A method for calibrating a quantum system that stabilizes a bosonic quantum bit

Abstract

The invention relates to a method of calibrating a quantum system stabilizing a so-called mooncat qubit. The method comprises: switching on (2200) a two-photon pump with a frequency of 2ωp and a longitudinal pump with a frequency of ωL; compensating (2210) for an undesired driving of the buffer mode; switching on (2220) a buffer drive with a frequency of ωB; for one or more amplitude values of the longitudinal pump, changing (2230) the phase difference between the longitudinal pump and the buffer drive while measuring the quantity Q, in order to derive a linear relationship between the amplitude of the longitudinal pump and the amplitude and setting (2260) the amplitude of the longitudinal pump to the value at which the amplitude is equal to a desired value and setting (2270) the phase difference to the value at which the phase difference is minimal.

Description

Cross-references to related applications

[0001] This application incorporates, by reference, the entire contents of priority application EP24305338.6, filed on March 5, 2024. Technical Field

[0002] This invention relates to stabilizing boson qubits. Background Technology

[0003] In general, superconducting qubits can be implemented as two-level systems of superconducting electronic circuits. Such qubits can be stored in boson modes, thus forming a specific class of superconducting qubits known as boson qubits.

[0004] It is known from existing technology that cat qubits, which are boson qubits defined by a quantum manifold spanned by the superposition of two coherent states, are quasi-classical states of boson modes. To this end, a specific dissipative stabilization mechanism can be implemented, which involves a nonlinear transition between two photons designed to carry the stabilizing quantum manifold in a first mode (also known as a memory mode or cat qubit mode) and a photon in a strongly dissipative second mode (also known as a buffer mode).

[0005] Cat qubits offer the advantage of an exponentially decreasing bit flip rate and a only linearly increasing phase flip rate. Therefore, stabilized cat qubits benefit from a high-noise bias, meaning that the bit flip probability is much smaller than the phase flip probability.

[0006] Due to its noisy structure, cat qubits can be coupled with repeating codes, using surface codes like ordinary superconducting qubits. However, the noise bias of cat qubits may not be sufficient for some large-scale algorithms to employ simple repeating codes, thus requiring the discovery of boson qubits with higher noise biases.

[0007] Therefore, recent research has focused on a specific class of cat qubits: squeezed cat qubits. For example, Q. Xu et al. (2022) proposed an autonomous quantum error correction (AQEC) scheme using squeezed cat codes to address the primary error source (excitation loss) in continuous variable systems in their paper “Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits” (arXiv:2210.13406). This paper claims to encode the cat state using only an average of four photons, with a noise bias of approximately 10. -15As another example, T. Hillmann et al. (2022) proposed and analyzed the error correction performance of dissipatively stabilized squeezed cat qubits in the article “Quantum error correction with dissipatively stabilized squeezed cat qubits” (arXiv:2210.13359, Phys.Rev.A 107, 032423).

[0008] However, the possibility of stabilizing squeezed cat qubits in practice faces several obstacles, and therefore remains purely theoretical. In particular, such stabilization would require designing a large number of Hamiltonian terms to generate the desired dissipatives, which in turn would necessitate the use of excessive pump sources, thereby jeopardizing the stability of the system. Furthermore, one of these terms... ,in, It is a first-mode photon annihilation operator, and It is a second-mode photon annihilation operator that requires a large amount of energy to be injected into the system, which impairs the system's coherence.

[0009] Against this backdrop, the applicant recently achieved the stabilization of a specific type of boson qubit, with performance comparable to or even slightly superior to that of a squeezed cat qubit. This stabilization relies not only on the nonlinear conversion between two photons in the first mode and one photon in the second mode, and the driving force of the second mode, but also on the longitudinal coupling between the first and second modes. The boson qubit stabilized in this manner is called the "moon cat qubit" by the applicant because its Wigner tomography reveals two crescent-shaped blobs.

[0010] Such a mooncat qubit enables a bit-flip probability up to six times lower than that of a standard cat qubit (i.e., a cat qubit stabilized by the aforementioned dissipation stabilization mechanism). This result represents a term in the Hamiltonian required to generate a compressed cat qubit. This was obtained under certain conditions, and therefore no corresponding pump is needed. Theoretically, the pump must operate at a frequency on the order of 15 gigahertz (GHz). Microwave delivery, in which, It is the resonant frequency of the first mode, and It is the resonant frequency of the second mode.

[0011] The calibration of a quantum system capable of stabilizing the Mooncat qubit presents several challenges, particularly due to the longitudinal coupling between the first and second modes. Specifically, this longitudinal coupling induces parasitic driving of the second mode and a Stark shift, resulting in a deviation in the corresponding resonant frequencies of the first and second modes. Furthermore, the relative phase of the longitudinal coupling and the driving of the second mode must be precisely tuned, and the number of photons in the memory can be controlled by adjusting the amplitude of the longitudinal coupling.

[0012] This invention aims to improve this situation. Summary of the Invention

[0013] To this end, the applicant proposed a method for calibrating quantum systems.

[0014] Such a quantum system is arranged to stabilize boson qubits and includes: - A command circuit comprising a first microwave source, a second microwave source, and a third microwave source, each microwave source being arranged to deliver microwave radiation; and - A nonlinear superconducting quantum circuit comprising an asymmetric threaded superconducting quantum interference device (FQFID) and at least one resonant section, the FQFID being connected to the at least one resonant section, the FQFID having flux lines through which radiation can be delivered to modulate a common flux and a differential flux, the nonlinear superconducting quantum circuit having a first mode and a second mode, the first mode having a first resonant frequency, the second mode having a second resonant frequency different from twice the first resonant frequency, and the second mode being dissipative.

[0015] An asymmetric threaded superconducting quantum interference device is arranged such that, under the following conditions: The first microwave source delivers radiation through the flux line, modulating the common flux at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency. The second microwave source delivers radiation through the flux line, modulating the common flux at a frequency equal to the second resonant frequency, and The third microwave source delivers radiation to the at least one resonant part (9) at a frequency equal to the second resonant frequency to drive the second mode.

[0016] The design of the nonlinear superconducting quantum circuit (3) is expressed as follows: The Hamiltonian H, where, Proportional to the amplitude of the first microwave source (11), It is the annihilation operator of the first mode (a). It is a complex number whose phase and amplitude are generated by the amplitude of the second microwave source (13), and each is defined relative to the phase and amplitude of the first microwave source (11). It is a complex number generated by the third microwave source (15) and defined relative to the first microwave source (11). It is the annihilation operator of the second mode (b), and It is Hermitian conjugation, and the Hamiltonian H produces an effective dissipative substituent through the dissipation of the second mode (b). The effective dissipative quanta stabilize the two-dimensional manifold carrying the boson qubits in the first mode (a).

[0017] The method includes the following operations: a) The first microwave source is turned on at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency, and the second microwave source is turned on at a frequency equal to the second resonant frequency. b) Compensate for the undesirable drive of the second mode caused by the second microwave source; c) Turn on the third microwave source at a frequency equal to the second resonant frequency; d) For one or more amplitude values ​​of the second microwave source, in relation to the quantity While performing the measurement, the phase difference between the second microwave source and the third microwave source is changed; e) Based on the amplitude value of the second microwave source, the quantity The evolution of the phase difference as a function determines the complex number corresponding to each amplitude value of the second microwave source. The corresponding value of the amplitude, and derive the amplitude of the second microwave source and the complex number. The linear relationship between the amplitudes; and f) Based on the linear relationship, the amplitude of the second microwave source is set such that the complex number... The amplitude is substantially equal to the value when the expected value is reached, and the phase difference is set such that the quantity... The minimum is the value

[0018] According to one or more embodiments, the flux lines of the asymmetric threaded superconducting quantum interference device include at least a left flux line and a right flux line. The quantum system further includes a compensation module arranged to couple a second microwave source to the left and right flux lines. The compensation module includes an RF power divider arranged to split the output of the second microwave source into a first power line and a second power line respectively connected to the left and right flux lines; an RF variable attenuator arranged on the first power line to change the amplitude difference between the common flux and the differential flux; and an RF phase shifter arranged on the second power line to change the phase difference between the common flux and the differential flux. Operation b) includes: b1) The amplitude difference between the common flux and the differential flux is changed using the RF variable attenuator, and the phase difference between the common flux and the differential flux is changed using the RF phase shifter, while simultaneously measuring the quantity. ; b2) Determine a pair of corresponding values ​​for the amplitude difference and the phase difference, wherein, due to compensation for the undesirable drive of the second mode (b), the quantity Zero; and b3) Set the amplitude difference and the phase difference to the pair of corresponding values.

[0019] Alternatively, the quantum system also includes an additional microwave source arranged to deliver radiation through the flux line, modulating the differential flux at a frequency equal to the second resonant frequency, operation b) comprising: b4) Turn on the additional microwave source at a frequency equal to the second resonant frequency; and b5) Tune the amplitude and phase of the additional microwave source to compensate for the undesirable drive of the second mode (b).

[0020] According to one or more embodiments, operation d) includes changing the phase of the third microwave source while keeping the phase of the second microwave source constant.

[0021] According to one or more embodiments, operation d) includes performing a longitudinal readout measurement of the quantity using a second microwave source. .

[0022] According to one or more embodiments, the method further includes the following operations: g) Set the phase difference between the first microwave source and the second microwave source to zero.

[0023] According to one or more embodiments, operation g) includes setting the corresponding phases of the first microwave source, the second microwave source, and the third microwave source to be equal to each other.

[0024] According to one or more embodiments, operation f) includes setting the amplitude of the second microwave source to such that a complex number of... The amplitude is less than or equal to 1.

[0025] According to one or more embodiments, operation f) includes setting the amplitude of the second microwave source to such that a complex number of... The magnitude is essentially equal to the value of 1.

[0026] The applicant also proposed a computer program including instructions that, when executed by at least one processor, cause the above-described method to be performed.

[0027] The applicant also proposed a computer-readable storage medium, including the aforementioned computer program stored thereon.

[0028] Finally, the applicant proposed a device for calibrating the aforementioned quantum system.

[0029] The device is arranged as follows: - The first microwave source is turned on at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency, and the second microwave source is turned on at a frequency equal to the second resonant frequency. - Compensate for the undesirable drive of the second mode caused by the second microwave source; - The third microwave source is turned on at a frequency equal to the second resonant frequency; - For one or more amplitude values ​​of the second microwave source, in relation to the quantity While performing the measurement, the phase difference between the second microwave source and the third microwave source is changed; -Based on the amplitude value of the second microwave source, the quantity The evolution of the phase difference as a function determines the complex number corresponding to each amplitude value of the second microwave source. The corresponding value of the amplitude, and derive the amplitude of the second microwave source and the complex number. The linear relationship between the amplitudes; and Based on the linear relationship, the amplitude of the second microwave source is set such that the complex number... The amplitude is substantially equal to the expected value, and the phase difference is set such that the quantity The minimum value. Attached Figure Description

[0030] Referring to the accompanying drawings, other features and advantages of the invention will become apparent from the following description, which is provided for illustrative and non-limiting purposes, wherein - Figure 1 A quantum system comprising a nonlinear superconducting quantum circuit and a command circuit is schematically illustrated. - Figure 2 The standard cat-state qubit and the qubit formed by the cat state are shown. Figure 1 The corresponding Wigner function of the boson qubits in the quantum system stabilized; - Figure 3 It shows Figure 1 A detailed schematic diagram of a quantum system; - Figure 4 It shows Figure 3 A local equivalent circuit diagram of an example implementation of the first current in a quantum system; - Figure 5 It shows Figure 3 A local equivalent circuit diagram of an example implementation of the second current in a quantum system; - Figure 6 It shows Figure 3 A partial equivalent circuit diagram of a capacitive example implementation of a quantum system; - Figure 7 It shows the result of Figure 1 The bit flip rate of the stabilized boson qubit in the quantum system is a function of the photon number; - Figure 8 It shows the result of Figure 1 The non-adiabatic error generated by implementing Z-gates in quantum systems; - Figure 9 It shows the result of Figure 1 A comparison of non-adiabatic errors between stabilized boson qubits in quantum systems and theoretically squeezed cat qubits; - Figure 10 It shows the result of Figure 1 The bit flip rate of the stabilized boson qubit in the quantum system; a function of the ratio of the corresponding zero-point fluctuations of the superconducting phase of the boson qubit mode and the buffer mode; - Figure 11 The asymmetric threaded superconducting quantum interference device (ATS) is shown in detail. - Figure 12 The compensation module coupled to the ATS is shown; - Figure 13 It shows the use of Figure 12 The compensation diagram obtained by the compensation module; - Figure 14 It shows Figure 13 A magnified view of the nebula region in the compensation map; - Figure 15 The evolution of the photon number as a function of the phase difference between the longitudinal pump and the buffer drive is shown for different amplitudes of the longitudinal pump. - Figure 16 The curve obtained by keeping the amplitude of the buffer drive constant is shown; - Figure 17The fit between the cat moon parameter amplitude and the longitudinal pump amplitude is shown; - Figure 18 Several experimental and theoretical Wigner tomography results are shown for different values ​​of the longitudinal pump amplitude; - Figure 19 It shows Figure 16 A magnified view of the curve; - Figure 20 Several Wigner tomography images are shown; each Wigner tomography image corresponds to Figure 19 The corresponding points of the curve; - Figure 21 The diagram illustrates the process for calibration. Figure 1 Devices for quantum systems; and - Figure 22 Calibration is illustrated schematically. Figure 1 Methods for quantum systems. Detailed Implementation

[0031] The accompanying drawings and the following description include most of the features used for their positive and clearly defined purpose. Therefore, they not only aid in understanding the invention, but can also be used to aid in its definition if desired. A. Cat qubit

[0032] To date, the applicant's work has generally focused on the stabilization of cat qubits. R. Lescanne et al. have demonstrated the possibility of realizing such qubits in "Exponential suppression of bit-flips in a qubit encoded in an oscillator" (Nature Physics, 2020), whereby such cat qubits can be stabilized by a nonlinear transition between two photons in a first mode a (memory mode or cat qubit mode) and one photon in a second mode b (buffer mode).

[0033] Cat qubits are defined as being composed of so-called cat states. Crossing a two-dimensional manifold, cat state There are two coherent states. and Superposition:

[0034] ,

[0035] in:

[0036] .

[0037] It is known that stabilized cat qubits benefit from high noise bias, meaning that the probability of a bit flip is exponentially smaller than the probability of a phase flip. More precisely, the effective error channel (e.g., bit error or "bit flip") increases with the "size" of the Schrödinger cat state of the cat qubit (i.e., the average number of photons). The phase flip is suppressed exponentially. As mentioned earlier, such exponential suppression of bit flips comes at the cost of a linear increase in the phase flip.

[0038] Based on current understanding, such suppression should apply to a large class of physical noise processes that have a local effect on the phase space of the harmonic oscillator. These include, but are not limited to, photon loss, thermal excitation, photon dephasing, and various nonlinearities caused by coupling to the Josephson junction.

[0039] Recent experiments in the field of superconducting quantum circuits have observed such bit flipping with exponential suppression of the average number of photons in the cat state. A.1 Stabilization Scheme

[0040] Cat qubits can be stabilized or restricted using the following exemplary schemes:

[0041] a) Parameter dissipation stabilization, with a jump operator. ,in, It is the two-photon dissipation rate. It is the photon annihilation operator for memory mode a, and It is a complex number that defines a cat qubit. It can be determined by considering the dissipation rate... The dissipative buffer mode b and the four-wave mixer (typically a Josephson junction or ATS) are coupled to the cat qubit mode a, and the Hamiltonian is designed... To implement this transition operator, where, It is the photon annihilation operator of buffer mode b, and It is the two-photon coupling rate, obtained by applying a frequency of [value] to the four-wave mixer. Pumping at frequency Drive buffer mode b=( This can be achieved under certain conditions.

[0042] b) Kerr Hamiltonian ,in, It is the amplitude of the Kerhammeter. It is the photon annihilation operator, and It is the average number of photons.

[0043] c) Detuned Kerheimian ,in, It is the amplitude of the Kerhammeter. It is the photon annihilation operator. It is the complex number that defines a cat qubit, and It is a detuning factor.

[0044] d) Two-photon exchange (TPE) Hamiltonian ,in, It is the complex two-photon coupling rate. It is the photon annihilation operator. It is the complex number that defines a cat qubit, and It is the decrement and elevation operator for a two-level system. This Hamiltonian can be designed in the same way as parameter dissipation stabilization a).

[0045] e) DC dissipation stabilization: The applicant filed European patent application EP 23306839.4 for this purpose. In this application, the cat qubit is stabilized according to the aforementioned stabilization scheme a), with the difference that the two-photon pump, which designs the nonlinear conversion between two photons in memory mode a and one photon in buffer mode b, is replaced by a DC voltage source. This DC voltage source is biased entirely by a nonlinear element formed by one or more Josephson junctions. Therefore, the two-photon coupling rate is... Amplitude of two-photon pumping: The restrictions, among which, It is the Josephson energy of one or more Josephson knots. It is the phase zero-point fluctuation of memory mode a, and It is the phase zero-point fluctuation of buffer mode b.

[0046] f) Resonant dissipation stabilization, with a migration operator ,in, It is the two-photon dissipation rate. It is the photon annihilation operator for memory mode a, and It is a complex number that defines a cat qubit. It can be determined by considering the dissipation rate... The dissipative buffer mode b and the three-wave mixer are coupled to the designed Hamiltonian. The transition operator is implemented using the cat qubit mode 'a', where, It is the photon annihilation operator of buffer mode b (which essentially satisfies the condition at the mode frequency). ,and and the frequency of adding it is (Under the condition of buffer mode driven).

[0047] The following sections focus on a specific stabilization scheme: dissipative compression stabilization. A.2 Compressed Cat Quantum Bits

[0048] Cat qubits possess the property of allowing the implementation of quantum gates (such as Z-gates or CNOT gates) while maintaining a noise bias. The properties used to evaluate the quality of a quantum gate are its execution time (i.e., the time it takes for the quantum gate to operate) and the associated error probability. For cat qubits, the optimal time for the gate to achieve a phase-flip error probability depends on a ratio... ,in, It is the single-photon loss rate (or error rate, because it causes phase-flipping errors) of the cat qubit used to perform quantum gates, and It is the two-photon dissipation rate (also known as the correction rate or stabilization rate) of these cat qubits. The smaller the value, the better the door fidelity.

[0049] It is generally accepted that using a single repeating code is sufficient to correct the remaining errors because bit-flip errors are rare enough; and more specifically, phase bit-flip error-correcting codes are sufficient to correct the remaining phase bit flips. This could be, for example, a repeating code defined in dibases or any other state-of-the-art error-correcting code.

[0050] However, even though cat qubits have a high noise bias, a particularly advantageous feature for achieving quantum error correction and designing reliable quantum computers, such a noise bias does not seem sufficient for large-scale quantum algorithms with simple repeating codes. Against this backdrop, recent research has pointed to a special class of cat qubits with even higher noise bias: compressed cat qubits.

[0051] Squeezed cat states also exhibit fewer nonadiabatic errors during the time interval of quantum gates (such as Z-gates or CNOT gates). Overall, reducing nonadiabatic errors allows for a reduction in the contrast ratio. Requirements.

[0052] Compression state Defined as:

[0053] ,

[0054] in, It is a shift operator:

[0055] ,

[0056] and It is a compression operator:

[0057] ,

[0058] in, It is a norm Complex compression parameters.

[0059] A compressed cat state is defined as the coherent superposition of two compressed states with opposite displacement amplitudes and the same degree of compression:

[0060] ,

[0061] in, It is a normalization constant.

[0062] Note that in order to obtain the proper compressed cat state, and The complex phase must satisfy:

[0063] ,

[0064] ,

[0065] Dissipative compression stabilization is based on the following transition operator:

[0066] ,

[0067] in, It is the two-photon dissipation rate. It is the photon annihilation operator. It is the complex number that defines a cat qubit. and Complex compression parameters The modulus and the argument.

[0068] By having a dissipation rate The lossy buffer mode b and a four-wave mixer (typically a Josephson junction or ATS) are coupled to the cat qubit mode, and the Hamiltonian is designed... To implement this transition operator, where, It is the photon annihilation operator for mode b.

[0069] The dissipation form of a cat qubit is as follows: The dissipation of theoretically squeezed cat qubits has the following more complex form: , in, and It is assumed to be a real number without loss of generality. More specifically, dissipative contraction stabilization is achieved through the interaction terms. It was designed by [the relevant authority].

[0070] Therefore, the theoretical implementation of stabilizing the compressed cat qubit depends on generating four specific terms: i. The first term corresponds to the nonlinear transition between two photons in the first mode a (memory mode) and one photon in the second mode b (buffer mode). This term requires a frequency of... The pump, among which, It is the resonant frequency of the first mode a, and It is the resonant frequency of the second mode b. ii. The second term corresponds to the longitudinal coupling between the first mode a and the second mode b. This term can be expressed at a frequency of... The pump is obtained. iii. The third item requires a frequency of: The pump. iv. The fourth item needs to be in frequency. Drive the second mode b.

[0071] It is important to note that the so-called "standard cat qubit" is generated only by generating the first term. and the fourth item To stabilize.

[0072] However, a significant obstacle to the application of squeezed cat qubits is the difficulty in designing such dissipative squeezed stabilizations. This obstacle stems primarily from the large number of terms involved in the pump design, which can jeopardize the system's stability, increase the hot particle number, or reduce the coherence time. Furthermore, it must be noted that generating the third term requires a very high frequency. Approximately 15 gigahertz (GHz), assuming frequency and Typically, these frequencies are around 5 GHz. The amount of energy required to bring the system to such a frequency negatively impacts the system's coherence. Furthermore, the frequency... Pumps (used to generate the third item) The phase and amplitude of the signal must be relative to the frequency. Pumps (used to generate the second item) The phase, amplitude, and frequency of ) are The second mode b driver (used to generate the fourth item) To perform precise tuning.

[0073] Therefore, although compressed cat qubits theoretically offer a higher noise bias than cat qubits, they are currently impossible to stabilize due to the numerous difficulties in achieving the required dissipation. On the other hand, cat qubits can be stabilized, but their use requires extremely high conditions to achieve a sufficient noise bias for running large-scale quantum algorithms. This fact is the subject of the recent publication "Computing 256-bit Elliptic CurveLogarithm in 9 Hours with 126133 Cat Qubits" by E. Gouzien et al. (2023) (arXiv: 2502.06639). B. Mooncat Quantum Bits

[0074] Figure 1 A schematic diagram of quantum system 1 is shown, which is arranged to stabilize a specific type of boson qubit: the mooncat qubit.

[0075] Quantum system 1 includes nonlinear superconducting quantum circuit 3 and command circuit 5.

[0076] The nonlinear superconducting quantum circuit 3 is arranged to enable at least four-wave mixing between the first mode a and the second mode b. In the following text, the first mode a carries the Mooncat qubit, while the second mode b is dissipative and serves as a buffer between the Mooncat qubit and the external environment.

[0077] In the remainder of the specification, the first mode a is referred to as memory mode, and the second mode b is referred to as buffer mode.

[0078] Memory mode a and buffer mode b correspond to the inherent resonant frequencies of the nonlinear superconducting quantum circuit 3. Therefore, memory mode a and buffer mode b each have their own resonant frequencies. Memory mode a has a resonant frequency. Furthermore, buffer mode b has a resonant frequency. ,in, and These are the corresponding angular frequencies of memory mode a and buffer mode b.

[0079] By referring to the "having" of memory modes and buffer modes, it should be understood that the nonlinear superconducting quantum circuit 3 comprises components operating by a superconducting mechanism, which independently or simultaneously carry modes. In other words, memory mode a and buffer mode b can be carried on different subsets of the components of the superconducting circuit, or on the same subset of the components of the superconducting circuit.

[0080] Memory mode a has a high quality factor Buffer mode b has a low quality factor. It should be understood that the quality factor (Q factor) can be determined in a variety of ways, such as by: (a) spectral linewidth measurement, where the quality factor is determined by... Given, among which, It is the resonant frequency and It is the spectral linewidth; or (b) via a time-domain measurement, wherein a single-tone signal is input and the return signal is measured after a predetermined time, wherein, , This refers to the characteristic decay time. Of course, those skilled in the art will be aware of many other methods used to determine the quality factor of a particular mode.

[0081] The nonlinear superconducting quantum circuit 3 is designed to withstand microwave radiation delivered by the instruction circuit 5 in order to implement various nonlinear interactions between memory mode a and buffer mode b. The frequency of each microwave radiation is tuned to select a specific term under the rotating wave approximation.

[0082] As detailed below, the nonlinear superconducting quantum circuit 3 is designed to interact with the instruction circuit 5 to design a specific Hamiltonian H, thereby generating an efficient dissipator through the dissipation of the buffer mode b, which stabilizes the two-dimensional manifold carrying the Mooncat qubit.

[0083] Such a Hamiltonian H can be expressed in the following form:

[0084] .

[0085] The following will explain and describe in detail each term of the Hamiltonian H.

[0086] The nonlinear superconducting quantum circuit 3 includes a four-wave mixing nonlinear element 7 and at least one resonant section 9.

[0087] The four-wave mixing nonlinear element 7 is arranged to be parametrically driven by the instruction circuit 5 so that the nonlinear superconducting quantum circuit 3 is designed with the required Hamiltonian H to stabilize the Mooncat qubit.

[0088] More specifically, the four-wave mixing nonlinear element 7 is an asymmetric threaded superconducting quantum interference device (or ATS hereinafter referred to as an ATS). As is known to those skilled in the art, the ATS can be used to design 2-to-1 photon conversions, i.e., the first term of the Hamiltonian H mentioned above. This is to enable the implementation of dissipative stabilization, as successfully demonstrated by R. Lescanne et al. (2020).

[0089] Unlike the first implementation of this stabilization scheme proposed by Z. Leghtas et al. in “Confining the state of light to a quantum manifold by engineered two-photon loss” (Science, Vol. 347, No. 6224, 2015) and S. Touzard et al. in “Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation” (Physical Review X8, 023005, 2018), where the superconducting circuit element used as a four-wave mixer is a transmon with a single Josephson junction, the solution developed by R. Lescanne et al. (2020) utilizes an ATS design with a much lower cross-Kerr term than the transmon, thus allowing the observation of exponential suppression of bit flipping.

[0090] ATS has a flux line through which radiation can be delivered to modulate common flux and / or differential flux.

[0091] By The frequency is used to parametrically pump the ATS to achieve a 2-to-1 photon conversion between memory mode a and buffer mode b. Advantageously, the pump frequency satisfies... To ensure that the pump operates as well as possible with this parameter, It is the two-photon coupling rate.

[0092] As stated in the applicant's European patent application EP 21306965.1, ( This is known as the resonant case and is a potentially advantageous specific case. However, in such a resonant case, the 2-to-1 photon conversion cannot be activated by parametrically pumping a four-wave mixing nonlinear element (such as an ATS). Instead, a three-wave mixing nonlinear element should be used. As will be seen later, four-wave mixing is still required to design the longitudinal term of the Hamiltonian H. Therefore, while the resonant case is compatible with the proposed Mooncat qubit stabilization, it requires an additional three-wave mixing nonlinear element. In other words, the resonant case requires both three-wave and four-wave mixing to generate the first term separately. Second item Three-wave mixing can be achieved through its usual operation. The ATS can be operated at different flux points, or generated by adding another nonlinear element, as described in the aforementioned European patent application EP 21306965.1.

[0093] In this invention, the applicant proposes using an ATS to stabilize the Mooncat qubit, thus achieving the desired result. Or an advantage outside the resonant range of 2-to-1 photon conversion.

[0094] The resonant section 9 is arranged to be coupled to or included in the ATS 7 to provide the nonlinear superconducting quantum circuit 3 with a corresponding resonant frequency. and The memory modes a and buffer modes b. More specifically, memory modes a and buffer modes b "participate" in ATS 7, meaning that some or all of the mode magnetic energy is stored in ATS 7. Such participation can be quantified by the zero-point fluctuations of the superconducting phase on ATS 7, denoted as memory mode a. For buffer mode b, denoted as .

[0095] exist Figure 1 In the schematic diagram of quantum system 1 shown, the nonlinear superconducting quantum system 3 includes only one resonant section, namely resonant section 9. A single resonant section can be configured to generate both memory mode a and buffer mode b. However, the nonlinear superconducting quantum system 3 typically includes two resonant sections to form memory mode a and buffer mode b, respectively.

[0096] Command circuit 5 is configured to deliver microwave radiation.

[0097] The instruction circuit 5 is arranged to parametrically drive the ATS 7 to achieve a nonlinear conversion between two photons in memory mode a and one photon in buffer mode b, to parametrically drive the ATS 7 to achieve longitudinal coupling between memory mode a and buffer mode b, and to drive buffer mode b.

[0098] Therefore, such as Figure 1 As shown, the instruction circuit 5 includes a first microwave source 11, a second microwave source 13, and a third microwave source 15.

[0099] The first microwave source 11 is arranged to parametrically drive the ATS 7. More specifically, the first microwave source 11 is used to achieve a frequency of The radiation is delivered to the parameter pump of ATS 7.

[0100] In the remainder of the specification, the first microwave source 11 is referred to as two-photon pump.

[0101] The second microwave source 13 is also arranged to parametrically drive the ATS 7. More specifically, the second microwave source 13 is used to achieve a frequency of The radiation is delivered to the parameter pump of ATS 7.

[0102] In the remainder of the specification, the second microwave source 13 is referred to as longitudinal pump.

[0103] Finally, the third microwave source 15 is arranged to deliver a frequency of to the resonant section 9. Radiation is used to drive buffer mode b.

[0104] In the remainder of the specification, the third microwave source 15 is referred to as the buffer driver.

[0105] As described above, the combined action of the two-photon pump 11 and the buffer drive 15 allows the nonlinear superconducting quantum circuit 3, more specifically the ATS 7, to perform the nonlinear conversion between two photons in memory mode a and one photon in buffer mode b, as well as the driving of buffer mode b.

[0106] Considering the need to stabilize the two-dimensional manifold carrying the Mooncat qubits (which is the goal of Quantum System 1), such a combination of actions should contribute to the generation of terms. and The Hamiltonian H is obtained so that it can be designed by nonlinear superconducting quantum circuit 3.

[0107] Furthermore, the parameter pump implemented using vertical pump 13 allows for vertical coupling between memory mode a and buffer mode b.

[0108] The result of such vertical coupling is the generation of terms. It also contributes to the Hamiltonian H, and thus helps to stabilize the two-dimensional manifold carrying the Mooncat qubit.

[0109] In response to radiation delivered by command circuit 5, nonlinear superconducting quantum circuit 3 designs a Hamiltonian H as follows:

[0110] ,

[0111] in: - It is the two-photon coupling rate or interaction strength that is proportional to the amplitude of the two-photon pump 11. - It is the annihilation operator for memory pattern a. - It is a complex number whose phase and amplitude are generated by the amplitude of radiation caused by longitudinal pump 13. - It is a complex number generated by buffer drive 15. - It is the annihilation operator for buffer mode b. - This indicates Hermitian conjugate.

[0112] In the expression for the Hamiltonian H, it should be noted that the parameter and These are all defined relative to two-photon pumping 11. Specifically, complex numbers The resulting phase and amplitude are each defined relative to the phase and amplitude of the two-photon pump 11.

[0113] In the remainder of this specification, the complex number It is known as the Moon Cat parameter.

[0114] It is worth noting that such a Hamiltonian H does not include terms. As mentioned earlier, such a term requires additional pumping, which increases complexity and threatens the stability of the system. Furthermore, this term implies a very high frequency (corresponding to...). Furthermore, a certain amount of energy is pumped into the system, which affects the coherence of the boson qubits.

[0115] Hamiltonian H generates efficient dissipatives through the dissipation of buffer mode b. This stabilizes the two-dimensional manifold that carries the Mooncat qubits.

[0116] The relative phase of the microwave source can be adjusted to obtain the desired number of photons in the memory.

[0117] More specifically, advantageously, the phase difference between the two-photon pump 11 and the longitudinal pump 13 is substantially zero. In other words, the two-photon pump 11 and the longitudinal pump 13 are configured such that their respective phases are substantially equal to each other.

[0118] Advantageously, the phase difference between the longitudinal pump 13 and the buffer drive 15 is substantially zero. In other words, the longitudinal pump 13 and the buffer drive 15 are configured such that their respective phases are substantially equal to each other.

[0119] Preferably, the two-photon pump 11, the longitudinal pump 13, and the buffer drive 15 are configured such that their respective phases are substantially equal to each other.

[0120] The phrase "substantially equal" implies that, ideally, the corresponding phases of related microwave sources are strictly equal to each other. However, achieving such equality is difficult in practice. Typically, the phase of one microwave source deviates from the phase of another by about 5%.

[0121] Figure 2 The corresponding Vig functions (or Wigner tomography) of the standard cat qubit and the moon cat qubit stabilized by quantum system 1 are shown.

[0122] It can be noted that the standard cat qubit and the mooncat qubit stabilized by quantum system 1 have the same number of photons. However, the latter has a larger separation in phase space than a standard cat qubit, meaning the two clumps are more separated. This increased separation, given the same number of photons, explains the increase in noise bias.

[0123] As can be seen, both clumps exhibit a crescent shape. This is why the boson qubit stabilized by quantum system 1 is called the "mooncat qubit". B.1 Example Implementation of Quantum Systems

[0124] Figure 3 It shows more clearly Figure 1 A schematic diagram.

[0125] The resonant section 9 adopts the form of a linear microwave network. This linear microwave network ensures that when coupled via the linear coupler 11 to the ATS 7, which acts as an inductive element, the nonlinear superconducting quantum circuit 3 has resonant frequencies of... and The ATS 7 participates in memory mode a and buffer mode b.

[0126] Two-photon pump 11 and longitudinal pump 13 are set to the common flux in modulated ATS 7.

[0127] exist Figure 3 In the example shown, the instruction circuit 5 also includes a microwave source 19 configured to modulate the differential flux in the ATS 7.

[0128] Such a microwave source 19 can be used to transmit the desired frequency at a frequency of 10 ... The radiation is delivered to the resonant section 9 to drive the buffer mode b. In the sense of this invention, the microwave source 19 can therefore also be considered a "third microwave source" or a "buffer driver" rather than the buffer driver 15.

[0129] To clearly distinguish the role of the source in the Hamiltonian, Figure 3 The diagram illustrates a microwave network 21 with the correct phase offset applied. Alternatively, each microwave source can be simply coupled to a single node of the ATS 7, and their relative phase and amplitude can be set to achieve the desired flux modulation. In such a case, the microwave sources require out-of-phase addressing circuitry to modulate the common flux, and in-phase addressing circuitry to modulate the differential flux.

[0130] As described above, the two-photon pump 11 is arranged to be substantially equal to The frequency of microwave radiation is delivered to the ATS 7 to enable the nonlinear superconducting quantum circuit 3 to perform a 2-to-1 photon conversion between memory mode a and buffer mode b, thereby designing the terms of the Hamiltonian H. To convert this 2-to-1 photon pair into two-photon dissipation, buffer mode b is configured via linear coupler 25 to have a frequency The microwave filter 27 of the bandpass filter is selectively coupled to the load 23.

[0131] Alternatively, microwave filter 27 can be configured to have a frequency of The band-stop filter can be placed between the external environment on one side and the memory mode a and the buffer mode b on the other side to isolate the memory mode a, thereby preventing the memory mode a from suffering additional losses due to unwanted coupling with the load 23.

[0132] Alternatively, if Then microwave filter 23 can be configured as a low-pass filter; if Then, microwave filter 23 can be configured as a high-pass filter. In other embodiments, microwave filter 23 can be omitted when coupling between load 19 and essentially only buffer mode b can be established. As mentioned above, memory mode a has a high quality factor. Buffer mode b has a low quality factor. .

[0133] As described above, the buffer drive 15 is arranged to operate at a frequency substantially equal to the second resonant frequency. The frequency of microwave radiation is delivered to the resonant part 9 to drive the buffer mode b, thereby designing the term of the Hamiltonian H. .

[0134] Alternatively, buffer mode b is set by frequency. Microwave source 19 driven.

[0135] In the above text, load 23 can be considered as Figure 1 The instruction circuit 5 is part of the instruction circuit, while the linear coupler 25 and microwave filter 27 can be regarded as part of the nonlinear superconducting quantum circuit 3.

[0136] As described above, the longitudinal pump 13 is arranged at a frequency substantially equal to the second resonant frequency. The frequency of microwave radiation is delivered to the ATS 7 to achieve longitudinal coupling between memory mode a and buffer mode b, thereby designing the Hamiltonian H. . B.1.1 Example Implementation of Current-Type Method

[0137] Figure 4 and Figure 5 An equivalent circuit diagram of a corresponding embodiment of a nonlinear superconducting quantum circuit 3 in the form of a current circuit is shown.

[0138] Such equivalent circuit diagrams are partial because they only represent ATS 7 and resonant section 9, and therefore do not represent either linear coupler 25 or microwave filter 27. More specifically, resonant section 9 includes first resonant section 29 and second resonant section 31.

[0139] The ATS 7 is implemented in a manner known in the art, for example, as described in R. Lescanne et al. (2020). The ATS 7 includes a first Josephson junction 33 and a second Josephson junction 35 connected in parallel, and an inductive element 37 connected in parallel between them. Thus, the ATS 7 has two connected loops, each including a Josephson junction 33, 35 connected in parallel with the parallel inductive element 37. The inductive element 37 can be implemented geometrically or via a chain of junctions. The ATS 7 biases the flux of both its loops in both DC and AC modes. The DC bias sets the operating point of the ATS 7. It can operate near a so-called saddle point, which is the optimal point of frequency and has a small cross-Kerr term.

[0140] Both the first resonant section 29 and the second resonant section 31 are currently coupled to the ATS 7. The first resonant section 29 will have a resonant frequency. The memory mode a imparts nonlinear superconducting quantum circuit 3, while the second resonant part 31 will have a resonant frequency. The buffer mode b imparts nonlinear superconducting quantum circuits 3.

[0141] Through "current coupling," it should be understood that there exists a short conductive portion connecting the first resonant section 29 and the second resonant section 31 to the ATS7, i.e., a short conductive trace or any other means ensuring a physically continuous conductive connection. The term "short" means connected to the ATS7 at a resonant frequency of... and Compared to the impedance of the first resonant section 29 and the second resonant section 31, the impedance of the conductive traces is negligible. These short conductive sections correspond to the linear coupler 17.

[0142] exist Figure 4 In one embodiment, the first resonant portion 29 includes a capacitive element 39 and an inductive element 41 connected in series. Similarly, the second resonant portion 31 includes a capacitive element 43 and an inductive element 45 connected in series.

[0143] exist Figure 5In one embodiment, the first resonant portion 29 further includes a capacitive element 39 and an inductive element 41. However, in such an embodiment, the capacitive element 39 and the inductive element 41 are connected in parallel. Similarly, the capacitive element 43 and the inductive element 45 of the second resonant portion 31 are connected in parallel.

[0144] exist Figure 4 and Figure 5 In a corresponding embodiment, the nonlinear superconducting quantum circuit 3 includes two resonant sections. However, as previously stated, the nonlinear superconducting quantum circuit 3 may include only one resonant section, which is arranged to generate both memory mode a and buffer mode b. B.1.2 Example Implementation of Capacitive Type

[0145] Figure 6 An equivalent circuit diagram of an embodiment of a nonlinear superconducting quantum circuit 3 in the form of a capacitor circuit is shown.

[0146] and Figure 4 and Figure 5 different, Figure 6 The external environment is shown. ATS 7 serves as the central reference point, and the remaining components are connected to this central reference point. For this purpose, there is also filtering for buffer mode b and the external environment. For simplicity, the microwave source is omitted, but its arrangement is similar to... Figure 3 The same as shown, used for the drive circuit.

[0147] exist Figure 6 In this linear microwave network, a capacitive element is current-coupled to ATS 7 to form buffer mode b, and a parallel LC resonator is strongly capacitively coupled to ATS 7 to form memory mode a. The coupling to ATS 7 corresponds to linear coupler 17. Both memory mode a and buffer mode b are strongly coupled to ATS 7, as shown by the phase zero fluctuations of the two modes in the center inductance of ATS 7. The buffer is coupled to the external environment through a capacitive element corresponding to linear coupler 25. B.2 Characterization of the Mooncat qubit

[0148] In this invention, the nonlinear superconducting quantum circuit 3 is designed as represented by The Hamiltonian H. The Hamiltonian H generates an efficient dissipative sub-process through the dissipation of buffer mode b. This stabilizes the two-dimensional manifold that carries the Mooncat qubits.

[0149] If the corresponding phases of the second microwave 13 and the buffer drive 15 (or alternatively 19) are properly tuned, then and They have the same complex phase, and therefore can take real numbers without loss of generality. Therefore, unless otherwise stated, it is assumed that... and It is a real number.

[0150] Even and odd cat states Similarly, the even-mooncat states (odd-mooncat states respectively) of mooncat qubits carried by a two-dimensional manifold stabilized using Quantum System 1 are a superposition of mooncat states containing only even-numbered (odd-numbered) Fock states. Even-mooncat states And the strange moon cat state The expansion under the Fockbasis is as follows (MCS stands for "Mooncat State"):

[0151] ,

[0152] in:

[0153] ,

[0154] ,

[0155] and:

[0156] ,

[0157] in:

[0158] ,

[0159] ,

[0160] in, and It is a normalization constant.

[0161] The mass factor of the implementation of quantum system 1 is a term The relative amplitude. In this respect, if a comparison can be established between the Moon Cat qubit of this invention and the theoretical compressed cat qubit, then It can be expressed as complex compression parameters The function is shown below:

[0162] .

[0163] Similar to compressed cats (qubits), by increasing... The value—or, for a compressed cat, equivalently increased. The numerical value—the probability of bit flipping decreases exponentially. B.3 Performance of Mooncat Quantum Bits

[0164] Figure 7 The bit-flipping probability is shown as the number of photons and for different Mooncat parameters. A function of the value of . More specifically, for the Mooncat parameter For each value, there exists a solid line corresponding to the bit flip rate of the Mooncat qubit stabilized by Quantum System 1, and a dashed line corresponding to the bit flip rate of the corresponding Compact Cat qubit. By "comparable," it should be understood here that for a given value... We consider using the parameters based on the previous formula. The obtained compressed cat qubits.

[0165] It can be seen that, for and in photon number At that point, the bit flip of the moon cat qubit stabilized by quantum system 1 is improved by six orders of magnitude compared to the bit flip of the standard cat qubit with the same number of photons.

[0166] Figure 7 As shown, in the Moon Cat parameters When the value is less than or equal to 1, the improvement in bit flipping of the Mooncat qubit (solid line) is the same as or even slightly better than that of the Compactcat qubit (dashed line).

[0167] As mentioned earlier, Moon Cat parameters Both the phase and amplitude are generated by the radiation amplitude caused by the longitudinal pump 13. Advantageously, the amplitude of the radiation caused by the longitudinal pump 13 is adjusted so that the lunar cat parameters... The value is equal to 1. Beyond this value, the mooncat qubit stabilized by quantum system 1 is affected by saturation, and therefore its performance is not as good as the theoretical performance of the compressed cat qubit.

[0168] Quantum System 1 also exhibits fewer non-adiabatic errors during gate implementation. The following description focuses primarily on Z-gates, but it can be directly generalized to CNOT gates.

[0169] Using known cat qubits (i.e., by generating only terms) and item During the implementation of the Z-gate using a stable cat qubit, two types of errors may occur: -Depend on The given single-photon loss is incorrect, where, It is the number of photons in the cat state. It is single-photon loss, and It is the duration of the door. -Because the door is in a limited time Non-adiabatic errors caused by internal execution, among which... This refers to the two-photon exchange rate. Non-adiabatic errors hinder the achievement of the goal of performing gate operations as quickly as possible to avoid increasing single-photon losses.

[0170] A trade-off must be made between single-photon loss errors and non-adiabatic errors, because the former is proportional to the duration of the gate operation, while the latter is proportional to the reciprocal of that duration.

[0171] Quantum system 1 has a smaller nonadiabatic error than known cat qubits. The nonadiabatic error of quantum system 1 during the Z-gate is given by the following formula:

[0172] .

[0173] Figure 8 This shows that quantum system 1 acts as a quantum system during the Z-gate period. It is a function of the gate time in units and for a fixed number of photons. The simulation of non-adiabatic errors. It can be seen that when the Moon Cat parameters... As the value of increases, the non-adiabatic error decreases. The solid line shows the numerical simulation, and the dashed line shows the above formula.

[0174] Figure 9 The diagram shows a comparison of non-adiabatic errors between the Mooncat qubit (solid line) stabilized by Quantum System 1 and the Compact Cat qubit (dashed line), demonstrating that the performance of Quantum System 1 is comparable to that of the Compact Cat qubit.

[0175] at last, Figure 10 The bit flip rate and ratio of the Mooncat qubit stabilized by Quantum System 1 are shown. The functional relationship, where the number of photons in memory mode a is approximately determined by... Given. In this diagram. The different approximations are due to the difficulty in fixing this value in practice. The figure clearly shows that as long as… The Mooncat qubit, stabilized by Quantum System 1, maintains its advantage over the Standard Cat qubit. More specifically, the curve corresponding to the Standard Cat qubit is for... The obtained curve.

[0176] It should be noted that, regarding This threshold depends in a non-trivial way on the noise parameter and ratio of quantum system 1. .

[0177] exist Figure 10 In the figure, the curves correspond to the following experimentally relevant parameters: -ratio , - Photon loss rate in buffer mode b MHz -Photon loss rate in memory mode a MHz - Dephasing rate of memory mode a MHz, and -Hotfilling in memory mode a . C. Calibration of quantum systems

[0178] Those skilled in the art know that when at its flux operating point ( Or conversely, when biased, the Hamiltonian of ATS 7 It has the following "sin-sin" form:

[0179] ,

[0180] in, - It is the total superconducting phase difference across ATS 7. - It is the zero-point fluctuation of the phase of memory mode a across ATS 7. - It is the zero-point fluctuation of the phase in buffer mode b across ATS 7. - It is the Josephson energy of the lateral junction. It is the induced energy of the central inductor. - Corresponding to the common flux modulation of the two loops of ATS 7, - Corresponding to the differential flux modulation of the two loops of ATS 7, and - It is a decreasing Planck constant.

[0181] Common flux modulation This can be implemented by delivering microwave radiation out of phase via the flux lines of ATS 7, while differential flux modulation This can be implemented by delivering microwave radiation in phase via the flux lines of ATS 7.

[0182] Parametric pumping in ATS 7 is typically accomplished by pumping a common flux, since pumping a differential flux simply replaces the mode coupled to ATS 7.

[0183] As an example, by frequency , Given the pump common flux, the nonlinear resonant part of the Hamiltonian can be written in the rotating coordinate system as:

[0184] ,

[0185] This is typically the 2-to-1 photon-exchange Hamiltonian required to design two-photon stabilization.

[0186] Hamiltonian of ATS 7 The Taylor expansion of the above "sin-sin" form gives the following about First-order terms:

[0187] .

[0188] When longitudinal pump 13 delivers radiation through the flux line of ATS 7 to a frequency When the common flux is modulated down to achieve vertical coupling between memory mode a and buffer mode b, the first-order term... In the Taylor expansion, it becomes the dominant term and acts as the linear driver of buffer mode b.

[0189] Such a driver in buffer mode b is a parasitic driver and must be compensated.

[0190] Furthermore, the derivation of the Taylor series also reveals the following about The third-order term:

[0191] .

[0192] As mentioned above, It is the total superconducting phase difference across ATS 7, and is defined as follows:

[0193] .

[0194] Therefore, the Hamiltonian of ATS 7 Writing now:

[0195] .

[0196] In a rotating coordinate system, at a frequency for memory mode a and the frequency for buffer mode b Below, the Hamiltonian of ATS 7 It can be approximated as follows:

[0197] .

[0198] Assume vertical coupling between active memory mode a and buffer mode b, and at a frequency Driving ATS 7, then common flux modulation and differential flux modulation It can be represented as follows:

[0199] ,

[0200] .

[0201] The first-order term used to remove the linear driving force that acts as buffer mode b. In the displacement reference frame, the Hamiltonian of ATS 7 writing:

[0202] ,

[0203] in: - ),and - ).

[0204] Under the rotating wave approximation (RWA), the Hamiltonian Written as:

[0205] ,

[0206] in: - It is a vertical item. - It is a cubic term. - It is the Stark shift of memory mode a, and - It is the Stark shift of buffer mode b.

[0207] in, It is the real part.

[0208] The last term corresponds to a stray and potentially harmful nonlinear term. Depending on the noise level that the stabilization of the Mooncat qubits must address, this can lead to a ratio... The constraints are designed to ensure that the last item does not cause excessive harm.

[0209] To achieve fine control over the drive of buffer mode b, adjustments must be made. and The corresponding amplitude and phase are used to eliminate the first-order term. In other words:

[0210] .

[0211] This situation can be considered "longitudinal pump compensation".

[0212] When this condition is met, it can be noted that ,because and All with Proportional. Under such circumstances, And therefore .

[0213] Therefore, the Stark shift in memory mode a and buffer mode b is eliminated. C.1 Longitudinal Pump Compensation

[0214] Turn on the two-photon pump 11 and the longitudinal pump 13.

[0215] As mentioned above, the uncalibrated longitudinal pump 13 will have a first-order term The linear drive is converted to buffer mode b. Therefore, all the necessary elements for generating the Mooncat qubit in memory mode a are now available: • The two-photon pump 11 delivers radiation through the flux line of the ATS 7 to achieve a frequency Modulate the common flux to design the project , • Longitudinal pump 13 delivers radiation through the flux line of ATS 7 to achieve a frequency Modulate the common flux to design the project ,and • Vertical pumping 13 also enables the first-order term Linearly driven buffer mode b. Such an undesirable buffer-driven design item. .

[0216] Generating mooncat-like qubits without longitudinal pump compensation. Number of photons in memory. The magnitude is proportional to the magnitude of the undesirable buffer drive:

[0217] ,

[0218] in: - It is a complex number generated by an undesirable buffer drive. - It is an unexpected buffer-driven amplitude, and - It is the two-photon coupling rate.

[0219] The goal is to perform longitudinal pump compensation, i.e., by adjusting... and The corresponding amplitude and phase are used to eliminate the parasitic buffer drive. To this end, the applicant has developed at least two different solutions: a compensation module and a compensation pump. C.1.1 Compensation Module

[0220] To explain the principle of the compensation module, reference is now made to the ATS 7 shown below. Figure 11 .

[0221] ATS 7 includes left (“L”) and right (“R”) flux lines. The left flux line senses the left flux. The right flux line senses the right flux. . left flux and Proportional, of which, It is the current in the left flux line, while the right flux line... and Proportional, of which, It is the current in the right flux line.

[0222] The left and right fluxes together generate a common flux. Sum of differential flux Public flux It is half the sum of the left and right fluxes, differential flux. It is half the difference between the right flux and the left flux. In other words:

[0223] ,

[0224] .

[0225] Figure 12 Compensation module 47 is shown.

[0226] On the one hand, the compensation module 47 is arranged to couple the longitudinal pump 13 to the ATS 7 via the left flux line (“left pump”) and the right flux line (“right pump”), and on the other hand, it is arranged to change and The relative amplitude and phase.

[0227] For this purpose, the compensation module 47 includes an RF power divider (or splitter) 49, an RF variable attenuator 51, and an RF phase shifter 53.

[0228] RF power divider 49 is arranged to split the output of longitudinal pump 13 into two signals of equal power. Figure 12 In the example, at the output of RF power divider 49, the power loss on each of power lines 1 and 2 is equal to 3dB.

[0229] RF variable attenuator 51 is arranged to change and The relative magnitude. and The amplitude difference depends on the voltage applied to the RF variable attenuator 51. .

[0230] RF phase shifter 53 is arranged to change and The relative phase. and The phase difference depends on the voltage applied to the RF phase shifter 53. .

[0231] exist Figure 12 In the example, the RF variable attenuator 51 is located on power line 1 at the output of the RF power divider 49, while the RF phase shifter 53 is located on power line 2 at the output of the RF power divider 49. However, their respective positions can be switched.

[0232] Furthermore, longitudinal pump 13 is not the only microwave source that needs to be coupled to ATS 7: two-photon pump 11 also needs to be coupled to ATS 7.

[0233] Therefore, the compensation module 47 also includes a first RF power combiner 55 and a second RF power combiner 57. Both the first RF power combiner 55 and the second RF power combiner 57 can combine two power signals into one power signal.

[0234] The dual-photon pump 11 is also equipped with an RF power divider (not shown) similar to the RF power divider 49, and the output of the dual-photon pump 11 is split into two signals of equal power. The first of the two power signals is combined using a first RF power combiner 55 with one of the two power signals at the output of the RF power divider 49, while the second of the two power signals is combined using a second RF power combiner 57 with the other power signal at the output of the power divider 49.

[0235] It should be noted that, in an absolute sense, four variables originally needed to be considered: amplitude, phase, amplitude and The phase. However, it is sufficient and simpler to treat only two variables: and The relative amplitude and and The relative phase.

[0236] Use compensation module 47 to change and The relative amplitude and relative phase were measured. Furthermore, the number of photons in the memory was measured. The result is a three-dimensional plot (a so-called compensation plot) showing the number of photons in the memory as... and A function of the amplitude difference and phase difference between them.

[0237] As is known to those skilled in the art, there are many techniques for measuring the number of photons in a memory. In the current situation, regarding the quantity... Measurements are performed to determine the number of photons in the memory when it is in a steady state. In known techniques, performing longitudinal readout to utilize the longitudinal coupling between memory mode a and buffer mode b is advantageous. In particular, longitudinal readout offers a high signal-to-noise ratio.

[0238] Figure 13 The compensation diagram is shown, i.e., quantity As and The evolution of the function of relative amplitude and relative phase between them.

[0239] More precisely, the x-axis of the compensation graph represents the voltage applied to the RF phase shifter 53. The y-axis is the voltage applied to the RF variable attenuator 51. .

[0240] In addition, Figure 13 In this example, the measurement method is longitudinal readout. The signal measured via longitudinal readout is as follows:

[0241] ,

[0242] in: - It is a measurement signal. - It is a signal from a static quantum system 1, and - When the voltage applied to the RF phase shifter 53 is And the voltage applied to the RF variable attenuator 51 is The slope read vertically.

[0243] The signal is obtained after the reset of quantum system 1. This is done to minimize the number of photons in the memory. For example, such a reset can be performed by enabling the interaction between memory mode a and buffer mode b, thus implementing a conversion between one photon in memory mode a and one photon in buffer mode b, allowing the memory to be cooled to the temperature of the buffer. It should be noted that even with such a reset, the memory is not completely emptied: a small number of photons remain due to thermal population.

[0244] It should be noted that quantity With photon number Proportional.

[0245] In the case of longitudinal pump compensation, the first-order term It no longer acts as the linear driver for buffer mode b. Therefore, only two of the three elements for the stabilization of the Mooncat qubit exist: the nonlinear transition between the two photons in memory mode a and the one photon in buffer mode b. Thus, the number of photons in the memory is extremely small; in particular, a small number of photons remain due to thermal population. Therefore, consider the zeros of the compensation graph.

[0246] Therefore, the analysis of the compensation map revealed three significant regions: , and .

[0247] Each of these regions contains several zeros, which are points in the memory where no photons are present. The question that arises is: which zero is the relevant zero, that is, the zero corresponding to the longitudinal pump compensation?

[0248] Vertical pump compensation is not the only case where the Mooncat qubit cannot be stabilized and therefore no photons are present in the memory. In fact, certain amplitude or phase differences can affect the frequency of memory mode a. Or the frequency of buffer mode b Stark shift occurs.

[0249] However, the vicinity of the point where the Stark shift occurs includes several other points where the Stark shift also occurs. It can be inferred that these all include regions with a large number of clustered nulls. and region Corresponding to the Stark frequency shift. On the compensation map, the region... and The regions appear as separate; however, due to periodicity, these two regions... and Together they form a single region. Therefore, these two regions and Abandoned.

[0250] Therefore, the sought zero point is located in the remaining region, which is nebula-like. middle.

[0251] Figure 14 For the area of ​​the compensation map A magnified view. In particular, Figure (a) shows... The evolution, and Figure (b) shows The evolution of, among which, It is the angle.

[0252] Figure (a) shows the two zero points. and These two zero points and This can be explained by the following facts: There are two factors and The product of factors. yes and The holomorphic function can be zero, while the factor This corresponds to the number of photons, and is therefore zero in the case of longitudinal pump compensation.

[0253] In order to identify points and points Which one corresponds to longitudinal pump compensation? It can be noted that such compensation is independent of the power of the two-photon pump 11 or the power of the longitudinal pump 13. Therefore, the sought zero is the point where the pump power remains constant. Alternatively, it can be noted that the sought zero is the point where there is no... The zero point of phase winding.

[0254] Figure (b) shows the zero point corresponding to longitudinal pump compensation. .

[0255] By selecting an appropriate voltage applied to the RF phase shifter 53 and the appropriate voltage applied to the RF variable attenuator 51 This can achieve the point corresponding to longitudinal pump compensation. C.1.2 Compensation Pump

[0256] As explained above in section B.1, buffer mode b can be driven using a microwave source configured to modulate the differential flux in ATS 7. Figure 3 In an example implementation, such a microwave source is microwave source 19.

[0257] In section B.1, microwave source 19 is used as an alternative to buffer drive 15. However, microwave source 19 can be used as an additional pump to compensate for the parasitic linear drive caused by longitudinal pump 13. In the remainder of the specification, microwave source 19 is referred to as a compensating pump.

[0258] Therefore, the compensating pump 19 delivers radiation through the flux line of the ATS 7 to achieve a frequency... Down-modulated differential flux. More specifically, the amplitude and phase of the compensated pump 19 are fine-tuned to compensate for the linear drive of the buffer mode b.

[0259] C.2 Phase difference calibration between longitudinal pump 13 and buffer drive 15 and amplitude calibration of longitudinal pump 13

[0260] Enable buffer driver 15. Such a buffer driver can be expressed as follows:

[0261] ,

[0262] in, It is a plural number. It is the angular frequency of the buffer drive 15, for example The amplitude and phase of the buffer drive 15 correspond to complex numbers. The amplitude and phase.

[0263] Therefore, in memory mode a, the remaining elements required to generate the Mooncat qubit exist: buffer drive 15 delivers a frequency of to resonant part 9. The radiation, and more specifically, the partial delivery radiation of the buffer mode b to the linear microwave network for the nonlinear superconducting quantum circuit 3.

[0264] The nonlinear superconducting quantum circuit 3 designs a Hamiltonian H, expressed as:

[0265] .

[0266] Hamiltonian H generates efficient dissipatives through the dissipation of buffer mode b. Its stabilization stabilizes the two-dimensional manifold of the mooncat qubit in the memory-carrying mode a.

[0267] Corresponding migration operator It can be represented as follows:

[0268] ,

[0269] in: - It is represented as: The two-photon dissipation rate, where, It is the single-photon loss rate of buffer mode b, and It is the two-photon coupling rate between the memory and the buffer. - It is a complex number generated by buffer drive 15, where, ,and - These are the Moon Cat parameters, whose phase and amplitude are generated by the amplitude of the longitudinal pump 13, where, .

[0270] During this calibration phase, the phase difference between the longitudinal pump 13 and the buffer drive 15, as well as the amplitude of the longitudinal pump 13, must be determined.

[0271] To this end, a set of one or more discrete values ​​of the amplitude of the longitudinal pump 13 is selected. For each of these discrete values, the amplitude of the longitudinal pump 13 is set to that discrete value, and then the relative phase of the longitudinal pump 13 and the buffer drive 15 is changed. Furthermore, similar to the case of the compensation map, the number of photons in the memory is measured.

[0272] Figure 15 Figures (a), (b), (c), and (d) are included, each corresponding to the amplitude value of the longitudinal pump 13. Furthermore, since the phase of the longitudinal pump 15 and the amplitude of the buffer drive 15 remain constant, each figure is obtained by changing the phase of the buffer drive 15 and thus changing the phase difference between the longitudinal pump 13 and the buffer drive 15.

[0273] More specifically, for each of Figures (a), (b), (c), and (d), the x-axis corresponds to the real part of the buffer drive 15, while the y-axis corresponds to the imaginary part of the buffer drive 15. In other words, for a given value of the amplitude of the longitudinal pump 15, each figure represents the evolution of the number of photons in the memory as the buffer drive 15 scans the complex plane.

[0274] exist Figure 15 In the example, the measurement method is longitudinal reading.

[0275] The analysis of Figures (a), (b), (c), and (d) yields two observations. The first observation is that the amplitude of the longitudinal pump 13 affects how the phase difference between the longitudinal pump 13 and the buffer drive 15 alters the number of photons in the memory. The second observation is that, although the amplitude of the longitudinal pump 13 is affected, at the center of the figure (i.e., for zero-buffer drive), the longitudinal pump compensation consistently results in no photons in the memory.

[0276] There is no need to change the amplitude of the buffer drive 15, because the quantum system 1 can be calibrated by keeping the amplitude of the buffer drive 15 constant. In the complex plane, a constant amplitude and a variable phase result in a displacement about a circle whose radius corresponds to the amplitude of the buffer drive 15.

[0277] The view can then be switched from a 3D plot to a curve representing the evolution of the number of photons in the memory as a function of the phase of the buffer drive 15, and thus the evolution of the phase difference between the longitudinal pump 13 and the buffer drive 15.

[0278] exist Figure 16 The diagram illustrates the transformation from a 3D plot to a curve by keeping the amplitude of buffer drive 15 constant, and therefore by changing only the phase of buffer drive 15. It should be noted that... Figure 16 In the middle, the three-dimensional graph corresponds to Figure 15 Figure (b).

[0279] exist Figure 16 In the middle, a circle corresponding to the constant amplitude of the buffer drive 15 is drawn with a dashed line.

[0280] The curves show that the number of photons in the memory decreases when the phase of buffer drive 15 is between -π and 0, and increases when it is between 0 and π. In particular, the number of photons in the memory is minimal when the phase of buffer drive 15 is zero.

[0281] As mentioned above, it should be noted that the amplitude of the longitudinal pump 13 has an impact. The evolution is a function of the phase difference between the longitudinal pump 13 and the buffer drive 15. Based on this observation, the Moon Cat parameter corresponding to the amplitude of the longitudinal pump 13 can be found. The amplitude of the Mooncat parameters is fitted to the amplitude of the longitudinal pump source 13, based on the fact that the stabilized boson qubits are Mooncat qubits that the applicant knows how to characterize. Therefore, as detailed in section B.2, the even Mooncat state And the strange moon cat state The expansion under the Fokk basis is as follows:

[0282] ,

[0283] in:

[0284] ,

[0285] ,

[0286] and:

[0287] ，

[0288] in,

[0289] ,

[0290] .

[0291] Figure 15 The Mooncat parameters corresponding to each amplitude of the longitudinal pump 13 are shown. The amplitude. Figure (a) corresponds to Figure (b) corresponds to Figure (c) corresponds to And Figure (d) corresponds to .

[0292] Figure 17 The parameters of the Moon Cat are shown. The amplitude of the pulse was fitted to the amplitude of the longitudinal pump 13. The results show that the amplitude of the pulse in the Mooncat parameter is... There is a linear relationship between the amplitude of the longitudinal pump 13 and the amplitude of the longitudinal term. According to the formula for the longitudinal term: Such a linear relationship can be expected.

[0293] Since the Mooncat qubit does not exist in the absence of longitudinal pump 13, the obtained straight line must pass through the point with coordinates (0, 0). Therefore, this straight line can be obtained from a single amplitude value of longitudinal pump 13, where the Mooncat parameters have been determined by characterizing the Mooncat qubit. The amplitude. Advantageously, a straight line is composed of several points.

[0294] The Mooncat parameters can be experimentally confirmed by performing Wigner tomography on each value of the amplitude of the longitudinal pump 13. The linear relationship between the amplitude of the pulse and the amplitude of the longitudinal pump 13. The Mooncat parameters can be calculated based on the aforementioned Wigner tomography and Mooncat qubit characterization. The range.

[0295] Figure 18 Several Wigner tomography images are shown. More specifically, Figure 18 Including Figures (a), (b), (c), and (d). In each figure, the Wigner tomography on the left is an experimentally performed Wigner tomography for a given value of the amplitude of the longitudinal pump 13, while the Wigner tomography on the right is the Mooncat parameter associated with the value of the amplitude of the longitudinal pump 13. The amplitude corresponds to the theoretical Wigner tomography.

[0296] Figure 18 The Mooncat parameters corresponding to the theoretical Wigner tomography for each schematic diagram are shown. The amplitude. Figure (a) corresponds to Figure (b) corresponds to Figure (c) corresponds to Figure (d) corresponds to .

[0297] because Figure 17 The curve in the image allows you to select an appropriate value for the amplitude of the vertical pump 13 in order to obtain the Mooncat parameters. The expected value of the amplitude.

[0298] As detailed in section B.3, when the amplitude of the Mooncat parameter is less than or equal to 1, the Mooncat qubit (solid line) achieves the same improvement, or even a slight advantage, in bit flipping as the Compact Cat qubit (dashed line). Advantageously, the value of the amplitude of the longitudinal pump 13 is chosen such that the Mooncat parameter... The amplitude is basically equal to 1: .

[0299] In addition, once the amplitude of the longitudinal pump 13 is set, use Figure 16Use the curve in the middle to select the quantity The relative phase between the longitudinal pump source 13 and the buffer drive source 15 minimizes the number of photons in the memory.

[0300] In fact, to increase the size of the Mooncat qubit, it is preferable to adjust the amplitude of the buffer drive 15 rather than its phase.

[0301] Figure 19 and Figure 20 The reason for choosing the buffer drive 15 to minimize the number of photons in the memory is explained.

[0302] Figure 19 It shows Figure 16 The enlarged graph of the curve shows four specific points, D1, D2, D3, and D4, each corresponding to a different value of the phase of the buffer drive 15.

[0303] Figure 20 Includes several figures (a), (b), (c), and (d), each corresponding to an experimental Wigner tomography. Each Wigner tomography image corresponds to... Figure 19 The corresponding points indicated above, and therefore correspond to different values ​​of the phase of the buffer drive 15. More specifically, Figure (a) corresponds to point D1, Figure (b) corresponds to point D2, Figure (c) corresponds to point D3, and Figure (d) corresponds to point D4.

[0304] Synchronization of different microwave sources in C.3 quantum systems

[0305] Further adjustments involve the synchronization of the microwave sources in the instruction circuit 5 of the quantum system 1, namely the synchronization of the two-photon pump 11, the longitudinal pump 13, and the buffer drive 15.

[0306] The principle is as follows: for each microwave source, determine the delay between the signal change of the microwave source and the arrival of that change at the nonlinear superconducting quantum circuit 3. To do this, each microwave source is turned on and its signal is significantly changed, while the resulting signal is measured at the nonlinear superconducting quantum circuit 3. In this way, the delays of the two-photon pump 11, the longitudinal pump 13, and the buffer drive 15 can be determined.

[0307] These different delays are used to improve the calibration of quantum system 1. C.4 Further Calibration

[0308] To improve the calibration of quantum system 1, the relative phases of the two-photon pump 11 and the longitudinal pump 13 can be adjusted. Optimal noise bias can be achieved when the phase of the two-photon pump 11 is equal to the phase of the longitudinal pump 13 (i.e., when the relative phases of the two-photon pump 11 and the longitudinal pump 13 are zero).

[0309] Ideally, the corresponding phases of the two-photon pump 11, the longitudinal pump 13, and the buffer drive 15 are equal to each other. This takes into account the two-photon coupling rate. Since it is a real number, the phase of buffer drive 15 should be equal to π in order to obtain the Mooncat qubit on the real axis; then, the phase of longitudinal pump 13 should be equal to 0.

[0310] Figure 21 A device 59 is shown that is arranged to calibrate the quantum system 1 to stabilize the Mooncat qubit.

[0311] For this purpose, device 59 includes memory 61, processor 63, controller 65, and calculator 67.

[0312] The memory 61 is configured to store instructions for a computer program that, when executed by the processor 63, causes the device 59 to run.

[0313] The memory 61 can also be arranged to store data related to the quantum system 1, especially data generated during the calibration of the quantum system 1.

[0314] Memory 61 can be any data storage medium arranged to receive and store digital data, such as a hard disk, a semiconductor disk, or more generally any computer component dedicated to storing data on flash memory. Memory 61 can also be random access memory (RAM) or a magneto-optical disk. Combinations of several types of data storage components are also conceivable.

[0315] The memory 61 is a computer-readable storage medium, which may or may not be non-transient.

[0316] Processor 63 may be a microprocessor, a programmable logic device (PLD), a field-programmable gate array (FPGA), a system-on-a-chip (SoC), a computer resource grid, a microcontroller, or any other specific form of device with the computational power required to implement the method of calibrating quantum system 1. One or more of these elements may also be implemented in the form of special-purpose electronic circuitry (such as application-specific integrated circuits (ASICs)). Combinations of processors and electronic circuitry are also envisioned.

[0317] The controller 65 is arranged to control the quantum system 1 for calibration purposes, in order to obtain information related to the quantum system 1 or to calibrate it.

[0318] The controller 65 is arranged to control the command circuit 5, and more specifically to control the two-photon pump 11, the longitudinal pump 13, the buffer drive 15, and the compensation pump 19 (if applicable).

[0319] In other words, the controller 65 is arranged to turn each pump or drive of the instruction circuit 5 on / off and tune their respective amplitude, phase and frequency.

[0320] In addition, the controller 65 can be arranged to control the compensation module 47 (if applicable) to change the amplitude difference and phase difference between the common flux and differential flux of the ATS 7.

[0321] Finally, calculator 67 is configured to numerically analyze the effect of the amplitude of longitudinal pump 13 on the evolution of the number of photons in the memory, which is a function of the phase difference between longitudinal pump 13 and buffer drive 15.

[0322] Calculator 67 was also configured to determine the amplitude of the longitudinal pump 13 and the parameters of the Mooncat qubit. The linear relationship between the amplitudes.

[0323] Figure 22 A method for calibrating quantum system 1 for the purpose of stabilizing the Mooncat qubit is shown.

[0324] In the following text, the method is performed using device 59.

[0325] In operation 2200, the controller 65's on-frequency is... The two-photon pump 11 and the on-time are Longitudinal pump 13.

[0326] As mentioned earlier, the longitudinal pump 13 causes the first-order term to... The buffer mode b is driven linearly. This undesirable buffer drive, combined with the nonlinear transformation between two photons in memory mode a and one photon in buffer mode b, and the longitudinal coupling between memory mode a and buffer mode b, results in the generation of a mooncat qubit carried in memory mode a.

[0327] In operation 2210, controller 65 and calculator 67 are used to compensate for undesirable buffer drives.

[0328] Such compensation can be implemented using compensation module 47 or compensation pump 19.

[0329] The compensation module 47 is used to change the amplitude difference between the common flux and differential flux of the ATS 7 using the RF variable attenuator 51, and to change the phase difference between the common flux and differential flux of the ATS 7 using the RF phase shifter 53, while simultaneously measuring the number of photons in the memory. Then, the compensation map obtained using the compensation module 47 is used to determine the relevant zero points, i.e., the points in the compensation map where the number of photons in the memory is zero due to compensation for the undesired buffer drive.

[0330] Alternatively, additional compensation module 19 is used to drive buffer mode b in order to compensate for undesirable buffer drive.

[0331] In operation 2220, the controller 65 is activated at a frequency of [frequency value missing]. The buffer driver 15.

[0332] Therefore, the nonlinear superconducting quantum circuit 3 is designed with a Hamiltonian H, which generates an efficient dissipative quantum through the dissipation of buffer mode b. This stabilizes the two-dimensional manifold carrying the Mooncat qubits in memory mode a.

[0333] In operation 2230, controller 65 changes the phase difference between longitudinal pump 13 and buffer drive 15 while simultaneously measuring the number of photons in the memory. To do this, the phase of buffer drive 15 is changed, and longitudinal readout can be performed since longitudinal coupling between memory mode a and buffer mode b has already been performed.

[0334] More specifically, such a phase difference scan is performed for one or more discrete values ​​of the amplitude of the longitudinal pump 13.

[0335] In operation 2240, based on the evolution of the number of photons in the memory as a function of the phase difference of the amplitude value of the longitudinal pump 13, calculator 67 determines the Mooncat parameter corresponding to each amplitude value of the longitudinal pump 13. The corresponding value of the amplitude.

[0336] In operation 2250, calculator 67 derived the amplitude of the vertical pump 13 and the Moon Cat parameters. A linear relationship between the amplitudes. Such a linear relationship exists in... Figure 17 The image shows: Moon Cat parameters The evolution of the amplitude as a function of the amplitude of the longitudinal pump 13 is linear.

[0337] In operation 2260, controller 65 sets the amplitude of longitudinal pump 13 at a value where the amplitude of the Mooncat parameter is substantially equal to the desired value, based on the linear relationship derived in operation 2250.

[0338] Finally, in operation 2270, the controller 65 sets the phase difference between the longitudinal pump 13 and the buffer drive 15 to the value when the number of photons in the memory is at its minimum.

Claims

1. A method for calibrating a quantum system (1), said quantum system (1) being arranged to stabilize boson qubits, and comprising: Command circuit (5), the command circuit (5) including a first microwave source (11), a second microwave source (13) and a third microwave source (15), each microwave source being arranged to deliver microwave radiation; and A nonlinear superconducting quantum circuit (3) includes an asymmetric threaded superconducting quantum interference device (7) and at least one resonant section (9). The asymmetric threaded superconducting quantum interference device (7) is connected to the at least one resonant section (9). The asymmetric threaded superconducting quantum interference device (7) has a flux line through which radiation is delivered to modulate a common flux and a differential flux. The nonlinear superconducting quantum circuit (3) has a first mode (a) and a second mode (b). The first mode (a) has a first resonant frequency, and the second mode (b) has a second resonant frequency that is different from twice the first resonant frequency. The second mode (b) is dissipative. The asymmetric threaded superconducting quantum interference device (7) is arranged such that, in the following case: The first microwave source (11) delivers radiation through the flux line, modulating the common flux at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency. The second microwave source (13) delivers radiation through the flux line, modulating the common flux at a frequency equal to the second resonant frequency, and The third microwave source (15) delivers radiation to the at least one resonant section (9) at a frequency equal to the second resonant frequency to drive the second mode (b). The design of the nonlinear superconducting quantum circuit (3) is expressed as follows: The Hamiltonian H, where, Proportional to the amplitude of the first microwave source (11), It is the annihilation operator of the first mode (a). It is a complex number whose phase and amplitude are generated by the amplitude of the second microwave source (13), and each is defined relative to the phase and amplitude of the first microwave source (11). It is a complex number generated by the third microwave source (15) and defined relative to the first microwave source (11). It is the annihilation operator of the second mode (b), and It is Hermitian conjugation, and the Hamiltonian H produces an effective dissipative substituent through the dissipation of the second mode (b). The effective dissipative quanta stabilize the two-dimensional manifold carrying the boson qubits in the first mode (a). The method includes the following operations: a) The first microwave source (11) is turned on (2200) at a frequency equal to the absolute value of the difference between the first resonant frequency and the second resonant frequency, and the second microwave source (13) is turned on at a frequency equal to the second resonant frequency. b) Compensate (2210) for the undesirable drive of the second mode (b) caused by the second microwave source (13); c) Turn on the third microwave source (15) at a frequency equal to the second resonant frequency (2220); d) For one or more amplitude values ​​of the second microwave source (13), in relation to the quantity While performing the measurement, the phase difference between the second microwave source (13) and the third microwave source (15) is changed (2230); e) Based on the amplitude value of the second microwave source (13), the quantity As an evolution of the phase difference, the complex number corresponding to each amplitude value of the second microwave source (13) is determined (2240). The corresponding value of the amplitude, and derive (2250) the amplitude of the second microwave source (13) and the complex number. The linear relationship between the amplitudes; and f) Based on the linear relationship, the amplitude of the second microwave source (13) is set (2260) to make the complex number The amplitude is substantially equal to the expected value, and the phase difference is set (2270) such that the quantity The minimum value.

2. According to claim 1, the flux lines of the asymmetric threaded superconducting quantum interference device (7) include at least a left flux line and a right flux line, and the quantum system (1) further includes a compensation module (47), the compensation module (47) being arranged to couple the second microwave source (13) to the left flux line and the right flux line, the compensation module (47) including an RF power divider (49), an RF variable attenuator (51), and an RF phase shifter (53), the RF power divider (49) being arranged to split the output of the second microwave source (13) into a first power line and a second power line respectively connected to the left flux line and the right flux line, the RF variable attenuator (51) being arranged on the first power line to change the amplitude difference between the common flux and the differential flux, and the RF phase shifter (53) being arranged on the second power line to change the phase difference between the common flux and the differential flux, wherein, Operation b) includes: b1) The amplitude difference between the common flux and the differential flux is changed using the RF variable attenuator (51), and the phase difference between the common flux and the differential flux is changed using the RF phase shifter (53), while the quantity is measured. ; b2) Determine a pair of corresponding values ​​for the amplitude difference and the phase difference, wherein, due to compensation for the undesirable drive of the second mode (b), the quantity Zero; and b3) Set the amplitude difference and the phase difference to the pair of corresponding values.

3. The method according to claim 1, wherein the quantum system (1) further comprises an additional microwave source (19) arranged to deliver radiation through the flux line to modulate the differential flux at a frequency equal to the second resonant frequency, wherein, Operation b) includes: b4) Turn on the additional microwave source (19) at a frequency equal to the second resonant frequency; and b5) Tune the amplitude and phase of the additional microwave source (19) to compensate for the undesirable drive of the second mode (b).

4. The method according to any one of the preceding claims, wherein, Operation d) includes changing the phase of the third microwave source (15) while keeping the phase of the second microwave source (13) constant.

5. The method according to any one of the preceding claims, wherein, Operation d) includes performing longitudinal readout measurement of the quantity using the second microwave source (13). .

6. The method according to any one of the preceding claims further comprises the following operations: g) Set the phase difference between the first microwave source (11) and the second microwave source (13) to zero.

7. The method according to claim 6, wherein, Operation g) includes setting the corresponding phases of the first microwave source (11), the second microwave source (13), and the third microwave source (15) to be equal to each other.

8. The method according to any one of the preceding claims, wherein, Operation f) includes setting the amplitude of the second microwave source (13) to such that the complex number The amplitude is less than or equal to 1.

9. The method according to any one of the preceding claims, wherein, Operation f) includes setting the amplitude of the second microwave source (13) to such that the complex number The magnitude is essentially equal to the value of 1.

10. A computer program comprising instructions which, when executed by at least one processor (63), cause to perform the method according to any one of the preceding claims.

11. A computer-readable storage medium (61) comprising a computer program according to claim 10 stored thereon.

12. An apparatus (59) for calibrating a quantum system (1), said quantum system (1) being arranged to stabilize boson qubits and comprising: Command circuit (5), the command circuit (5) including a first microwave source (11), a second microwave source (13) and a third microwave source (15), each microwave source being arranged to deliver microwave radiation; and A nonlinear superconducting quantum circuit (3) includes an asymmetric threaded superconducting quantum interference device (7) and at least one resonant section (9). The asymmetric threaded superconducting quantum interference device (7) is connected to the at least one resonant section (9). The asymmetric threaded superconducting quantum interference device (7) has a flux line through which radiation is delivered to modulate a common flux and a differential flux. The nonlinear superconducting quantum circuit (3) has a first mode (a) and a second mode (b). The first mode (a) has a first resonant frequency, and the second mode (b) has a second resonant frequency that is different from twice the first resonant frequency. The second mode (b) is dissipative. The asymmetric threaded superconducting quantum interference device (7) is arranged such that, in the following case: The first microwave source (11) delivers radiation through the flux line, modulating the common flux at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency. The second microwave source (13) delivers radiation through the flux line, modulating the common flux at a frequency equal to the second resonant frequency, and The third microwave source (15) delivers radiation to the at least one resonant section (9) at a frequency equal to the second resonant frequency to drive the second mode (b). The design of the nonlinear superconducting quantum circuit (3) is expressed as follows: The Hamiltonian H, where, Proportional to the amplitude of the first microwave source (11), It is the annihilation operator of the first mode (a). It is a complex number whose phase and amplitude are generated by the amplitude of the second microwave source (13), and each is defined relative to the phase and amplitude of the first microwave source (11). It is a complex number generated by the third microwave source (15) and defined relative to the first microwave source (11). It is the annihilation operator of the second mode (b), and It is Hermitian conjugation, and the Hamiltonian H produces an effective dissipative substituent through the dissipation of the second mode (b). The effective dissipative quanta stabilize the two-dimensional manifold carrying the boson qubits in the first mode (a). The device (59) is arranged as follows: The first microwave source (11) is turned on at a frequency equal to the absolute value of the difference between the first resonant frequency and the second resonant frequency, and the second microwave source (13) is turned on at a frequency equal to the second resonant frequency. Compensate for the undesirable drive of the second mode (b) caused by the second microwave source (13); The third microwave source (15) is turned on at a frequency equal to the second resonant frequency; For one or more amplitude values ​​of the second microwave source (13), in relation to the quantity While performing the measurement, the phase difference between the second microwave source (13) and the third microwave source (15) is changed; Based on the amplitude value of the second microwave source (13), the quantity As an evolution of the phase difference, the corresponding value of the amplitude of the complex number λ corresponding to each amplitude value of the second microwave source (13) is determined (2240), and a linear relationship between the amplitude of the second microwave source (13) and the amplitude of the complex number λ is derived; and Based on the linear relationship, the amplitude of the second microwave source (13) is set such that the amplitude of the complex number λ is substantially equal to the desired value, and the phase difference is set such that the quantity... The minimum value.

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