Apparatus and method for reducing cat qubit phase flips

Abstract

An electronic device for storing quantum information is -resonant frequency ω a a cat qubit electromagnetic resonator (10) having -resonant frequency ω b a buffer electromagnetic resonator (20); - a nonlinear coupling element (30), and a frequency ω b Coupling means for coupling electromagnetic waves of frequency 2ω a -ω b a coupling means for coupling the electromagnetic waves; a dissipation device (40) coupled to the cat qubit resonator (10) and the buffer resonator (20) via a nonlinear coupling element (30); It is equipped with: -frequency ω a Two photons of frequency ω b and one photon of frequency 2ω a -ω b Four-wave mixing occurs, involving one photon of the electromagnetic wave. The coupling means (60) has a frequency (2n+1)ω a +ω b -ω c and further configured to couple a third electromagnetic wave of ω c is the resonant frequency of the lossy mode, and n is an integer.

Description

[Technical Field]

[0001] The present invention is in the field of quantum information processing and quantum computing. The present invention relates to an apparatus and method for storing and / or processing quantum information in the form of quantum confined cat qubits while reducing first-order phase reversal errors. The apparatus and method apply to all such confined cat qubits, and in particular to compressed cat qubits. The apparatus and method are based on a pattern of feedback from the cat qubits, where the cat qubits provide such feedback autonomously.

[0002] Quantum computing is an emerging field at the intersection of physics, mathematics, and computer science. Quantum computing is based on building circuits that manipulate qubits, the basic units of quantum information, which are fundamental two-state quantum mechanical systems. The circuits can be electronic or based on photons, atoms, or trapped ions. The properties of qubits allow them to be in a superposition of two states simultaneously. In a quantum computer, quantum logic gates, or quantum gates, are operations on a small number of qubits and are the building blocks for larger quantum computations.

[0003] Quantum computers exploit quantum properties such as superposition, interference, and entanglement to solve certain complex computational problems more easily and faster than non-quantum computers. [Background technology]

[0004] (Physical means used to build circuits - cat qubits and their characteristics) There are several approaches to creating quantum computer qubits and gates, one of which is based on superconducting circuits cooled to a few millikelvins (mK).

[0005] In the field of superconducting circuits, it is known to encode data using anharmonic oscillators, consisting of Josephson junctions connected in parallel with capacitance. These circuits are called transmon qubits, where transmon stands for "transmission line shunt plasma oscillation." Anharmonicity allows energy levels to be separated by non-identical energy differences, so that only the transitions between two distinct levels |0> and |1> can be activated in a controlled manner with a signal of a given frequency.

[0006] However, a later and highly useful approach utilizes harmonic LC oscillators, i.e., an electrical circuit consisting of an inductor L and a capacitor C, which function as an electrical resonator. This refers to a system in a quantum superposition of classical-like states, common in non-quantum (i.e., classical) models, encoding information as Schrödinger's cat states. So-called cat qubits typically use quantum superpositions of coherent states with equal weights and opposite phases, for example. More generally, such information can be encoded in so-called bosonic modes, creating bosonic codes or continuously variable codes. This is typically realized in photons, but is also possible with other types of oscillators on photons and other physical platforms. This approach was first developed in a collaboration between the applicant and Yale University and is being pursued by several academic institutions and private companies. In general, bosonic codes exploit redundancy to reduce the impact of physical errors on the encoded logical information, without the need for active monitoring, due to the high dimensionality of harmonic oscillators. This is one of the reasons why bosonic codes are so attractive.

[0007] Cat qubits are interesting because, as qubits with a noise bias, the effects of physical errors are reduced: one of the two fundamental errors that can occur in a qubit, bit flips and phase flips, is suppressed exponentially 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 grows linearly, offering attractive scaling. In the context of quantum error correcting codes, qubits with an exponential error bias can dramatically reduce the required overhead, i.e., the number of physical qubits per logical qubit, to reach a satisfactory or given level of information protection.

[0008] However, it is important to keep the rate of unprotected types of errors—those between bit flips and phase flips that are not exponentially suppressed by a single cat qubit—as low as possible. Indeed, quantum error-correcting codes are only efficient if these errors, regardless of their type, are below a certain threshold compared to the error correction period. Furthermore, even below the threshold, the higher the error rate, the more overhead the code requires. Even if the overhead is lower for cat qubits than for qubits without noise bias, it still represents a significant complexity in terms of practical construction and the operation of logical operations on the encoded information.

[0009] The present invention describes the situation where the bits are of the exponentially protected type of quantum information and the phase is of the exponentially unsuppressed type of quantum information, but it can also be applied to the reverse situation.

[0010] (confinement to code space) In quantum processors, the confinement into a two-dimensional code space necessary for the operation of quantum bits, which are essentially multi-valued systems, has been experimentally demonstrated with cat qubits.

[0011] Two methods are known to confine the state 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 on engineered two-photon dissipation and the self-Kerr nonlinearity of the junction in the Hamiltonian of the harmonic oscillator, respectively.

[0012] The first method (dissipation-based), disclosed in Mirrahimi, 2014, and Lescanne, 2020, is based on a confinement scheme resulting from engineered two-photon dissipation, confining the dynamics to only two steady states (the cat qubit computational states) in an ideal system. Bit flips are exponentially suppressed. This confinement is achieved by a nonlinear superconducting circuit element called an Assymetrically Threaded Superconducting Quantum Interference Device, or Assymetrically Threaded SQUID, or ATS, as disclosed in U.S. Pat. No. 11,302,856. It can also be achieved using other such elements, such as the Superconducting Nonlinear Asymmetric Inductive Elements parametric amplifier, or SNAIL, as disclosed by Fratini et al. in Phys. Rev. Applied (2018) and U.S. Patent Publication No. 2021 / 0021245. Alternatively, it can be realized using transmons as nonlinear circuit elements (see Leghtas et al., Science (2015)). A cat qubit encoded in a linear resonator is coupled to a buffer mode using this nonlinear circuit element, which is highly dissipative and decays in energy much faster than the lifetime of the cat qubit. The buffer mode does not need to be harmonic, since only its two lowest states are essential for device operation. In a paper by Chamberland, 2020, the authors further propose coupling a single buffer mode to multiple cat qubits, rather than using a buffer mode for each cat qubit. More precisely, in this dissipative approach, a two-photon-to-one-photon exchange Hamiltonian is designed via a nonlinear circuit element between the cat qubit mode and the short-lived buffer mode, respectively, in the rotational frame of both modes.

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[0013] Methods for performing single-qubit Z rotations, two-qubit CNOT gates, also called CX gates, and three-qubit CCNOT gates, also called CCX or Toffoli gates, on such dissipative Cat qubits are described in Guillaud, 2019.

[0014] The feedforward Hamiltonian, which simultaneously "pushes" the state of the system, is used in synergy with two-photon dissipation, which is said to "pull" the state of the system. In practice, the dissipation term remains implemented using coupling with the buffer mode via a nonlinear circuit element. The feedforward term in the Z gate is simply a standard drive on the Cat qubit mode, while the feedforward term in the CNOT and CCNOT gates can be implemented via a driving nonlinear coupling between the Cat modes involved.

[0015] The second method to confine the cat qubit state is pure Hamiltonian confinement based on two-photon drive and the Kerr nonlinearity, as disclosed in Puri, 2017 and Grimm, 2020. This approach is called the Kerr cat qubit. In the rotating frame of the cat qubit mode, it can be modeled by the following Hamiltonian:

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[0016] In these confinement schemes, improved mechanisms to reduce gate-induced phase errors are disclosed in Gautier, 2022 and Xu, 2022-1 through two-photon dissipation or Kerr-cat qubit approaches.

[0017] The present invention is based on a dissipative confinement setup.

[0018] (Phase reversal, especially gate-induced phase error) Furthermore, phase reversals, also known as phase errors, are of particular interest to the present invention, the two main causes of which are briefly described below.

[0019] The first source of phase error is the natural decoherence mechanism due to spontaneous single-photon loss. This is the dominant perturbation acting on an idle harmonic oscillator. Its effect on the information bit is well-cancelled by the confinement of the cat. Its effect on the phase bit is that the logic value flips with each photon loss. Thus, two consecutive losses revert the logic value to its original value. However, with just one cat qubit, there is no way to measure how many photon losses have occurred without destroying the information bit, so over time, the uncertainty about how many photon losses have occurred and therefore what the encoded phase value was grows.

[0020] The second source of phase error appears when applying certain logical operations to the cat qubit through gates. Indeed, the displacement Hamiltonian H gate =u(t)(a+a + ) only leads to imperfect phase control. The phase shifts by a well-controlled amount, but is inevitably smeared because the physics cannot precisely align with the cat qubit code space. This leads to further phase-flipping errors, since while the transient displacement from the cat qubit subspace is offset by two-photon dissipation, it is still an unprotected part of the encoded quantum information.

[0021] Although techniques exist to mitigate this effect, it is difficult to completely suppress it. In particular, this effect worsens with faster gates, including the CNOT gates that are actually used for phase error correction. Although improved mechanisms to reduce gate-induced phase errors were recently proposed in Gautier, 2022 and Xu, 2022-1, further phase protection mechanisms are of interest to reach a satisfactory combination of speed and accuracy in quantum computing.

[0022] (Squeezed Cats and other cats - a short comparison with the standard cat qubit) A variant of the cat qubit, termed "squeezed cats," is known, which is realized by a superposition of squeezed coherent states, which has a less complex confinement mechanism than the standard cat qubit. The present invention also applies to these particular cat qubits.

[0023] In a standard cat qubit, the dominant perturbation mechanism, spontaneous photon loss, is undetectable because it causes a phase inversion while remaining within code space. Unlike a standard cat qubit, spontaneous photon loss in a squeezed cat is detectable in principle because it displaces the state outside code space. Moreover, it is still the dominant error source causing the phase inversion of the quantum information. Therefore, detecting and correcting this part of the error process is conceivable and highly useful. The reduction of the squeezed cat phase error due to this observation is discussed in Carde, 2021, Schlegel, 2022, and Xu, 2022-2.

[0024] In other non-squeezed-cat types of encoding of quantum information, such as cats containing multiple harmonic oscillators (Albert, 2019) or cats containing two or more coherent state components (Ofek, 2016), the spontaneous loss of a photon displaces the quantum state out of code space, as in squeezed cats, and thus could in principle be detected by well-adapted measurements. However, this "displacement" takes a more specialized form than the perturbations discussed above for two-component (squeezed or non-squeezed) cats. These are not addressed in this invention, and comparable proposals for such cat types appear to be currently unknown.

[0025] Displacement of the two components (squeezed or unsqueezed) of the Cat qubit from code space induces a response in the buffer mode displaced from vacuum. The intentionally created strong dissipation of the buffer mode quickly induces photon loss due to the buffer mode as the Cat qubit mode mimics its return to code space. Because this is a designed process, it is in principle possible to detect the photon lost by the buffer mode, thereby detecting when the Cat qubit mode has deviated from code space and consequently applying corrective action to the Cat qubit phase. However, based on currently available technology, methods for repeatedly measuring and correcting photons lost by the buffer mode, such as those proposed by Carde, 2021 and Schlegel, 2022, do not seem very promising in practice.

[0026] (Autonomous feedback and measurement-based feedback) Indeed, implementing a phase correction operation based on an actual quantum measurement followed by a correction operation would likely involve very complex and inefficient physics. In particular, measurement devices typically have a "detection efficiency" of a few tens of percent, which translates directly into the same inefficiency for feedback correction of the phase error, at least in the context of dissipative confinement. Furthermore, there are decoupling complexities involved in sending signals back and forth from the quantum computer to a classical computer. Therefore, measurement-based feedback is not an attractive solution.

[0027] The concept of "autonomous feedback" is a natural way to avoid doubts about the fidelity of measurement loops at the quantum level, especially in contexts where dissipative stabilization already exists. The principle, as explained in more detail below, is to design a physical mechanism that packages the deviation to be detected and the action to be taken. The challenge is how to design such a mechanism using simple physical components. Early coherent feedback principles were proposed by Mabuchi, 2008, and James and Gough, 2010. In Xu, 2022, a specific "autonomous feedback" controller was proposed for the current task, with the key observation being that it is applied to squeezed-cat feedback, with the side benefit of reducing non-adiabatic gate-induced errors.

[0028] Although the standard cat qubit method reduces the bit-flip error rate, it does not provide a satisfactory solution to the phase-flip error.

[0029] The present invention proposes a physical mechanism that automatically corrects the phase error in situ, at least to first order.

[0030] The present invention applies a correction to the dissipative cat qubit confinement mechanism, while automatically correcting some of the phase error by operating back into cat qubit space.

[0031] More precisely, in all cat qubits, including the standard cat qubit, the present invention corrects to first order the phase error induced by the Hamiltonian used to implement the gate.

[0032] Moreover, specifically for squeezed-cat qubits, the present invention also provides first-order correction of phase errors induced by spontaneous single-photon loss or gain, which is often the dominant decoherence process. Thus, the present invention has particular advantages for squeezed-cat qubits.

[0033] Furthermore, whatever the nature of the cat qubit used, whether it be a standard cat qubit, a squeezed cat qubit, or a cat qubit that may be neither standard nor squeezed, the present invention can be combined with other topological protection methods.

[0034] Compared to Xu, 2002-2, the present invention proposes different specific implementations of autonomous feedback for this task. These two implementations feature different advantages and disadvantages with respect to the problems faced in the specific implementation, both in terms of robustness against secondary effects and practicality for manufacturing processes.

[0035] For example, the autonomous feedback targeted by Xu, 2022-2 requires the design of a large number of microwave pumps. Their proposed practical implementation, detailed in their equation n16, requires five microwave pumps (one or two between each pair of resonators) and two microwave drives (on separate resonators). Such a large number of pumps and drives presents practical challenges due to frequency collisions or the large number of qubit connections required, as hundreds of qubits will ultimately be built on a chip, each requiring such a large number of pumps and drives. The present invention offers a simpler design, using fewer pumps and drives, with roughly similar performance. Summary of the Invention [Problem to be solved by the invention]

[0036] In this context, the invention relates to an electronic device for storing quantum information, the electronic device comprising: - first resonant frequency ω a With cat qubit electromagnetic resonator; a second resonant frequency ω different from the first resonant frequency b a buffer electromagnetic resonator having: a nonlinear coupling element coupling the cat qubit electromagnetic resonator to the buffer electromagnetic resonator; -frequency ω ba coupling means (e.g., including a coaxial cable having an appropriate bandwidth) configured to couple a first electromagnetic wave of frequency 2ω to the nonlinear coupling element; a -ω b a coupling means (e.g., including the same coaxial cable as mentioned for the first electromagnetic wave, or a different coaxial cable) configured to couple the second electromagnetic wave to the nonlinear coupling element; a dissipation device coupled to the cat qubit electromagnetic resonator and the buffer electromagnetic resonator via the nonlinear coupling element; It is equipped with The nonlinear coupling element is a Two photons of frequency ω b and one photon of frequency 2ω a -ω b to generate a photon of the second electromagnetic wave at a frequency ω a The above two photons are b The photon is then exchanged with the photon of the first order photon.

[0037] This device is unique because it has at least the following features: the device has coupling means (for example also the same coaxial cable as described above for the first electromagnetic wave, or another coaxial cable), which coupling means is coupled to a frequency (2n+1)ω a +ω b -ω c to the nonlinear coupling element; and c is ω a and ω b is the resonant frequency of a lossy mode of the dissipative device, where n is a non-negative integer (e.g., n=0), and this lossy mode embodies the dissipative nature of the device, but unlike standard cat qubits, the buffer mode is non-dissipative here.

[0038] The nonlinear coupling element is configured to couple the cat qubit electromagnetic resonator to a frequency ω a(2n+1) photons at frequency ω in the buffer electromagnetic resonator b 1 photon of the above loss mode at frequency ω c and one photon of the third electromagnetic wave, wherein the (2n+4)-wave mixing dissipates a positive odd number of photons of the cat qubit electromagnetic resonator relative to one photon of the buffer electromagnetic resonator through the dissipation device. In a more general manner, the 2n+4-wave mixing is performed at a frequency ω a can exist within a larger wave-mixing ensemble that performs exchanges involving an odd number of photons.

[0039] The present invention is also embodied in a method for storing quantum information, the method comprising: - first resonant frequency ω a and a cat qubit electromagnetic resonator having a second resonant frequency ω different from the first resonant frequency. b a buffer electromagnetic resonator having the same frequency as the input signal, using a nonlinear coupling element; -frequency ω b and the first electromagnetic wave of frequency 2ω a -ω b coupling the second electromagnetic wave to the nonlinear coupling element; - coupling a dissipative device to the cat qubit electromagnetic resonator and the buffer electromagnetic resonator via the nonlinear coupling element; It contains The method for storing quantum information comprises: frequency ω a Two photons of frequency ω b and one photon of frequency 2ω a -ω b performing four-wave mixing by the nonlinear coupling element including one photon of the second electromagnetic wave at a frequency ω a The above two photons are b The method further includes the step of exchanging the one photon of the first photon with the one photon of the second photon.

[0040] This method is unique because it has the following features: A method for storing quantum information is a +ω b -ω c further comprising coupling a third electromagnetic wave of ω c is ω a and ω b is the resonant frequency of a loss mode of the dissipative device different from The method for storing quantum information comprises generating a quantum signal at a frequency ω a (2n+1) photons at frequency ω in the buffered electromagnetic resonator b 1 photon of the above loss mode at frequency ω c and the third electromagnetic wave of frequency (2n+1)ω a +ω b -ω c performing (2n+4)-wave mixing by the nonlinear coupling element including one photon of the cat qubit electromagnetic resonator, wherein the (2n+4)-wave mixing dissipates a positive odd number of photons of the cat qubit electromagnetic resonator relative to one photon of the buffer electromagnetic resonator through the dissipation device.

[0041] Joint dissipation inverts the phase value of the cat qubit as it returns to the steady-state subspace. The present invention inverts the phase value back to its original value when correcting for displacement from the steady-state subspace.

[0042] In this way, the new design combines the exponential protection against bit-flip errors inherent in the properties of the cat qubit with its own improved protection against phase-flip errors, by autonomously correcting the dominant order of the phase error during gate operations on the cat qubit. This allows the use of faster gates without incurring high uncorrected error rates.

[0043] More precisely, it should be recognized that the present invention provides first-order correction, which generally allows gains of one to two orders of magnitude in phase accuracy by eliminating not all but a dominant part of the effect of the dominant error channel.

[0044] For a standard cat qubit, it is conceivable to implement the present invention only during certain gate operations, while maintaining standard dissipation otherwise.

[0045] The present invention is suitable for combination with other schemes to improve phase protection during gate operation, such as anti-adiabatic drives as disclosed in Xu, 2022-1.

[0046] In the case of squeezed cat qubits, the same design also provides first-order correction for the phase reversal associated with spontaneous single-photon loss, the dominant error source inherent in cat qubits.

[0047] The additional engineering complexity is low because the number of microwave pumps and drives required is limited: four pumps and one drive for the minimum Squeezed Cats setup, and two pumps and one drive for the non-Squeezed Cats setup.

[0048] Even if this additional engineering introduces other perturbations to the phase error, these are of much lower order than the errors caused by gate-induced noise or spontaneous decoherence, and the phase is clearly better preserved overall.

[0049] Other features are optional but advantageous and are listed below. said dissipation device is adapted to dissipate heat at a frequency ω c may further include a third electromagnetic resonator resonating at and coupled to the transmission line; The dissipation device may further include a nonlinear resonator; The cat qubit electromagnetic resonator, the buffer electromagnetic resonator, and the dissipation device may be constructed as a superconducting circuit; -frequency ωb a generator for the first electromagnetic wave of frequency 2ω a -ω b a generator for the second electromagnetic wave of frequency (2n+1)ω a +ω b -ω c and all or some of the third electromagnetic wave generators may be microwave generators; the cat qubit electromagnetic resonator is a squeezed cat qubit resonator, and the coupling means is coupled to a frequency 2ω a +ω b to the nonlinear coupling element; and -The above coupling means has a frequency (2n'+1)ω a +ω b -ω c (or there may be several such waves) to the nonlinear coupling element, where n′ is a strictly negative integer, and the nonlinear coupling element couples a fifth electromagnetic wave of frequency ω a an odd number of photons of frequency ω in the buffer electromagnetic resonator b of photons, the frequency of the loss mode above ω c and the fifth electromagnetic wave of frequency (2n'+1)ω a +ω b -ω c wherein an odd number of photons are added to the cat qubit electromagnetic resonator while the buffer electromagnetic resonator is reset to a vacuum state; The cat qubit electromagnetic resonator can be a squeezed cat qubit resonator, and the method can include generating a qubit at a frequency of 2ω. a +ω b coupling a fourth electromagnetic wave to the nonlinear coupling element; and - Frequency 2ω a +ω b Generator for the fourth electromagnetic wave at frequency (2n'+1)ω a +ω b -ω csome or all of the generators for the fifth electromagnetic wave in may be microwave generators, and the nonlinear coupling element may include a capacitive coupling element that couples the cat qubit electromagnetic resonator to the buffer electromagnetic resonator; - coupling means at frequency 2ω a -ω b may include an inductive coupling means configured to couple the second electromagnetic wave to the nonlinear coupling element; The nonlinear coupling element may comprise an asymmetrically threaded superconducting quantum interference element (ATS), or a superconducting nonlinear asymmetric inductive element (SNAIL), or a transmon device as a coupler, or other nonlinear elements such as superconducting nanowires as described in Ku, 2010.

[0050] For method and process characteristics, -(2n+4) wave mixing may be a second four-wave mixing (n=0); -frequency ω a Two photons of frequency ω b and one photon of frequency 2ω a +ω b Further wave mixing including one photon of the fourth electromagnetic wave of frequency ω a The two photons of frequency ω b and exchange them with one photon of this fourth electromagnetic wave, a +ω b -ω c a fifth electromagnetic wave is further coupled to the nonlinear coupling element, n′ being a strictly negative integer, and having a frequency ω a -(2n'+1) photons of frequency ω in the buffer electromagnetic resonator b 1 photon of the above loss mode at frequency ω c and the fifth electromagnetic wave of frequency (2n'+1)ω a +ω b -ω cAnother further wave mixing including one photon of the above is carried out in the nonlinear coupling element; In particular, it is possible that n'=-1 and / or n=0.

[0051] Several of the processes described can occur simultaneously. In particular, (2n+4) wave mixing can occur simultaneously for several values ​​of n.

[0052] For the purposes of this disclosure, microwaves are considered to be waves between 300 MHz and 300 GHz, or subsidiarily between 1 GHz and 30 GHz. The invention may also use high frequency or very high frequency waves outside these ranges.

[0053] Further features and advantages of the present invention will become apparent from the following detailed description of illustrative embodiments thereof and by reference to the accompanying drawings. [Brief explanation of the drawings]

[0054] [Figure 1] 1 is an overall schematic diagram of the present invention; [Figure 2] FIG. 10 is a lumped parameter model of a photon dissipative confinement cat qubit setup with a correlated dissipative device, where the phase inversion reduction method is implemented and ATS is used, according to one embodiment of the present invention. [Figure 3] FIG. 10 is a lumped parameter model of a photon dissipative confinement cat qubit setup with a correlated dissipative device, where the phase inversion reduction method is implemented and ATS is used, according to one embodiment of the present invention. [Figure 4] FIG. 10 is a lumped parameter model of a photon dissipative confinement cat qubit setup with a correlated dissipative device according to another embodiment of the invention, again implementing the phase inversion reduction method. This embodiment uses a SNAIL as the nonlinear coupler. [Figure 5] 7 is a model of the same cat qubit setup (an example embodiment with ATS) as in FIG. 6, but without the phase inversion reduction method implemented. [Figure 6]6 is a model of the same cat qubit setup (an example embodiment with SNAIL) as in FIG. 5, but without the phase inversion reduction method implemented. [Figure 7] Figure 8 shows a model of the same cat qubit setup, but for a squeezed cat, with the phase inversion reduction method implemented. In this exemplary embodiment, ATS is used. [Figure 8] Figure 7 shows a model of the same cat qubit setup, but for a squeezed cat, with the phase inversion reduction method implemented. In this exemplary embodiment, SNAIL is used. [Figure 9] FIG. 10 is a lumped parameter model of a photon dissipative confinement cat qubit setup with a correlated dissipative device in accordance with another embodiment of the present invention, again implementing the phase inversion reduction method. This embodiment uses transmons as nonlinear couplers. [Figure 10] 1 illustrates the effectiveness of the present invention in the context of a single qubit Z gate. [Figure 11] We demonstrate the effectiveness of the present invention in the context of a two-qubit CNOT gate. DETAILED DESCRIPTION OF THE INVENTION

[0055] (Physical explanation) In the described embodiment, the invention builds on the physical implementation of a photon dissipative confined cat qubit based on two resonators and a nonlinear coupling device, and introduces an additional feature for dissipation.

[0056] Thus, a standard cat qubit is stabilized in a high-quality harmonic oscillation mode, labeled A, coupled to an oscillation mode, labeled B, via a two-photon exchanger TPE.

[0057] Furthermore, the correlation dissipation device CDD performs joint (or correlated) dissipation of mode A and B photons.

[0058] (Figure 1) Such a setup is shown in Fig. 1. The harmonic oscillator mode A is composed of a photon annihilation operator a and a photon creation operator a † and the oscillator mode B is associated with the photon annihilation operator b and the photon creation operator b † is associated with.

[0059] In this diagram, the A mode couples to the B mode in two ways. First, a two-photon exchanger, the TPE, converts a pair of photons from the A mode into a single photon in the B mode, and vice versa. Such an exchanger performs so-called "four-wave mixing." The "4" represents the three photons involved in the exchange plus one photon from an external, frequency-tunable pump.

[0060] Second, the correlated dissipation device CDD, as shown in Figure 1, has the required form Q(a)b for joint dissipation, or more generally Q(Aa,a + )b allows for the correlation dissipation of photons A and B.

[0061] Therefore, the dissipator used in the present invention is as follows: Dissipator[Q(a,a + )b](ρ) ρ is the density matrix of the cat qubit, and a and a + The total output of the operator must be odd.

[0062] When this dissipator annihilates a photon of B, it always co-modifies an odd number of photons of A.

[0063] where α is the complex amplitude of the coherent state (eigenstate a of the operator) of the cat qubit harmonic oscillator, and the resulting equation is for the coupled Hamiltonian that models the TPE:

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[0064] Operator Q(a,a + ) realizes autonomous feedback: if buffer mode B detects a deviation via Hcoupling, the subsequent relaxation of B triggers an action on mode A via Q(), without the need for external intervention such as measurement or feedback manipulation.

[0065] While the embodiment of FIG. 1 features Q(a)=a, meaning that one photon in mode A is annihilated simultaneously with one photon in mode B, other embodiments may feature Q(a)=a. + Any polynomial of an odd power of can be used for Q.

[0066] The physical mechanism used is wave mixing, involving one photon of each type, but the setup will work if other processes involving more photons are involved, as long as the number of photons exchanged with the cat resonator is odd. If Q(a) = a and we assume nominal behavior in the other waves, this is four-wave mixing, or more generally, if Q corresponds to the annihilation of (2n + 1) photons in mode A, it is (2n + 4)-wave mixing.

[0067] In terms of implementation, the proposed dissipation is of sufficiently low complexity to meet the standard dissipation engineering capabilities of the devices for which the cat qubit is designed.

[0068] The second embodiment uses a squeezed cat qubit. The squeezed cat qubit is stabilized by H coupling In S(a), a and a + If a high squeezing effect is desired, a and a + It has similar coefficients for

[0069] Dissipator[Q(a)b] can be further replaced by Dissipator[S(a)b], or more generally by Dissipator[Q(S(a))b], where Q is a polynomial of an odd power.

[0070] Again, as in the unsqueezed setup, the spurious phase reversal typically associated with actuation induced leaving the cat steady-state subspace is reversed by subtracting or adding exactly one photon while jumping back into the cat qubit space.

[0071] However, this embodiment based on squeezed cats has an important additional advantage: indeed, unlike standard cats, squeezed cats are designed to escape from the steady-state cat qubit space under the action of spontaneous single-photon loss, which is the dominant error source in the absence of any manipulation. Therefore, this scheme also automatically reverses the phase inversion associated with this spontaneous photon loss.

[0072] (Practical Implementation) As already mentioned, the present invention is based on the physical implementation of a photon dissipative confinement cat qubit based on two resonators and a nonlinear coupling element (called ATS as an example).Using superconducting circuits, such a device can be designed in various ways.

[0073] (Figure 2) 2 to 9, the cat qubit resonator 10 is modeled by a harmonic LC-oscillator, i.e., an inductor and a capacitor attached in parallel with one another. This has a first resonant frequency ω a This is a cat qubit electromagnetic resonator with a resonant frequency of . This is also the Mode A oscillator shown in and described above in connection with FIG. 1.

[0074] Figure 2 shows the following elements: -10: Cat qubit (a) resonator -20: Buffer mode (b) resonator -41: Dissipative mode (c) resonator -30: Nonlinear coupling element, capable of mixing 4, 6, 8 or more waves (even wave mixing possible) -40: Dissipative device having at least one loss mode -35,45: Capacitive or inductive coupling element -50: Microwave coupling means -55:ω b Frequency drive (microwave drive) -60: High frequency pump (having a different frequency and amplitude than the microwave drive 55) -65:2ω a -ω b Frequency Pump -66:2ω a +ω b Frequency Pump (for Squeeze Cat) -75:(2n+1)ω a +ω b -ω c Frequency Pump -76:(2n'+1)ω a +ω b -ω c Frequency Pump (for Squeeze Cat)

[0075] (Figure 3) 3, the buffer resonator 20 is shown modeled as a harmonic LC oscillator, but may also operate as a non-harmonic oscillator, which has a second resonant frequency ω that is different from the first resonant frequency. b This is also the Mode B oscillator shown in and described above in connection with FIG.

[0076] To physically design the TPE Hamiltonian, a coupling element between the cat qubit mode (A) and the buffer mode (B) is required. This is achieved via an ATS 30, consisting of two Josephson junctions, with two current loops, coupled to the cat qubit resonator 10 via capacitive coupling 35. The ATS 30 provides the B mode. The ATS 30 embodies the TPE described above in connection with FIG. 1.

[0077] Furthermore, a dissipative oscillator 40 is coupled to the ATS 30 via a capacitive coupling element 45. This dissipative oscillator 40 is of mode C, and in the illustrated example is made of a harmonic LC oscillator coupled to a transmission line, but it may also be an anharmonic oscillator such as mode B, and its dissipation may be realized by any means. a Yaω b A different resonant frequency ω c This has a loss mode with a photon annihilation operator c and a photon creation operator c † is related to.

[0078] The coupling Hamiltonian that models the CDD is:

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[0079] The ATS 30 and dissipative oscillator 40 embody the CDD described in connection with FIG.

[0080] The third oscillator C has significant losses, for example because it is coupled to a waveguide.

[0081] This device also operates at a frequency ω bThe device also comprises coupling means 50 for coupling the first electromagnetic wave of frequency ω to the ATS 30 and the resonators 10, 20 through inductive or capacitive means. This is embodied by a printed circuit designed to have a wave-guiding effect and may include a director and a capacitance or (cross) inductance receiving the wave by means of a coaxial cable. The device also comprises coupling means 50 for coupling the first electromagnetic wave of frequency ω b The system comprises a generator 55 for the first electromagnetic wave or is comprised in a system comprising a generator 55.

[0082] This device also operates at a frequency of 2ω a -ω b The inductive coupling means 60 is provided for coupling a second electromagnetic wave of frequency (2n+1)ω to the nonlinear coupling element ATS 30. A magnetic field is required in each of the two loops of the ATS, and for this purpose the inductive coupling means 60 generates a magnetic field in the first loop by a first portion of the inductive coupling means 60, while generating a second magnetic field in the second loop of the ATS by a second portion of the inductive coupling means 60, and the two magnetic fields generate different magnetic fluxes in these loops. The inductive coupling means 60 is provided with a frequency (2n+1)ω a +ω b- ω c The device is also used to couple a third electromagnetic wave of the second electromagnetic wave to the nonlinear coupling element ATS 30. The device also includes a generator 65 for the second electromagnetic wave and a generator 75 for the third electromagnetic wave, or is included in a system that includes these.

[0083] The TPE embodied by the ATS 30 is a resonator 10 receiving energy (at a frequency ω a ) and the energy received from the resonator 20 (at frequency ω b ) and the wave received from generator 65 (with frequency 2ω a -ω b Four-wave mixing is performed between the photon and the electron (one photon at a time).

[0084] The CDD embodied by the ATS 30 and the dissipative oscillator 40 generates a a 2n+1 photons at frequency ωb ) and the frequency of the loss mode ω c and the frequency of the electromagnetic wave generated by the generator 65 is (2n+1)ω a +ω b -ω c Wave mixing, for example four-wave mixing, is performed between one photon and another photon. Figures 3 to 5 show three operating points of the same circuit.

[0085] In Figure 3, this circuit is composed of a dissipator [ab](ρ) and a two-photon exchange H between the A and B modes. coupling Since the parity of the photon number of A is not conserved, this is a parity-switching setup.

[0086] Therefore, the second electromagnetic wave has a frequency of 2ω a -ω b and the third electromagnetic wave has frequency (2n+1)ω a +ω b -ω c is.

[0087] (Figure 4) Figure 4 shows an embodiment similar to Figure 3, but using a SNAIL instead of an ATS. Frattini, 2018, is a paper that mentions such a SNAIL. The ATS 30 in Figure 3 has been replaced with a SNAIL.

[0088] (Figure 5) In Figure 5, this circuit designs the Dissipator[b](ρ) with the same two-photon exchange, which is a parity-preserving setup.

[0089] Indeed, it is conceivable that a standard cat qubit would implement the present invention only during certain gate operations, while maintaining standard dissipation otherwise.

[0090] Because this dissipator was designed for a regular cat qubit, this setup shows how to turn off the parity-switching device while keeping the same circuit layout. This change in the setup can actually be done by turning on and off various wave sources.

[0091] Therefore, the second electromagnetic wave has a frequency of 2ω a -ω b and the third electromagnetic wave has frequency ω b -ω c is.

[0092] (Figure 6) In FIG. 6, an embodiment similar to FIG. 5 is shown using a SNAIL instead of an ATS.

[0093] (Figure 7) In Figure 7, the circuit design is Dissipator[S(a)b](ρ), which is a parity switch setup for the squeezed cat state.

[0094] Therefore, the second electromagnetic wave has a frequency of 2ω a -ω b and the third electromagnetic wave has frequency (2n+1)ω a +ω b -ω c However, the frequency 2ω coupled to the nonlinear coupling element ATS30 by the inductive coupling means 60 is a +ω b The fourth electromagnetic wave, and the frequency (2n'+1)ω a +ω b -ω c There is also a fifth electromagnetic wave n′, where n′ is a strictly negative integer coupled to the nonlinear coupling element ATS 30 by inductive coupling means 60. These waves are generated by generators 65 and 75, respectively, or by other generators or generator assemblies.

[0095] Similarly, it is possible to design a parity-preserving setup for Squeezed Cats, and thus available as an option when not running gates (not shown).

[0096] (Figure 8) In FIG. 8, an embodiment similar to FIG. 7 is shown using a SNAIL instead of an ATS.

[0097] (Figure 9) Figure 9 shows an embodiment similar to Figures 3 and 4, but using a transmon coupler instead of the ATS or SNAIL. Leghtas, 2015, discloses an experimental realization of a cat qubit using a transmon coupler as shown in Figure 9.

[0098] (Figure 10) Figure 10 shows the ab / |α| 2 = 8g2 (gray: thin line) and the autonomous feedback design of the present invention b This shows the gate error of the Z gate compared to the normal design at =8g2 (black: thick line). Left: fixed cat size, |α| 2 =8. Right: fixed gate time, T=10 / g2.

[0099] Figure 10 shows the error induced by a regular gate and our correlation dissipator Z-gate for both phase and bit reversal errors. For phase reversal errors, we observe an improvement by a constant factor of about μ≈0.02, independent of both gate time and cat size.

[0100] (Figure 11) Figure 11 shows the ab / |α| 2 = 8g2 and the autonomous feedback design of the present invention. b The gate error of the CNOT gate at =8g2 is shown compared to the normal design (black: thick line). Left: fixed cat size, |α| 2 =8. Right: fixed gate time, T=10 / g2. The gray (thin) dashed line indicates the non-adiabatic phase error.

[0101] Figure 11 explores such a setup for a two-qubit CNOT gate, where our correlation dissipator is activated on the control qubit. Here, performance is similar to a single-qubit Z gate, with phase fidelity improved by 1 / μ≈50.

[0102] The variation of the microwave pump through the loop of nonlinear circuit elements can be done in a real-time setup.

[0103] In other embodiments, this C-mode is engineered using a transmon qubit or other nonlinear resonator.

[0104] Further additional features may be present in embodiments of the present invention.

[0105] In particular for logic gate implementations, the optional use of an additional feedforward Hamiltonian can further enhance the conservation of quantum information.

[0106] The present invention has been described through exemplary embodiments using n=0, and for Squeezed Cats, n=0, n'=-1, and Q(a)=a. Other values ​​of n can be used, provided that n is not a negative integer, where n is any positive integer including 0. The value of n is determined by the way the circuit is constructed, in particular the order of nonlinearity 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. Q can also be determined by the order of a and a + It can be a polynomial of an odd power of .

[0107] Oscillator 40 can be anharmonic, up to the qubit made of an anharmonic oscillator. It is also possible that oscillator 40 is not present, with transmission lines directly coupled to resonators 10 and 20 in a special way that induces the joint dissipation required by the present invention.

[0108] Furthermore, B-mode can be either harmonic or inharmonic.

[0109] (Bibliography) Mirrahimi, 2014:Mirrahimi et al., New J. Physics, 16, 045014, 2014. Lescanne, 2020:Lescanne et al., Nature Physics, 16, 509, 2020. Chamberland, 2020:Chamberland et al. arXiv:2012.04108, 2020. Guillaud, 2019: Guillaud et al., Physical Review X 9 (4), 041053, 2019. Puri, 2017:Puri et al, npj Quantum Information, 3, 18, 2017. Grimm,2020:Grimm et al, Nature, 584, 205, 2020. Gautier, 2022: Gautier et al, PRX Quantum 3, 020339, 2022. Xu, 2022-1: Xu et al., Phys. Rev. Res. 4, 013082, 2022. Carde, 2021: Carde et al., Master of Sciences thesis, Inria Quantic & ENS Paris, 2021. Schlegel, 2022: Schlegel et al, arXiv:2201.02570, 2022. Xu, 2022-2: Xu et al., arXiv:2210.13406, 10 / 2022. Albert, 2019: Albert et al., Quantum Science and Technology 4, 035007, Nature 536, 441–445, 2016:Ofek et al. Mabuchi , 2008 : Mabuchi , Phys. Rev. Fr. A 78 , 032323 , James and Gough, 2010:James and Gough in IEEE Transactions on Automatic Control, vol. 55, no. 8, pp. Science, 347.6224 (2015): 853–857. Frattini,2018:Frattini et al., Applied Physical Review 10.5 (2018):054020 On, 2010:J. Ku, et al. Phys. Rev. Fr. B 82 , 134518 -13 October

Claims

1. 1. An electronic device for storing quantum information, comprising: - first resonant frequency ω ａ a cat qubit electromagnetic resonator (10) having a second resonant frequency ω different from said first resonant frequency ｂ a buffer electromagnetic resonator (20) having: a nonlinear coupling element (30) that couples the cat qubit electromagnetic resonator (10) to the buffer electromagnetic resonator (20); -Frequency ω ｂ a coupling means (50) configured to couple a first electromagnetic wave of frequency 2ω to said nonlinear coupling element (30); ａ -ω ｂ a coupling means (60) configured to couple a second electromagnetic wave of the second wavelength to the nonlinear coupling element (30); a dissipation device (40) coupled to the cat qubit electromagnetic resonator (10) and the buffer electromagnetic resonator (20) via the nonlinear coupling element (30); It is equipped with The nonlinear coupling element (30) is ａ Two photons of frequency ω ｂ and one photon of frequency 2ω ａ -ω ｂ to perform four-wave mixing including one photon of the second electromagnetic wave at a frequency ω ａ The two photons of frequency ω ｂ and the combining means (60) is configured to exchange a photon of frequency (2n+1)ω ａ +ω ｂ -ω ｃ to the nonlinear coupling element (30), and ｃ is ω ａ and ω ｂ is a resonant frequency of a lossy mode of the dissipative device (40) that is different from the frequency ω ａ (2n+1) photons at frequency ω ｂ , one photon of the loss mode at frequency ω ｃ and one photon of the third electromagnetic wave of frequency (2n+1)ω ａ +ω ｂ -ω ｃ The (2n+4) wave mixing is further configured to perform (2n+4) wave mixing including one photon of the cat qubit electromagnetic resonator (10), wherein the (2n+4) wave mixing dissipates a positive odd number of photons of the cat qubit electromagnetic resonator (10) relative to one photon of the buffer electromagnetic resonator (20) through the dissipation device. electronic equipment.

2. The further dissipation device (40) is ｃ a third electromagnetic resonator coupled to the transmission line, the third electromagnetic resonator resonating at The electronic device of claim 1 .

3. The buffer electromagnetic resonator (20) and / or the further dissipation device (40) comprise a nonlinear resonator. The electronic device of claim 1 .

4. The cat qubit electromagnetic resonator (10), the buffer electromagnetic resonator (20), and the dissipation device (30) are constructed as a superconducting circuit.

4. An electronic device according to any one of claims 1 to 3.

5. frequency ω ｂ a generator (55) for said first electromagnetic wave of frequency 2ω ａ -ω ｂ and a generator (65) for said second electromagnetic wave of frequency (2n+1)ω ａ +ω ｂ -ω ｃ and a generator (75) for the third electromagnetic wave.

5. An electronic device according to any one of claims 1 to 4.

6. frequency ω ｂ for the first electromagnetic wave, frequency 2ω ａ -ω ｂ and the frequency (2n+1)ω ａ +ω ｂ -ω ｃ The generator (55, 65, 75) for the third electromagnetic wave is a microwave generator.

6. The electronic device of claim 5.

7. The cat qubit electromagnetic resonator (10) is a squeezed cat qubit resonator, and the coupling means (60) is a coupling means for coupling a cat qubit electromagnetic resonator having a frequency of 2ω ａ +ω ｂ a fourth electromagnetic wave to the nonlinear coupling element (30), The nonlinear coupling element (30) is ａ Two photons of frequency ω ｂ and one photon of frequency 2ω ａ +ω ｂ to perform further wave mixing involving one photon of the fourth electromagnetic wave at frequency ω ａ The two photons of frequency ω ｂ and further configured to exchange the one photon of The coupling means (60) has a frequency (2n'+1)ω ａ +ω ｂ -ω ｃ to the nonlinear coupling element (30), where n′ is a strictly negative integer, and the nonlinear coupling element couples a fifth electromagnetic wave of frequency ω ａ -(2n'+1) photons of frequency ω in the buffer electromagnetic resonator ｂ , one photon of the loss mode at frequency ω ｃ and one photon of the fifth electromagnetic wave of frequency (2n'+1)ω ａ +ω ｂ -ω ｃ and further configured to perform another further wave mixing including one photon of 7. An electronic device according to any one of claims 1 to 6.

8. The nonlinear coupling element (30) includes a capacitive coupling element (35) that couples the cat qubit electromagnetic resonator (10) to the buffer electromagnetic resonator (20).

8. An electronic device according to any one of claims 1 to 7.

9. The coupling means (60) is ａ -ω ｂ and an inductive coupling means configured to couple the second electromagnetic wave of the second wavelength to the nonlinear coupling element (30).

9. An electronic device according to any one of claims 1 to 8.

10. The nonlinear coupling element (30) includes an asymmetrically threaded superconducting quantum interference element or a superconducting nonlinear asymmetric inductive element parametric amplifier.

10. An electronic device according to any one of claims 1 to 9.

11. 1. A method for storing quantum information, comprising: - first resonant frequency ω ａ and a cat qubit electromagnetic resonator having a second resonant frequency ω different from the first resonant frequency. ｂ a buffer electromagnetic resonator having the same frequency as the input signal, by a nonlinear coupling element; -Frequency ω ｂ and a first electromagnetic wave of frequency 2ω ａ -ω ｂ coupling a second electromagnetic wave of the second wavelength to the nonlinear coupling element; - coupling a dissipative device to the cat qubit electromagnetic resonator and the buffer electromagnetic resonator via the nonlinear coupling element; It contains The method for storing quantum information comprises: The nonlinear coupling element couples the frequency ω ａ Two photons of frequency ω ｂ and one photon of frequency 2ω ａ -ω ｂ to perform four-wave mixing including one photon of the second electromagnetic wave at a frequency ω ａ The two photons of frequency ω ｂ and exchanging the one photon with the one photon of frequency (2n+1)ω ａ +ω ｂ -ω ｃ to the nonlinear coupling element; and coupling a third electromagnetic wave at a frequency ω ａ (2n+1) photons at frequency ω ｂ , one photon of the loss mode at frequency ω ｃ and one photon of the third electromagnetic wave of frequency (2n+1)ω ａ +ω ｂ -ω ｃ performing (2n+4) wave mixing involving one photon of It further includes ω ｃ is ω ａ and ω ｂ is a resonant frequency of a lossy mode of the dissipative device different from The (2n+4) wave mixing dissipates a positive odd number of photons of the cat qubit electromagnetic resonator relative to one photon of the buffer electromagnetic resonator through the dissipation device. method.

12. The (2n+4) wave mixing is the second four-wave mixing.

12. A method for storing quantum information according to claim 11.

13. The cat qubit electromagnetic resonator (10) is a squeezed cat qubit resonator, and the method includes: ａ +ω ｂ a fourth electromagnetic wave into the nonlinear coupling element (30), frequency ω ａ Two photons of frequency ω ｂ and one photon of frequency 2ω ａ +ω ｂ Further wave mixing is performed in the nonlinear coupling element (30) including one photon of the fourth electromagnetic wave at frequency ω ａ The two photons of frequency ω ｂ and exchanges it with the one photon of frequency (2n'+1)ω ａ +ω ｂ -ω ｃ a fifth electromagnetic wave is further coupled to the nonlinear coupling element (30), n′ being a strictly negative integer, and a fifth electromagnetic wave of frequency ω ａ -(2n'+1) photons of frequency ω in the buffer electromagnetic resonator ｂ , one photon of the loss mode at frequency ω ｃ and one photon of the fifth electromagnetic wave of frequency (2n'+1)ω ａ +ω ｂ -ω ｃ Another further wave mixing including one photon of 13. A method for storing quantum information according to claim 11 or claim 12.

14. n'=-1 14. A method for storing quantum information according to claim 13.

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