Asymmetric repeat code for cat qubits

Abstract

The present invention relates to a cat qubit repetition code that includes a number d of data cat qubits (4) and at least (d-1) auxiliary cat qubits (6), where the number d is greater than or equal to 3, and where each auxiliary cat qubit (6) is connected to two data cat qubits (4) by two respective CNOT gates (8) such that no data cat qubit (4) is connected to more than two auxiliary cat qubits (6), and where the two-photon dissipation factor of the auxiliary cat qubit is ensured to be greater than the two-photon dissipation factor of the data cat qubit. The repetition code comprises, for each auxiliary cat qubit, at least the following steps: a) putting the auxiliary cat qubit (6) into a state suitable for operator X: TIFF2025509669000046.tif6150 or, TIFF2025509669000047.tif6150, b) activating one of two CNOT gates (8) connected to the ancillary CAT qubit (6), c) activating the other CNOT gate (8) connected to the ancillary CAT qubit (6), and d) performing an error correction cycle that includes measuring the parity of the photon number of the ancillary CAT qubit (6).

Description

[Technical Field]

[0001] The present invention relates to the fields of quantum computing, boson quantum error correcting codes, and repetition codes. [Background technology]

[0002] Large-scale quantum computers are difficult to produce because noise induced by uncontrolled interactions between the quantum computer's components and its environment destroys the fragile quantum properties responsible for quantum acceleration. Indeed, all algorithms for which quantum acceleration has been theoretically proven require some level of protection against decoherence.

[0003] The theory of fault-tolerant quantum computing addresses this problem. Quantum error correcting codes (QECCs or "Quantum error correcting codes" in English) are designed to prevent environmentally induced errors from affecting quantum information. These codes work according to the principle of "countering entanglement with entanglement." Since natural errors that occur in physical systems are generally local, the quantum information to be protected is encoded in a non-local entangled state, which is less likely to be corrupted by errors. The most popular QECCs are surface codes.

[0004] Central to quantum fault tolerance theory is the threshold theorem: quantum computations of any length can be performed reliably if the noise affecting the physical components of the computer is below a certain value called the fault-tolerance error threshold.

[0005] In theory, when functioning below the fault-tolerant error threshold, QECC provides arbitrarily good protection against noise and solves the problem of decoherence. However, implementation in the physical world requires significant physical resources to achieve a sufficient level of protection. The trade-off between the degree of protection guaranteed by QECC and the increase in components required for its implementation is defined as the "resource overhead problem."

[0006] A realistic approach to quantum computing must address this issue. For this reason, continuous variable systems (such as harmonic oscillators), which can easily utilize infinite-dimensional Hilbert spaces to protect and process quantum information, appear to be superior to discrete variable systems (DVs), which only have finite-dimensional Hilbert spaces. There are different types of continuous variable encodings, which generally involve a superposition of several specific states of a harmonic oscillator, such as position-motion momentum eigenstates (GKP qubits), Fock states, or coherent states (cat qubits).

[0007] More specifically, the present invention relates to cat qubits.

[0008] Pumped (or stabilized) cat qubits are known to benefit from noise bias. More specifically, the effective error channel (e.g., bit error or "bit flip" error) is suppressed exponentially with the "size" (i.e., the average number of photons) of the Schrödinger cat state of the cat qubit. Current knowledge suggests that this suppression should apply to a large class of physical noise processes that have local effects on the phase space of a harmonic oscillator. This includes, but is not limited to, photon loss, thermal excitation, photon phase shifts, and various nonlinearities induced by coupling to Josephson junctions. Recent experiments in the field of quantum superconducting circuits have observed an exponential suppression of bit errors with the average number of photons in the cat state.

[0009] Because of this noise structure, quantum error correction has the same complexity as classical error correction and can be performed using repetition codes. In fact, if we want to correct only phase jumps, we only need to use phase jump error correcting codes. For example, this can consist of a repetition code defined in a dual base, or any other classical error correcting code. The code space is defined by d-1 stabilizers. TIFF2025509669000001.tif6150 The logical operators of the repeated cat qubit are TIFF2025509669000002.tif6150. Logical state TIFF2025509669000003.tif6150 and TIFF2025509669000004.tif6150 is Given by TIFF2025509669000005.tif6150.

[0010] A cat qubit repetition code is constructed using d cat qubits, called data cat qubits, in which logical information is encoded. The repetition code is implemented, i.e., errors are detected, by repeatedly measuring the stabilizer of the repetition code. This is done using d-1 further cat qubits, called auxiliary cat qubits. The quantum circuit for the repetition code has the state This requires preparation in TIFF2025509669000006.tif6150 (in the case of the cat qubit, the Schrödinger cat state), measurement of the Pauli operator X (which in the case of the cat qubit is the parity of the photon number), and a CNOT gate between the auxiliary cat qubit and the data cat qubit.

[0011] The difficulty in implementing this repetition code is how to achieve code functionality below the fault-tolerant error threshold, which means that the fidelity of the quantum operations in this circuit must be sufficiently high. More specifically, if the repetition code operates above the threshold—that is, if the fidelity of the physical operations that make up the repetition code is not sufficiently high—the lifetime of the logical information decreases as the number of physical data qubits, d, increases. This means that new errors introduced by adding quantum systems cannot be compensated for by the error correction strategy. However, if the code operates below the error correction threshold—that is, if the fidelity of the physical operations is sufficiently high—the lifetime of the logical information increases exponentially with the number of physical data qubits, d, which corresponds to the distance, d, of the repetition code.

[0012] Cat qubits are implemented in the laboratory by dissipative stabilization (through artificial two-photon dissipation at a rate of κ) or by Hamiltonian confinement using a Kerr-type Hamiltonian of amplitude K or a two-photon exchange Hamiltonian (or TPE, short for "two photon exchange" in English) of amplitude g.

[0013] "Repetition Cat Qubits for Fault-Tolerant Quantum Computation" by Jeremie Guillaud and Mazyar Mirrahimi in Phys. Rev. X, 9,041053, on December 12, 2019; "Bias-preserving gates with stabilized cat qubits" by Shruti et al. in SCIENCE ADVANCES, Vol. 6, No. 34, on August 21, 2020; "Error rates and resource overheads of repetition cat qubits" by Jeremie Guillaud and Mazyar Mirrahimi in Phys. Rev. A, 103,042413, on April 13, 2021; "Building a Fault-Tolerant Quantum Computer Using Concatenated Cat" by Christopher Chamberland et al. in PRX Quantum, 3,010329, on February 23, 2022 Codes,” or “Practical Quantum Error Correction with the XZZX Code and Kerr-Cat Qubits” by Andrew S. Darmawan et al. in PRX Quantum 2, 030345, September 16, 2021. Some literature suggests using cat qubits in QECC, either with codes dedicated to phase errors (or “phase reversals”) or with codes that are more tolerant of phase errors than bit errors (such as rectangular surface codes or bias-noise adjusted codes of the XZZX surface code type).

[0014] In a cat qubit-based architecture, the quality of the hardware is measured by the ratio of two time scales: 1 / κ2 and 1 / κ1. κ2 is the two-photon dissipation rate that stabilizes the qubit, and κ1 is the one-photon loss rate. Other time scales include the rate phase shift κ Φ , thermal excitation n thThere are other sources of error such as self-Kerr interactions, cross-Kerr interactions, or other undesired couplings with other quantum systems present in the vicinity of the memory. However, one-photon loss is the dominant error mechanism, and for simplicity, only this physical error mechanism will be considered below. In the general case, all of the following holds by replacing the κ1 / κ2 ratio with the sum of the error mechanism rates divided by κ2:

[0015] In the prior art (published papers), experimentally obtained κ1 / κ2 ratios ranged from 1 to 10 -2 (the smaller the better). However, for quantum error correction to work, theory predicts that this ratio κ1 / κ2<5x10 -3 It is estimated that for large-scale quantum computing, this ratio needs to be designed to be lower than [10 -5 ;10 -4 It will need to be within the range of

[0016] Therefore, currently, no solution exists that can implement a cat qubit repetition code that is compatible with a fault-tolerant error threshold. Summary of the Invention

[0017] The present invention improves on this situation. To this end, the invention provides a repetition code for cat qubits, characterized as comprising a number d of data cat qubits and at least (d-1) auxiliary cat qubits, where d is 3 or greater, each auxiliary cat qubit connected to two data cat qubits by two respective CNOT gates such that no data cat qubit is connected to more than two auxiliary cat qubits, and the two-photon dissipation rate of the auxiliary cat qubits is strictly greater than the two-photon dissipation rate of the data cat qubit. This repetition code comprises at least the following operations: a) Put the auxiliary cat qubit into a state suitable for operator X: TIFF2025509669000007.tif6150 or Prepare it with TIFF2025509669000008.tif6150, b) activating one of the two CNOT gates connected to the auxiliary cat qubit; c) activating the other CNOT gate connected to the auxiliary cat qubit; and d) measuring the parity of the photon number of the auxiliary cat qubit; and This is implemented by performing for each auxiliary cat qubit error correction cycle, including

[0018] This device is particularly advantageous because it can implement cat qubit repetition codes that are compatible with fault-tolerant error thresholds.

[0019] According to various embodiments, the present invention comprises the following features: the two-photon dissipation rate of the ancillary cat qubit is selected to be substantially equal to a multiple of the two-photon dissipation rate of the data qubit, the multiple being selected from the group including 2, 5, 20, 30, and 50; - operations a) through d) are repeated for each auxiliary Cat qubit a number of times substantially equal to the ratio of the two-photon dissipation rate of the data Cat qubit to the two-photon loss rate of the auxiliary Cat qubit, followed by a refresh operation having a duration within the reciprocal of the two-photon dissipation rate of the data Cat qubit; the error correction cycle is performed substantially simultaneously for all of the auxiliary cat qubits; and -for each auxiliary cat qubit, operations a) through d) are performed sequentially; and -the data cat qubit is stabilized in the mode of the 3D cavity using an ATS circuit; -The auxiliary cat qubit is a resonant cat qubit; and The auxiliary cat qubit is a cat qubit stabilized in the mode of a 2D resonator using an ATS circuit; may have one or more of:

[0020] The present invention also relates to a surface code for cat qubits, comprising a number d of data cat qubits and at least (d-1) auxiliary cat qubits, where the number d is 3 or greater; each auxiliary cat qubit is connected to four data cat qubits by four respective CNOT gates, such that no data cat qubit is connected to more than four auxiliary cat qubits; The two-photon dissipation rate of the auxiliary cat qubit is definitely larger than the two-photon dissipation rate of the data cat qubit, The surface code performs at least the following operations for each auxiliary cat qubit: a) Set the auxiliary cat qubit to state X TIFF2025509669000009.tif6150 or, Prepare it with TIFF2025509669000010.tif6150, b) sequentially activating the CNOT gates connected to the auxiliary cat qubits; c) measuring the parity of the photon number of the auxiliary cat qubit; and The method is characterized in that it is implemented to execute a cycle including: [Brief explanation of the drawings]

[0021] Other characteristics and advantages of the invention will be better understood from reading the following description based on an embodiment given as a non-limiting example and from the drawings, in which:

[0022] [Figure 1] FIG. 1 shows a block diagram of a repetition code according to the present invention. [Figure 2] FIG. 2 shows the error probability diagram for the CNOT gate on the auxiliary cat qubit of the repetition code of FIG. 1 on the one hand and the data cat qubit on the other hand. [Figure 3] FIG. 3 shows an implementation diagram of the repeat code of FIG. 1 according to the first embodiment. [Figure 4] FIG. 4 shows an implementation diagram of the repeat code of FIG. 1 according to a second embodiment. [Figure 5]FIG. 5 shows the distortion curves of a data cat qubit in the context of the implementation of FIG. [Figure 6] FIG. 6 shows a top view of another practical embodiment of the repeat code of FIG. [Figure 7] FIG. 7 shows a side view of the repeating cord of FIG. [Figure 8] FIG. 8 shows a top view of another practical embodiment of the repeat code of FIG. [Figure 9] FIG. 9 shows a side view of the repeating cord of FIG. [Figure 10] Figure 10 shows the phase error probability of state-of-the-art symmetric repetition codes. [Figure 11] FIG. 11 shows the phase error probability of an asymmetric repetition code according to the invention using the correction cycle of FIG. [Figure 12] FIG. 12 shows a block diagram of a surface code according to the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0023] The following drawings and description inherently contain elements of a specific nature and, as such, can be used not only to better understand the invention, but also, where appropriate, to contribute to the definition of the invention.

[0024] 1 shows a block diagram of a repetition code 2 according to the present invention. In the example described herein, the repetition code 2 is three-dimensional, i.e. it comprises three data Cat qubits 4 and two auxiliary Cat qubits 6.

[0025] By cat qubit, we mean any implementation of a cat qubit, in particular a two-photon dissipative Schrödinger cat qubit. Alternatively, other cat qubits may be employed. In some embodiments, the data cat qubit 4 and the auxiliary cat qubit 6 may be made of different types of cat qubits.

[0026] By data cat qubit we should understand the fact that this physical qubit contains the quantum information that the repetition code 2 is intended to protect. By auxiliary cat qubit we should understand the complement of the data cat qubit in the repetition code, i.e. this physical qubit is used to detect phase errors in the data cat qubit.

[0027] The repetition code 2 comprises a conventional repetition code architecture for cat qubits, with d data cat qubits 4, a number d greater than or equal to 3, and d-1 auxiliary cat qubits 6. In some embodiments, it is possible to have d auxiliary cat qubits 6 for d data cat qubits 4. Each auxiliary cat qubit 6 is connected to two data cat qubits 4 by CNOT gates 8. The connections between the data cat qubits 4 and the auxiliary cat qubits 6 are such that one data cat qubit 4 is connected to at most two auxiliary cat qubits 6. Each auxiliary cat qubit 6 is also connected to a device for measuring a parity operator with photon number 10, which is intended to detect phase errors as cycles of the error repetition code are implemented.

[0028] As explained at the beginning, the implementation of the repeat code is as follows: - for each auxiliary cat qubit 6, a state that is a suitable state for the Pauli operator X TIFF2025509669000011.tif6150 or Preparation in TIFF2025509669000012.tif6150 and - applying each CNOT gate 8, where the CNOT gates 8 associated with the same auxiliary Cat qubit 6 are applied sequentially, i.e., one after the other without overlapping, such that the Cat qubit 6 receives the state of the data Cat qubit 4 connected by the respective CNOT gate 8; - for each auxiliary cat qubit, a measurement of the parity of the photon number is performed; and This is carried out by

[0029] All known systems use the same cat qubit for the data cat qubit 4 and for the auxiliary cat qubit 6. Much of the focus has been on improving the κ1 / κ2 ratio of the cat qubit. However, this is complex, and currently, all efforts to improve κ2 result in a proportional increase in κ1. More specifically, there are several techniques for stabilizing cat qubits. In general, techniques that allow for a very low κ1 ratio (such as 3D cavities) are difficult to strongly couple the cat qubit to, and therefore result in high values ​​of κ2. Conversely, some techniques (such as 2D resonators or resonant cat-like circuits) allow for much higher values ​​of κ2 because it is easier to strongly couple the cat, but these circuits are much more difficult to isolate from the environment and therefore result in a high one-photon loss rate κ1.

[0030] Applicants have found that it may be interesting to use different cat qubits for the data cat qubit 4 and the auxiliary cat qubit 6. Indeed, in iteration code 2, the roles of the data cat qubit 4 and the auxiliary cat qubit 6 are very different. This is explained in principle and then in detail in FIG. 2, where, for the same fixed value of κ / κ, there are advantages to using a higher value of κ for the auxiliary cat qubit 6 compared to κ for the data cat qubit 4.

[0031] The interest of such a choice can be explained as follows: As explained with reference to Figure 1, the typical time T of an error correction cycle depends mainly on the time scale set by the two-photon dissipation rate of the ancillary cat qubit 6. Thus, TIFF2025509669000013.tif9150, where C is in the range [0.1;10]. However, the typical error rate for the data cat qubit 4 during this cycle is The file is TIFF2025509669000014.tif6150.

[0032] Assume that the ratio of one-photon loss to two-photon dissipation is the same for the auxiliary cat qubit 6 and the data cat qubit 4. TIFF2025509669000015.tif6150, but there is an asymmetry between the auxiliary cat qubit 6 and the data cat qubit 4, The file is TIFF2025509669000016.tif6150.

[0033] However, what matters most during a code cycle is the total probability of a phase shift error for the data cat qubit 4, and this probability is Given as TIFF2025509669000017.tif6150.

[0034] Figure 2 shows the consequences of this asymmetry.

[0035] As shown in this figure, we can digitally evaluate the error introduced into the system (auxiliary cat qubit and data cat qubit) by performing a CNOT gate between the two cats, with different asymmetries Δ (along the x-axis) and two different photon numbers α 2 = 4, 7 with a constant relative ratio δ = 10 -3 There is a one photon loss at . Of course, other values ​​of δ and α can be considered. For example, α 2 The range of interest for large-scale quantum computers is from 2 to 20-30 photons at most. The time for a CNOT gate is It is set as TIFF2025509669000018.tif6150.

[0036] The resulting errors are divided into two categories: there are 12 quantum errors (IX, IY, XI, XX, XY, XZ, YI, YX, YY, YZ, ZX, ZY), and at least one or both of the cats contain a specific bit error component, and these errors are expressed as α 2 is exponentially suppressed by , which can be seen in the green curve on a logarithmic scale.

[0037] What is interesting is the behavior of the remaining three quantum errors, which are pure phase changes and are not exponentially suppressed: the auxiliary cat qubit qubit Z a(the top curve of the graph, almost flat), the phase change of qubit Z of the data cat qubit d Phase change of (bottom curve of the graph, almost flat), Z a Z d The phase change (qubit Z d α when passing under the curve 2 (This is the curve with the largest change between the other two curves except for Δ = 4). Figure 2 is presented on a logarithmic scale. A linear scale representation would show that the error of the data cat qubit decreases linearly with increasing asymmetry Δ.

[0038] As mentioned above, the phase error of the data qubit (the two superimposed orange curves) decreases linearly as the asymmetry Δ decreases, while the pure phase change of the control qubit increases slightly, but this only introduces a measurement error that does little damage to the error correction.

[0039] Therefore, the applicant We propose a first embodiment of the repetition code 2 according to FIG. 1 with an asymmetry such that TIFF2025509669000019.tif6150 is in the range [1;50] for all possible values ​​of the range, including 2, 5, 20, 30 and 50.

[0040] This repetition code 2 implements the correction cycle shown in Figure 3, i.e. the repetition of the following operations: a) Set auxiliary cat qubit 6 to state X TIFF2025509669000020.tif6150 or Prepare with TIFF2025509669000021.tif6150, b) activating one of the two CNOT gates 8 connected to that auxiliary cat qubit 6; c) activating other CNOT gates 8 connected to that auxiliary cat qubit 6; and d) Measuring the parity of the photon number of the auxiliary cat qubit 6.

[0041] In Figure 3, three successive modification cycles are shown, with time progressing from left to right. Thus, the leftmost element represents the operation performed first, and two vertically adjacent elements indicate simultaneous or near-simultaneous operations. The operation involving data cat qubit 4 is denoted "data cat qubit," and the operation involving auxiliary cat qubit 6 is denoted "auxiliary cat qubit."

[0042] Applicants have found this embodiment to be highly advantageous, and can improve the error tolerance threshold by a factor of two or more.

[0043] Also, in this implementation, the asymmetry Δ in the two-photon dissipation rate results in It was also discovered that slight distortions ("leakage" in English) can occur in the data cat qubit because the gates are too fast compared to the timescale of the data cat qubit given by TIFF2025509669000022.tif6150.

[0044] In fact, the gate time is approximately TIFF2025509669000023.tif11150. As Δ increases, the typical time scale The gates are faster compared to TIFF2025509669000024.tif6150. This can lead to significant distortion of the data cat qubit. The fact that the data cat qubit is distorted (a significant portion of the probability density of the data cat qubit no longer lies within the cat qubit subspace) can lead to two undesirable effects: the introduction of exponentially unsuppressed bit errors, and an increase in the logic error rate due to time correlation in the measurement errors.

[0045] Therefore, the applicant has implemented a second embodiment of Repetition Code 2, the correction cycle of which is shown in Figure 4. In this figure: TIFF2025509669000025.tif6150 is It is shown as TIFF2025509669000026.tif6150, TIFF2025509669000027.tif6150 is The reconvergence, denoted TIFF2025509669000028.tif6150 and described below, is denoted "refresh time."

[0046] As shown in this figure, the cycles are very similar to those of FIG. 3, but with a refresh time between Δ conventional error cycles.

[0047] The idea behind this second embodiment is to insert a "wait time" or "refresh / reconvergence time" after performing a predetermined number of error correction cycles (an error correction cycle in the repeated code consists of preparing the auxiliary Cat qubit, applying two CNOT gates, and measuring the auxiliary Cat qubit).

[0048] During these refresh times, the two-photon pumping of the data Cat qubits is turned on for a period of time sufficient for the state of these qubits to return to the Cat qubit subspace, i.e., for distortions of the data Cat qubits induced by the previous measurement cycle to be suppressed.

[0049] A typical duration of the refresh time for a data cat qubit is These wait times inevitably introduce additional phase errors into the data cat qubits, as they are always subject to error mechanisms during these "long" convergence times. Nevertheless, applicants have found that concatenating "fast" error correction cycles and refreshing the data cat qubits after the distortions caused by these fast cycles before restarting results in higher code performance than symmetric modes of operation, where the error correction cycles are slow but cause little or no distortion to the data cat qubits, and therefore no refresh time is required. The number of error correction cycles that can be performed before a refresh is required typically depends on the asymmetric The range is TIFF2025509669000030.tif6150.

[0050] Figure 6 shows a curve illustrating the distortion of a data cat qubit that occurs during the implementation of the repeating code according to the correction cycle of Figure 4. TIFF2025509669000031.tif6150 is Shown in TIFF2025509669000032.tif6150, TIFF2025509669000033.tif6150 is TIFF2025509669000034.tif6150. The vertical axis, referenced "Leakage," represents the distortion rate, i.e., the probability density of the data cat qubit lying outside the cat's subspace as a function of cycle time. This number varies between 0 and 1, being 0 when the qubit's state is completely within the subspace, and 1 when it is no longer. The higher this number, the more distortion there is in the cat qubit. The horizontal axis is time, measured in units of The file is TIFF2025509669000035.tif6150.

[0051] Thus, this figure shows the distortion rate obtained for three different ratios Δ. After each refresh period, the distortion rate appears to return to the lower bound, indicating that the correction cycle in Figure 4 is effective in suppressing the distortion caused by the high speed of the quantum gates.

[0052] Applicants have found this second embodiment to be highly advantageous, and can improve the error tolerance threshold by a factor of four or more.

[0053] Figure 10 shows the evolution of the phase error probability as a function of the value of the ratio δ as a function of the dimension d of the repetition code when the ratio Δ is 1. Since the ratio Δ is equal to 1, we are dealing with a "traditional" repetition code, which is considered "symmetric", and this figure represents state-of-the-art performance.

[0054] For comparison, when δ is 0.001 and d is 3, the probability is approximately 0.02. When δ is 0.003, the probability is between 0.02 and 0.06 for all values ​​of d.

[0055] Figure 11 shows the variation of the phase error probability as a function of the value of the ratio δ as a function of the dimension d of the repetition code when the ratio Δ is 21. Since the ratio Δ is equal to 1, the repetition code is one of the present invention and is considered "asymmetric".

[0056] Considering again the state-of-the-art values ​​shown in Figure 10, -If δ is 0.001 and d is 3, the probability is 0.002 (a gain ratio of 10 compared to the state of the art), When -δ is 0.003, the probability is 0.02 if d is 3 (a gain ratio of 3 compared to the state-of-the-art), the probability is 0.005 if d is 5 (a gain ratio of 10 compared to the state-of-the-art), and the probability is 0.001 if d is 7 (a gain ratio of 50 compared to the state-of-the-art).

[0057] Figures 6 and 7 show the "physical" implementation of Repeat Code 2 of Figures 1-5.

[0058] In this first embodiment, performed in the laboratory, the repeating cord 2 comprises an electromagnetic isolating device 60 including a base 62 made of an artificial magnetic conductor, from which rises a plurality of protrusions forming a bed of nails 64. The electromagnetic device 60 includes a portion that fits over the bed of nails to form an interdiction electromagnetic band structure. The bed of nails has a regular pattern of nails 64. The device 60 is the subject of a patent application bearing application number FR2111275.

[0059] The electromagnetic isolation device 60 is intended to confine the electromagnetic field within the 3D cavity of the data cat qubit 4 described below, limiting radiative loss of the data qubit trapped therein (which reduces single-photon loss).

[0060] Thus, the repetition code 2 contains three data cat qubits 4, which here are cat qubits stabilized in 3D cavity modes, with typical values Typical values ​​of κ1 achieved by this design are The file is TIFF2025509669000037.tif6150.

[0061] 7, these qubits are mounted in a cavity 66 with a finger 68 extending down the center in the same direction as the nail 62. The data cat qubit 4 is created by an ATS (Asymmetrically Threaded SQUID) circuit 70.

[0062] The ATS circuit 70 includes a SQUID (Superconducting Quantum Interference Device) shorted in the middle by a large inductance, forming two loops, and surrounded on either side by two pads 72 made of superconducting material. The ATS circuit 70 is powered by three lines 74, two of which carry the pumping current for the data cat qubit 4 and flow to the ATS circuit 70 to stabilize the qubit. The third line allows a return current for the flow. The ATS circuit 70 is the subject of U.S. patent application published under US2021 / 0234086.

[0063] The state of data cat qubit 4 can be read by a conventional device 76. In the example described herein, device 76 is formed by a transmon comprising two pads and a Josephson junction coupled to a measurement resonator of a transmon coupled to a transmission line. Alternatively, device 76 can be fabricated in many other ways that are conventional in the current state of the art.

[0064] CNOT gate 8 is created by a transmission line 78 connecting one of pads 72 to the auxiliary Cat qubit 6. The transmission line acts as a "coupler," increasing the participation of the auxiliary Cat qubit 6's modes in the Josephson junction of ATS 70 and enabling nonlinear coupling between the auxiliary Cat qubit 6 and the data Cat qubit 4. CNOT gate 8 can be activated by adding one or more signals to line 74.

[0065] In the examples described herein, the auxiliary cat qubit 6 has a typical value TIFF2025509669000038.tif8150 is a 2D resonant cat qubit80. Typical values ​​of κ1 achieved by this design are TIFF2025509669000039.tif6150. More specifically, the 2D resonant cat qubit has two modes, wa and wb, such that wb = 2wa. The Schrödinger cat state is stable in the wa mode, and the wb mode is an auxiliary mode. The auxiliary cat qubit is also powered by a transmission line, which can provide a direct current to control the flow applied to the auxiliary cat qubit's circuit and can also couple to an auxiliary mode located in the auxiliary cat qubit's circuit. 2D resonant cat qubits are the subject of European Patent Application EP21306965.1. Device 81 allows the state of auxiliary cat qubit 6 to be read and implements Device 10. Device 81 can be fabricated in a manner similar to Device 76.

[0066] In this illustration, some nails 64 are intentionally not shown below cavities 66 to make line 74 easier to see, but these are in fact much smaller than nails 64 and are located between nails 64, and the pattern of the bed of nails 64 is periodic except where cavities 66 are located.

[0067] Figures 8 and 9 show an alternative implementation. For brevity, we will only describe the differences from Figures 6 and 7. In this variant, the cat qubit 6 is always 2D, but this time it is not resonant and is stabilized by the ATS 82.

[0068] As mentioned above, data cat qubits are always identical to each other. To limit the risk of crosstalk due to frequency crowding phenomena, the frequencies of the data cat qubit modes are clearly distinguishable between spatially adjacent qubits. This crosstalk causes control of one qubit to affect neighboring qubits whose resonant modes are at similar frequencies. Furthermore, data cat qubits can be fabricated in different ways than cat qubits stabilized in the modes of a 3D cavity. The embodiments of Figures 6-9 are intended to illustrate the generality of the present invention and should not be construed as limiting.

[0069] The present invention also relates to architectures in which cat qubits are used in error-correcting codes that are different from repetition codes. More specifically, the present invention also relates to surface code architectures based on cat qubits.

[0070] In fact, the strategy of using a repetition code to correct phase errors in cat qubits is appropriate when the noise bias of the cat qubits in question is very high, i.e., when the probability of a single bit error occurring in the entire system (across all cat qubits in the system, over the entire typical operating period of the system; i.e., during the typical execution time of a quantum algorithm on the architecture in question) is very low compared to the probability of a logical phase error.

[0071] If the noise bias is not high enough (e.g., because the size of the cat qubit measured in number of photons is not high enough; or the bit error rate saturates and does not increase with cat size, which occurs for large numbers of photons when the physical phenomena causing the bit errors are no longer local), it may be interesting to use, instead of a repetition code, a surface code that exclusively corrects only phase errors, or another quantum error-correcting code that can also tolerate a small number of bit errors.

[0072] In these embodiments, the use of auxiliary cat qubits whose two-photon dissipation rate is ensured to be greater than that of the data cat qubit is also advantageous for the same reasons as above. Indeed, for the surface code, the stabilizer (the quantum operator measured by the data qubit to detect errors) is TIFF2025509669000040.tif6150 and The format is TIFF2025509669000041.tif6150. Stabilizer S j For the measurement of x, an error correction cycle is performed, which involves preparing the auxiliary cat, applying four CNOT gates, and measuring the auxiliary cat's operator X. As with repetition codes, the typical speed at which this cycle is performed depends primarily on the stabilization speed (two-photon dissipation) of the auxiliary cat. Therefore, using two different technologies for the auxiliary cat and the data cat improves the performance of the code and increases the value of the error correction threshold.

[0073] FIG. 12 shows a block diagram of such a surface code.

Claims

1. A cat qubit repetition code, comprising a number d of data cat qubits (4) and at least (d-1) auxiliary cat qubits (6), the number d being 3 or greater; each auxiliary cat qubit (6) is connected to two data cat qubits (4) by two respective CNOT gates (8) such that no data cat qubit (4) is connected to more than two auxiliary cat qubits (6); the two-photon dissipation rate of the auxiliary Cat qubit is greater than the two-photon dissipation rate of the data Cat qubit; The repetition code performs at least the following operations for each auxiliary cat qubit (6): a) The auxiliary cat qubit (6) is put into a state suitable for operator X: or To prepare with b) activating one of the two CNOT gates (8) connected to that auxiliary cat qubit (6); c) activating the other CNOT gate (8) connected to that auxiliary cat qubit (6); d) measuring the parity of the photon number of the auxiliary cat qubit (6); [0033] Implemented by performing an error correction cycle including: A cat qubit repetition code characterized by:

2. 2. The repetition code of claim 1, wherein the two-photon dissipation rate of the ancillary Cat qubit (6) is selected to be substantially equal to a multiple of the two-photon dissipation rate of the data Cat qubit, the multiple being selected from the group consisting of 2, 5, 20, 30, and 50.

3. 3. The repetition code of claim 1 or claim 2, wherein operations a) through d) are repeated for each auxiliary Cat qubit (6) a number of times substantially equal to the ratio of the two-photon dissipation rate of the data Cat qubit (4) to the two-photon loss rate of the auxiliary Cat qubit (6), followed by a refresh operation having a duration within the reciprocal of the two-photon dissipation rate of the data Cat qubit (4).

4. 3. The repetition code of claim 1 or claim 2, wherein the error correction cycle is performed substantially simultaneously for all of the auxiliary cat qubits (6).

5. 5. The repetition code of claim 4, wherein for each auxiliary cat qubit (6), operations a) to d) are performed sequentially.

6. 3. The repetition code of claim 1 or claim 2, wherein the data cat qubits (4) are stabilized in the mode of a 3D cavity using an ATS circuit (70).

7. 3. The repetition code of claim 1 or claim 2, wherein the auxiliary cat qubit (6) is a resonant cat qubit (80).

8. 3. The repetition code of claim 1 or 2, wherein the auxiliary cat qubit (6) is a cat qubit stabilized in the mode of a 2D resonator using an ATS circuit (82).

9. a surface code for cat qubits, comprising a number d of data cat qubits (4) and at least (d-1) ancillary cat qubits (6), the number d being 3 or greater; each auxiliary cat qubit (6) is connected to four data cat qubits (4) by four respective CNOT gates (8) such that no data cat qubit (4) is connected to more than four auxiliary cat qubits (6); the two-photon dissipation rate of the auxiliary Cat qubit is greater than the two-photon dissipation rate of the data Cat qubit; The surface code includes at least the following operations for each auxiliary cat qubit (6): a) Put the auxiliary cat qubit (6) into state X or To prepare with b) sequentially activating the CNOT gates (8) connected to the auxiliary cat qubits (6); c) measuring the parity of the photon number of the auxiliary cat qubit (6); This is implemented by executing a cycle containing The cat qubit surface code is characterized by:

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