ERROR-TOLERANT QUBITS VIA MULTIMOD RESONATORS

Abstract

A quantum computing system may include one or more multimode resonators and one or more superconducting control circuits, where each of the one or more superconducting control circuits is coupled to one or more multimode resonators, and where each of the one or more superconducting control circuits includes a superconducting nonlinear circuit. The system may also include a controller. The controller can create, in at least one of the one or more multimode resonators, multiple cat qubits associated with multiple acoustic modes by parametric coupling to at least one of the one or more superconducting control circuits.The controller can also implement, in at least one of the one or more multimode resonators, a logic qubit based on multiple error-correcting chat qubits using parameter-driven interactions with at least one of the one or more superconducting control circuits. Selected figure: Fig. 1A.

Description

Title of the invention: ERROR-TOLERANT QUBITS VIA MULTIMOD RESONATORS technical field

[0001] The present disclosure relates generally to quantum computing and, more particularly, to the provision of error-corrected logic bits based on multiple qubits of cat in an acoustic resonator by parametric coupling to a superconducting nonlinear circuit. Context of the invention

[0002] Quantum computers consist of qubits that are controlled and coupled via quantum circuits. Quantum computers are subject to errors that produce undesirable changes in the state of the qubits. Therefore, error-correcting algorithms must be used to combine multiple physical qubits into a single logical qubit, where errors can be detected and corrected. The number of resources required for error-correcting algorithms increases with the error rate. Hardware improvements have plateaued, as physical error rates are too high to be practical. Cat qubits use a continuous-variable quantum system to encode a qubit and are able to exponentially suppress one of the error channels (e.g., bit inversions) by using this additional degree of freedom.However, the current state of the art uses large single-mode resonators to encode each chat qubit, which are therefore not scalable. Consequently, a scalable physical platform is needed to overcome the above limitations. Summary

[0003] In embodiments, the techniques described herein relate to a quantum computing system, including one or more multimode resonators; one or more superconducting control circuits, wherein each of the one or more superconducting control circuits is coupled to one or more multimode resonators, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit; and a controller including one or more processors configured to execute program instructions causing the one or more processors to create, in at least one of the one or more multimode resonators, multiple cat qubits associated with multiple acoustic modes by parametric coupling to at least one of the one or more superconducting control circuits; and implementing, in at least one of the one or more multimode resonators, a logic qubit based on multiple qubits of cat error correction using parameter-driven interactions with at least one of one or more superconducting control circuits.

[0004] In embodiments, the techniques described here relate to a quantum computer system, in which at least one of the one or more superconducting control circuits further includes a read resonator coupled to the superconducting nonlinear circuit for reading a state of at least one of any of the multiple cat qubits or any of the logic qubits.

[0005] In embodiments, the techniques described here relate to a quantum computer system, in which one or more multimode resonators and one or more superconducting control circuits are fabricated on a common substrate.

[0006] In embodiments, the techniques described here relate to a quantum computer system, in which the one or more multimode resonators are epitaxial high harmonic volume elastic wave (HBAR) resonators.

[0007] In some embodiments, the techniques described here relate to a quantum computer system, where the superconducting nonlinear circuit includes a Josephson junction.

[0008] In embodiments, the techniques described here relate to a quantum computer system, where the creation of a particular cat qubit among the multiple cat qubits includes at least one of the preparation of a particular multimode resonator among the one or more multimode resonators in one of two cat states or the stabilization of the particular multimode resonator in a manifold generated by the two cat states.

[0009] In embodiments, the techniques described here relate to a quantum computer system, in which the logic qubit in a particular multimode resonator among one or more multimode resonators is coded using the multiple chat qubits in the particular multimode resonator by means of a non-local error-correcting code.

[0010] In some embodiments, the techniques described here relate to a quantum computer system, where the non-local error correction code is a low-density parity checking (LDPC) error correction code.

[0011] In some embodiments, the techniques described here relate to a quantum computer system, where error correction is biased by noise.

[0012] In some embodiments, the techniques described here relate to a quantum computer system, where the controller includes one or more excitation generators to provide excitation signals to any of the nonlinear circuits superconductors for at least one of the following: the creation of multiple chat qubits, the stabilization of multiple chat qubits, or the implementation of error correction.

[0013] In embodiments, the techniques described here relate to a quantum computing system, where the one or more multimode resonators include two or more multimode resonators coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, where a particular superconducting coupling circuit among the one or more superconducting coupling circuits includes an additional superconducting nonlinear circuit coupled to two of the two or more multimode resonators.

[0014] In embodiments, the techniques described here relate to a quantum computer system, where one or more processors are further configured to execute program instructions causing one or more processors to implement additional error correction on any of the logical qubits in any of two or more multimode resonators.

[0015] In embodiments, the techniques described here relate to a quantum computer system, where one or more processors are further configured to execute program instructions causing one or more processors to implement one or more quantum logic operations on any one of the logical qubits in any one of two or more multimode resonators.

[0016] In embodiments, the techniques described here relate to a quantum computer system, where the particular superconducting coupling circuit among one or more superconducting coupling circuits further includes an additional readout resonator.

[0017] In embodiments, the techniques described here relate to a quantum computer system, where the controller includes one or more excitation generators to provide excitation signals to any of the superconducting nonlinear circuits for at least one of the creation of multiple chat qubits, the implementation of error correction or the control of interactions between any of two or more multimode resonators.

[0018] In embodiments, the techniques described herein relate to a quantum computing system, including a controller comprising one or more processors configured to execute program instructions causing the one or more processors to create, in at least one of the one or more multimode resonators, multiple chat qubits associated with multiple acoustic modes by parametric coupling to one or more superconducting control circuits, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit coupled to one of the one or more multimode resonators; and implement, in at least one of the one or more multimode resonators, a logic qubit based on multiple chat qubits by error correction using parameter-driven interactions with the coupled superconducting control circuit.

[0019] In embodiments, the techniques described here relate to a quantum computer system, in which at least one of the one or more superconducting control circuits further includes a read resonator coupled to the superconducting nonlinear circuit for reading a state of at least one of any of the multiple cat qubits or the logic qubit.

[0020] In embodiments, the techniques described here relate to a quantum computing system, where the one or more multimode resonators include two or more multimode resonators coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, where a particular superconducting coupling circuit among the one or more superconducting coupling circuits includes an additional superconducting nonlinear circuit coupled to two of the multimode resonators.

[0021] In embodiments, the techniques described herein relate to a quantum computing method, including the creation, in at least one of the one or more multimode resonators, of multiple chat qubits associated with multiple acoustic modes by parametric coupling to one or more superconducting control circuits, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit coupled to one of the one or more multimode resonators; and the implementation, in at least one of the one or more multimode resonators, of a logic qubit based on the multiple chat qubits by error correction using parameter-driven interactions with the one or more superconducting control circuits.

[0022] In embodiments, the techniques described herein relate to a quantum computing method, wherein the two or more multimode resonators are coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, wherein a particular superconducting coupling circuit among the one or more superconducting coupling circuits includes an additional superconducting nonlinear circuit coupled to two of the two or more multimode resonators, wherein the method further includes the implementation of at least one of an additional error correction or a quantum logic operation on any one of the logic qubits in any one of the two or more multimode resonators.

[0023] It is understood that both the preceding general description and the following detailed description are given by way of example and explanation only and do not limit not the scope of the present invention. The drawings in the appendix, which are incorporated into this document and form part thereof, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. Brief description of the drawings

[0024] The many advantages of disclosure can be better understood by a person skilled in the art with reference to the attached figures.

[0025] Figure [Fig.1A] illustrates a functional diagram of a quantum computer system, in accordance with one or more embodiments of the present disclosure.

[0026] Fig. 1B illustrates a schematic diagram of part of a superconducting control circuit and schemes of operations realizable via parametric interactions, according to one or more embodiments of this disclosure.

[0027] Fig. 2 represents a Bloch sphere representing a state of a cat qubit, in an illustrative embodiment.

[0028] Figure 3 illustrates a diagram showing details of the multimode resonator, in accordance with one or more embodiments of this disclosure.

[0029] Fig. 4 is a diagram illustrating a parametric coupling between the superconducting nonlinear circuit and the multimode resonator.

[0030] Fig. 5 is a graph of the reflection spectrum of the multimode resonator.

[0031] Figure 6 illustrates a chain of multimode resonators that are controlled by superconducting control circuits and coupled to superconducting coupling circuits, according to one or more embodiments of this disclosure.

[0032] Figure 7 illustrates a fault-tolerant quantum computing method, in accordance with one or more embodiments of this disclosure. Detailed description

[0033] Reference will now be made in detail to the disclosed object, which is illustrated in the accompanying drawings. The present disclosure has been particularly represented and described with respect to certain embodiments and their specific features. The embodiments shown here are considered illustrative rather than limiting. It should be obvious to those skilled in the art that various changes and modifications to the form and details can be made without departing from the spirit and scope of the disclosure.

[0034] Embodiments of this disclosure relate to systems and methods providing fault-tolerant quantum computing. In some embodiments, a quantum computing system can create and / or stabilize Multiple cat qubits in a single multimode resonator, such as an acoustic resonator, are interacted with a superconducting control circuit, including a superconducting nonlinear circuit (e.g., a Josephson junction, or similar). The quantum computing system can further implement a logic qubit in each multimode resonator associated with the multiple cat qubits via an error-correcting code using parameter-driven interactions with a superconducting control circuit.

[0035] It is envisaged here that this configuration could provide an architecture for stable and scalable quantum computing. Cat states are biased by noise and can naturally suppress bit inversion errors, constituting a promising avenue for efficient error tolerance. In particular, the use of cat states can provide a form of hardware suppression of bit inversion errors so that error-correcting codes can focus entirely or primarily on phase inversion errors. Furthermore, parametric interactions between the superconducting control circuit and the multimode resonator can enable the use of non-local error-correcting codes for the efficient implementation of a single error-tolerant logic qubit in a single multimode resonator based on multiple cat qubits stabilized in the multimode resonator.In addition, multiple multimode resonators can be coupled in a one-dimensional (1D) chain configuration via superconducting coupling circuits that also include superconducting nonlinear circuits to provide additional error correction and / or quantum logic operations on the error-tolerant logic qubits.

[0036] With reference now to [Fig.1A]-7, the systems and methods providing error-tolerant quantum computing are described in accordance with one or more embodiments of this disclosure.

[0037] Figure 1A illustrates a functional diagram of a quantum computing system 100, according to one or more embodiments of this disclosure. In some embodiments, a quantum computing system 100 includes one or more multimode resonators 102 and one or more superconducting control circuits 104 suitable for parametric coupling to the multimode resonators 102.

[0038] A superconducting control circuit 104 may include a superconducting nonlinear circuit 106 suitable for providing parametric interactions with modes in a multimode resonator 102. The superconducting nonlinear circuit 106 may include any superconducting element, including, but not limited to, a Josephson junction. The superconducting control circuit 104 may further include a reading resonator 108, which can be considered as part of the superconducting nonlinear circuit 106 or as a separate element.

[0039] The multimode resonator 102 may include any type of resonator suitable for supporting multiple modes that can be manipulated through parametric interactions with the superconducting nonlinear circuit 106. For example, the multimode resonator 102 may include, but is not limited to, an acoustic resonator. In some embodiments, the multimode resonator 102 is an epitaxial high-harmonic volume elastic wave (HBAR) resonator.

[0040] The quantum computing system 100 may further include one or more superconducting coupling circuits 110 for connecting multimode resonators 102 in a chain configuration. For example, [Fig. 1A] shows two multimode resonators 102 coupled by a single superconducting coupling circuit 110. A superconducting coupling circuit 110 may also include an additional superconducting nonlinear circuit 112 and an additional readout resonator 114. In some cases, the superconducting coupling circuits 110 have the same design as a superconducting control circuit 104, except that they are configured to be coupled to two multimode resonators 102.

[0041] The multimode resonators 102, the superconducting control circuits 104 and / or the superconducting coupling circuits 110 can be fabricated on a single chip (e.g., on a common substrate), which can reduce cost and complexity while improving performance.

[0042] The quantum computing system 100 may further include a controller 116 comprising one or more processors 118 configured to execute program instructions stored in a memory 120. In this way, the controller 116 (for example, via the processors 118) can perform any operation or step disclosed herein directly or through excitation signals. For example, the controller 116 may include an excitation generator 122 to generate excitation signals for the superconducting control circuits 104 and / or the superconducting coupling circuits 110 to perform parametric interactions in any of the multimode resonators 102.

[0043] The one or more processors 118 of a controller 116 may include any processing element known in the art. In this sense, the one or more processors 118 may include any microprocessor-type device configured to execute algorithms and / or instructions. For example, the processors 118 may include a digital signal processor (DSP), a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a central processing unit (CPU), or a graphics processing unit (GPU). The memory 120 may include any storage medium known in the art suitable for storing program instructions executable by the associated processor(s). For example, memory may include non-transient memory. As another example, memory may include, but is not limited to, read-only memory, random access memory, magnetic or optical storage devices (e.g., disks), magnetic tape, solid-state drives, and the like.

[0044] The excitation generator 122 may include any type of signal generator known in the art suitable for generating excitation signals of any type suitable for inducing parametric interactions between a multimode resonator 102 and a superconducting control circuit 104 and / or a superconducting coupling circuit 110. For example, the excitation generator 122 may be an electrical signal generator that can generate electrical excitation signals at selected frequencies to provide parametric interactions between modes in or between any of the multimode resonators 102. Furthermore, the excitation generator 122 may be incorporated as a standalone component or integrated with other components in the controller 116 such as, but not limited to, the processors 118.

[0045] A superconducting control circuit 104 can perform multiple functions to achieve both physical and coding efficiency. For example, the superconducting control circuit 104 can use parametric interactions (e.g., based on excitation signals from the excitation generator 122) to create and stabilize multiple cat qubits in a single multimode resonator 102, where a particular cat qubit is created and stabilized by preparing the multimode resonator 102 in one of two cat states and then maintaining a manifold generated by the two cat states. The superconducting control circuit 104 can use any type of stabilization technique, including, but not limited to, dissipative stabilization or nonlinear stabilization.

[0046] By way of further example, the superconducting control circuit 104 can use parametric interactions to measure (e.g., read) the state of a cat qubit via the superconducting nonlinear circuit 106 and a readout resonator 108. As another example, the superconducting control circuit 104 can implement an error-correcting code to train a logic qubit in a single multimode resonator 102 based on the multiple cat qubits in the multimode resonator 102. This error-correcting code can be a non-local code that provides arbitrary interactions between cat qubits in the same multimode resonator 102, thus allowing the correction of more errors per qubit than is possible with local codes (e.g., based on planar interactions). Any type of non-local code can be used, including, but not limited to, an error-correcting code low-density parity checking errors (LDPC). As another example, the superconducting control circuit 104 can measure (e.g., read) a state of a logic qubit associated with a multimode resonator 102.

[0047] A superconducting coupling circuit 110 may also include a superconducting nonlinear circuit 112 (for example, a Josephson junction or similar) and a readout resonator 114, but may provide parametric interactions with two multimode resonators 102. In this way, superconducting coupling circuits 110 can provide various error-correcting operations on logic qubits. For example, superconducting coupling circuits 110 can provide an additional error-correcting code on the logic qubits. As another example, superconducting coupling circuits 110 can implement error-tolerant quantum logic operations.

[0048] Fig. 1B illustrates a schematic diagram of part of a superconducting control circuit 104 and schemes of operations realizable via parametric interactions, according to one or more embodiments of this disclosure.

[0049] A panel 124 represents a schematic diagram of a superconducting control circuit 104 that includes a superconducting nonlinear circuit 106 and a multimode resonator 102. In some embodiments, the superconducting nonlinear circuit 106 includes a superconducting playback resonator 108 and a Josephson junction element 126 (element marked JJ) to provide a source of nonlinearity and allow parametric coupling to one or more modes of the multimode resonator 102. In FIG. IB, the acoustic modes of the multimode resonator 102 are represented by and the superconducting nonlinear circuit 106 has a natural radio frequency of w <l. Les panneaux 130-134 illustrent trois exemples non limitatifs de contrôles paramétriques, où les encarts 136-140 illustrent les différents modes impliqués dans l’interaction effective que le signal de contrôle paramétrique produit, la flèche pleine représentant le taux d’interaction pertinent.

[0050] In FIG. IB, the quantum degrees of freedom are represented as circles. For example, FIG. IB represents a mode a of a superconducting nonlinear circuit 106 as well as acoustic resonator modes bn).

[0051] The excitation signals 128 (for example, from the excitation generator 122) may include parametric tones (for example, frequencies) which can be used to perform various functions such as, but not limited to, creating cat qubits, stabilizing cat qubits, implementing gates on cat qubits, and / or measuring cat qubit states by inducing coupling (for example, parametric coupling) with the superconducting nonlinear circuit 106. In some embodiments, the excitation signals 128 are provided in the form of external flux passing through the Josephson junction element 126 of the superconducting control circuit 104.

[0052] Panel 130 represents a technique for preparing and / or stabilizing cat qubits. Cat qubits can be encoded in multiples of the modes of the multimode resonator 102 ^2,^3, • • •)• A cat qubit can be created and / or stabilized in an oscillating mode by supplying an excitation signal 128 to the superconducting nonlinear circuit 106 at a frequency 2a»n or a frequency close to it which represents twice the desired frequency, which is illustrated in box 136 and the arrow indicating the coupling K2n between the mode and T2. For example, an excitation signal suitable for preparing and / or stabilizing a cat qubit may exhibit a frequency ojp ~ r2cün- COq+ Ôp^ where Ôpp is a mismatch between the acoustic mode frequencies and the control circuit frequency.

[0053] Panel 132 represents a technique for making gates on cat qubits. Excitation signals 128 can be supplied to the superconducting nonlinear circuit 106 in order to realize gates on the cat qubits encoded in the multimode resonator 102. In some embodiments, the control of a cat qubit encoded in a mode is achieved by modulating the stabilizing excitation signal 128 (for example, an electrical signal) at 2wn as described above, and by producing additional tones at frequencies close to. For example, gates between a pair of cat qubits in modes with frequencies and 0^2 can be realized by supplying an electrical signal at the differential frequency ^2 " ^1 via a pair of parametric tones close to ^2 " ^1 " ^qct. As another example, Box 138 illustrates a ZiZ2 gate, which can be realized via the two tones œq+6zz} , where 6ZZ is a disagreement frequency. In this example, the ZiZ2 gate implies at, gt, 15 in order to produce an interaction plus a Hermitian conjugate.

[0054] Panel 140 represents a technique for performing a measurement (e.g., a reading) of cat qubits. In some embodiments, the reading resonator 108 can be used to measure the quantum states of the cat qubits stored in the multimode oscillator 102, which can be used for various operations, including, but not limited to, error correction. In some embodiments, the measurement can be performed using an excitation signal 128 to induce coupling between the multimode resonator 102 containing the cat qubit of interest and the reading resonator 108. By way of illustration, one may consider A case in which the readout resonator 108 has a natural radio frequency of and the polled cat qubit is encoded with a frequency of 0¾. An efficient coupling can be produced that transfers information in the polled cat qubit state to the readout resonator 108 via the nonlinear mode by applying a pair of tones close to the frequencies 2Wq - and . For example, inset 140 represents a readout operation based on excitation signals 128 with two tones: { MP} ~ {2Wç - + dM> Mq + ÔM} , where is a detuning frequency and Qr is a coupling between ^2f and

[0055] By implementing a series of gates and measurements as described above, the controller 116 can implement a quantum error-correcting code and thus encode one or more logic qubits using the state of several chat qubits in a single oscillator. Due to the high bias caused by chat qubit noise, where hardware error suppression exponentially reduces the bit inversion rate, a large portion of the error-correcting resources can be devoted to a single error channel, thereby increasing its efficiency. In various embodiments, this error-correcting code can be a quantum low-density parity control (LDPC) code due to the possibility of arbitrary chat qubit connectivity in a single oscillator.

[0056] Figure 2 illustrates a Bloch 200 sphere representing a state of a cat qubit, in an illustrative embodiment. A cat qubit is a qubit encoded in a variety of doubly degenerate ground states of a continuous-variable quantum system. In various embodiments, this quantum system can be an acoustic resonator mode coupled to a superconducting nonlinear circuit. Its degenerate pair of ground states can be written on the basis of coherent states {l+"h l-": I ±) =4| + a) ±| -a) (1) which are chosen to be the qubit states | + ) (for example, the eigenstates X as shown on the Bloch sphere). The computational basis states are therefore given by: | 0) = I +a) (2) And | 1) «| -a) (3) which form the poles of the Bloch sphere.

[0057] Cat qubits exponentially reduce the bit inversion error rate at the hardware level. By increasing the state amplitude fundamental a, the rate of bit inversions induced by the environment (between the states of equations (2) and (3)) decreases exponentially: « k| a| 2et'^ This is one of the two possible error channels that affect qubits. The other source of error comes from phase inversions, which excite transitions between the states |q-J and |I_) shown in equation (1). These states are separated by a single Fock space excitation (a photon, or in this case a phonon), and thus the bit inversion rate increases linearly with the number of excitations: IV.aK|a|2^

[0058] In standard quantum computing approaches, it is assumed that bit and phase inversion errors occur with approximately equal probability. However, according to equations (4) and (5), the cat qubit reduces both the overall error rate and produces biased noise, which can be corrected more efficiently. This is achieved by increasing |Ct| at the hardware level of the quantum computing system, which can be done in various embodiments by increasing the amplitude of the stabilizing tone or by reducing a theoretical dissipation rate. This then eliminates the computational bit inversion rate, making it possible to use efficient error-correcting codes that focus on eliminating the phase inversion error rate.

[0059] Figure 3 illustrates a schematic diagram 300 showing details of the multimode resonator 102, according to one or more embodiments of this disclosure. The schematic diagram 300 illustrates a cylindrical section of a larger substrate, indicating where the modes are supported. In various embodiments, the multimode resonator 102 is a composite high-harmonic volume elastic resonator (HBAR), comprising a piezoelectric transducer 304 on a low-loss substrate 302. The substrate, of thickness ts below the piezoelectric transducer 304, forms a phononic Fabry-Perot cavity that supports acoustic modes with frequencies: o>a = n where vs is the speed of sound in the substrate and n is the mode number. In various embodiments, the transducer may consist of a composite epitaxial structure to maximize acoustic impedance matching, including a piezoelectric material 306 of thickness tr that couples directly to the nonlinear superconducting circuit 106. The piezoelectric material converts electrical energy into acoustic energy, generating phonons in the acoustic modes of the cavity.

[0060] Figure 4 is a schematic diagram 400 illustrating parametric coupling between the superconducting nonlinear circuit 106 and the multimode resonator 102. A Josephson nonlinear element 402 is represented in the superconducting nonlinear circuit 106, and the coupling between the superconducting nonlinear circuit 106 and the piezoelectric transducer 304 is represented by a capacitor 404. The acoustic resonator consists of multiple modes 406 at frequencies that are generally far from the resonance of the superconducting nonlinear circuit 106 but which can be strongly coupled by parametric modulation of the Josephson nonlinear element 402. The generation of the acoustic modes 406 by piezoelectric coupling is represented by the first coupling arrow 408. The reading of the acoustic modes 406 is represented by the second coupling arrow 410.The interaction between the nonlinear superconducting circuit 106 and the acoustic modes is represented by equation (7): . H= cock a^â+^d2£clco^üjdt)( ât+ â)+2n«nîf,tS2i-2EjCos( (t))cos(ç)(r(u?( â++ â) +Snua( + (7) where at and are nonlinear mode creation and annihilation operators of circuit (for example a transmon), with an excitation frequency wa, and O are HU 71 creation and annihilation operators for the phononic mode with resonance a>b+nv^ is the free spectral domain (FSR) and 50 represents a shift of static flux. Here, the sum describes tones applied to the circuit mode nonlinear via the readout resonator, and the last term represents the interaction generated by the nonlinear Josephson 402 element, where and are hybridization coefficients. Different nonlinear terms can be controlled here by the 124 gates (i.e., an applied flux dependent on the time O(t)) and are explicitly represented with this dependence. The applied electrical signal can generally be written as: ^(t) = O0+2 p ^pcos( ü)pt\ (8) The final term in equation (7) describes the interaction between the nonlinear superconducting circuit 106 and the phononic modes provided by the piezoelectric transducer.

[0061] FIG. 5 is a graph 500 of the reflection spectrum of the multimode resonator 102. The frequency is shown along the x-axis in gigahertz (GHz) and a reflection coefficient is shown along the y-axis in decibels. The reflection spectrum combines the transduction envelope with the bare acoustic cavity modes of equation (6), and thus represents the phononic density of the states with which the superconducting nonlinear circuit 106 interacts. A box 502 shows a large spectrum plane from approximately 9 GHz to approximately 9.5 GHz, a region of mode factors of particularly high quality and therefore with a low phononic loss rate. This is of ideal modes for encoding cat qubits, because their loss rate naturally low K K~ 2Q will result in low phase inversion error rates (equation (5)) even with a high l^l value.

[0062] Figure 6 illustrates a chain of 600 multimode resonators 102a-102d that are controlled by superconducting control circuits 104a-104d and coupled to superconducting coupling circuits 110a-110c, according to one or more embodiments of this disclosure. This architecture can be used as a fault-tolerant universal quantum computer. Each of the superconducting control circuits 104a-104d is shown with an individual superconducting nonlinear circuit 106a-106d and a readout resonator 108a-108d. In this way, each control circuit 104a-104d can create, stabilize, read, and error-correct chat qubits in the associated multimode resonator 102a-d, and further generate logic qubits in the associated multimode resonators 102a-d as described in FIGS. 1 and 4. Similarly, the control circuits 110a-110c are each represented with additional individual superconducting nonlinear circuits 112a-112c and an additional readout resonator 114a-114c. In this way, the superconducting coupling circuits HOa-c can achieve intra-resonator interactions and thus provide additional error correction and / or quantum logic operations based on the logic qubits in the multimode resonators 102a-d. For example, the superconducting coupling circuits 110a-c (or the 600 chain in general) can implement a gauge code.

[0063] Figure 7 illustrates a fault-tolerant quantum computing method 700, according to one or more embodiments of this disclosure. The embodiments and enabling technologies described in the context of the superposition metrology quantum computing system 100 can be interpreted as extending to the method 700. For example, the method 700 can be implemented using the quantum computing system 100 described herein. However, the method 700 may not be limited to the specific architecture of the quantum computing system 100.

[0064] In some embodiments, the method 700 includes a step 702 of creating, in at least one of one or more multimode resonators, multiple chat qubits associated with multiple acoustic modes by parametric coupling to one or more control circuits. For example, as described with respect to the quantum computing system 100, step 702 may include the excitation of a superconducting nonlinear circuit 106 with excitation signals that induce parametric interactions to create and / or stabilize multiple chat qubits in a multimode resonator 102. In some embodiments, the method 700 includes a step 704 of implementing, in at least one of the one or more multimode resonators, a logic qubit based on the multiple chat qubits by error correction using parameter-driven interactions with the one or more control circuits. For example, as described with respect to the quantum computing system 100, step 704 may include the implementation of non-local error-correcting codes (e.g., via excitation signals) to implement a logic qubit in a multimode resonator 102 based on the multiple chat qubits in the multimode resonator 102. Furthermore, although not explicitly shown in [Fig.7], the method 700 may include the implementation of an additional error correction and / or quantum logic operation on any of the logic qubits in any of two or more multimode resonators 102 coupled by superconducting coupling circuits 110. .

[0065] Any of the methods described herein may include storing in memory the results of one or more steps of the process embodiments. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results have been stored, the results may be retrieved from memory and used by any of the process or system embodiments described herein, formatted for presentation to a user, used by another software module, process, or system, and so on. Furthermore, the results may be stored "permanently," "semi-permanently," "temporarily," or for a certain period of time.For example, the memory can be random access memory (RAM), and the results do not necessarily persist indefinitely in memory.

[0066] It is further envisaged that each embodiment of the process described above may include any other step of any other process described herein. Furthermore, each embodiment of the process described above may be carried out by any of the systems described herein.

[0067] Those skilled in the art will recognize that the components, operations, devices, and objects described herein, and the accompanying discussion, are used by way of example for the sake of conceptual clarity and that various configuration modifications are envisaged. Therefore, as used herein, the specific examples set forth and the accompanying discussion are intended to be representative of their more general classes. In general, the use of any example specific is intended to be representative of its class, and the non-inclusion of specific components, operations, devices and objects should not be considered limiting.

[0068] As used herein, directional terms such as "up," "down," "above," "below," "superior," "upward," "inferior," and "downward" are intended to provide relative positions for descriptive purposes and are not intended to designate an absolute frame of reference. Various modifications to the described embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments.

[0069] As regards the use of virtually any term in the plural and / or singular here, a person skilled in the art can translate from plural to singular and / or from singular to plural depending on the context and / or application. The various singular / plural permutations are not expressly set out here for the sake of clarity.

[0070] The object described herein sometimes illustrates different components contained within or connected to other components. It should be understood that the architectures shown are only examples and that it is in fact possible to implement many other architectures that achieve the same functionality. Conceptually, any arrangement of components to achieve the same functionality is effectively "linked" so that the desired functionality is achieved. Thus, any two components combined here to achieve a particular functionality can be considered "linked" to each other so that the desired functionality is achieved, regardless of the architectures or intermediate components.Similarly, any two components thus associated can also be considered as being "connected" or "coupled" to each other to achieve the desired functionality, and any two components capable of being thus associated can also be considered as being "couplingable" to each other to achieve the desired functionality. Specific examples of couplingable components include, but are not limited to, physically pairable and / or physically interacting components and / or components that can interact wirelessly and / or interact wirelessly and / or components that interact logically and / or can interact logically.

[0071] Furthermore, it should be understood that the invention is defined by the appended claims. It will be understood by those skilled in the art that, in general, the terms used herein, and in particular in the appended claims (for example, the bodies of the appended claims), are generally intended to be "open" terms (for example, the term "including" should be interpreted as "including, but not limited to", the term "having" should be interpreted as "having at least", the term "includes" should be interpreted as "includes, but not limited to", and the like). It will also be understood by those skilled in the art that if a specific number from an introduced list of claims is targeted, such an intention will be explicitly stated in the claim, and that in the absence of such a statement, no such intention is present. For example, to facilitate understanding, the following appended claims may contain the use of the introductory phrases "at least one" and "one or more" to introduce lists of claims.However, the use of such phrases should not be interpreted as implying that the introduction of a claim enumeration by the indefinite articles "a" or "an" limits any particular claim containing such an introduced claim enumeration to inventions containing only such an enumeration, even when the same claim includes the introductory phrases "one or more" or "at least one" and the indefinite articles such as "a" or "an" (for example, "a" and / or "an" should typically be interpreted as meaning "at least one" or "one or more"); the same applies to the use of definite articles used to invoke claim enumerations.Furthermore, even if a specific number from an introduced claim enumeration is explicitly quoted, a person skilled in the art will recognize that this enumeration should typically be interpreted as meaning at least the quoted number (for example, the simple enumeration of "two enumerations," without further modifiers, typically means at least two enumerations or two or more enumerations). Moreover, in cases where a convention analogous to "at least one of A, B, and C, and similar" is used, such a construction is generally employed in the sense that a person skilled in the art would understand the convention (for example, "a system having at least one of A, B, and C" would include, but not be limited to, systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, and similar).In cases where a convention analogous to "at least one of A, B, or C, and similar" is used, such a construction is generally employed in the sense that a person skilled in the art would understand the convention (for example, "a system having at least one of A, B, or C" would include, but not be limited to, systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, and similar). It will further be understood by a person skilled in the art that virtually every disjunctive word and / or disjunctive phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood as considering the possibilities of including one of the terms, either of the terms, or both terms. For example, the expression "A or B" will be understood as including the possibilities of "A" or "B" or "A and B".

[0072] It is considered that the present disclosure and many of the associated benefits will be understood from the preceding description, and it will be evident that various modifications can be made to the form, construction, and arrangement of the components without departing from the disclosed object or sacrificing any of its material advantages. The described form is purely explanatory, and it is intended that the following claims will encompass and include such modifications. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

Demands

1. Quantum computing system, comprising: one or more multimode resonators; one or more superconducting control circuits, wherein each of the one or more superconducting control circuits is coupled to one of the one or more multimode resonators, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit; and a controller including one or more processors configured to execute program instructions causing the one or more processors to: create, in at least one of the one or more multimode resonators, multiple chat qubits associated with multiple acoustic modes by parametric coupling to at least one of the one or more superconducting control circuits;and implement, in at least one of the one or more multimode resonators, a logic qubit based on multiple error-correcting chat qubits using parameter-driven interactions with at least one of the one or more superconducting control circuits.

2. Quantum computing system according to claim 1, wherein at least one of one or more superconducting control circuits further comprises a read resonator coupled to the superconducting nonlinear circuit for reading a state of at least one of any of the multiple cat qubits or any of the logic qubits.

3. Quantum computing system according to claim 1, wherein one or more multimode resonators and one or more superconducting control circuits are fabricated on a common substrate.

4. Quantum computing system according to claim 3, wherein the one or more multimode resonators are epitaxial high harmonic volume elastic wave (HBAR) resonators.

5. Quantum computing system according to claim 1, wherein the superconducting nonlinear circuit includes a Josephson junction.

6. Quantum computing system according to claim 1, wherein the creation of a particular cat qubit among the multiple cat qubits comprises: at least one of the preparation of a particular multimode resonator among the one or more multimode resonators in one of two cat states or the stabilization of the particular multimode resonator in a manifold generated by the two cat states.

7. Quantum computing system according to claim 1, wherein the logic qubit in a particular multimode resonator among one or more multimode resonators is encoded using multiple chat qubits in the particular multimode resonator via a non-local error-correcting code.

8. Quantum computer system according to claim 7, wherein the non-local error correction code is a low-density parity checking (LDPC) error correction code.

9. Quantum computer system according to claim 1, wherein error correction is biased by noise.

10. Quantum computing system according to claim 1, wherein the controller includes one or more excitation generators to provide excitation signals to any of the superconducting nonlinear circuits for at least one of the following: the creation of multiple chat qubits, the stabilization of multiple chat qubits, or the implementation of error correction.

11. Quantum computing system according to claim 1, wherein the one or more multimode resonators include two or more multimode resonators coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, wherein a particular superconducting coupling circuit among the one or more superconducting coupling circuits includes an additional superconducting nonlinear circuit coupled to two of the two or more multimode resonators.

12. Quantum computer system according to claim 11, wherein one or more processors are further configured to execute program instructions causing one or more processors to implement additional error correction on any of the logical qubits in any of two or more multimode resonators.

13. Quantum computer system according to claim 11, wherein one or more processors are further configured to execute program instructions causing one or more processors to implement one or more quantum logic operations on any one of the logical qubits in any one of two or more multimode resonators.

14. Quantum computing system according to claim 11, wherein the particular superconducting coupling circuit among one or more superconducting coupling circuits further includes an additional readout resonator.

15. Quantum computing system according to claim 11, wherein the controller includes one or more excitation generators to provide excitation signals to any of the superconducting nonlinear circuits for at least one of the creation of multiple chat qubits, the implementation of error correction or the control of interactions between any one of two or more multimode resonators.

16. Quantum computing system, comprising: a controller including one or more processors configured to execute program instructions causing the one or more processors to: create, in at least one of one or more multimode resonators, multiple chat qubits associated with multiple acoustic modes by parametric coupling to one or more superconducting control circuits, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit coupled to one of the one or more multimode resonators; and implement, in at least one of the one or more multimode resonators, a logic qubit based on the multiple chat qubits by error correction using parameter-driven interactions with the coupled superconducting control circuit.

17. Quantum computing system according to claim 16, wherein at least one of one or more superconducting control circuits further comprises a read resonator coupled to the superconducting nonlinear circuit for reading a state of at least one of any of the multiple cat qubits or the logic qubit.

18. Quantum computing system according to claim 16, wherein the one or more multimode resonators include two or more multimode resonators coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, wherein a particular superconducting coupling circuit among the one or more superconducting coupling circuits includes an additional superconducting nonlinear circuit coupled to two of the multimode resonators.

19. A quantum computing method, comprising: the creation, in at least one of the one or more multimode resonators, of multiple chat qubits associated with multiple acoustic modes by parametric coupling to one or more superconducting control circuits, wherein each of the one or more superconducting control circuits includes a superconducting nonlinear circuit coupled to one of the one or more multimode resonators; and the implementation, in at least one of the one or more multimode resonators, of a logic qubit based on the multiple chat qubits by error correction using parameter-driven interactions with the one or more superconducting control circuits.

20. A quantum computing method according to claim 19, wherein the two or more multimode resonators are coupled in a one-dimensional chain configuration by one or more superconducting coupling circuits, wherein a particular superconducting coupling circuit among the one or more superconducting coupling circuits comprises an additional superconducting nonlinear circuit coupled to two of the two or more multimode resonators, wherein the method further comprises: the implementation of at least one of an additional error correction or a quantum logic operation on any of the logic qubits in any of the two or more multimode resonators.

Images