reference to the first aspect of the present application, another possible implementation manner is that, calculating a function value according to a current candidate parameter value and a target function, and calculating a gradient of the target function with respect to the candidate parameter value, further includes: setting of auxiliary quantities
Calculate U and A separatelyi(t) a gradient with respect to a current candidate parameter value; according to U and Ai(t) calculating a gradient of the objective function relative to the candidate parameter values relative to a gradient of the current candidate parameter values.
By adopting the method and adopting the mode of setting the auxiliary value, the calculation steps can be reduced, thereby increasing the calculation efficiency of the control pulse.
With reference to the first aspect of the present application, another possible implementation manner is that, after outputting the current candidate parameter value as a parameter value of the control pulse, the method further includes: and adjusting the numerical value of the coefficient a.
By adjusting the value of the coefficient a, the resulting control pulse can be adjusted. In particular, when the value of a is smaller, the resulting control pulse performs a quantum gate operation more accurately; the larger the value of a, the more non-adiabatic and harmonic conditions are met by the resulting control pulse.
In a second aspect, embodiments of the present invention provide a computer apparatus for controlling a quantum computer to perform a quantum gate operation, the computer apparatus comprising: a first processing module for receiving operation information, wherein the operation information comprises Hamiltonian of quantum system of quantum computer, type U of quantum gatewantAnd operation time determined based on the operation informationDetermining the objective function O ═ O1-aO2A is a coefficient; a second processing module for determining an objective function O ═ O according to the operation information1-aO2A is a coefficient; obtaining a current candidate parameter value; calculating a function value according to the current candidate parameter value and the target function, and calculating the gradient of the target function relative to the candidate parameter value; and when the output condition is met, outputting the current candidate parameter value as the parameter value of the control pulse, wherein the output condition comprises that the difference value between the calculated gradient and 0 is less than or equal to a first preset value and the difference value between the calculated function value and 1 is less than or equal to a second preset value, the output parameter value is used for representing the intensity of the control pulse in N channels in the operation time, the N channels are mutually independent, and N is a positive integer.
With reference to the second aspect of the present application, in one possible implementation manner, the second processing module is further configured to: when the output condition is not met, updating the candidate parameter values, recalculating the function values according to the updated current candidate parameter values and the target function, recalculating the gradient of the target function relative to the updated candidate parameter values, and repeating the steps until the output condition is met; and outputting the current candidate parameter value adopted when the output condition is met as the parameter value of the control pulse.
With reference to the second aspect of the present application, another possible implementation manner is that, when the candidate parameter value is updated, the second processing module is specifically configured to: when the difference value between the gradient calculated at the previous time and 0 is greater than a first preset value and the difference value between the function value calculated at the previous time and 1 is greater than a second preset value, multiplying the gradient calculated at the previous time by a preset coefficient to obtain a gradient adjustment value, and taking the sum value of the gradient adjustment value and the candidate parameter value before updating as the updated candidate parameter value; or when the difference between the previously calculated gradient and 0 is less than or equal to a first preset value and the difference between the previously calculated function value and 1 is greater than a second preset value, randomly acquiring updated candidate parameter values.
In combination with the second aspect of the present application, another possible implementation manner is that when the function is calculated according to the current candidate parameter value and the objective functionThe second processing module is specifically configured to, when calculating the value of the target function relative to the gradient of the candidate parameter value: setting of auxiliary quantities
Wherein the operating time is divided into n time segments, HiIs the Hamiltonian of the quantum system in the ith time period, Ti-1In the (i-1) th time period, n is a positive integer, and i is a positive integer not greater than n; calculating an objective function
Where U is the actual evolution function of the quantum gate, ISThe computation subspace for the quantum system is shown at L as the dimension of the computation subspace.
With reference to the second aspect of the present application, another possible implementation manner is that, when the function value is calculated according to the current candidate parameter value and the objective function, and the gradient of the objective function with respect to the candidate parameter value is calculated, the second processing module is further configured to: setting of auxiliary quantities
Calculate U and A separatelyi(t) a gradient with respect to a current candidate parameter value; according to U and Ai(t) calculating a gradient of the objective function relative to the candidate parameter value relative to a gradient of the current candidate parameter value.
With reference to the second aspect of the present application, another possible implementation manner is that the computer device further includes a third processing module, configured to adjust the value of a after outputting the current candidate parameter value as the parameter value of the control pulse.
In a third aspect, the present application provides a computer apparatus comprising a memory for storing a computer program and a processor for executing the computer program to implement the method of calculating a control pulse as in the first aspect.
Drawings
Fig. 1 is a schematic diagram of a quantum computer in the prior art using states of particles to represent eigenstates and stacking states.
Fig. 2 is a schematic diagram of the energy level structure of an Λ -configured quantum system.
Fig. 3A is a schematic diagram of a computer device according to an embodiment of the present application.
Fig. 3B is a schematic diagram of a computer device and a quantum computer provided by an embodiment of the present application.
FIG. 4 is a schematic flow chart diagram of an embodiment of the present application.
Fig. 5 is a schematic flow chart of another embodiment of the present application.
Fig. 6 is a schematic diagram of modules of a computer device according to an embodiment of the present application.
Figure 7 is a schematic diagram of the structure of a computer device provided by an embodiment of the present application,
Detailed Description
In order to solve the problems of influence caused by errors in quantum computation and slow evolution process and high environmental requirements of adiabatic and harmonic quantum computation in practice, the prior art provides a theoretical scheme of non-adiabatic and harmonic quantum computation and a practical method of non-adiabatic and harmonic computation for quantum systems with Λ configuration.
FIG. 2 is a schematic representation of the energy level structure of an Λ -configured quantum system, as shown in FIG. 2, comprising 3 substantially bare states, i.e., atomic intrinsic quantum states when no driving laser is applied, each identified as |0>、|1>、|e>Corresponding characteristic energy level w0、w1、we. Based on this configuration, at a suitable frequency V0、V1Respectively independently driving two lower energy states |0>、|1>And excited state | e>The transition between.
The Hamiltonian of this laser interaction with the system in a rotating coordinate system is expressed as:
H(t)＝Δ0|0><0|+Δ1|1><1|+Ω(t)(ω0|e><0|+ω1|e><1| + h.c.). Wherein, ω is0And ω1The real part and the imaginary part of the phase difference of the two laser pulses respectively satisfy the condition of omega0|2+|ω1|21. Delta is called the detuning term and is the difference between the transition frequency and the laser frequency, i.e. Delta0＝we0-V0，Δ1＝we1-V1(ii) a Omega (t) refers to the function of the change of the contrast ratio frequency along with time, when laser pulses are driven into a substance, particles in a medium are caused to periodically oscillate between upper and lower energy levels, and the frequency of the particle oscillation is the contrast ratio frequency; h.c. refers to the matrix in parentheses (i.e. ω)0|e><0|+ω1|e><1|) was subjected to hermitian conjugation.
According to the technical scheme, on the basis of the formula, the Hamiltonian quantity of the system can be adjusted to a form capable of realizing a desired harmonic quantum gate by setting a proper driving laser parameter, and the drive method specifically comprises the following steps:
for a single-bit quantum gate, for example, to implement a Pagli gate, the amount of detuning of the Λ -type quantum system is first made 0, i.e., Δ0＝Δ 10. In this case, the expression of the Hamiltonian can be reduced to H(1)(t)＝Ω(t)(ω0|e><0|+ω1|e><1| + h.c.). By setting a suitable evolution time tau, the integral multiple is satisfied0 τΩ (t) dt ═ pi. The unitary thus derived evolves at |0>、|1>The projection of the open subspace is equivalent to a rotation of a 2-dimensional Hilbert space, i.e.
Wherein, ω is0＝sin(θ/2)eiφ、ω1＝-cos(θ/2)、
Namely, by adjusting parameters such as frequency, phase difference and control evolution time of the driving laser, any single-bit non-adiabatic quantum gate can be realized in the specific quantum system.
Similarly, for a two-bit quantum gate, appropriate Control parameters may be found to form a controlled-Not gate (CNOT), where the CNOT gate operates in two operationsA qubit, the second qubit being |1 only in the first qubit>The prior art provides a non-harmonic quantum computing scheme that adjusts the amount of laser detuning for two similar Λ -configuration quantum systems, such that at | e0>、|0e>、|e1>、|1e>In the subspace where the four independent basis vectors are open, the Hamiltonian of the system is in the form of:
wherein η is the L amb Dicke parameter, and η2<<1，σ0(Φ)＝eiΦ/4|e＞＜0|+h.c.， σ1(-Φ)＝e-iΦ/4E > < 1| + h.c., and the intensity ratio is set to
Under the condition of the Hamiltonian, the control system evolves a pi pulse, namely
The unitary evolution operator is represented as
The prior art provides that in a specific type of quantum system (e.g. the Λ -configured quantum system described above), an analytic form for controlling the hamiltonian is found by a manual analysis method, and then parameters of the control pulse are obtained in turn, when the controlled quantum system is changed, an optimal control method needs to be found again, which brings about the following problems.
Since the parameters of the control pulse are found in an artificial way for a specific type of quantum system in the existing calculations regarding non-adiabatic and harmonic quanta, it is inefficient to re-find the optimal control method when the quantum system of the controlled quantum system is changed. The application provides a method for calculating the parameters of the non-adiabatic quantum control pulse in any quantum system, and has feasibility and universality.
The technical scheme provided by the application is applied to a computer device. Fig. 3A is a schematic diagram of a computer device that can implement the technical solution of the present application.
As shown in FIG. 3A, computer device 300 includes a processor 302, a memory 304, an input/output interface 306, a communication interface 308, and a bus 310. The processor 302, the memory 304, the input/output interface 306, and the communication interface 308 are communicatively connected to each other via a bus 310. The processor 302 is a control center of the computer device 300, and is used for executing relevant programs to implement the technical solutions provided by the embodiments of the present invention. The memory 304 may store an operating system and other application programs, and when the technical solution provided by the embodiment of the present invention is implemented by software or firmware, a program code for implementing the technical solution provided by the embodiment of the present invention is stored in the memory 304 and executed by the processor 302. The memory 304 may be integrated with the processor 302 or integrated within the processor 302, or may be one or more memory units separate from the processor 302. The input/output interface 306 may be used to receive input data and information, and output operation results and the like. The communication interface 308 enables communication between the computer apparatus 300 and other devices or communication networks using transceiver means such as, but not limited to, a transceiver. Bus 310 is used to transfer information between the various components of computer device 300, such as processor 302, memory 304, input/output interface 306, and communication interface 308.
In the technical solution provided in the present application, the parameters of the control pulse may be calculated by the computer device 300 and manually input into the quantum computer for quantum calculation, or the quantum computer may be connected to the computer device 300, so that the quantum computer may directly utilize the parameters of the control pulse calculated by the computer device 300.
As shown in fig. 3B, the computer apparatus 300 is connected to a quantum computer 320, and the quantum computer 320 includes a control unit 322, an evolution unit 324, a measurement unit 326, and an output unit 328. The control unit 322 is configured to receive a parameter of a control pulse sent by the computer apparatus 300, and generate the control pulse according to the parameter; the evolution unit 324 is a space where the quantum system in the quantum computer 320 exists, and the particle is located in the evolution unit 324 and receives the control pulse sent by the control unit 322; the measurement unit 326 is configured to measure the state of the particle in the evolution unit 324 when the particle evolves to the final state, so as to obtain the result of quantum computation; the output unit 328 is used for outputting the result of the quantum computation.
It should be noted that the above description of the structures of the computer device 300 and the quantum computer 320 is only an example, and the computer device 300 and the quantum computer 320 may also be composed of more or less components, and the above description does not limit the technical solution provided in the present application.
FIG. 4 is a schematic flow chart diagram of an embodiment of the present application.
As shown in fig. 4, the present application includes the following steps:
s401: receiving type U of quantum gatewantHamiltonian of quantum system
And operation information such as operation time τ.
The technical scheme provided by the application is a numerical method for calculating the parameter sequence of the non-adiabatic and harmonic control pulse in any quantum system (the non-adiabatic and harmonic evolution path exists). For any quantum system, when a laser pulse is input into the quantum system, the hamiltonian of the system can be expressed as follows:
i.e., an expression for the variation of the intensity of each channel of a sequence of laser pulses over time, resulting in a variation of the hamiltonian of the system. Wherein, the type U of the evolution Hamiltonian quantity and quantum gate of the systemwantThe operating time τ and the quantum system.
A quantum gate (qubit gate) refers to a unitary operator on a qubit. There are various types of quantum gates, including the Adadral (Hadamard) gate, the Pauli-X gate, the Pauli-Y gate, the Pauli-Z gate, the control NOT gate, and the like. For example, an Addall gate is a gate that operates on only one qubit, which will be in the base state |0>Become into
And will be in a basic state |1>Become into
The Pally-X gate operates on one qubit and can gate |0>Becomes |1>Will |1>Becomes |0>. For different types of quantum gates, this is achieved by control pulses of different parameter values. Therefore, in order to calculate the parameter values of the control pulses used, the computer device first needs to calculateThe next quantum gate type is received.
When the control pulse controls the quantum computer to perform quantum gate operation, the intensity of each channel can change along with time. In a typical operation, a predetermined operation time τ for the quantum computer to complete the quantum gate operation is given, and the predetermined operation time τ is divided into n segments, where each control pulse includes n pulse segments. Different preset operation times correspond to different pulse intensities. For example, when the given preset operation time is shorter, the intensity of the control pulse to be used is generally stronger; the longer a given preset operating time is, the weaker the intensity of the control pulse employed will generally be.
S402: determining an objective function
Expressing Hamiltonian of quantum system
Combining non-adiabatic and thermal conditions: (i)
(ii)<φk(t)|H(t)|φl(t)>l, the objective function provided by the present application can be obtained as 0, k, l, 1,2
Wherein O is1Refers to an optimized objective function related to the general quantum optimization control theory of any quantum system, and the function includes the details of the system Hamiltonian, the type of quantum gate, the selected computation subspace and the operation time, i.e. the fidelity of the quantum gate operation, O2Is a function obtained according to non-adiabatic and harmonic conditions, a is a set coefficient used for balancing the front term and the rear term, and when the set value of a is larger, the obtained result conforms to the non-adiabatic and harmonic conditions; the smaller the value of a set, the more accurate the result is. In one implementation of the embodiments of the present application, this can be achieved by adjusting the value of aThe result obtained is more consistent with the expected result, wherein the value of a may be adjusted when the objective function is determined in S402, or may be adjusted at other suitable times in the process, which is not limited herein.
Specifically, the non-adiabatic and harmonic conditions include two expressions. For the first expression
This condition requires that the subspace S (τ) ═ k ═ 1L Φ k τ><Φ k τ satisfies the condition S τ ═ S (0). The similarity of S (τ) and S (0) can be quantified as the fidelity of a mixed state. Is provided with
Then
From the above calculations, the first expression for the non-adiabatic and harmonic conditions can be converted to:
with respect to the second expression, it is,<Φk(t)|H(t)|Φl(t)>0, k, l 0,1,2 … L. this expression can be translated to ∑k∑lαkl(t)·αkl(t)*＝0，t∈[0,τ]And can continue to be converted into
Wherein when set αkl(t)＝<Φk(t)|H(t)|Φl(t)>When it is, α is satisfiedkl(t)αkl(t)*≥0。
For simplicity of calculation, the summation calculation can be converted into a calculation of the traces of the matrix, as follows:
s403: and acquiring the current candidate parameter value.
Unlike the prior art in which the analytic form of the hamiltonian is calculated by manual analysis and guessing, in the present application, the parameters of the control pulse are found by a gradient optimization method. Therefore, after the objective function is determined, the value and the gradient of the objective function are calculated according to the initial candidate parameter values of the pulse intensity sequence of each channel to be calculated, and then the candidate parameter values are adjusted according to the obtained gradient, wherein the pulse sequence comprises N channels which are independent of each other, and the candidate parameter values of the pulse sequence comprise the intensities of the pulses on each channel in the preset operation time. According to the technical scheme provided by the application, the initial candidate parameter value used for calculation can be random when circulating for the first time because the candidate parameter value is calculated and then adjusted according to the feedback of the result. In the technical solution provided in the present application, the initial candidate parameter value may be stored in the computer device in advance, or may be obtained by a method of receiving an external input, and the present application does not limit this.
S404: according to the current candidate parameter value
Calculating a value of an objective function and calculating a gradient of the objective function with respect to a candidate parameter value
And calculating the value of the target function and calculating the gradient of the target function relative to the candidate parameter value according to the current parameter value. The gradient is a vector, and indicates that the directional derivative of a certain function at the point takes the maximum value along the direction, that is, the function changes the fastest along the direction at the point, and the change rate is the maximum.
S405: and judging whether the difference between the gradient and 0 is less than or equal to a first preset value and whether the difference between the value of the objective function and 1 is less than or equal to a second preset value.
In this scheme, the parameter value that maximizes the result of the objective function needs to be found, so an optimization method of gradient ascent is adopted. Since the gradient is a vector, it means that the directional derivative of a certain function at the point takes the maximum value along the direction in which the gradient points, i.e. the function changes the fastest at the point along the direction in which the gradient points, and the change rate is the maximum. Therefore, whether the difference between the gradient value obtained by the judgment and 0 is smaller than or equal to a first preset value or not can be judged, whether the objective function obtains a local maximum value under the condition that the current candidate parameter value is adopted or not can be judged, and whether the objective function is a global optimum value or not can be effectively judged according to whether the difference between the value of the objective function and 1 is smaller than or equal to a second preset value or not, wherein the first preset value and the second preset value are preset. The smaller the values of the first preset value and the second preset value are set, the more accurate the candidate parameter values are finally obtained, but the number of required calculations may increase accordingly.
Because the gradient represents the direction in which the value of the scalar field at a certain point in the scalar field changes fastest, if the difference between the obtained gradient value and 0 is less than or equal to a first preset value, it is indicated that the target function obtains a local maximum value under the condition of the current parameter value, under this condition, it is further determined whether the difference between the value of the target function and 1 is less than or equal to a second preset value, if the difference between the obtained gradient value and 0 is less than or equal to the first preset value and the difference between the value of the target function and 1 is less than or equal to the second preset value, step S406 is executed to output the current candidate parameter value, that is, the output condition of the parameter is that the difference between the gradient and 0 is less than or equal to the first preset value and the difference between the value of the target function and 1 is less than or equal; if the difference between the obtained gradient value and 0 is greater than the first preset value or the difference between the value of the objective function and 1 is greater than the second preset value, it indicates that the objective function does not obtain the optimal value under the condition of the current candidate parameter value, and can be further optimized, then step S407 is executed.
S406: and outputting the current candidate parameter value.
When the objective function obtains an optimum value under the condition of the current parameter value, the current candidate parameter value is output as the parameter of the control pulse. In the implementation manner of the present application, the computer device may be connected to a quantum computer, and the output parameter value may be directly used to generate a corresponding control pulse in the quantum computer; the parameter value may also be manually input to the quantum computer according to the parameter value output by the computer device, so that the quantum computer generates the corresponding control pulse according to the parameter value, which is not limited in the present application.
S407: the current candidate parameter values are updated.
When the difference between the gradient value and 0 is greater than the first preset value and the difference between the value of the objective function and 1 is greater than the second preset value, it is indicated that the objective function does not reach the local maximum value under the condition of the current candidate parameter value, because the gradient represents the direction in which the scalar field value at a certain point in the scalar field increases fastest, the gradient value can be multiplied by a preset coefficient to serve as a gradient adjustment value, and the sum of the gradient adjustment value and the candidate parameter value before updating serves as the candidate parameter value after updating, and the step S404 is returned, and the value of the objective function and the gradient value of the objective function relative to the current candidate parameter value are recalculated by using the candidate parameter value after updating.
It should be noted that in the gradient rise optimization algorithm, the candidate parameter value is usually updated by multiplying the gradient value by a certain coefficient (learning rate) and then adding the current candidate parameter value, but other similar actions may be taken in practical operation, such as multiplying the gradient value by a coefficient matrix (in particular, such as newton's method) and then adding the current candidate parameter value. The updating of candidate parameter values in the former manner is only used for illustrating the technical solutions provided in the present application, and is not limited.
When the difference between the gradient value and 0 is less than or equal to the first preset value and the difference between the value of the objective function and 1 is greater than the second preset value, it indicates that the objective function obtains the local maximum value under the condition of the current candidate parameter value, but does not obtain the global optimum value, in this case, the candidate parameter value is updated by randomly obtaining the updated candidate parameter value, and the step 404 is returned, and the value of the objective function and the corresponding gradient value are recalculated by using the updated candidate parameter value.
Since the objective function cannot obtain the global optimum value without obtaining the local maximum value, under the condition that the first preset value and the second preset value are reasonably set, the situation that the difference between the gradient value and 0 is greater than the first preset value and the difference between the value of the objective function and 1 is less than or equal to the second preset value cannot occur, and the application is not discussed about the situation.
Fig. 5 is a schematic flow chart of another embodiment of the present application.
S501: receiving type U of quantum gatewantHamiltonian of quantum system
And operation information such as operation time τ.
S502: determining an objective function
Referring to step S402, an expression of the objective function is determined as
S503: and setting an auxiliary quantity and optimizing an objective function.
In step S403, it has been explained that the non-adiabatic and harmonic conditions can be converted from a calculation sum to a trace of a calculation matrix, i.e. a trace of a calculation matrix
Because the current non-adiabatic and le analytic conditions are not convenient for directly being applied to the numerical gradient optimization algorithm, three auxiliary quantities are set in the method, the non-adiabatic analytic conditions are convenient for numeralization, the utilization rate of intermediate variables can be improved in the gradient optimization process, and the calculation complexity is reduced. The set auxiliary amounts are specifically as follows:
where τ refers to the total time of the control pulse sequence, which is divided into n control pulse segments, thus Ti-1～TiRefers to the time of the ith pulse train. The U function refers to the actual control evolution. I isSRefers to the computation subspace in the complete Hilbert space
Refers to the hamiltonian of the system in the ith time slice. In order to realize correct quantum gate operation, the actual control evolution function U needs to be made to correspond to the target evolution function U of the quantum gatewantThe same is true.
With the aid of the above-mentioned auxiliary quantities, the non-adiabatic sum-mean condition (i) is combined with the objective evolution function UwantAnd actually controlling the evolution function U to obtain:
wherein, ISThe computation subspace for the quantum system is shown at L as the dimension of the computation subspace.
The non-adiabatic and le conditions (ii) in combination with the above auxiliary amounts, can be converted into:
the objective of the gradient optimization is to be at Tr [ AI ]S]On the premise of 0, let F1With the maximum value of (A), combined with prior knowledge Tr [ AI ]s]≧ 0, the optimization objective function can therefore be rewritten in the form:
s504: and acquiring the current candidate parameter value.
S505: according to the current candidate parameter value
Calculating the value of the objective function and the gradient of the objective function with respect to the candidate parameter values
In the above expression of the objective function, only the U function and the auxiliary quantity a contain variables, so that calculating the gradient for the objective function can be converted into calculating the gradient for the U function and the auxiliary quantity a, wherein the gradient calculation mainly comprises the following steps:
and
according to the calculation, the auxiliary quantities A, B and C are set, so that in the process of gradient calculation, gradient operation on an O function is converted into iterative product operation of relatively simple intermediate variables A, B and C, the calculation is simplified, and the efficiency of calculating the gradient and iterating by a computer device to optimize the control pulse sequence is improved.
It should be noted that the above-mentioned expression for the objective function and the expressions for the auxiliary quantities A, B and C are only used to illustrate the technical solutions of the present application, and similar methods for adding non-adiabatic and harmonic terms to the general quantum control optimization objective function and converting the gradient calculation into the multiplication and addition operation by setting the auxiliary quantities are all within the scope of protection of the present application.
S506: and judging whether the difference between the gradient and 0 is less than or equal to a first preset value and whether the difference between the value of the objective function and 1 is less than or equal to a second preset value.
When the difference between the obtained gradient value and 0 is less than or equal to the first preset value and the difference between the value of the objective function and 1 is less than or equal to the second preset value, executing step S507; when the difference between the obtained gradient value and 0 is greater than the first preset value or the difference between the value of the objective function and 1 is greater than the second preset value, step S508 is performed.
S507: and outputting the current candidate parameter value as the parameter of the control pulse.
S508: the current candidate parameter values are updated.
When the difference between the gradient value and 0 is greater than the first preset value and the difference between the value of the objective function and 1 is greater than the second preset value, it is indicated that the objective function does not reach the local maximum value under the condition of the current candidate parameter value, because the gradient represents the direction in which the scalar field value at a certain point in the scalar field increases fastest, the gradient value can be multiplied by a preset coefficient to serve as a gradient adjustment value, the sum of the gradient adjustment value and the candidate parameter value before updating serves as an updated candidate parameter value, and the step S505 is returned, and the value of the objective function and the gradient value of the objective function relative to the current candidate parameter value are recalculated by using the updated candidate parameter value.
When the difference between the gradient value and 0 is less than or equal to the first preset value and the difference between the value of the objective function and 1 is greater than the second preset value, it indicates that the objective function obtains the local maximum value under the condition of the current candidate parameter value, but does not obtain the global optimum value, in this case, the updated candidate parameter value is randomly obtained, and the step 505 is returned, and the value of the objective function and the corresponding gradient value are recalculated by using the updated candidate parameter value.
Fig. 6 is a schematic diagram of modules of a computer device according to an embodiment of the present application.
As shown in fig. 6, the computer apparatus 600 includes:
a first processing module 610 for: receiving operation information, wherein the operation information comprises Hamiltonian of quantum system of quantum computer, type U of quantum gatewantAnd operating time; according to the aboveOperation information determination target function O ═ O1-aO2Wherein O is1For the fidelity of the operation of the quantum gate, O2In the non-adiabatic condition, a is a coefficient;
a second processing module 620, configured to obtain a current candidate parameter value; calculating the value of the target function and the gradient of the value of the target function relative to the candidate parameter value according to the current candidate parameter value; when an output condition is met, outputting the current candidate parameter value as a parameter value of the control pulse, wherein the output condition comprises that the difference value between the calculated gradient and 0 is less than or equal to a first preset value and the difference value between the calculated function value and 1 is less than or equal to a second preset value, the output parameter value is used for expressing the intensity of the control pulse in N channels in the operation time, the N channels are mutually independent, and N is a positive integer;
and a third processing module 630, configured to adjust the value of a.
The first processing module 610, the second processing module 620 and the third processing module 630 can also be used for executing the flows shown in fig. 4 and 5, specifically, the first processing module 610 is used for executing steps S401, S402, S501 and S502; the second processing module 620 is configured to execute steps S403 to S407 and S503 to S508, which are not described herein again.
Fig. 7 is a schematic structural diagram of a computer device 700 according to an embodiment of the present application. The computer device 700 in this embodiment may be a specific implementation manner of the computer device in each of the above embodiments.
As shown in FIG. 7, the computer device 700 includes a processor 701, the processor 701 being coupled to a memory 705. The Processor 701 may be a Field Programmable Gate Array (FPGA), a Digital Signal Processor (DSP), or any combination thereof. Processor 701 may also be a single core processor or a multi-core processor.
The memory 705, which may be a RAM memory, a flash memory, a ROM memory, an EPROM memory, an EEPROM memory, a register, or any other form of storage medium known in the art, may be used to store program instructions that, when executed by the processor 701, the processor 701 performs the methods described in the embodiments above.
The connection line 709 is used to transmit information between the components of the communication device, and the connection line 709 may be a wired connection or a wireless connection, which is not limited in this application. The connection 709 is also connected to a network interface 804.
The network interface 704 enables communication with other devices or networks 711 using connection means such as, but not limited to, cables or twisted pair wires, and the network interface 704 may also be interconnected with the network 711 in a wireless fashion.
Some of the features of the embodiments of the present application may be performed/supported by the processor 701 executing program instructions or software code in the memory 705. The software components loaded on the memory 705 may be summarized functionally or logically, for example, the first processing module 610, the second processing module 620, and the third processing module 630 shown in fig. 6.
In one embodiment of the present application, when the memory 705 is loaded with program instructions, the processor 701 performs transactions associated with the above-described functional/logic modules in the memory 705.
Moreover, FIG. 7 is merely an example of a computing device 700, and the computing device 700 may include more or fewer components than shown in FIG. 7, or have a different arrangement of components. Also, the various components illustrated in FIG. 7 may be implemented in hardware, software, or a combination of hardware and software. For example, the memory and the processor may be implemented in one module, and the instructions in the memory may be pre-written into the memory, or may be loaded by a subsequent processor during execution, which is not limited in this application.
Claims (13)
1. A method of calculating a control pulse for use in a computer device, the control pulse for controlling a quantum computer to perform a quantum gate operation, the method comprising:
receiving an operation messageWherein the operation information comprises Hamiltonian of quantum system of the quantum computer, type U of the quantum gatewantAnd operating time;
determining an objective function O ═ O according to the operation information1-aO2Wherein O is1For the fidelity of the operation of the quantum gate, O2In the non-adiabatic condition, a is a coefficient;
obtaining a current candidate parameter value;
calculating a function value according to the current candidate parameter value and the objective function, and calculating the gradient of the objective function relative to the candidate parameter value;
and when an output condition is met, outputting the current candidate parameter value as the parameter value of the control pulse, wherein the output condition comprises that the difference value between the calculated gradient and 0 is less than or equal to a first preset value and the difference value between the calculated function value and 1 is less than or equal to a second preset value, the output parameter value is used for representing the intensity of the control pulse in N channels in the operation time, the N channels are mutually independent, and N is a positive integer.
2. The method of claim 1, further comprising:
when the output condition is not met, updating the candidate parameter value, recalculating the function value according to the updated current candidate parameter value and the target function, recalculating the gradient of the target function relative to the updated candidate parameter value, and repeating the steps until the output condition is met;
and outputting the current candidate parameter value adopted when the output condition is met as the parameter value of the control pulse.
3. The method of claim 2,
when the output condition is not satisfied, updating the candidate parameter value, including:
when the difference value between the previously calculated gradient and 0 is greater than the first preset value and the difference value between the previously calculated function value and 1 is greater than the second preset value, multiplying the previously calculated gradient by a preset coefficient to obtain a gradient adjustment value, and taking the sum of the gradient adjustment value and the candidate parameter value before updating as the updated candidate parameter value; alternatively, the first and second electrodes may be,
and when the difference value between the gradient calculated at the previous time and 0 is less than or equal to the first preset value and the difference value between the function value calculated at the previous time and 1 is greater than the second preset value, randomly acquiring updated candidate parameter values.
4. A method according to any one of claims 1 to 3, wherein calculating a function value from the current candidate parameter value and the objective function, and calculating a gradient of the objective function with respect to the candidate parameter value, comprises:
setting of auxiliary quantities
Wherein the operation time is divided into n time segments, HiIs the Hamiltonian, T, of the quantum system in the ith time periodi-1In the (i-1) th time period, n is a positive integer, and i is a positive integer not greater than n;
calculating the objective function
Wherein U is the actual evolution function of the quantum gate, ISFor the computation subspace corresponding to the quantum system, L is the dimension of the computation subspace.
5. The method of claim 4, wherein calculating a function value from the current candidate parameter value and the objective function, and calculating a gradient of the objective function with respect to the candidate parameter value, further comprises:
setting of auxiliary quantities
Calculate U and A separatelyi(t) a gradient with respect to the current candidate parameter value;
according to the U and Ai(t) calculating a gradient of the objective function relative to the candidate parameter values relative to a gradient of the current candidate parameter value.
6. The method according to any of claims 1-5, wherein after outputting the current candidate parameter value as the parameter value of the control pulse, the method further comprises:
and adjusting the value of the a.
7. A computer apparatus for controlling pulses used to control a quantum computer to perform quantum gate operations, the computer apparatus comprising:
a first processing module to: receiving operation information, wherein the operation information comprises Hamiltonian of a quantum system of the quantum computer, type U of the quantum gatewantAnd operating time;
determining an objective function O ═ O according to the operation information1-aO2Wherein O is1For the fidelity of the operation of the quantum gate, O2In the non-adiabatic condition, a is a coefficient;
a second processing module to: acquiring a current candidate parameter value;
calculating a function value according to the current candidate parameter value and the objective function, and calculating the gradient of the objective function relative to the candidate parameter value;
and when an output condition is met, outputting the current candidate parameter value as the parameter value of the control pulse, wherein the output condition comprises that the difference value between the calculated gradient and 0 is less than or equal to a first preset value and the difference value between the calculated function value and 1 is less than or equal to a second preset value, the output parameter value is used for representing the intensity of the control pulse in N channels in the operation time, the N channels are mutually independent, and N is a positive integer.
8. The computer device of claim 7, wherein the second processing module is further configured to:
when the output condition is not met, updating the candidate parameter value, recalculating the function value according to the updated current candidate parameter value and the target function, recalculating the gradient of the target function relative to the updated candidate parameter value, and repeating the steps until the output condition is met;
and outputting the current candidate parameter value adopted when the output condition is met as the parameter value of the control pulse.
9. The computer device of claim 8,
when updating the candidate parameter value, the second processing module is specifically configured to:
when the difference value between the previously calculated gradient and 0 is greater than the first preset value and the difference value between the previously calculated function value and 1 is greater than the second preset value, multiplying the previously calculated gradient by a preset coefficient to obtain a gradient adjustment value, and taking the sum of the gradient adjustment value and the candidate parameter value before updating as the updated candidate parameter value; alternatively, the first and second electrodes may be,
and when the difference value between the gradient calculated at the previous time and 0 is less than or equal to the first preset value and the difference value between the function value calculated at the previous time and 1 is greater than the second preset value, randomly acquiring updated candidate parameter values.
10. The computer device according to any one of claims 7 to 9,
when calculating a function value according to the current candidate parameter value and the objective function, and calculating a gradient of the objective function with respect to the candidate parameter value, the second processing module is specifically configured to:
setting of auxiliary quantities
Wherein the operation time is divided into n time segments, HiIs the Hamiltonian, T, of the quantum system in the ith time periodi-1In the (i-1) th time period, n is a positive integer, and i is a positive integer not greater than n;
calculating the objective function
Wherein U is the actual evolution function of the quantum gate, ISFor the computation subspace corresponding to the quantum system, L is the dimension of the computation subspace.
11. The computer device of claim 10,
when calculating a function value from the current candidate parameter value and the objective function, and calculating a gradient of the function with respect to the candidate parameter value, the second processing module is further configured to:
setting of auxiliary quantities
Calculate U and A separatelyi(t) a gradient with respect to the current candidate parameter value;
according to the U and Ai(t) calculating a gradient of the objective function relative to the candidate parameter values relative to a gradient of the current candidate parameter value.
12. The computer device of any one of claims 7-11, wherein the computer device further comprises:
and the third processing module is used for adjusting the value of the a after the current candidate parameter value is taken as the parameter value of the control pulse to be output.
13. A computer arrangement, characterized in that the computer arrangement comprises a memory for storing a computer program and a processor for executing the computer program for implementing the method according to any of claims 1-6.
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