Apparatus and method for phase flip reduction in cat qubits

Abstract

An electronic device for storing quantum information, the electronic device comprising:-a cat qubit electromagnetic resonator (10), the cat qubit electromagnetic resonator having a first resonant frequency [omega] a; -a buffer electromagnetic resonator (20) having a resonant frequency [omega] b; -a non-linear coupling element (30); the coupling device is used for coupling electromagnetic waves with the frequency of omega b; the coupling device is used for coupling electromagnetic waves with the frequency of 2 omega a-omega b; and-a dissipative device (40) coupled to the cat qubit resonator (10) and to the buffer resonator (20) by means of a non-linear coupling element (30); -wherein a four-wave mixing is carried out with respect to two photons at a frequency [omega] a, one photon at a frequency [omega] b and photons of an electromagnetic wave at a frequency of 2 [omega] a-[omega] b. The coupling device (60) is further configured to couple a third electromagnetic wave at a frequency of (2n + 1) [omega] a + [omega] b-[omega] c to the nonlinear element (30), wherein [omega] c is the resonant frequency of the loss mode and n is an integer.

Description

Technical Field

[0001] The present invention belongs to the field of quantum information processing and quantum computing. The present invention relates to a device and method for storing and / or processing quantum information in the form of restricted quantum cat qubits while reducing first-order phase flip errors. The present invention is applicable to all such restricted cat qubits, and in particular to squeezed cat qubits. The device and method are based on a feedback pattern from the cat qubit, where the cat qubit autonomously performs this feedback.

[0002] Quantum computing is an emerging field at the intersection of physics, mathematics, and computer science. It is based on constructing circuits that address qubits or quantum bits. A qubit is the fundamental unit of quantum information or a basic two-state quantum mechanical system. The circuit can be an electronic circuit or a circuit based on photons, atoms, or trapped ions. Due to its properties, a qubit can be in a superposition of two states simultaneously. In a quantum computer, a quantum logic gate or quantum gate is an operation performed on a small number of qubits and is thus a building block for larger-scale quantum computing.

[0003] Quantum computers utilize quantum properties such as superposition, interference, and entanglement and can solve certain complex computational problems more easily and quickly than non-quantum computers.

[0004] Background Art - State of the Art

[0005] Physical means for constructing a circuit - cat qubits and their characteristics

[0006] There are several methods for constructing qubits and gates for quantum computers, one of which is based on superconducting circuits cooled to a few millikelvin (mK).

[0007] In the field of superconducting circuits, a known method is to encode data in a non-harmonic oscillator circuit composed of a Josephson junction in parallel with a capacitor. These circuits are called transmon qubits, where the name transmon stands for "transmission line shunted plasma oscillation". The anharmonicity allows the energy levels to be separated by unequal energy differences, so that in a controlled manner, only the transition between two identified levels |0> and |1> can be operated using a signal at a given frequency.

[0008] However, a very advantageous approach later on is to utilize a harmonic LC oscillator, i.e., a circuit consisting of an inductor L and a capacitor C connected together and acting as an electrical resonator. It encodes information into a Schrödinger cat state, which refers to a quantum superposition of a system being in its classical-like state as commonly found in non-quantum (i.e., classical) models. Thus called cat qubits typically use, for example, a quantum superposition of coherent states with equal weights and opposite phases. More generally, such information can be encoded in so-called boson modes, thereby creating boson codes or continuous variable codes - typically photons, but also phonons or other types of oscillators on other physical platforms. Several academic and private players have pursued this approach, which was initially developed by the applicant and Yale University in a collaborative effort. Generally, in boson codes, the high dimensionality of the harmonic oscillator implies redundancy, which is used to reduce the impact of physical errors on the encoded logical information without the need for active monitoring, and this is one of the very attractive reasons for boson codes.

[0009] Cat qubits are of interest because they exhibit a reduced impact of physical errors compared to qubits with noisy biases, which means that one of the two fundamental errors that occur in qubits - namely, bit flips and phase flips - is exponentially suppressed in the cat qubit size - the size of a cat qubit is the average number of photons in the oscillator - while the other fundamental error only increases linearly, thus providing an attractive scaling. In the context of quantum error correction codes, qubits with exponential error biases can significantly reduce the overhead required, i.e., the number of physical qubits per logical qubit, to achieve a satisfactory or given level of information protection.

[0010] Nonetheless, it is important to keep the error rate of the unprotected type as low as possible, i.e., keep the error rate between bit flips and phase flips that is not exponentially suppressed in a single cat qubit as low as possible. In fact, quantum error correction codes are only effective when these errors (regardless of their type) are below a certain threshold rate compared to the error correction cycle. Moreover, even below the threshold, a higher error rate requires a code with a larger overhead. Even though the overhead of cat qubits is lower than that of qubits without noisy biases, it still implies significant complexity in terms of actual construction and performing logical operations on the encoded information.

[0011] The present invention describes the case where the bits are of the exponentially protected type of quantum information and the phase is of the type not exponentially suppressed. But it also applies to the opposite case.

[0012] Restriction to the code space

[0013] For cat qubits, experimentally, confinement to a two-dimensional code space has been shown, which is necessary for operating qubits that are essentially multi-level systems.

[0014] Two methods are known for confining the states of a quantum harmonic oscillator to a two-dimensional manifold corresponding to the logical states of a cat qubit. These two confinement methods are based respectively on engineered two-photon dissipation and self-Kerr nonlinearity of a junction in the harmonic oscillator Hamiltonian.

[0015] The first method - the dissipation-based method - is disclosed in Mirrahimi, 2014 and Lescanne, 2020, and this method is based on a confinement scheme arising from engineered two-photon dissipation and confines dynamics to only two stable states of an ideal system, namely the cat qubit computational states. Bit flips are exponentially suppressed. This confinement is achieved by a non-linear superconducting circuit element called an asymmetric threaded superconducting quantum interference device, or asymmetric threaded SQUID or ATS, disclosed in US11302856B2. It can also be achieved by using another such element, such as a superconducting non-linear asymmetric inductive element parametric amplifier or SNAIL, as disclosed in Frattini et al., Phys.Rev Applied (2018) and US2021 / 0021245A1. Alternatively, a transmon can also be used as the non-linear circuit element to achieve this, see Leghtas et al., Science (2015). The cat qubit encoded in a linear resonator is coupled to a buffer mode using this non-linear circuit element, where the buffer mode is highly dissipative and the energy decays much faster than the lifetime of the cat qubit. The buffer mode does not need to be harmonic, as only its two lowest levels are required for device operation. In the Chamberland, 2020 paper, the authors further proposed coupling a single buffer mode to multiple cat qubits instead of using a buffer mode for each cat qubit. More precisely, in this dissipation method, the two-photon to one-photon exchange Hamiltonian is engineered in the rotating frame of the two modes between the cat qubit mode and the short-lived buffer mode respectively via the non-linear circuit element:

[0016]

[0017] Here, a denotes the photon annihilation operator of the cat qubit mode, and b denotes the photon annihilation operator of the buffer mode. Additionally, and are the associated photon creation operators. Thus, two photons in mode a are exchanged with a single photon in mode b. Additionally, δ represents the rate of this exchange and can be adjusted by the amplitude of the microwave pump applied to the nonlinear circuit element. The buffer mode must also be driven in its resonant state. In the rotating frame of the buffer mode, this can be modeled by the following Hamiltonian:

[0018]

[0019] The drive amplitude can be related to the effective amplitude in the cat qubit mode via the equation ∈ = g2α 2 Thus, the total interaction Hamiltonian can be written as:

[0020]

[0021] The strong dissipation in mode b is then transformed into effective dissipation of the form This is called two-photon dissipation and is regarded as a way to pull the system state to confine the harmonic oscillator state to the two-dimensional space spanned by the coherent states |±ɑ>, thus defining the confined cat qubit.

[0022] A method for performing single qubit Z rotations, two qubit CNOT gates (also known as CX gates), and three qubit CCNOT gates (also known as CCX or Toffoli) on such dissipative cat qubits is described in Guillaud 2019.

[0023] The feedforward Hamiltonian that "pushes" the system state simultaneously is used in conjunction with the two-photon dissipation that is said to "pull" the system state. In fact, the dissipation term is still implemented through the nonlinear circuit element and using the coupling to the buffer mode; the feedforward term for the Z gate is just a standard drive on the cat qubit mode, and the feedforward terms for the CNOT and CCNOT gates can be implemented through the driven nonlinear coupling between the involved cat modes.

[0024] The second method for confining the cat qubit state is a pure Hamiltonian confinement based on two-photon drive and Kerr nonlinearity, as disclosed in Puri, 2017 and Grimm, 2020. This method is called the Kerr cat qubit. In the rotating frame of the cat qubit mode, it can be modeled by the Hamiltonian:

[0025]

[0026] Here K represents the strength of the Kerr effect, and Kɑ 2is the two - photon - driven amplitude. The manifold associated with the cat qubit state corresponds to the degenerate eigenspace of the Hamiltonian designed above and is separated from the rest of the spectrum by a gap proportional to the strength of the Kerr nonlinearity K. In these publications, the nonlinearity is indeed implemented using SNAIL.

[0027] In both of these confinement schemes, improved mechanisms for reducing gate - induced phase errors have been disclosed in Gautier, 2022 and Xu, 2022 - 1, either through two - photon dissipation or through the Kerr cat qubit method.

[0028] The present invention is based on a dissipative confinement setup.

[0029] Phase flip, and in particular phase errors caused by gates

[0030] Furthermore, the present invention specifically targets phase flips, also known as phase errors. Therefore, their two main sources are briefly discussed below.

[0031] The first source of phase error is the natural decoherence mechanism through spontaneous single - photon loss. This is the main perturbation acting on the idle harmonic oscillator. Its effect on the information - qubit part is well - cancelled by the cat confinement. In the phase part, its effect is that each photon loss causes the logical value to be inverted. Thus, after two consecutive losses, the logical value returns to its original value. However, since there is only a single cat qubit, the number of photon losses cannot be measured without destroying the information - qubit part, and over time, the uncertainty about how many photon losses have occurred grows, and thus the uncertainty about what the encoded phase value is also grows.

[0032] The second source of phase error occurs when certain logical operations are applied to the cat qubit through a gate. In fact, standard Hamiltonians, such as the applied displacement Hamiltonian N 门 = u(t)(a + a + ) only result in imperfect phase control: the amount of the phase shift, while well - controlled, is also necessarily blurred because the physical operation cannot be precisely aligned with the cat - qubit code space. This leads to additional phase - flip errors because this is the unprotected part of the encoded quantum information, and the instantaneous displacement outside the cat - qubit subspace is cancelled by two - photon dissipation.

[0033] There are techniques to mitigate this effect, but completely suppressing it is challenging. In particular, for faster gates, the effect is worse. This includes the CNOT gates that are actually used for phase error correction. Although improved mechanisms for reducing gate-induced phase errors have been proposed recently in Gautier, 2022 and Xu, 2022-1, any further phase protection mechanism would be of interest for achieving a satisfactory combined level of speed and accuracy in quantum computing.

[0034] Squeezed cats and other cats - brief comparison with standard cat qubits

[0035] A variant of the cat qubit known as the squeezed cat is known, and this variant is achieved by superposing squeezed coherent states. It has a limiting mechanism that is not much more complex than that of the standard cat qubit. The present invention also applies to this particular cat qubit.

[0036] In the standard cat qubit, the main perturbation mechanism, namely spontaneous photon loss, causes a phase flip within the code space and thus cannot be detected. Different from the standard cat qubit, the spontaneous loss of photons in the squeezed cat can in principle be detected because it moves the state out of the code space. Moreover, this remains the main error source causing phase flips on the quantum information. Therefore, the process of detecting and correcting this part of the error can be considered and would be very useful. The reduction of phase errors in the squeezed cat via such observations has been discussed in Carde, 2021, Schlegel, 2022 and Xu, 2022-2.

[0037] In other non-squeezed cat-type quantum information encodings, such as the cat involving several harmonic oscillators in Albert, 2019, or the cat involving more than two coherent state components in Ofek, 2016, the spontaneous loss of photons can in principle be detected by appropriately adjusted measurements because it moves the quantum state out of the code space, just as in the squeezed cat. However, this "displacement" has a more specific form than the perturbations of the two-component (squeezed or non-squeezed) cats discussed above; the present invention does not address these issues, and it currently does not seem clear what the equivalent proposals are for this type of cat.

[0038] The removal of a two-component (squeezed or unsqueezed) cat from its code space causes a reaction in the buffer mode, which is removed from the vacuum. The strong dissipation of the buffer mode is deliberately designed, and when the cat qubit mode returns to the code space simultaneously, the strong dissipation of the buffer mode will rapidly cause photon loss in the buffer mode. In principle, the photons lost by the buffer mode can be detected because this is a designed process, so as to detect when the cat qubit mode has moved out of the code space and apply a correction action to the cat qubit phase accordingly. However, based on currently available technologies, the method of repeatedly measuring the photons lost by the buffer mode and making corrections based on Carde, 2021, or Schlegel, 2022, seems to have little prospect in practice.

[0039] Autonomous feedback and measurement-based feedback

[0040] In fact, implementing a phase correction action based on actual quantum measurements and then performing a correction operation may involve highly complex and inefficient physical elements. In particular, measurement devices usually have a "detection efficiency" of several tens of percent, and at least in the context of dissipation limits, this directly translates into the same low efficiency of feedback correction for phase errors. In addition, there are also isolation complexities when signals are transmitted from the quantum computer to the classical computer and back. Therefore, measurement-based feedback is not an attractive solution.

[0041] The concept of "autonomous feedback" is a natural way to circumvent the question of measuring the loop fidelity at the quantum level, especially in the context where dissipation stabilization already exists. The principle will be further elaborated below, that is, to design a physical mechanism that combines the deviation to be detected and the action to be taken. The challenge lies in how to design such a mechanism using simple physical building blocks. The early coherent feedback principle was proposed by Mabuchi, 2008 and James and Gough, 2010. In Xu, 2022-2, a special "autonomous feedback" controller was proposed for the current task, and the main observation is that it is applicable to squeezed cat feedback and has the incidental benefit of reducing errors caused by non-adiabatic gates.

[0042] Problems solved by the invention

[0043] The standard cat qubit method reduces the bit flip error rate, but there is no satisfactory solution to deal with the phase flip error.

[0044] The present invention proposes a physical mechanism for automatically performing in-situ correction of phase errors, at least to first-order correction.

[0045] The present invention modifies the dissipative cat qubit confinement mechanism such that the actions that simultaneously return to the cat qubit space automatically correct some phase errors.

[0046] More precisely, on all cat qubits including the standard cat qubit, the present invention corrects the phase errors caused by the Hamiltonian used to perform the gates to first order.

[0047] And specifically on the squeezed cat qubit, the present invention also corrects the phase errors caused by spontaneous single-photon loss or gain, which is often the main decoherence process, to first order. Therefore, the present invention has special advantages for the squeezed cat qubit.

[0048] In addition, regardless of the nature of the cat qubit used, whether it is a standard cat qubit, a squeezed cat qubit, or a cat qubit that may be neither a standard cat qubit nor a squeezed cat qubit, the present invention can be combined with other phase protection methods.

[0049] Compared with Xu, 2002-2, the present invention proposes a different specific implementation of autonomous feedback for this task. These two implementations have different advantages and disadvantages in terms of the problems faced in the specific implementation, both in terms of the robustness to side effects and the practicality in the manufacturing process.

[0050] For example, the autonomous feedback targeted by Xu, 2022-2 requires the design of a large number of microwave pumps. In the actual implementation proposed in that paper, as detailed in its formula n°16, five microwave pumps are required - one or two microwave pumps between each pair of resonators - and two microwave drivers - the two microwave drivers are located on different resonators. This large number of pumps and drivers presents practical difficulties, such as frequency conflicts, or due to the need for a large number of qubit connectivities, because ultimately hundreds of cat qubits are built on the chip and each qubit requires this number of pumps and drivers. The present invention provides a more direct design that uses fewer pumps and drivers but has generally similar performance.

[0051] In this context, the present invention includes an electronic device for storing quantum information, the electronic device comprising:

[0052] - A cat qubit electromagnetic resonator having a first resonance frequency ω a ;

[0053] - A buffer electromagnetic resonator having a second resonance frequency ω b , the second resonance frequency ω b being different from the first resonance frequency;

[0054] - A non - linear coupling element that couples a cat qubit resonator to a buffer resonator;

[0055] - Coupling means configured to couple a first electromagnetic wave having a frequency of ω b to the non - linear coupling element - for example, including a coaxial cable having an appropriate bandwidth, and coupling means configured to couple a second electromagnetic wave having a frequency of 2ω a - ω b to the non - linear coupling element - for example, the same coaxial cable as the first wave, or a different coaxial cable; and

[0056] - A dissipative device that is coupled to the cat qubit resonator and to the buffer resonator through the non - linear coupling element;

[0057] wherein the non - linear coupling element is configured to perform four - wave mixing with respect to two photons having a frequency of ω a , one photon having a frequency of ω b , and photons of a second electromagnetic wave having a frequency of 2ω a - ω b to exchange two photons having a frequency of ω a in the cat qubit resonator with a photon having a frequency of ω b .

[0058] The device is original due to having at least the following features:

[0059] - The device has coupling means - also for example the same coaxial cable as used for the first wave above, or a different coaxial cable, and the coupling means is further configured to couple one or more third electromagnetic waves having a frequency of (2n + 1)ω a + ω b - ω c to the non - linear coupling element, where ω c is the resonance frequency of the loss mode of the dissipative device and ω c is different from ω a and ω b , and n is a non - negative integer (e.g., n = 0); this loss mode now embodies the dissipative characteristics of the device, and unlike a standard cat qubit, the buffer mode is non - dissipative here.

[0060] - The non - linear coupling element is further configured to perform with respect to 2n + 1 photons having a frequency of ω a in the cat qubit resonator, one photon having a frequency of ω b in the buffer resonator, and photons at the frequency of ω cOne or several instances of 2n + 4 wave mixing of a photon of a first electromagnetic wave and a photon of a third electromagnetic wave, said 2n + 4 wave mixing causing an odd number of photons in the cat qubit resonator to be dissipated correlatively with a photon in the buffer resonator through a dissipative device. In a more general way, such 2n + 4 wave mixing can occur in a larger set of wave mixings, performing the exchange of an odd number of photons with frequency ω in the cat qubit resonator. a The odd number of photons is exchanged.

[0061] The present invention also embodies a method for storing quantum information, said method comprising:

[0062] - Coupling a cat qubit electromagnetic resonator having a first resonance frequency ω a to a buffer electromagnetic resonator having a second resonance frequency ω b , said second resonance frequency ω b being different from said first resonance frequency;

[0063] - Coupling a first electromagnetic wave with frequency ω b and a second electromagnetic wave with frequency 2ω a - ω b to the non - linear coupling element; and

[0064] - Coupling a dissipative device to the cat qubit resonator and to the buffer resonator through the non - linear coupling element;

[0065] wherein the method for storing information further comprises performing four - wave mixing with respect to two photons with frequency ω a , one photon with frequency ω b , and a photon of a second electromagnetic wave with frequency 2ω a - ω b by means of the non - linear coupling element, so as to exchange two photons with frequency ω a in the cat qubit resonator with a photon with frequency ω b .

[0066] This method is original due to having at least the following characteristics:

[0067] - The method for storing information further comprises coupling a third electromagnetic wave with frequency (2n + 1)ω a + ω b - ω c to the non - linear coupling element, where ω c is the resonance frequency of the loss mode of the dissipative device and ω c is different from ω a and ω b , and n is a non - negative integer;

[0068] - And the method for storing information further includes performing (2n + 4)-wave mixing on (2n + 1) photons with frequency ω in the cat resonator, one photon with frequency ω in the buffer resonator, one photon with frequency ω in the loss mode, and one photon with frequency (2n + 1)ω + ω - ω of the third electromagnetic wave, where the (2n + 4)-wave mixing causes the dissipation of an odd number of photons in the cat qubit resonator and one photon in the buffer resonator through the dissipation device in a correlated manner. a of the buffer resonator, one photon with frequency ω b of the loss mode, and one photon with frequency (2n + 1)ω c of the third electromagnetic wave, where the (2n + 4)-wave mixing causes the dissipation of an odd number of photons in the cat qubit resonator and one photon in the buffer resonator through the dissipation device in a correlated manner. a + ω b - ω c of the buffer resonator, one photon with frequency ω

[0069] The joint dissipation causes the phase value of the cat qubit to flip, and at the same time it jumps back to the subspace of its stable state; therefore, when the present invention corrects the displacement outside the stable state subspace, it flips the phase back to its original value.

[0070] In this way, the new design can autonomously correct the main order of the phase error during the gate operation on the cat qubit, so that it can combine the exponential protection of the bit flip error benefited from the characteristics of the cat qubit with the original improved protection against the phase flip error. This allows the use of faster gates when the uncorrected error rate is not too high.

[0071] More precisely, it must be admitted that the present invention provides a first-order correction, which, although it cannot eliminate all the effects of the typically main error channels, can eliminate the main part of them, so that an order of magnitude of one or two can be obtained in terms of phase accuracy.

[0072] In a standard cat qubit, it can be considered to implement the present invention only during certain gate operations, and otherwise maintain the standard dissipation.

[0073] The present invention can be combined with other schemes for improving the phase protection during the gate operation, such as the anti-adiabatic drive disclosed in Xu, 2022-1.

[0074] For the squeezed cat qubit, the same design also corrects the phase flip associated with the spontaneous single-photon loss to the first order, and the spontaneous single-photon loss is the main error source inherent in the cat qubit.

[0075] The additional design complexity is low because it requires a finite number of microwave pumps and drivers, that is, for the squeezed cat, four pumps and one driver are required in the minimum setup; for the non-squeezed cat, two pumps and one driver are required in the minimum setup.

[0076] Even though this additional design introduces some other perturbations into the phase error, the order of these other perturbations is much lower than the errors caused by the noise and spontaneous decoherence introduced by the gates. Therefore, overall, the phase is clearly better protected.

[0077] Other features are optional and advantageous and are indicated below.

[0078] - The additional dissipative device may include a third electromagnetic resonator that resonates at a frequency ω c and is coupled to the transmission line;

[0079] - The additional dissipative device may include a nonlinear resonator;

[0080] - The cat qubit resonator, the buffer resonator, and the dissipative device may be constructed as a superconducting circuit;

[0081] - The electronic device may further include a generator for a first electromagnetic wave at a frequency ω b and a generator for a second electromagnetic wave at a frequency 2ω a - ω b and a generator for a third electromagnetic wave at a frequency (2n + 1)ω a + ω b - ω c ; these generators may be the same device that generates several waves;

[0082] - The generator for a first electromagnetic wave at a frequency ω b and the generator for a second electromagnetic wave at a frequency 2ω a - ω b and the generator for a third electromagnetic wave at a frequency (2n + 1)ω a + ω b - ω c may be a microwave generator - all or only some of them;

[0083] - The cat qubit resonator may be a squeezed cat qubit resonator, and wherein the coupling means is further configured to couple a fourth electromagnetic wave at a frequency 2ω a + ω b to the nonlinear coupling element; and

[0084] - In this case, the nonlinear coupling element may further be configured to perform additional wave mixing on photons of two photons at a frequency ω a of one photon at a frequency ω b and a fourth electromagnetic wave at a frequency 2ω a + ω b to cause the frequency ω aTwo photons of which are exchanged with photons of frequency ω b The coupling device is further configured to couple a fifth electromagnetic wave of frequency (2n'+1)ω a +ω b -ω c to the nonlinear coupling element, where n' is a strictly negative integer, and the nonlinear coupling element is further configured to perform another additional wave mixing regarding an odd number of photons of frequency ω a in the cat resonator, one or several photons of frequency ω b in the buffer resonator, one or several photons of frequency ω c in the loss mode, and one or several photons of frequency (2n'+1)ω a +ω b -ω c of the fifth electromagnetic wave, wherein, while resetting the buffer resonator to vacuum, an odd number of photons are added to the cat resonator;

[0085] - The cat qubit resonator is a squeezed cat qubit resonator, and wherein the method includes coupling a fourth electromagnetic wave of frequency 2ω a +ω b to the nonlinear coupling element; and

[0086] - A generator for the fourth electromagnetic wave of frequency 2ω a +ω b and a generator for the fifth electromagnetic wave of frequency (2n'+1)ω a +ω b -ω c can be a microwave generator - all or only part of it - and the nonlinear coupling element can include a capacitive coupling element that couples the cat qubit resonator to the buffer resonator;

[0087] - The coupling device can include an inductive coupling device configured to couple a second electromagnetic wave of frequency 2ω a -ω b to the nonlinear coupling element;

[0088] - The nonlinear coupling element can include an asymmetric threaded superconducting quantum interference device (ATS), or a superconducting nonlinear asymmetric inductive element (SNAIL), or a transmon device as a coupler, or possibly any other nonlinear component, such as the superconducting nanowire mentioned in Ku, 2010.

[0089] For method and process features,

[0090] - The (2n + 4) wave mixing can be the second four-wave mixing (n = 0);

[0091] - Additional wave mixing can be performed in the nonlinear coupling element for two photons with frequency ω a , one photon with frequency ω b , and a photon of a fourth electromagnetic wave with frequency 2ω a + ω b to jointly obtain two photons with frequency ω a in the cat qubit resonator and a photon with frequency ω b , and exchange them with a photon of the fourth electromagnetic wave. A fifth electromagnetic wave with frequency (2n’ + 1)ω a + ω b - ω c is also coupled to the nonlinear coupling element, where n’ is a strictly negative integer, and another additional wave mixing is performed in the nonlinear coupling element (30) for -(2n’ + 1) photons with frequency ω a in the cat resonator, one photon with frequency ω b in the buffer resonator, one photon with frequency ω c in the loss mode, and a photon with frequency (2n’ + 1)ω a + ω b - ω c of the fifth electromagnetic wave;

[0092] - In particular, n’ = -1 and / or n = 0 are possible.

[0093] Several of the described processes can occur simultaneously. In particular, (2n + 4) wave mixing can occur simultaneously for several values of n.

[0094] In the present disclosure, microwaves are considered to be waves between 300 MHz and 300 GHz, or, subsidiarily, microwaves are considered to be waves between 1 and 30 GHz. The present invention can also use radio frequencies or high frequencies outside these ranges. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Additional features and advantages of the present invention will become apparent by reference to the following detailed description of exemplary embodiments and from the figures, wherein:

[0096] Figure 1 is a general schematic diagram of the present invention.

[0097] Figure 2 and Figure 3 are lumped element models of a photon dissipation-limited cat qubit setup with associated dissipation devices according to an embodiment of the present invention, where a phase flip reduction method is performed and ATS is used.

[0098] Figure 4 and Figure 9is a lumped element model of a photon dissipation-limited cat qubit setup with associated dissipation devices according to two further embodiments of the invention, in which the phase flip reduction method is also carried out. These two embodiments use a SNAIL and a transmon, respectively, as the non-linear coupler.

[0099] Figure 5 and Figure 6 are models of the same cat qubit setup (exemplary embodiments using an ATS and a SNAIL, respectively), but the phase flip reduction method is not carried out.

[0100] Figure 7 and Figure 8 show models of the same cat qubit setup, but the cat is squeezed and the phase flip reduction method is carried out. These exemplary embodiments use an ATS and a SNAIL, respectively.

[0101] Figure 9 has been mentioned above.

[0102] Figure 10 shows the effect of the invention in the context of a single qubit Z gate.

[0103] Figure 11 shows the effect of the invention in the context of a two qubit CNOT gate. Detailed Description

[0104] Physical description

[0105] In the described embodiments, the invention is based on the physical implementation of a photon dissipation-limited cat qubit based on two resonators and a non-linear coupling element, and additional features for dissipation are introduced.

[0106] Thus, the standard cat qubit is stabilized in a high-quality harmonic oscillator mode labeled A and coupled to an oscillator mode labeled B via a two-photon exchanger TPE.

[0107] Additionally, the associated dissipation device CDD performs joint (or correlated) dissipation on the photons in modes A and B.

[0108] Figure 1 Figure 1 This setup is represented in . The harmonic oscillator mode A is associated with the photon annihilation operator labeled a and the photon creation operator labeled and the oscillator mode B is associated with the photon annihilation operator b and the photon creation operator labeled

[0109] ​​In this figure, mode A is coupled to mode B in two ways. First, the two-photon exchanger TPE converts pairs of photons from mode A into single photons of mode B and vice versa. This exchanger performs so-called "four-wave mixing", where the "four" represents the three photons involved in the exchange and one photon from an external pump with an adjustable frequency.

[0110] Second, the correlated dissipative device CDD can achieve the correlated dissipation of photons in A and B, and the required joint dissipation Q(a)b is in the form as Figure 1 shown, or more generally Q(a, a+)b.

[0111] Therefore, the dissipator used in the present invention is:

[0112] Dissipator[Q(a,a + )b](ρ).

[0113] ρ is the density matrix of the cat qubit, where the total power of the a operator and the a + operator must be odd.

[0114] When this dissipator annihilates photons in B, it always jointly changes an odd number of photons in A.

[0115] Where α is the complex amplitude of the coherent state of the cat qubit harmonic oscillator (the eigenstate of the a operator), the resulting equation is the equation for the coupled Hamiltonian used to model TPE:

[0116] H 耦合 =(a 2 -α 2 )b + +(a 2 -α 2 )+b

[0117] For the evolution of ρ, the density matrix of the cat qubit is:

[0118] d / dtρ=-i[H 耦合 , ρ]+Dissipator[Q(a,a + )b](ρ).

[0119] The result of the two couplings is that two photons in A are converted into a single photon in B, and then this photon dissipates, but it has an impact on A, and the exact impact is determined by the choice of Q. Therefore, the joint dissipation changes how the system converges back to the subspace of its stable state when perturbed.

[0120] The operator Q(a, a + ) realizes autonomous feedback: whenever the buffer mode B passes through H 耦合When a deviation is detected, the subsequent relaxation of B triggers the Q() action on mode A without any external intervention such as measurement and feedback actions.

[0121] Figure 1 The implementation is characterized by Q(a)=a, which means that one photon in mode A co-annihilates with one photon in mode B, but in an alternative implementation, any polynomial of odd powers of a and a + can be used for Q.

[0122] The physical mechanism used is wave mixing, where one photon of each type is involved, but if other processes involving more photons are involved, as long as the number of photons exchanged with the cat resonator is odd, the setup can also work. If Q(a)=a and assuming other waves operate normally, this is four-wave mixing, and more generally, when Q corresponds to the annihilation of (2n + 1) photons in mode A, this is (2n + 4)-wave mixing.

[0123] Regarding the implementation, the proposed dissipation has a low enough complexity to meet the standard dissipation design capabilities of devices for designing cat qubits.

[0124] The second implementation uses a squeezed cat. If a higher squeezing effect is required, the stability of the squeezed cat qubit involves replacing a with S(a) in H 耦合 and a linear combination of a and a + that has similar coefficients for a and a + .

[0125] The dissipator Dissipator[Q(a)b] is also replaced by Dissipator[S(a)b], or more generally by Dissipator[Q(S(a))b] where Q is a polynomial of odd powers.

[0126] Again, as in the non-squeezed setup, the erroneous phase flips typically associated with actuation that cause departure from the cat's stable state subspace are reversed by precisely subtracting or adding one photon when jumping back into the cat qubit space.

[0127] However, this implementation based on the squeezed cat has an important additional benefit. In fact, unlike the standard cat, the squeezed cat leaves the stable state cat qubit space under the action of spontaneous single-photon loss, which is the main error source in the absence of any operations. Therefore, this scheme also automatically reverses the phase flips associated with self-emitted photon loss.

[0128] Practical implementation

[0129] As previously mentioned, the present invention is based on the physical implementation of a photonic dissipation-limited cat qubit based on two resonators and a non-linear coupling element, namely referred to as ATS in one example. Using superconducting circuits, such a device can be designed in different ways.

[0130] Figure 2 In Figures 2 to 9 , the cat qubit resonator 10 is modeled by a resonant LC oscillator, i.e., an inductor and a capacitor mounted in parallel with each other. It is a cat qubit electromagnetic resonator having a resonant frequency as the first resonant frequency ω a . It is also an oscillator of mode A, as Figure 1 shown and discussed with respect to the Figure 1 .

[0131] Figure 2 The following elements are represented in

[0132] - 10: Cat qubit (a) resonator

[0133] - 20: Buffer mode (b) resonator

[0134] - 41: Dissipation mode (c) resonator

[0135] - 30: Non-linear coupling element capable of mixing 4, 6, 8 waves or more waves (mixing an even number of waves)

[0136] - 40: Dissipation device having at least one loss mode

[0137] - 35, 45: Capacitive or inductive coupling element

[0138] - 50: Microwave coupling device

[0139] - 55: ω b Frequency drive (microwave drive)

[0140] - 60: RF pump (the frequency and amplitude of the RF pump are different from the frequency and amplitude of the microwave driver 55)

[0141] - 65: 2ω a - ω b Frequency pump

[0142] - 66: 2ω a + ω b Frequency pump (for squeezing the cat)

[0143] - 75: (2n + 1)ω a + ω b - ω c Frequency pump

[0144] ​-76: (2n’ + 1)ω a + ω b -ωc frequency pump (for squeezing the cat).

[0145] Figure 3 Also as Figure 3 shown, the buffer resonator 20 is shown modeled as a resonant LC oscillator, although it can behave as a non-harmonic oscillator. It is a buffer electromagnetic resonator having a resonant frequency as the second resonant frequency ω b which is different from the first resonant frequency. It is also an oscillator in mode B, as b shown and discussed above with respect to Figure 1 the Figure 1 .

[0146] For the physical design of the TPE Hamiltonian, a coupling element between the cat qubit mode (A) and the buffer mode (B) is needed. This is accomplished by the ATS 30, which consists of two Josephson junctions and has two current loops, and the ATS 30 is capacitively coupled to the cat qubit resonator 10 by the capacitive coupling 35. The ATS 30 supports mode B. The ATS 30 embodies the TPE discussed above with respect to Figure 1 .

[0147] In addition, the dissipative oscillator 40 is capacitively coupled to the ATS 30 by the capacitive coupling 45. The dissipative oscillator 40 is in mode C. In the example shown, the dissipative oscillator 40 consists of a resonant LC oscillator coupled to a transmission line, but similar to mode B, the dissipative oscillator 40 can also be a non-harmonic oscillator, and its dissipation can be embodied in any way. The dissipative oscillator 40 has a loss mode having a resonant frequency ω c which is different from ω c and ω a . It is associated with the photon annihilation operator c and the photon creation operator labeled b .

[0148] The coupling Hamiltonian for modeling the CDD is:

[0149] H associated with Dissipator[c] 耦合2 = Q(a, a + )bc + +(Q(a, a + )b) + c

[0150] The ATS 30 and the dissipative oscillator 40 embody the CDD discussed with respect to Figure 1 . ​​

[0151] The third oscillator C has significant losses because it is coupled, for example, to a waveguide.

[0152] The device further includes coupling means 50 for coupling a first electromagnetic wave of frequency ω b to the ATS 30 and the resonators 10 and 20 by inductive or capacitive means. This may include a waveguide and a capacitor or (cross) inductor, embodied by a printed circuit designed to have waveguide effects, and receiving the wave via a coaxial cable. The device further includes the following system, or is included in the following system, which includes a generator 55 for the first electromagnetic wave of frequency ω b

[0153] The device further includes inductive coupling means 60 for coupling a second electromagnetic wave of frequency 2ω a -ω b to the non-linear coupling element ATS 30; a magnetic field is required in each of the two loops of the ATS. To this end, the inductive coupling means 60 generates a magnetic field in the first loop through a first part of the inductive coupling means 60, while a second part of the inductive coupling means 60 generates a second magnetic field in the second loop of the ATS, and these two fields generate different magnetic fluxes in these loops. The inductive coupling means 60 is also used to couple a third electromagnetic wave of frequency (2n + 1)ω a +ω b -ω c to the non-linear coupling element ATS 30. The device further includes the following system, or is included in the following system, which includes a generator 65 for the second electromagnetic wave and a generator 75 for the third electromagnetic wave.

[0154] The TPE embodied by the ATS 30 performs four-wave mixing between the energy received from the resonator 10 (two photons of frequency ω a ), the energy received from the resonator 20 (one photon of frequency ω b ), and the wave received from the generator 65 (one photon of frequency 2ω a -ω b ).

[0155] The CDD embodied by the ATS 30 and the dissipative oscillator 40 performs wave mixing, such as four-wave mixing, between the energy received from the resonator 10 (2n + 1 photons of frequency ω a ), the energy received from the resonator 20 (one photon of frequency ωb), one photon of frequency ω c of the loss mode, and one photon of frequency (2n + 1)ω a +ω b -ω c of the electromagnetic wave generated by the generator 65.​Figures 3 to 5 Shows three operating points of the same circuit.

[0156] In Figure 3 , the circuit designs Dissipator[a b](ρ), and two - photon exchange between mode A and mode B, H 耦合 . This is a parity - switching setting because the parity of the number of photons in A is not conserved.

[0157] Therefore, the frequency of the second electromagnetic wave is 2ω a - ω b , and the frequency of the third electromagnetic wave is (2n + 1)ω a + ω b - ω c .

[0158] Figure 4 In Figure 4 , an embodiment similar to that of Figure 3 is shown, but SNAIL is used instead of ATS. Frattini, 2018 is the article that mentions this SNAIL. Figure 3 The ATS 30 in

[0159] Figure 5 In Figure 5 , the circuit designs Dissipator[b](ρ) and the same two - photon exchange, and this is a parity - preserving setting.

[0160] In fact, in a standard cat qubit, it is possible to consider implementing the present invention only during certain gate operations and otherwise maintaining standard dissipation.

[0161] This dissipator is designed for a conventional cat qubit, so this setting shows how to turn off the parity - switching device while maintaining the same circuit layout. In fact, this setting change can be performed by turning on and off various wave sources.

[0162] Therefore, the frequency of the second electromagnetic wave remains 2ω a - ω b , and the frequency of the third electromagnetic wave is ω b - ω c .

[0163] Figure 6 In Figure 6 , an embodiment similar to that of Figure 5 is shown, but SNAIL is used instead of ATS.

[0164] Figure 7 In Figure 7 ​​​​In it, the circuit design Dissipator[S(a)b](ρ) is for the parity switching setting of squeezing the cat state.

[0165] Therefore, the frequency of the second electromagnetic wave is 2ω a -ω b , and the frequency of the third electromagnetic wave is (2n + 1)ω a +ω b -ω c . However, there is also a fourth electromagnetic wave with a frequency of 2ω a +ω b coupled to the nonlinear coupling element ATS 30 through the inductive coupling device 60, and a fifth electromagnetic wave with a frequency of (2n'+1)ω a +ω b -ω c coupled to the nonlinear coupling element ATS 30 through the inductive coupling device 60, where n' is a strictly negative integer. These waves are generated by the generators 65 and 75 respectively, or by other generators or generator components.

[0166] Similarly, a parity-preserving setting can be designed for squeezing the cat, so it can be an option when the gate is not executed; however, it is not shown.

[0167] Figure 8 In Figure 8 , an embodiment similar to that of Figure 7 is shown, but SNAIL is used instead of ATS.

[0168] Figure 9 Figure 9 shows an embodiment similar to those of Figure 3 and Figure 4 , but a transmon coupler is used instead of ATS or SNAIL. Leghtas, 2015 discloses an experimental implementation of a cat qubit using a transmon coupler as depicted in Figure 9 .

[0169] Figure 10 Figure 10 shows the gate error (gray) of the Z gate with the autonomous feedback design of the present invention at K ab / |α| 2 = 8g2, and the gate error (black) of the Z gate with a conventional design at K b = 8g2.

[0170] Left: Fixed cat size, |α| 2 = 8.

[0171] Right: Fixed gate time, T = 10 / g2.​​​​​

[0172] Figure 10 Shows the errors for both phase flips and bit flips for a conventional gate and for the associated dissipator of the present invention caused by the Z gate. For the phase flip error, an improvement with a constant factor of approximately μ≈0.02 was found, independent of the gate time and the cat size.

[0173] Figure 11 Figure 11 Shows the gate error of a CNOT gate with the self-feedback design of the present invention at K ab / |α| 2 = 8g2, and the gate error of a CNOT gate with a conventional design at K b = 8g2 (black).

[0174] Left: Fixed cat size, |α| 2 = 8.

[0175] Right: Fixed gate time, T = 10 / g2.

[0176] The dashed gray line represents the non-adiabatic phase error.

[0177] Figure 11 This setup of the two-qubit CNOT gate was studied. The associated dissipator of the present invention was activated on the control qubit. Here, the performance is similar to that of a single-qubit Z gate, where the phase fidelity is improved by 1 / μ≈50.

[0178] The microwave pump passing through the loop of the nonlinear circuit element can be modified by real-time settings.

[0179] In other embodiments, the mode C employs a transmon qubit or another nonlinear resonator design.

[0180] Additional features may be present in the embodiments of the present invention.

[0181] In particular, for logic gate implementations, an additional feedforward Hamiltonian can be used as an optional feature to better preserve quantum information.

[0182] The present invention has been described by way of exemplary embodiments. In particular, for n = 0, and for the squeezed cat, n = 0 and n' = -1, and Q(a) = a. Other values of n can also be used, provided that n is a non-negative integer; n can be any positive integer, including 0. The value of n is determined by the way the circuit is constructed, and in particular by the nonlinear order of the ATS or any nonlinear coupling element replacing the ATS. Other values of n' can also be used, provided that n' is a negative integer, different from 0. And Q can be a polynomial of odd powers of a and a + and a†. ​​

[0183] The oscillator 40 can be non-harmonic, up to qubits made from non-harmonic oscillators. It can also be absent, where the transmission line is directly coupled to the resonators 10 and 20 in a specific way, thus causing their joint dissipation as required by the present invention.

[0184] In addition, mode B can be harmonic or can also be non-harmonic.

[0185] Bibliography

[0186] Mirrahimi, 2014: Mirrahimi et al., New J. Physics, 16, 045014, 2014

[0187] Lescanne, 2020: Lescanne et al., Nature Physics, 16, 509, 2020

[0188] Chamberland, 2020: Chamberland et al. arXiv:2012.04108, 2020

[0189] Guillaud, 2019: Guillaud et al., Physical Review X 9(4), 041053, 2019

[0190] Puri, 2017: Puri et al., npj Quantum Information, 3, 18, 2017

[0191] Grimm, 2020: Grimm et al., Nature, 584, 205, 2020

[0192] Gautier, 2022: Gautier et al., PRX Quantum 3, 020339, 2022

[0193] Xu, 2022 - 1: Xu et al., Phys. Rev. Res. 4, 013082, 2022

[0194] Carde, 2021: Carde et al., Master of Sciences thesis, Inria Quantic & ENS Paris, 2021

[0195] Schlegel, 2022: Schlegel et al., arXiv:2201.02570, 2022

[0196] Xu, 2022-2: Xu et al., arXiv:2210.13406, 10 / 2022

[0197] Albert, 2019: Albert et al., Quantum Science and Technology 4, 035007, 2019

[0198] Ofek, 2016: Ofek et al., Nature 536, 441–445, 2016

[0199] Mabuchi, 2008: Mabuchi, Phys. Rev. A78, 032323, 2008

[0200] James and Gough, 2010: James and Gough in IEEE Transactions on Automatic Control, vol. 55, no. 8, pp. 1806-1821, 2010

[0201] Leghtas, 2015: Leghtas et al., Science, 347.6224(2015): 853-857

[0202] Frattini, 2018: Frattini et al., Physical Review Applied 10.5(2018): 054020

[0203] Ku, 2010: J. Ku, et al. Phys. Rev. B 82, 134518–13 October 2010。

Claims

1. An electronic device for storing quantum information, the electronic device comprising: - Cat qubit electromagnetic resonator (10), the cat qubit electromagnetic resonator having a first resonance frequency ω a ; - A buffer electromagnetic resonator (20) having a second resonance frequency ω b , said second resonance frequency ω b being different from the first resonance frequency; - A non-linear coupling element (30) that couples the cat qubit resonator (10) to the buffer resonator (20); - configured to couple a first electromagnetic wave having a frequency of ω b to the nonlinear coupling element (30), and a coupling device (50) configured to couple a second electromagnetic wave having a frequency of 2ω a - ω b to the nonlinear coupling element (30); And - A dissipative device (40) that is coupled to the cat qubit resonator (10) and to the buffer resonator (20) through the non-linear coupling element (30); wherein the non-linear coupling element (30) is configured to perform four-wave mixing on photons of two photons with frequency ω a , one photon with frequency ω b and photons of the second electromagnetic wave with frequency 2ω a - ω b such that two photons with frequency ω a in the cat qubit resonator (10) are exchanged with a photon with frequency ω b , characterized in that the coupling device (60) is further configured to couple a third electromagnetic wave with frequency (2n + 1)ω a + ω b - ω c to the non-linear coupling element (30), where ω c is the resonance frequency of the loss mode of the dissipative device (40) and ω c is different from ω a and ω b , and n is a non-negative integer, and wherein the non-linear coupling element (30) is further configured to perform (2n + 4)-wave mixing on (2n + 1) photons with frequency ω a in the cat qubit resonator (10), one photon with frequency ω b , one photon with the frequency ω c of the loss mode, and one photon with frequency (2n + 1)ω a + ω b - ω c of the third electromagnetic wave, and the (2n + 4)-wave mixing causes an odd number of positive photons in the cat qubit resonator (10) to be dissipated through the dissipative device in association with a photon in the buffer resonator (20).

2. The electronic device according to claim 1, wherein, Another dissipative device (40) includes a third electromagnetic resonator that resonates at a frequency ω c and is coupled to a transmission line.

3. The electronic device according to claim 1, wherein, The buffer resonator (20) and / or an additional dissipative device (40) includes a non-linear resonator.

4. The electronic device according to any one of claims 1 to 3, wherein, The cat qubit resonator (10), the buffer resonator (20), and the dissipative device (30) are constructed as a superconducting circuit.

5. The electronic device according to any one of claims 1 to 4, wherein the electronic device further comprises a generator (55) for a first electromagnetic wave having a frequency of ω b and a generator (65) for a second electromagnetic wave having a frequency of 2ω a - ω b and a generator (75) for a third electromagnetic wave having a frequency of (2n + 1)ω a + ω b - ω c .

6. The electronic device according to claim 5, wherein, for the first electromagnetic wave having a frequency of ω b and for the second electromagnetic wave having a frequency of 2ω a -ω b and for the third electromagnetic wave having a frequency of (2n + 1)ω a +ω b -ω c the generators (55, 65, 75) are microwave generators.

7. The electronic device according to any one of claims 1 to 6, wherein, The cat qubit resonator (10) is a squeezed cat qubit resonator, and wherein the coupling device (60) is further configured to couple a fourth electromagnetic wave having a frequency of 2ω a +ω b to the nonlinear coupling element (30); and wherein the non-linear coupling element (30) is further configured to perform additional wave mixing on two photons with frequency ω a , one photon with frequency ω b , and a fourth electromagnetic wave photon with frequency 2ω a +ω b to exchange two photons with frequency ω a in the cat qubit resonator (10) with a photon with frequency ω b . The coupling device (60) is further configured to couple a fifth electromagnetic wave with frequency (2n'+1)ω a +ω b -ω c to the non-linear coupling element (30), where n' is a strictly negative integer. The non-linear coupling element is further configured to perform yet another additional wave mixing on -(2n'+1) photons with frequency ω a in the cat resonator, one photon with frequency ω b in the buffer resonator, one photon with frequency ω c in the loss mode, and one photon with frequency (2n'+1)ω a +ω b -ω c of the fifth electromagnetic wave.

8. The electronic device according to any one of claims 1 to 7, wherein, The non-linear coupling element (30) includes a capacitive coupling element (35) that couples the cat qubit resonator (10) to the buffer resonator (20).

9. The electronic device according to any one of claims 1 to 8, wherein, The coupling device (60) includes an inductive coupling device configured to couple a second electromagnetic wave having a frequency of 2ω a - ω b to the nonlinear coupling element (30).

10. The electronic device according to any one of claims 1 to 9, wherein, The non-linear coupling element (30) includes an asymmetric threaded superconducting quantum interference device, or a superconducting non-linear asymmetric inductive element parametric amplifier.

11. A method for storing quantum information, the method comprising: - Coupling a cat qubit electromagnetic resonator having a first resonant frequency ω a to a buffer electromagnetic resonator having a second resonant frequency ω b using a non - linear coupling element, where the second resonant frequency ω b is different from the first resonant frequency; -Couple a first electromagnetic wave with a frequency of ω b and a second electromagnetic wave with a frequency of 2ω a -ω b to the nonlinear coupling element; And - Coupling a dissipative device to the cat qubit resonator and to the buffer resonator through the non-linear coupling element; Wherein, the method for storing information further includes performing four-wave mixing using the non-linear coupling element on two photons with a frequency of ω a one photon with a frequency of ω b and a photon of the second electromagnetic wave with a frequency of 2ω a -ω b so that two photons with a frequency of ω a in the cat qubit resonator are exchanged with a photon with a frequency of ω b . It is characterized in that the method for storing information further includes coupling a third electromagnetic wave with a frequency of (2n + 1)ω a +ω b -ω c to the non-linear coupling element, where ω c is the resonance frequency of the loss mode of the dissipation device and ω c is different from ω a and ω b , and n is a non-negative integer; and wherein, the method for storing information further includes performing (2n + 4)-wave mixing using the non-linear coupling element on (2n + 1) photons with a frequency of ω a in the cat resonator, one photon with a frequency of ω b , one photon with a frequency of ω c of the loss mode, and one photon with a frequency of (2n + 1)ω a +ω b -ω c of the third electromagnetic wave. The (2n + 4)-wave mixing causes an odd number of photons in the cat qubit resonator to dissipate through the dissipation device in correlation with one photon in the buffer resonator.

12. The method for storing quantum information according to claim 11, wherein, The (2n + 4)-wave mixing is second four-wave mixing.

13. The method for storing quantum information according to claim 11 or claim 12, wherein, The cat qubit resonator (10) is a squeezed cat qubit resonator, and wherein the method includes coupling a fourth electromagnetic wave having a frequency of 2ω a +ω b to the nonlinear coupling element (30); and wherein, in the non-linear coupling element (30), additional wave mixing is performed on two photons with a frequency of ω a , one photon with a frequency of ω b , and photons of the fourth electromagnetic wave with a frequency of 2ω a +ω b so that two photons with a frequency of ω a in the cat qubit resonator (10) are exchanged with photons with a frequency of ω b . The fifth electromagnetic wave with a frequency of (2n'+1)ω a +ω b -ω c is also coupled to the non-linear coupling element (30), where n' is a strictly negative integer, and in the non-linear coupling element (30), additional wave mixing is performed on -(2n'+1) photons with a frequency of ω a in the cat resonator, one photon with a frequency of ω b in the buffer resonator, one photon with a frequency of ω c in the loss mode, and one photon with a frequency of (2n'+1)ω a +ω b -ω c of the fifth electromagnetic wave.

14. The method for storing quantum information according to claim 13, wherein, n’＝-1。

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