Quantum system with low resonant frequency memory for stabilizing cat qubits

Abstract

The invention relates to a nonlinear superconducting quantum circuit comprising at least one resonant part having a first mode with a first resonance frequency and a second mode with a second resonance frequency, and a nonlinear element (7) coupled to the at least one resonant part or at least partially comprised in the at least one resonant part. The at least one resonant part has a resonator (27) comprising a capacitive element (29) and an inductive element (31) jointly generating the first mode, the capacitive element (29) having a capacitance between 1 and 10 pF and / or the inductive element (31) having an inductance between 0.3 and 5 nH, such that the first resonance frequency is less than or equal to 3.5 GHz.

Description

Cross-reference to related applications

[0001] The entire contents of European patent application EP 24305343.6, filed on 6 March 2024, are incorporated herein by reference. Technical Field

[0002] This invention relates to the field of stable cat 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 Bose modes, thus forming a specific class of superconducting qubits known as Bose qubits.

[0004] According to existing technology, cat qubits, defined as Bose qubits, are stabilized by a quantum manifold spanned by the superposition of two coherent states, which are quasi-classical states of the Bose mode. To achieve this, a specific dissipative stabilization mechanism can be implemented, involving a nonlinear transition between two photons implementing a first mode (also known as a memory mode or cat qubit mode) carrying the stable quantum manifold, and one photon implementing a strongly dissipative second mode (also known as a buffer mode).

[0005] R. Lescanne et al. demonstrated the possibility of realizing such qubits in “Exponential suppression of bit-flips in a qubitencoded in an oscillator” (Nature Physics, 2020). As mentioned above, cat qubits rely on a mechanism of dissipating photons in pairs. This process locks two coherent states to separate locations in phase space. By increasing this interval, experiments have shown an exponential decrease in the bit-flip rate, while only a linear increase in the phase-flip rate. As a result, stable cat qubits have been shown to benefit from a high-noise bias, meaning that the bit-flip probability is exponentially smaller than the phase-flip probability. Specifically, this is achieved by using an asymmetric flux-through superconducting quantum interference device (“ATS”) as a four-wave mixing nonlinear element to implement a 2-to-1 photon conversion.

[0006] This 2-to-1 photon conversion occurs through frequency... The following parameters are used for pumping, among which... It is the resonant frequency of the memory mode, and It is the resonant frequency of the buffer mode.

[0007] Cat qubits possess the property of allowing the implementation of quantum gates (such as Z or CNOT gates) while maintaining a noisy 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 phase-flip probability at the optimal gate time depends on the ratio... ,in, It is the single-photon loss rate of the cat qubit used to execute this quantum gate—or, because it causes phase flipping, the error rate. It is the two-photon dissipation rate of these cat qubits—also known as the correction rate or stabilization rate. The higher the value, the better the door fidelity.

[0008] Used to reduce single-photon loss rate One possible solution is to reduce the resonant frequency of the memory mode as much as possible. However, this solution faces several limitations.

[0009] First, the resonant frequency of the buffer mode. While maintaining values ​​within the existing technology range (i.e., approximately 5 GHz), the resonant frequency of the memory mode is reduced. This will quickly lead to a high frequency of pumping using the aforementioned parameters. However, it is known that the energy value injected into a quantum system designed to stabilize cat qubits to reach a given frequency can adversely affect the coherence of such a quantum system because the given frequency to be reached is very high. Furthermore, lowering the resonant frequency of the buffer mode is not possible because this would result in an excessively high thermal population of photons in the buffer.

[0010] In addition, reducing the resonant frequency of the memory mode It will significantly increase thermal noise. In fact, even if the resonant frequency of the memory mode is reduced... It will reduce the single-photon loss rate This reduction will also significantly increase the heat population of the bath. .

[0011] To date, these difficulties have led those hoping to implement dissipative stabilization mechanisms to instead choose high resonant frequencies for memory modes. .

[0012] As an example, the resonant frequency of the memory mode equal: -7.58 GHz, in the article "Confining the state of light to a quantum manifold by engineered two-photon loss" by Z. Leghtas et al. (Science, vol. 347, No. 6224, 2015); -8 GHz, in the above discussion by R. Lescanne et al. (2020); -4 GHz, in C. Berdou et al., “One Hundred Second Bit-Flip Time in a Two-Photon Dissipative Oscillator” (PRXQuantum 4, 020350, 2023); -5.26 GHz, in U. Réglade et al. "Quantum control of a cat-qubit with bit-flip times exceeding ten seconds" (arXiv: 2307.06617); -6 GHz, as described in A. Grimm et al.'s "The Kerr-Cat Qubit: Stabilization, Readout, and Gates" (Nature 584, pp. 205-209, 2020), and... -4.3497 GHz, in G. Beauplace et al., “Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerrresonator” (arXiv:2310.13636).

[0013] This invention attempts to improve this situation. Summary of the Invention

[0014] To this end, the applicant has proposed a nonlinear superconducting quantum circuit, comprising: - At least one resonant component, having a first mode with a first resonant frequency and a second mode with a second resonant frequency; and - A nonlinear element coupled to or at least partially included in the at least one resonant part.

[0015] At least one resonant section has a resonator comprising a capacitive element and an inductive element that jointly generate the first mode, the capacitive element having a capacitance between 1 and 10 pF, and / or the inductive element having an inductance between 0.3 and 5 nH, such that the first resonant frequency is less than or equal to 3.5 GHz.

[0016] According to one or more embodiments, the nonlinear element is a four-wave mixing nonlinear element.

[0017] According to one or more embodiments, the nonlinear element is an asymmetric flux-through superconducting quantum interference device.

[0018] According to one or more embodiments, a nonlinear element is included in at least one resonant portion and is used as an inductive element within said at least one resonant portion.

[0019] According to one or more embodiments, the capacitive element is formed by stacking a dielectric substrate and a superconducting material layer, the superconducting material layer being etched to define a four-leaf clover shape.

[0020] According to one or more embodiments, the capacitive element has a capacitance between 1 and 2 pF, and preferably equal to 1.4 pF.

[0021] According to one or more embodiments, the capacitive element is a planar capacitor formed by a dielectric substrate sandwiched between a first conductive plate and a second conductive plate.

[0022] According to one or more embodiments, the inductive element is a Josephson knot.

[0023] According to one or more embodiments, the first resonant frequency is between 1 and 3.5 GHz.

[0024] According to one or more embodiments, the first resonant frequency is less than or equal to 1 GHz.

[0025] According to one or more embodiments, the first resonant frequency is substantially equal to 1 GHz.

[0026] According to one or more embodiments, the phase zero fluctuation of the first mode across the nonlinear element and the phase zero fluctuation of the second mode across the nonlinear element are each between 0.005 and 0.3, and preferably between 0.01 and 0.15.

[0027] Finally, the applicant also proposed a quantum system for stabilizing cat qubits, comprising: The command circuit includes at least a first microwave source and a second microwave source, each microwave source being arranged to deliver microwave radiation; and A nonlinear superconducting quantum circuit includes a nonlinear element and at least one resonant section, wherein the nonlinear element is coupled to or at least partially included in the at least one resonant section, and the at least one resonant section has a first mode with a first resonant frequency and a second mode with a second resonant frequency.

[0028] At least one resonant section has a resonator comprising a capacitive element and an inductive element that jointly generate the first mode, the capacitive element having a capacitance between 1 and 10 pF, and / or the inductive element having an inductance between 0.3 and 5 nH, such that the first resonant frequency is less than or equal to 3.5 GHz.

[0029] A quantum system is arranged such that, under the following conditions, The first microwave source delivers microwave radiation to the nonlinear element 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 microwave radiation at a frequency equal to the second resonant frequency to the resonant region to drive the second mode.

[0030] A two-dimensional manifold stably carrying the cat qubits via a nonlinear superconducting quantum circuit. Attached Figure Description

[0031] 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 schematic diagram of a quantum system comprising a nonlinear superconducting quantum circuit and an instruction circuit according to the present invention is shown; - Figure 2 It was shown as Figure 1 The evolution of the decay rate as a function of the resonant frequency of the memory in a quantum system; - Figure 3 It was shown as Figure 1 The evolution of dielectric loss as a function of the resonant frequency of the memory in a quantum system; - Figure 4 A capacitor with a four-leaf clover design is shown; - Figure 5 A capacitor with a planar design is shown; - Figure 6 An inductor formed by a Josephson junction is shown; - Figure 7The Hilbert inductor is shown; - Figure 8 It shows Figure 1 A local equivalent circuit diagram of a current-mode example implementation of a quantum system; - Figure 9 It shows the relationship with Figure 8 The circuit equivalent to the circuit; - Figure 10 It shows Figure 1 A partial equivalent circuit diagram of a capacitive example implementation of a quantum system; - Figure 11 It shows the use of Figure 6 A partial equivalent circuit diagram of an example implementation of an inductor formed by a Josephson junction; - Figure 12 It shows the use of having Figure 4 The capacitor with a four-leaf clover design Figure 1 The performance of quantum system 1; and - Figure 13 The evolution of the phase reversal rate as a function of the number of photons is shown. Detailed Implementation

[0032] The accompanying drawings and the following description consist largely of well-defined and specific features. Therefore, they not only aid in understanding the invention, but can also be used to help define it if needed. A. Cat qubit

[0033] To date, the applicant's work has generally concerned the stabilization of cat qubits. As previously mentioned, R. Lescanne et al. (2020) demonstrated that 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).

[0034] 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:

[0035] ,

[0036] in:

[0037] .

[0038] It is known that stable 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). This is suppressed exponentially. As mentioned earlier, this exponential suppression of bit flips comes at the cost of a linear increase in phase flips.

[0039] Based on current understanding, this 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.

[0040] Recent experiments in the field of superconducting quantum circuits have observed that this bit flipping is exponentially suppressed by the average number of photons in the cat state.

[0041] It is generally believed that, since bit flips are rare enough, a single repeating code is sufficient to correct other errors; and more specifically, a phase flip correction code is sufficient to correct other phase flips. For example, this could be a repeating code defined in a dual basis or any other existing error-correcting code. A.1 Stabilization Scheme

[0042] The following exemplary schemes can be used to stabilize or limit cat qubits:

[0043] 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 Hamiltonian is implemented. To implement this transition operator, where, It is the photon annihilation operator of buffer mode b, and It is the two-photon coupling rate, determined by applying a frequency of [value] to a four-wave mixer. The pump and the frequency are The driver for buffer mode b (in) This can be achieved under certain conditions.

[0044] 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.

[0045] 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.

[0046] 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. The Hamiltonian can be implemented in the same way as the parameter dissipative stability a).

[0047] e) Dissipative compression stabilization with transition operator ,in, It is to compress the two-photon dissipation rate. It is the photon annihilation operator for memory mode a. It is the complex number that defines a cat qubit. and Complex compression parameters The modulus and argument. This can be achieved by using a 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 Hamiltonian is implemented. To implement this transition operator, where, It is the photon annihilation operator of buffer mode b, and It is the compressed two-photon coupling rate, utilizing a frequency of , and Several pumps, and a frequency of The driver for buffer mode b (in) This can be achieved under certain conditions.

[0048] f) A variant of the aforementioned stabilization scheme e), for which the applicant has filed European patent application EP23175147.0, wherein the Hamiltonian is implemented... To stabilize the Bose qubit (called the "mooncat qubit" because its two blobs of Wigner function are crescent-shaped), in which, The frequency is The amplitude of the pump, It is the annihilation operator for memory mode a. It is a complex number (its phase and amplitude are determined by the frequency). The amplitude of longitudinal coupling generated by the pump. It is composed of frequency The complex number generated by the driver of buffer mode b, and It is the annihilation operator for buffer mode b; by... Represented as complex compression parameters The function (as shown below): This allows for a comparison between the Mooncat qubit and the Compressed Cat qubit.

[0049] g) 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), except that the two-photon pump, which performs the nonlinear conversion between two photons in memory mode a and one photon in buffer mode b, is replaced by a DC voltage source biased entirely by a nonlinear element formed by one or more Josephson junctions. This DC-biased nonlinear element acts as a voltage-to-frequency converter, which, under appropriate voltage bias, provides the frequency necessary to achieve dissipation stabilization. The required parameters for interaction. Specifically, the two-photon coupling rate. Therefore, the amplitude is not affected by two-photon pumping: The restrictions, among which, It is the Josephson energy of one or more Josephson junctions. It is the phase zero-point fluctuation of memory mode a, and It is the phase zero-point fluctuation of buffer mode b.

[0050] h) Resonant dissipation stabilization, with 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 implementation of 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).

[0051] This invention is general and not limited to any specific stabilization scheme. In particular, the teachings of this invention can be used to at least implement the stabilization schemes a) to g) listed above. In any case, this invention is situated in a context where at least the following needs to be generated: - 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. - The second item requires a frequency of The driver for the second mode b. A.2 Quantum systems for stabilizing cat qubits

[0052] Figure 1 A quantum system 1 arranged as stable cat qubits is shown.

[0053] Quantum system 1 includes nonlinear superconducting quantum circuit 3 and command circuit 5.

[0054] The nonlinear superconducting quantum circuit 3 is arranged to perform at least four-wave mixing between the first mode a and the second mode b.

[0055] 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.

[0056] 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.

[0057] 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.

[0058] 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.

[0059] 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.

[0060] The nonlinear superconducting quantum circuit 3 includes a nonlinear element 7 and at least one resonant part 9.

[0061] exist Figure 1 In the example, nonlinear element 7 is a four-wave mixing nonlinear element, and more specifically, an asymmetrically threaded superconducting quantum interference device, or ATS as referred to below.

[0062] As is known to those skilled in the art, ATS can be used to implement 2-to-1 photon conversion, i.e., the first item mentioned above. This is to enable the implementation of dissipative stabilization, as successfully demonstrated by R. Lescanne et al. (2020).

[0063] Unlike the first implementation of this stabilization scheme proposed by Z. Leghtas et al. (2015) and S. Touzard et al. in the paper “Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation” (Physical Review X 8, 023005, 2018), in which 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 for the observation of exponential suppression of bit flips.

[0064] ATS has a flux line through which radiation can be delivered to modulate common flux and / or differential flux.

[0065] In the remainder of the specification, and without loss of generality, nonlinear element 7 is an ATS. However, it should be noted that the invention can relate to several stabilization schemes for cat qubits, and therefore nonlinear element 7 is not necessarily an ATS; it can also be another four-wave mixing nonlinear element, or a nonlinear element for higher-order mixing.

[0066] For example, parameter dissipation stabilization (which corresponds to stabilization scheme a described in detail in section A.1 above) can be implemented using a Josephson junction without the use of an ATS. On the other hand, DC dissipation stabilization (which corresponds to stabilization scheme g in the same section A.1) can be implemented using one or more Josephson junctions that are only subject to appropriate DC bias, thereby achieving the desired four-wave mixing.

[0067] By The ATS is parameterized by pumping at a frequency 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.

[0068] Those skilled in the art know that when the flux operating point ( Or conversely, when biased, the Hamiltonian of ATS 7 It has the following "sin-sin" form:

[0069] ,

[0070] in, - 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 of 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; Differential flux modulation corresponding to the two loops of ATS 7; and - It is a decreasing Planck constant.

[0071] 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.

[0072] 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.

[0073] As an example, by frequency Pump common flux, The nonlinear resonant part of Hamiltonian can be written in a rotating coordinate system as:

[0074] ,

[0075] This is typically the 2-to-1 photon exchange Hamiltonian required to implement two-photon stabilization.

[0076] 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. This 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 .

[0077] 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.

[0078] The resonant section 9 adopts the form of a linear microwave network. This linear microwave network allows the nonlinear superconducting quantum circuit 3 to exhibit resonant frequencies at the resonant frequencies when coupled via the linear coupler 11 to the ATS 7, which acts as an inductive element. and The following are the memory modes a and buffer modes b of ATS 7.

[0079] Command circuit 5 is configured to deliver microwave radiation.

[0080] More specifically, the instruction circuit 5 is arranged to at least parametrically drive the ATS 7 to implement a nonlinear conversion between two photons in memory mode a and one photon in buffer mode b, and to drive buffer mode b.

[0081] Therefore, such as Figure 1 As shown, the instruction circuit 5 includes at least microwave source 13 and microwave source 15.

[0082] Microwave source 13 is set to modulate the common flux in ATS 7.

[0083] For this purpose, microwave network 17 is used to separate the radiation emitted by microwave source 13 and apply it to each node of ATS 7 with the correct phase. Alternatively, two different microwave sources can be used, each simply coupled to a single node of ATS 7, and their relative phase and amplitude can be set to achieve the desired flux modulation.

[0084] Microwave source 13 is arranged to be equal to The frequency will deliver radiation to ATS 7, causing the nonlinear superconducting quantum circuit 3 to perform a 2-to-1 photon conversion between memory mode a and buffer mode b, thereby implementing the first term. To convert the 2-to-1 photon pair into two-photon dissipation, buffer mode b is selectively coupled to load 19 via linear coupler 21 and microwave filter 23, the microwave filter 23 being configured to have a frequency The bandpass filter.

[0085] In the remainder of the specification, microwave source 13 is referred to as two-photon pump.

[0086] Alternatively, microwave filter 23 can be configured as having a frequency of The band-stop filter can be placed between the external environment on one side and the memory mode a and buffer mode b on the other side to isolate memory mode a, thereby preventing memory mode a from suffering additional losses from undesirable coupling with load 19.

[0087] Alternatively, if Then microwave filter 23 can be configured as low-pass (correspondingly, if If so, it is 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. .

[0088] Microwave source 15 is arranged to drive the second mode b to implement the second item. Therefore, microwave source 15 is arranged to be equal to The frequency of the microwave radiation is delivered to the resonant part 9.

[0089] In the remainder of the instruction manual, microwave source 15 is referred to as buffer drive.

[0090] In the above text, load 19 can be considered as Figure 1 It is part of the instruction circuit 5, while the linear coupler 21 and microwave filter 23 can be regarded as part of the nonlinear superconducting quantum circuit 3.

[0091] Finally, Figure 1 In addition, the instruction circuit 5 also includes a microwave source 25, which is configured to modulate the differential flux in the ATS7 via the microwave network 17.

[0092] Furthermore, microwave network 17 is used for convenience, but it can be omitted, and microwave source 25 can be applied directly to the two nodes of ATS 7 by setting their relative phase and amplitude to achieve the desired flux modulation.

[0093] For completeness, it can also be noted that microwave source 25 can be used instead of microwave source 15 to achieve a frequency of Microwave radiation is delivered to the resonant section 9 to drive the buffer mode b.

[0094] It should be noted that quantum system 1 can be adapted to the stabilization scheme to be implemented. For example, in order to implement the stabilization scheme f) described in section A.1, instruction circuit 5 includes an additional microwave source (not shown here) to achieve longitudinal coupling between memory mode a and buffer mode b.

[0095] This additional microwave source (hereinafter referred to as longitudinal pump) is configured to modulate the common flux in ATS 7.

[0096] The longitudinal pumps are arranged to be equal to The frequency will deliver microwave radiation to ATS 7 to generate additional items. .

[0097] This additional item The first term generated by two-photon pump 13 and the second term generated by buffer drive 15 The combination causes the nonlinear superconducting quantum circuit 3 to implement the Hamiltonian H as follows:

[0098] ,

[0099] in, - It is the two-photon coupling rate (or interaction strength) that is proportional to the amplitude of the two-photon pump 13. - It is the annihilation operator for memory mode a; - The phase and amplitude of the radiation caused by longitudinal pumping are complex numbers. - It is a complex number generated by buffer drive 15; - It is the annihilation operator for buffer mode b; - It represents Hermitian conjugate.

[0100] Hamiltonian H generates efficient dissipatives through the dissipation of buffer mode b. It is a two-dimensional manifold that stably carries a specific type of Bose qubit, namely the Mooncat qubit. B. Low resonant frequency memory

[0101] The applicant has studied the quality of memory mode a and its resonant frequency. The relationship between them.

[0102] Therefore, relaxation time should be considered. Yes, it is related to the relaxation time. The decay of quantum states (especially cat states) is typically quantized. More specifically, the relaxation time. Characterizes the probability of a cat qubit transitioning from an excited state to its ground state.

[0103] Relaxation time Limited by the photon loss mechanism of memory mode a. Therefore, relaxation time It can be represented as follows:

[0104] .

[0105] Typically, the attenuation rate is expressed as However, the symbol here This is used to emphasize that the attenuation rate is the sum of all loss channels, whether it is inherent loss or loss due to the coupling of memory mode a with the external environment.

[0106] Figure 2 The attenuation rate is shown as the resonant frequency of memory mode a. The evolution of the function. Therefore, the resonant frequency of memory mode a can be seen. The lower the attenuation rate The lower.

[0107] As described in the description, the resonant frequency of memory mode a is reduced. This enables a reduction in single-photon loss rate. .

[0108] Single photon loss rate This is especially important in the context of cat qubits because of the ratio The phase-flip probability must be kept as low as possible. Since cat qubits have enabled an exponential decrease in the bit-flip rate that can be observed, reducing the phase-flip probability has become a major challenge.

[0109] Therefore, compared with known solutions in the prior art, the resonant frequency of memory mode a is reduced. It has advantages.

[0110] Therefore, the applicant has discovered that making memory mode a have a low resonant frequency (i.e., resonant frequency less than or equal to 3.5 GHz) It has potential.

[0111] However, this observation must be weighed against the fact that the resonant frequency of memory mode a is reduced. It also increases the thermal population of photons. The effect. Attenuation rate. Fluctuations in the voltage (especially a one-time increase or decrease in shutdown) can cause phase reversal. Without any theoretical constraints, the phase reversal rate... It can be represented as follows:

[0112] .

[0113] This phenomenon can be observed in Figure 2 As seen in the text, Figure 2 The gain saturation at the lowest frequency is clearly shown, when the resonant frequency of memory mode a is... The platform is reached at speeds below 1 GHz.

[0114] Based on this observation, two possible options should be considered: a frequency range from 1 to 3.5 GHz with low resonant frequencies. At the same time, maintain a thermal population higher than that of photons. Platforms; or frequency ranges below 1 GHz with even lower resonant frequencies. To reduce the attenuation rate, but it cannot outperform the thermal population of photons. The platform.

[0115] In addition to the aforementioned considerations, the applicant has sufficient reason to believe that, due to the surface dielectric loss in the relaxation mechanism (and therefore in the relaxation time) Dominated by low resonant frequency To improve the quality factor of memory mode a It has made a more significant contribution.

[0116] The paper by C. Wang et al., “Surface participation and dielectric loss in superconducting qubits” (Appl. Phys. Lett. 107, 162601, 2015), points out that the relaxation of resonators can be caused by various dissipation channels (such as dielectric loss), and indicates that the strong proportional relationship between the qubit decay rate and the surface participation ratio (representing the proportion of electric field energy stored in the dissipative surface layer) strongly suggests that surface dielectric loss is the main relaxation mechanism of superconducting transport qubits.

[0117] Figure 3 The resonant frequency as memory mode a is shown. The evolution of dielectric loss as a function of the function. It can be seen that dielectric loss is related to the resonant frequency of memory mode a. It is proportional to the square of.

[0118] Therefore, this invention proposes a nonlinear superconducting quantum circuit 3, which includes an ATS 7 and at least one resonant section 9 having a resonant frequency. Memory mode a, less than or equal to 3.5 GHz.

[0119] This frequency range, far below that of existing technologies, allows for both a reduction in phase-flipping probability and a reduction in relaxation time. (Especially when surface dielectric loss is dominant), and without suffering the adverse effects of excessive and unnecessary increase in photonic thermal population.

[0120] exist Figure 1 In the schematic diagram, there is a microwave filter 23 for the resonant frequency of memory mode a. Filtering is performed. However, considering the resonant frequency of memory mode a... In the frequency range, this microwave filter 23 is redundant and can be omitted.

[0121] Many stabilization schemes are related to this resonant frequency of memory mode a. Compatibility, especially with the stabilization schemes a) to g) detailed in subsection A.1 above.

[0122] For this purpose, a nonlinear superconducting quantum circuit 3, and more specifically at least one resonant section 9, includes a resonator 27 having a capacitive element 29 and an inductive element 31.

[0123] The following subsections elaborate on how to realize such a nonlinear superconducting quantum circuit 3, both in terms of the electronic components that can be used for this purpose and in terms of possible lumped circuits. B.1 Capacitors and Inductors

[0124] As mentioned above, resonant frequency Memory mode a with a frequency of 3.5 GHz or less is generated by a resonator 27 having a capacitive element 29 and an inductive element 31. Typically, the capacitive element 29 is a capacitor, and the inductive element 31 is an inductor.

[0125] This resonator 27 can be referred to as an LC circuit.

[0126] The capacitive element 29 and the inductive element 31 can be connected in series or in parallel within the resonator 27. In any case, it is well known that the resonant frequency of such a resonator 27 is:

[0127] ,

[0128] in, - It is a capacitor of capacitive element 29: and - It is the inductance of inductive element 31.

[0129] Therefore, in order to obtain the resonant frequency within the target frequency range Parallel or series connection can be used, and the capacitance of capacitive element 29 can be adjusted. and / or the inductance of the inductive element 31 .

[0130] In particular, the applicant used materials with extremely high capacitance in the research. The capacitive element 29, and more specifically the capacitor Between 1 and 10 picofarads (pF), and / or using high inductance The inductive element 31, and more specifically the inductor Between 0.3 and 5 Nahens (nH). B.1.1 Capacitor

[0131] In the examples in this section, a high capacitance is used. The capacitive element 29 is used to obtain the low resonant frequency of memory mode a. .

[0132] Figure 4 An embodiment of resonator 27 is shown, wherein the capacitive element 29 is a capacitor with a cloverleaf design.

[0133] More generally, in addition to resonator 27, Figure 4 The circuit also includes other components of ATS 7 and nonlinear superconducting quantum circuit 3 (not shown in the figure).

[0134] The nonlinear superconducting quantum circuit 3 is made of a dielectric substrate on which at least one superconducting material layer 33 is deposited.

[0135] Dielectric substrates can be, for example, silicone or sapphire. Of course, other materials can also be considered for dielectric substrates. Superconducting materials are, for example, aluminum (Al), tantalum (Ta), or niobium (Nb), and more generally, all conventional superconducting metals.

[0136] Figure 4 Orthogonal X, Y, and Z axes are provided. The Z axis corresponds to the stacking direction of the dielectric substrate and the superconducting material layer 33.

[0137] The capacitive element 29 of the resonator 27 is fabricated by etching a superconducting material layer 33 to isolate a "fractal island" 35 within the superconducting material layer 33. This fractal island 35 is defined by a peripheral groove 37, which gives it a clover-like shape.

[0138] The peripheral groove 37 has a constant width e surrounding the fractal island 35. This width e is typically equal to 30 micrometers (μm). At the peripheral groove 37, the fractal island 35 and the remainder of the superconducting material layer 33 (corresponding to the ground plane) face each other and are thus separated by the width e, thereby jointly defining the capacitive element 29. The fractal island 35 and the remainder of the superconducting material layer 33 lie in the same XY plane. This capacitive element 29 can therefore be described as a coplanar capacitor.

[0139] In this cloverleaf design, increasing the length of the peripheral groove 37, and thus increasing the perimeter of the fractal island 35, allows for an increase in the capacitance of the capacitive element 29. Therefore, by adjusting the length of the peripheral groove 37, the capacitance of the capacitive element 29 is increased. Between 1 and 10 pF.

[0140] This four-leaf clover shape makes the capacitance of capacitive element 29... This design maximizes the field size while minimizing its footprint on the superconducting material layer 33. Furthermore, it offers the advantage of reducing electric field concentration and thus reducing loss channels such as dielectric losses. It also minimizes the self-inductance of the capacitive element 29, resulting in the absence of resonant modes within the capacitive element 29 at low frequencies.

[0141] In order to complete Figure 4 As should be noted, the inductive element 31 is formed by an array of Josephson junctions. Advantageously, this Josephson junction array contains as many Josephson junctions as possible to limit the nonlinearity introduced into the nonlinear superconducting quantum circuit 3. The number of Josephson junctions is limited by manufacturing process constraints.

[0142] Finally, transmission line 39 is used to couple buffer mode b to microwave filter 23, which may be, for example, a Purcell filter (not shown). Transmission line 39 can be adapted to achieve a loss rate between 5 and 50 MHz for buffer mode b. .

[0143] It should be noted that designs other than the four-leaf clover design can be etched on the superconducting material layer 33.

[0144] Figure 5 An embodiment of a capacitor with a planar design is shown, in which the capacitive element 29 is formed by a stack of three layers: a first conductive plate 41, a second conductive plate 43, and a dielectric substrate 45.

[0145] The dielectric substrate 45 is sandwiched between the first conductive plate 41 and the second conductive plate 43.

[0146] The dielectric substrate 45 is, for example, silicone or sapphire. Of course, other materials can be considered for the dielectric substrate 45. The first conductive plate 41 and the second conductive plate 43 are made of, for example, aluminum (Al), tantalum (Ta), niobium (Nb), and more generally all conventional superconducting metals.

[0147] In this configuration, since the first conductive plate 41 and the second conductive plate 43 are not located in the same plane, the capacitive element 29 is a planar capacitor rather than a coplanar capacitor.

[0148] and Figure 4 similar, Figure 5 The system is equipped with orthogonal X, Y, and Z axes. The Z axis corresponds to the stacking direction of the first conductive plate 41, the dielectric substrate 45, and the second conductive plate 43.

[0149] Capacitor of capacitive element 29 The capacitance depends on the surface areas of the first conductive plate 41 and the second conductive plate 43, as well as the distance between them (i.e., the thickness of the dielectric substrate 45). Therefore, by adjusting the surface areas of the first conductive plate 41 and the second conductive plate 43, and the distance between them, the capacitance of the capacitive element 29 is increased. Between 1 and 10 pF.

[0150] Those skilled in the art should know that, having high capacitance The capacitive element 29 can be implemented using processes and configurations other than those described in this subsection. B.1.2 Inductor

[0151] In the examples in this section, a high inductance is used. The inductive element 31 is used to obtain the low resonant frequency of memory mode a. .

[0152] Figure 6 The diagram shows that the inductive element 31 is composed of a Josephson junction. i An example of an inductor formed by a chain.

[0153] This Josephson knot JJ i The chain is used as a transmission line to form what is called Resonator.

[0154] As described in subsection A.2 above, a single resonant section (9) can have several modes—at least memory mode a and buffer mode b. This is precisely what is achieved here by the Josephson junction JJ i The chain formed The case of resonators.

[0155] Depend on The resonator 27, formed by the resonator and capacitive element 29 (not shown here), has several modes, each with a corresponding resonant frequency. The first mode of resonator 27 (i.e., the mode with the lowest resonant frequency) can be used as memory mode a; and the Josephson junction JJ i The chain can be configured such that the inductance of the inductive element 31 Between 0.3 and 5 Nahens (nH).

[0156] like Figure 6 As shown, each Josephson junction JJ i Coupled to the corresponding grounding capacitor. These additional capacitors implement several modes. The value of each additional capacitor can be between 0.01 and 1 fenfarad (fF).

[0157] Generally speaking, the resonant frequency of the nth mode of resonator 27 The definition is as follows:

[0158] .

[0159] Any k-th mode can be chosen as buffer mode b, where k is a natural number greater than 1. For example, a convenient approach is to choose the second mode (k=2). The resonant frequency of buffer mode b is... Then it is:

[0160] .

[0161] In this case, it should be noted that the two-photon pump 13 must be equal to The frequency of the microwave radiation is delivered to the ATS 7. In other words, the two-photon pump 13 delivers microwave radiation at the resonant frequency of memory mode a. Pumping is performed.

[0162] Then, as Figure 6 As shown, capacitive element 29 is needed to ground the transmission line. More specifically, capacitive element 29 is placed in the Josephson junction. i The end of the chain is between the ground and the ground. This effectively changes the mode frequency and yields... This solved the above problem.

[0163] Figure 7 An embodiment of resonator 27 is shown, wherein the inductive element 31 is a Hilbert inductor.

[0164] exist Figure 7 In the image, the metal is black, while the substrate is white.

[0165] This design was inspired by the paper “Miniaturization of superconducting filters using Hilbert fractal curves” by M. Barra et al. (IEEE Transactions on Applied Superconductivity, Vol. 15, No. 3, September 2005).

[0166] In this configuration, capacitive element 29 is a Hilbert capacitor. Specifically, as... Figure 7 As shown, both capacitive element 29 and inductive element 31 have a Hilbert design, which is because both are formed by labyrinthine metal traces, so that capacitive element 29 and inductive element 31 can be described as an end capacitor and an end inductor, respectively.

[0167] This design is given as an example to emphasize its potential use in implementing inductors. Several designs for the inductive element 31 are between 0.3 and 5 nanohenries (nH). In addition, an article by M. Barra et al. (2005) describes another design—the meander design—which can also be used to implement the resonator 27. B.2 Lumped Circuits

[0168] Just as different capacitors and inductors can be used to implement capacitances between 1 and 10 picofarads (pF) and inductances between 0.3 and 5 nanohenries (nH), different lumped circuits (and including such capacitors and / or inductors) can be implemented to benefit from the resonant frequency of memory mode a at less than or equal to 3.5 GHz. .

[0169] In the following text, Figures 8-11Each figure partially illustrates the nonlinear superconducting quantum circuit 3. More specifically, each of these figures illustrates a lumped circuit with memory mode a, buffer mode b, and nonlinear element 7.

[0170] In the example described below, nonlinear element 7 is a four-wave mixing nonlinear element, and more specifically, an ATS. However, as mentioned above, nonlinear element 7 can be another four-wave mixing nonlinear element, or a nonlinear element used to achieve higher-order mixing. Nonlinear element 7 can be a single Josephson junction or multiple Josephson junctions, if the stabilization scheme allows or requires it.

[0171] Figure 8 A circuit is shown in which resonator 27 is current-coupled to resonator 49.

[0172] Through "current coupling," it should be understood that there exists a short conductive section connecting resonators 27 and 49, i.e., a short conductive trace or any other means that ensures a physical, continuous conductive connection. The expression "short" means connected to resonators 27 and 49 at their resonant frequencies. and Compared to the impedance below, the impedance of the conductive traces is negligible. These short conductive sections correspond to... Figure 1 Linear coupler 11.

[0173] As previously described, resonator 27 includes a capacitive element 29 and an inductive element 31. The capacitive element 29 and the inductive element 31 together produce a resonant frequency with a frequency less than or equal to 3.5 GHz. The memory mode is a. In other words, resonator 27 corresponds to memory mode a.

[0174] The resonator 27 can be composed of a capacitive element 29 with high capacitance and / or an inductive element 31 with high inductance. Section B.1 presents different designs for implementing such a capacitive element 29 and / or such an inductive element 31.

[0175] exist Figure 8 In the example, capacitive element 29 and inductive element 31 are connected in series. Alternatively, capacitive element 29 and inductive element 31 can be connected in parallel.

[0176] Resonator 49 includes a capacitive element 51 and an ATS 7. ATS 7 includes a first Josephson junction 53, a second Josephson junction 55, and an inductive element 57. ATS 7 acts as the inductive element within resonator 49. Resonator 49 corresponds to buffer mode b.

[0177] Such a circuit can be described as "minimal" in that it involves as few components as possible to have both memory mode a and buffer mode b: two capacitive elements (29, 51) and two inductive elements (31, 7). In effect, ATS 7 acts both as the inductive element generating buffer mode b and as the four-wave mixing nonlinear element generating the nonlinear conversion between two photons in memory mode a and one photon in buffer mode b. Furthermore, ATS 7 can also be used as the inductive element for memory mode a.

[0178] Figure 9 shows a circuit equivalent to the circuit in Figure 8, and thus shows another possible representation of this minimized circuit.

[0179] The applicant has already implemented the four-leaf clover design presented in section B.1.1 above. Figure 8 The circuitry. Specifically, the applicant has adjusted the parameters to ensure that each of the memory mode a and buffer mode b has sufficiently high participation in the ATS 7, i.e., low corresponding zero-point fluctuations. and When the phase of memory mode a crosses the zero-point fluctuation of ATS 7... Typically, the zero-point fluctuation of the phase of memory mode a is considered to be between 0.005 and 0.3, and preferably between 0.01 and 0.15. The level is low enough to ensure that the participation of memory mode a in ATS 7 is sufficient; such that the phase of memory mode b crosses the zero-point fluctuations of ATS 7. Typically, the zero-point fluctuation of the phase of buffer mode b is considered to be between 0.005 and 0.3, and preferably between 0.01 and 0.15. It is low enough that the participation of buffer mode b in ATS 7 is sufficient.

[0180] In this case, the applicant selected the following values ​​or ranges for different parameters: - Capacitor of capacitive element 29 : 1 to 2 picofarads (pF), and preferably 1.4 picofarads (pF); - The capacitance of capacitive element 51 is 0.4 to 1 picofarad (pF), and preferably 0.6 picofarad (pF); -Inductance of inductive element 31 : 2 to 20 nanohenries (nH), and preferably 6.1 nanohenries (nH); - The inductance of the inductive element 57 is 2 to 10 nanohenries (nH), and preferably 6.6 nanohenries (nH); - The coupling rate of the Pussel filter is 5 to 50 MHz, and preferably 80 MHz; -Pusser filter loss rate: 2 GHz; - Zero-point fluctuations in the phase of memory mode a : 0.02 to 0.15; and -Zero-point fluctuations in the phase of buffer mode b : 0.1 to 0.3.

[0181] Figure 10 The circuit diagram shows resonator 27 capacitively coupled to resonator 49. In particular, resonator 27 and resonator 49 are coupled together via capacitive element 59.

[0182] It should be noted that the same reference numerals have been retained for ease of understanding.

[0183] As in Figure 8 and Figure 9 As shown, resonator 27 corresponds to memory mode a, while resonator 49 corresponds to buffer mode b.

[0184] The applicant has adjusted the parameters to ensure that each of memory mode a and buffer mode b has sufficiently high participation in ATS 7, i.e., low zero-point fluctuations respectively. and .

[0185] In this case, the applicant selected the following values ​​or ranges of values ​​for different parameters: - Capacitor of capacitive element 29 : 1 to 10 picofarads (pF); - Capacitance of capacitive element 51: 1 to 10 picofarads (pF). -Inductance of inductive element 31 : 5 to 15 Nahens (nH); - Inductance of inductive element 57: 5 to 15 nanohenries (nH); - Capacitance of capacitive element 59: 1 to 10 picofarads (pF); - Coupling rate of Pussel filter: 5 to 50 MHz; -Pusser filter loss rate: 2 GHz; - Zero-point fluctuations in the phase of memory mode a : 0.02 to 0.15; and -Zero-point fluctuations in the phase of buffer mode b : 0.1 to 0.3.

[0186] at last, Figure 11 Corresponding to Figure 6The circuit of the embodiment, wherein the inductive element 31 of the resonator 27 is a Josephson junction JJ i chain.

[0187] The resonator 49 present in Figures 8, 9 and 10 is omitted here, because as described above, the resonator 27 alone generates the memory mode a and the buffer mode b.

[0188] It should be noted that the resonator 27 (corresponding to Figure 1 the resonant portion 9) is current-coupled to the ATS 7.

[0189] Again, the applicant has adjusted the parameters to ensure that each of the memory mode a and the buffer mode b has a sufficiently large participation in the ATS 7, that is, respectively low zero-point fluctuations and .

[0190] In the present case, the applicant has selected the following values or ranges of values for different parameters: - Capacitance of the capacitive element 29 : 10 to 1000 femtofarads (fF); - Number of Josephson junctions JJ of the inductive element 31 i : 100 to 1000; - Inductance of the inductive element 57: approximately 10 nanohenries (nH); - Coupling rate of the Purcell filter: 5 to 20 megahertz (MHz); - Phase zero-point fluctuation of the memory mode a : 0.01 to 0.05; and - Phase zero-point fluctuation of the buffer mode b : 0.02 to 0.1.

[0191] In addition, additional capacitors connected to ground and respectively coupled to the Josephson JJ i junctions typically have a capacitance between 0.01 and 1 femtofarad (fF). For the sake of clarity, these additional capacitors are omitted in Figure 11 , but are shown for example in Figure 6 .

[0192] B.3 Performance of Low Resonant Frequency Memory

[0193] Figure 12 illustrates the performance of a cat qubit stabilized by the quantum system 1 according to the operation mechanism proposed by the present invention (i.e., the resonant frequency of the memory mode a is less than or equal to 3.5 gigahertz (GHz)).

[0194] More specifically, these performances are obtained according to Figure 4The four-leaf clover design is implemented using memory pattern a, and has the features described above for... Figure 8 and Figure 9 The circuit shown lists the parameters.

[0195] Figure (a) shows the population evolution of resonator 27 over time. Figure (a) shows that resonator 27 has a relaxation time of approximately 68 microseconds (μs). .

[0196] Figure (b) shows the dimensions. Wigner tomography of a cat qubit with 2.9 photons, an angle of -75.7 degrees, and a stabilization time of 250 microseconds (μs) corresponds to a deep steady state. To reiterate, the angle of the cat qubit depends on the phase of the buffer driver 15. This stabilization of the cat qubit is performed using a resonator 27.

[0197] Figure 13 The cat qubit phase flip rate is shown as a function of the number of photons in the memory. The evolution. Through measurement. The number of photons in the transient and steady states of the memory was determined. The results show that the modification time... This is equal to 27.47 microseconds (μs). This modified time... Corresponding to the best-fit linear relationship The time value. This modifies the relaxation time. Stray effects caused by parameter pumping have been taken into account.

[0198] In order to utilize the operating mechanism (i.e., the resonant frequency of memory mode a) which is the subject of this invention For signals less than or equal to 3 GHz, it is recommended to first clear the memory to ensure that there are as few photons as possible in the memory.

[0199] For example, this memory reset can be performed by enabling the interaction between memory mode a and buffer mode b, thereby 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 this reset, the memory is not completely cleared: a small percentage of photons remain due to thermal population.

Claims

1. A nonlinear superconducting quantum circuit (3), comprising: At least one resonant part (9) has a first mode (a) with a first resonant frequency and a second mode (b) with a second resonant frequency. as well as A nonlinear element (7), said nonlinear element being coupled to or at least partially included in said at least one resonant portion (9), The at least one of the resonant components has a resonator (27) comprising a capacitive element (29) and an inductive element (31) that together generate the first mode (a), the capacitive element (29) having a capacitance between 1 and 10 pF, and / or the inductive element (31) having an inductance between 0.3 and 5 nH, such that the first resonant frequency is less than or equal to 3.5 GHz.

2. The nonlinear superconducting quantum circuit (3) according to claim 1, wherein, The nonlinear element (7) is a four-wave mixing nonlinear element.

3. The nonlinear superconducting quantum circuit (3) according to claim 2, wherein, The nonlinear element (7) is an asymmetric flux-through superconducting quantum interference device.

4. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The nonlinear element (7) is included in the at least one resonant portion (9) and serves as an inductive element (31) within the at least one resonant portion (9).

5. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The capacitive element (29) is formed by stacking a dielectric substrate and a superconducting material layer (33), which is etched to define a four-leaf clover shape.

6. The nonlinear superconducting quantum circuit (3) according to claim 5, wherein, The capacitive element (29) has a capacitance between 1 and 2 pF, and preferably equal to 1.4 pF.

7. The nonlinear superconducting quantum circuit (3) according to any one of claims 1 to 4, wherein, The capacitive element (29) is a planar capacitor formed by a dielectric substrate (45) sandwiched between the first conductive plate and the second conductive plate (41, 43).

8. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The inductive element (31) is a Josephson knot.

9. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The first resonant frequency is between 1 and 3.5 GHz.

10. The nonlinear superconducting quantum circuit (3) according to any one of claims 1 to 8, wherein, The first resonant frequency is less than or equal to 1 GHz.

11. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The first resonant frequency is approximately equal to 1 GHz.

12. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The phase zero fluctuations of the first mode (a) on the nonlinear element (7) and the phase zero fluctuations of the second mode (b) on the nonlinear element (7) are each between 0.005 and 0.3, and preferably between 0.01 and 0.

15.

13. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The first mode (a) is used to carry a boson qubit, and wherein the nonlinear element (7) is arranged to nonlinearly couple the first mode (a) and the second mode (b), optionally wherein the boson qubit is a cat qubit.

14. The nonlinear superconducting quantum circuit (3) according to any one of the preceding claims, wherein, The first mode (a) has a quality factor, and the second mode (b) has a quality factor, wherein the quality factor of the first mode (a) is higher than the quality factor of the second mode (b).

15. A quantum system (1) for stabilizing cat qubits, comprising: Command circuit (5), the command circuit (5) including at least a first microwave source (13) and a second microwave source (15), each microwave source being arranged to deliver microwave radiation; and A nonlinear superconducting quantum circuit (3) includes a nonlinear element (7) and at least one resonant part (9), wherein the nonlinear element (7) is coupled to or at least partially included in the at least one resonant part (9), and the at least one resonant part (9) has a first mode (a) with a first resonant frequency and a second mode (b) with a second resonant frequency. The at least one of the resonant components has a resonator (27) comprising a capacitive element (29) and an inductive element (31) that jointly generate the first mode (a), the capacitive element (29) having a capacitance between 1 and 10 pF, and / or the inductive element (31) having an inductance between 0.3 and 5 nH, such that the first resonant frequency is less than or equal to 3.5 GHz. The quantum system (1) is arranged such that the nonlinear superconducting quantum circuit (3) stably carries the two-dimensional manifold of the cat qubits when: The first microwave source (13) delivers microwave radiation to the nonlinear element (7) 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 (15) delivers microwave radiation at a frequency equal to the second resonant frequency to the at least one resonant part (9) to drive the second mode (b).

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