Method and arrangement for optimally designing complex resonator networks - Patents.com

Abstract

To fabricate a quantum microwave circuit, a network model is provided. Each resonator element of the network model is characterized by one or more respective physical quantities that define the contribution of the respective resonator element to one or more resonator modes of the microwave circuit. The values ​​of the respective parameters (x) constitute a vector (1), whose initial form is (2). The characteristic of the microwave circuit in the i-th resonator mode as a quantity s i The real part is defined relative to the target damping constant and the imaginary part relative to the target resonant frequency of the respective resonator mode. Starting from the initial form (2) above, a numerical optimization method finds the vector (1) that gives an extremum of the objective function that depends on the quantities above. A physical instance of the microwave circuit is fabricated such that each physical quantity has the found value of the parameter (x).

Description

[Technical field]

[0001] The present disclosure relates to quantum computing. More particularly, the present disclosure relates to methods and arrangements for optimally designing complex resonator networks for use in quantum computing systems. Further, the present disclosure relates to quantum computing systems. [Background technology]

[0002] A quantum computing system includes one or more quantum processing units (QPUs), which are placed in a cryostat to operate them at temperatures very close to absolute zero. A QPU typically includes multiple qubits and supporting circuitry, e.g., multiple microwave resonator elements, built on one or more substrate materials, such as sapphire, fused silica, or crystalline quartz. The microwave resonator elements often form complex resonator networks that must be carefully designed to exhibit the required frequency characteristics. Parameters of interest include the target frequency and lifetime, the latter of which may be said to represent the linewidth in the frequency spectrum.

[0003] FIG. 1 shows a network model of a simple microwave circuit. A transmission line 101 runs between an input port 102 and an output port 103. Coupled to the transmission line 101 are three resonator elements 104, 105, and 106. Each of the resonator elements 104, 105, and 106 is characterized by one or more respective physical quantities that define the contribution of the respective resonator element to one or more resonator modes of the microwave circuit. Examples of such physical quantities include, but are not limited to, the physical dimensions of the resonator element components, the lengths of the transmission line sections from the coupling points of the resonator elements to the input port 102 and the output port 103, and the distances between adjacent resonator element components from each other.

[0004] The values ​​of said physical quantities may be regarded as degrees of freedom or free parameters in the overall problem of making the microwave circuit perform its intended task as effectively as possible. Since the influence of the various free parameter values ​​is intricately intertwined, it is not easy to find a combination of parameter values ​​that gives the optimal result. Summary of the Invention [Problem to be solved by the invention]

[0005] This Summary is provided to introduce selected concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

[0006] It is an objective to provide a method and arrangement for optimally designing complex resonator networks for efficient use in quantum computing systems. The method and arrangement should make it possible to find the optimal combination of free parameter values ​​in the design accurately and with reasonable computational effort. [Means for solving the problem]

[0007] These and further advantageous objects are achieved by solving a multidimensional optimization problem in which the impedance of a microwave circuit is evaluated in the Laplace domain using complex-valued frequencies whose real part is the target decay constant of the appropriate resonator mode and whose imaginary part is the corresponding target resonant frequency. The objective function, whose extremum is to be found by the numerical optimization, depends on both the complex-valued frequencies and the free parameter values.

[0008] According to a first aspect, there is provided a method for manufacturing a microwave circuit for use in a quantum computing system, the method comprising the steps of providing a network model of the microwave circuit, the network model comprising at least a plurality of resonator elements, each of the resonator elements being characterized by one or more respective physical quantities defining the contribution of the respective resonator element to one or more resonator modes of the microwave circuit. The method further comprises the steps of:

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[0009] According to an embodiment, the quantity is the impedance of the microwave circuit in the i-th resonator mode.

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[0010] According to an embodiment, the impedance of the microwave circuit in the i-th resonator mode

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[0011] According to an embodiment, using the numerical optimization method comprises:

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[0012] According to an embodiment, the microwave circuit includes k ports, k being a positive integer, and the impedance between the nth port and the mth port of the microwave circuit is expressed by a matrix element Z of a k×k square matrix such that n ∈ [1, k] and m ∈ [1, k]. nm The method may be written as: nn )

[0013] According to an embodiment, the quantity is the admittance of the microwave circuit in the i-th resonator mode.

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[0014] According to an embodiment, the microwave circuit includes k ports, k being a positive integer. The admittance between the nth port and the mth port of the microwave circuit is expressed by a matrix element Y of a k×k square matrix, such that n ∈ [1, k] and m ∈ [1, k]. n,m and the method further comprises: n,n )

[0015] According to an embodiment, using the numerical optimization method comprises:

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[0016] According to an embodiment, the microwave circuit includes k ports, k being a positive integer. The quantity may be a scattering characteristic S of the microwave circuit, the scattering parameter between the nth port and the mth port in the ith resonator mode being:

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[0017] The accompanying drawings, which are included to provide a further understanding of the invention and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. [Brief description of the drawings]

[0018] [Figure 1] FIG. 1 shows a network model of a simple microwave circuit. [Diagram 2] FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] In the following description, reference is made to the accompanying drawings, which form a part of this disclosure, and in which are shown by way of example specific aspects in which the present disclosure may be incorporated. It is understood that other aspects may be used and structural or logical changes may be made without departing from the scope of the present disclosure. Thus, the following detailed description should not be taken in a limiting sense, since the scope of the present disclosure is defined by the appended claims.

[0020] For example, it is understood that disclosure related to a described method may also apply to a corresponding device or system configured to perform the method, and vice versa. For example, where certain method steps are described, the corresponding device may include units for performing the described method steps, even if such units are not explicitly described or shown in the figures. On the other hand, for example, where a particular apparatus is described in terms of functional units, the corresponding method may include steps for performing the described functions, even if such steps are not explicitly described or shown in the figures. Furthermore, it is understood that features of various exemplary aspects described herein may be combined with each other, unless otherwise specified.

[0021] A microwave circuit, such as the one whose network model is shown in FIG. 1, generally has k ports, k being a positive integer. In the case of FIG. 1, k=2. What is of interest may be the impedance of any of the microwave circuits, i.e. the impedance of any of said ports, or between any pair of ports. In general, the impedance between the nth and mth ports of a microwave circuit is given by the matrix element Z of a k×k square matrix, such that n∈[1, k] and m∈[1, k]. nm If we consider the admittance Y or scattering characteristic S instead of the impedance Z, the matrix element Y of the admittance matrix n,m or the matrix element S of the scattering matrix n,mmay be used to describe a general k-port microwave network.

[0022] Frequency itself is a real-valued quantity. Thus, the frequency characteristics of microwave circuits are often described using graphs showing parameter values, such as the S21 scattering parameter or other S-parameters or the impedance Z value, as a function of frequency. Such frequency characteristics of microwave circuits depend, as mentioned above, on the values ​​chosen for several physical quantities in the circuit elements. The values ​​of said quantities are expressed in terms of their respective parameters x and collected into the vector

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[0023] However, it has been found that such approaches can lead to the use of objective functions in the numerical optimization that are highly irregular and therefore poorly suited to standard numerical optimization methods.

[0024] It is therefore proposed to evaluate the impedance of the microwave circuit in the Laplace domain using a complex-valued frequency s, where the real part of s is related to the damping constants of the resonator modes of the microwave circuit and the imaginary part of s is related to the real-valued resonant frequencies.

[0025] 2 shows a schematic diagram of a method for manufacturing a microwave circuit for use in a quantum computing system. Step 201 of the method involves selecting a target value for a complex-valued frequency s. Given that the microwave circuit to be designed may have multiple resonator modes of interest, the target values ​​s for each of the multiple i where the index i ranges from 1 to the total number of resonator modes of interest.

[0026] Step 202 of the method comprises providing a network model of the microwave circuit. Very often, an experienced designer of microwave circuits can predict very accurately the approximate influence of various circuit elements on the frequency characteristics, and therefore it is not unreasonable to assume that, at least qualitatively, the network model provided in step 202 can already be said to represent a relatively feasible practical implementation. The network model provided in step 202 comprises at least a number of resonator elements. Furthermore, the network model may comprise other circuit elements such as transmission lines, and / or even optical or (micro)mechanical elements, and / or any combination of any of the elements listed above.

[0027] Each of said resonator elements is characterized by one or more respective physical quantities that define the contribution of the respective resonator element to one or more resonator modes of the microwave circuit. It may be possible to model the influence of not only pure resonator elements but also other kinds of circuit elements on the resonator modes through their respective physical quantities. Step 203 of the method comprises identifying the relevant physical quantities of at least the resonator elements and expressing the values ​​of said physical quantities by respective parameters. These parameters are represented above as parameters x and together form the vector

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[0028] Step 205 of the method comprises:

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[0029] Step 206 of the method includes performing a numerical optimization part, where the impedance Z of the microwave circuit at the i-th resonator mode is given by:

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[0030] The use of an objective function is typical of a numerical optimization method. The objective function represents a quantity that, due to the selected form of the objective function, takes an extreme value when the best possible combination of free parameter values ​​is found. In one embodiment, the use of a numerical optimization method in step 206 is:

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[0031] Step 207 of the method is the output step of the numerical optimization process, where the target value s i provides the best match with (vector

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[0032] If the numerical optimization in step 206 fails to provide final parameter values ​​x that sufficiently converge the optimization to the goal, one can return to step 202 and redesign the network model, then repeat steps 203, 204, 205, and 206. This loop can be repeated until sufficient convergence is achieved.

[0033] The target damping constant for each resonator mode is s i The target resonance frequency of each resonator mode is s i Instead of directly using the imaginary part of

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[0034] Returning to the impedance matrix approach discussed above, a microwave circuit to be designed may include k ports, where k is a positive integer. As explained above, the impedance between the nth and mth ports of such a microwave circuit is given by the matrix elements Z nm Experiments have demonstrated that the method described above can be written as nn ) is roughly 2 times slower than the other elements of the matrix. k It has been shown that the computational cost can be reduced by an order of magnitude.

[0035] It has already been pointed out above that instead of the impedance, the admittance or scattering properties of the microwave network may be considered. In such cases, the use of numerical optimization methods can be

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[0036] It is obvious to those skilled in the art that with the advancement of technology, the basic idea of ​​the present invention may be implemented in various ways. Therefore, the present invention and its embodiments are not limited to the above examples, but rather may vary within the scope of the claims. [Explanation of symbols]

[0037] 101 Transmission Line 102 input ports 103 Output Port 104 Resonator element 105 Resonator element 106 Resonator element

Claims

1. 1. A method for manufacturing a microwave circuit for use in a quantum computing system, comprising: providing a network model of the microwave circuit, the network model including at least a plurality of resonator elements, each of the resonator elements being characterized by one or more respective physical quantities defining a contribution of the respective resonator element to one or more resonator modes of the microwave circuit; Vector [0010] expressing the value of said physical quantity in terms of respective parameters (x) which together constitute The vector [0025] Early form of [0030] selecting initial values ​​for the parameters (x) to form The characteristic of the microwave circuit in the i-th resonator mode is expressed as a complex number s having a real part and an imaginary part. i as a quantity that depends on s i the real part of is defined relative to a target damping constant of each resonator mode, s i wherein the imaginary part of is defined relative to a target resonant frequency of the respective resonator mode; The initial form [0045] Starting from , we use a numerical optimization method to find the vector , which gives an extremum of an objective function that depends on the quantities. [0050] finding values ​​of said parameters (x) constituting fabricating a physical instance of said microwave circuit, said respective physical quantity having said found value of said parameter (x); A method comprising:

2. The quantity is an impedance of the microwave circuit in the i-th resonator mode. [006] and s i is the target damping constant of each of the resonator modes, and s i 2. The method of claim 1 , wherein the imaginary part of is the target resonant frequency of the respective resonator mode.

3. The impedance of the microwave circuit in the i-th resonator mode [0070] is the sum over j points around the i-th resonator mode of interest [0080] and each s i,j is the damping constant of each resonator mode at each j-th point, and each s i,j The method of claim 2, wherein the imaginary part of is the resonant frequency of the respective resonator mode at each jth point.

4. Using the numerical optimization method, [0097] The vector that minimizes [0010] finding values ​​of said parameters (x) constituting 4. The method of claim 1, wherein the index i varies across multiple resonator modes.

5. the microwave circuit includes k ports, k being a positive integer; The impedance between the nth port and the mth port of the microwave circuit is expressed as a matrix element Z of a k × k square matrix, where n ∈ [1, k] and m ∈ [1, k]. nm It is described as The method further comprises: nn 5. The method according to claim 1 , wherein the method is performed on a

6. The quantity is the admittance of the microwave circuit in the i-th resonator mode ##EQU00011## and s i is the target damping constant of each of the resonator modes, and s i 2. The method of claim 1 , wherein the imaginary part of is the target resonant frequency of the respective resonator mode.

7. the microwave circuit includes k ports, k being a positive integer; The admittance between the nth port and the mth port of the microwave circuit is expressed as a matrix element Y of a k × k square matrix, where n ∈ [1, k] and m ∈ [1, k]. n,m It is described as The method further comprises: n,n 7. The method of claim 6, wherein the method is performed on

8. Using the numerical optimization method, ##EQU00012## The vector that minimizes ##EQU00013## finding values ​​of said parameters (x) constituting 8. The method of claim 7, wherein the index i varies across multiple resonator modes.

9. the microwave circuit includes k ports, k being a positive integer; The quantity is a scattering characteristic S of the microwave circuit, and a scattering parameter between the nth port and the mth port in the i-th resonator mode is expressed as 1≦n≦k and 1≦m≦k. ##EQU00014## is represented by the matrix s i is the target damping constant of the respective resonator mode, s i is the target resonant frequency of the respective resonator mode, Using the numerical optimization method, ##EQU00015## The vector that minimizes ##EQU00016## finding values ​​of said parameters (x) constituting 2. The method of claim 1, wherein the index i varies across multiple resonator modes.

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