Techniques for performing entanglement gates on logical qubits and related systems and methods

Abstract

Techniques for performing two qubit gates on logical qubits are described. The two-qubit gate may be performed in a manner that is fault tolerant and / or produces an indication of whether an error has occurred during the gate. Robustness of the described techniques to errors is provided at the hardware level by designing a system in which secondary qubits act as flag states for certain errors. Thus, it may not be necessary to manipulate the state of the system to counteract errors; instead, when an error occurs, the results of the gate may be filtered out or executed again. In other cases, the error state may be simply recorded as an indication of the quality of the system state. The techniques described herein for performing two-qubit gates may also be compatible with different viton coding of logical qubits, illustrative examples thereof are described.

Description

[0001] Government funding

[0002] This invention was made with Government support under W911NF-18-1-0212 awarded by the U.S. Army Research Office. The Government has certain rights in this invention. Background Art

[0003] Quantum information processing techniques perform calculations by manipulating one or more quantum objects. These techniques are sometimes referred to as "quantum computing". In order to perform calculations, quantum information processors use quantum objects to reliably store and retrieve information. According to some quantum information processing methods, quantum simulations of classical computing "bits" (equal to 1 or 0) have been developed, which are called quantum bits (quantum bits) or "qubits". A quantum bit can be composed of any quantum system with two different states (which can be considered as a 1 state and a 0 state), but also has the special property that the system can be placed in a quantum superposition and therefore potentially exists in these two states at the same time. Summary of the invention

[0004] In some aspects, the technology described herein relates to a system for implementing an entanglement gate that operates on two logical quantum bits, the system comprising: a first quantum oscillator; a second quantum oscillator; a coupling element coupled to the first quantum oscillator and the second quantum oscillator; an auxiliary quantum bit coupled to the first quantum oscillator; at least one energy source; a readout resonator coupled to the auxiliary quantum bit; and at least one controller, the at least one controller being configured to: perform an entanglement gate between logical states of the first quantum oscillator and the second quantum oscillator by operating the at least one energy source one or more times to direct energy to the coupling element and / or to the auxiliary quantum bit; measure the state of the auxiliary quantum bit measured after performing the entanglement gate; and determine whether the entanglement gate has produced an error based on the measured state of the auxiliary quantum bit.

[0005] In some aspects, the technology described herein relates to a system for implementing an entanglement gate that operates on two dual-rail qubits, the system comprising: a first dual-rail qubit, including: a first quantum oscillator; a second quantum oscillator; a first coupling element coupled to the first quantum oscillator and the second quantum oscillator; and an auxiliary qubit coupled to the second quantum oscillator; a second dual-rail qubit, including: a third quantum oscillator; a fourth quantum oscillator; and a second coupling element coupled to the third quantum oscillator and the fourth quantum oscillator; a third coupling element coupled to the second quantum oscillator and the third quantum oscillator; at least one energy source; and at least one controller, the at least one controller being configured to: perform an entanglement gate between a dual-rail state of the first dual-rail qubit and a dual-rail state of the second dual-rail qubit by operating the at least one energy source one or more times to direct energy to the third coupling element and / or to the auxiliary qubit; measure the state of the auxiliary qubit measured after performing the entanglement gate; and determine whether the entanglement gate has generated an error based on the measured state of the auxiliary qubit.

[0006] The foregoing device and method embodiments can be implemented with any appropriate combination of the aspects, features and actions described above or in more detail below. These and other aspects, embodiments and features of the present teaching can be more fully understood according to the following description in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Various aspects and embodiments will be described with reference to the following drawings. It should be understood that the drawings are not necessarily drawn to scale. In the drawings, each identical or nearly identical component shown in the various figures is represented by the same reference numeral. For the purpose of clarity, not every component may be labeled in every drawing.

[0008] Figure 1 depicts diagrams suitable for practicing the techniques described herein, according to some embodiments;

[0009] Figure 2A Depicted is a microwave cavity according to some embodiments Figure 1 illustrative implementation of a system;

[0010] Figure 2B Depicted according to some embodiments Figure 2A Coupling between components;

[0011] Figure 2C and Figure 2D depicts illustrative operator Bloch Sphere trajectories for designing entanglement gates for bosonic qubits according to some embodiments;

[0012] FIG. 3A to FIG. 3Ddepicts illustrative operator Bloch sphere trajectories for entanglement gates ZZ, SWAP, and uSWAP according to some embodiments;

[0013] Figure 4A is an illustrative circuit for applying an error-detecting bosonic entanglement gate according to some embodiments;

[0014] FIG. 4B to FIG. 4D is an illustrative circuit for applying ZZ, eSWAP, and Z-gate according to some embodiments;

[0015] Figure 5A depicts a circuit for parameterizing a general excitation preserving two-qubit gate according to some embodiments;

[0016] FIG. 5B to FIG. 5D Depicted according to some embodiments Figure 5A Illustrative examples of circuits;

[0017] Fig. 6A Depicted is a schematic diagram of a system including two dual-track logic qubits implemented with a microwave cavity according to some embodiments. Figure 1 illustrative implementation of a system;

[0018] Figure 6B Depicted according to some embodiments Fig. 6A coupling between elements of the

[0019] Figure 7 Depicted is a method for providing Fig. 6A An illustrative circuit for a two-rail qubit application of a ZZ gate. DETAILED DESCRIPTION

[0020] Quantum multilevel systems such as superconducting qubits exhibit quantum states that decoherence within about 100 μs based on current experimental practice. Although experimental technology will undoubtedly improve this and produce qubits with longer decoherence times, it may be beneficial to couple the multilevel system with another system that exhibits a longer decoherence time. Systems configured with bosonic modes may be particularly desirable for coupling to multilevel systems. Through this coupling, the state of the multilevel system can be represented by the bosonic mode instead, thereby maintaining the same information in a longer state than would otherwise exist alone in the multilevel system. When used in this manner, bosonic systems are sometimes referred to as "logical" qubits.

[0021] Nonetheless, the quantum information stored in the bosonic modes may still have a finite lifetime, so that errors will still occur within the bosonic system. Therefore, when errors occur in its state, it may be desirable to manipulate the bosonic system to effectively correct these errors and thus regain the previous state of the system. If a wide range of types of errors can be corrected, the state of the bosonic system can be preserved indefinitely (or at least for long periods of time) by correcting any type of error that may occur.

[0022] The fields of cavity quantum electrodynamics (QED) and circuit QED (cQED) represent an illustrative experimental approach to achieving quantum error correction. In these methods, one or more qubit systems are each coupled to a resonator cavity in a manner that allows the quantum information contained in the qubit to be mapped to and / or mapped from the resonator. The resonator will generally have a longer stable lifetime than the qubit. The quantum state can later be retrieved in the qubit by mapping the state from each resonator back to the qubit. When a multi-level system such as a qubit is mapped to the state of a bosonic system coupled thereto, a specific method must be selected to encode the qubit state in the state of the bosonic system. This choice of encoding is often referred to as a "code".

[0023] While using logical qubits to store quantum information has the potential to reduce the hardware required to perform quantum error correction, resonators used as logical qubits must generally be designed to have a high quality factor, and operations on logical qubits (e.g., error correction operations or algorithmic operations) should ideally be insensitive to errors. The latter requirement is sometimes referred to as the "fault tolerance" requirement.

[0024] The inventors have recognized and understood the techniques for performing two-qubit gates on logical qubits. The two-qubit gate can be performed in a manner that is fault-tolerant and / or produces an indication of whether an error has occurred during the gate. By designing a system in which an auxiliary (ancilla) qubit acts as a flag state for certain errors, the robustness of the described technology to errors is provided at the hardware level. Thus, it may not be necessary to manipulate the state of the system to offset errors; instead, when an error occurs, the result of the gate can be filtered out or executed again. In other cases, the error state can simply be recorded as an indication of the quality of the system state. The techniques described herein for performing two-qubit gates can also be compatible with different bosonic encodings of logical qubits, an illustrative example of which is described below. As used herein, a "two-qubit gate" refers to an entanglement gate that works between two logical qubits.

[0025] According to some embodiments, the techniques described herein can be applied to a system in which two bosonic modes are coupled via a programmable beam splitter interaction (e.g., implemented by a coupling element between the two bosonic systems), and in which the auxiliary qubit is divergently coupled to one of the bosonic modes. The techniques can provide a two-qubit gate to be applied to the bosonic modes while providing a natural means of detecting errors through the state of the auxiliary qubit. For example, the state of the auxiliary qubit can act as a "flag" for an error, such that a measurement of the state of the auxiliary qubit after a two-qubit gate can indicate whether an error occurred during the two-qubit gate, where one or more states of the auxiliary qubit are associated with an error, and one or more states of the auxiliary qubit are associated with no error.

[0026] According to some embodiments, a system in which two bosonic modes are coupled via a programmable beam splitter interaction can be implemented as a cQED system, which includes two quantum oscillators (e.g., microwave cavity resonators) coupled together via a suitable coupling element, such as a superconducting transmon qubit, a superconducting nonlinear asymmetric inductor element (SNAIL), or a superconducting quantum interference device (SQUID). One of the quantum oscillators can be coupled to an auxiliary qubit (e.g., a superconducting transmon qubit). Although the auxiliary qubit is only coupled to one of the bosonic modes of the system, due to the beam splitter interaction provided by the coupling element, both bosonic modes interact with the auxiliary qubit, thereby achieving various dual-mode operations. As further described below, a two-qubit gate can be performed on the bosonic mode by the application of energy (e.g., microwave pulses) applied to the auxiliary qubit and / or the coupling element.

[0027] According to some embodiments, a system in which two bosonic modes are coupled via a programmable beam splitter interaction can be implemented as a cQED system, which includes two dual-rail qubits, each implemented as a pair of quantum oscillators (e.g., microwave cavity resonators). In dual-rail encoding, photons are stored in one of the two oscillators; the photon in the first oscillator is considered a logical 0, and the photon in the other oscillator is considered a logical 1. Therefore, the two oscillators together form a single logical dual-rail qubit. The dual-rail encoding arrangement has several benefits: (i) photon losses appear as erase errors; (ii) the single-photon state is the lowest energy state of the oscillator and therefore has the lowest error rate of any state of the oscillator, and therefore dual-rail encoding minimizes the loss error rate; and (iii) photon gain or loss can be easily detected by measuring the joint parity of the oscillators. Each dual-rail qubit acts as one of the bosonic modes, and the two dual-rail qubits can be coupled together via a suitable coupling element - in particular, one of the oscillators in one dual-rail qubit is coupled to one of the oscillators in the other dual-rail qubit. One of the oscillators coupled to an oscillator in another dual-rail qubit may also be coupled to the auxiliary qubit. As described further below, a two-qubit gate may be performed on a bosonic mode by application of energy (e.g., a microwave pulse) to the auxiliary qubit and / or to a coupling element that couples the two dual-rail qubits to each other.

[0028] According to some embodiments, the auxiliary qubit may be driven to its ground state prior to executing a two-qubit gate. Certain gates described further below may rely on the auxiliary qubit being initially in its ground state prior to executing the gate, although at least one example is provided below where this is not a requirement.

[0029] According to some embodiments, after executing the two-qubit gate, the state of the auxiliary qubit is measured (e.g., by readout of a readout resonator that is dispersion coupled to the auxiliary qubit). In some cases, when the state of the auxiliary qubit is measured to be in a ground state after executing the two-qubit gate, this indicates that no errors (or at least no instances of certain types of errors) occurred during the two-qubit gate. Conversely, when the state of the auxiliary qubit is measured to be in an excited state (including a first excited state or a second excited state) after executing the two-qubit gate, this indicates that an error occurred during the two-qubit gate.

[0030] According to some embodiments, a two-qubit gate may be performed in part by applying energy to a coupling element that couples two bosonic systems together, and the energy has an amplitude, frequency, and duration selected based on the type of gate being performed. In some cases, in addition to the type of gate being performed, the amplitude, frequency, and duration (also collectively referred to herein as "control parameters") may be selected based on the bosonic encoding used to store logical information in the bosonic system. In addition to such operations, the two-qubit gate may also include one or more operations applied to an auxiliary qubit, such as one or more rotations of the auxiliary qubit state, which may be performed by suitable control techniques. In general, a two-qubit gate may include applying energy to an auxiliary qubit in one or more steps, and applying energy to the coupling element (using appropriate control parameters) in one or more steps different from the step of applying energy to the auxiliary qubit.

[0031] Below is a more detailed description of various concepts and embodiments related to techniques for performing error-detectable two-qubit gates. It should be understood that the various aspects described herein can be implemented in any of a variety of ways. Examples of specific implementations are provided herein for illustrative purposes only. In addition, the various aspects described in the following embodiments can be used alone or in any combination, and are not limited to the combinations explicitly described herein.

[0032] Figure 1 An illustrative system suitable for practicing the techniques described herein according to some embodiments is shown. In system 100, logical qubits 101 and 102 are coupled to each other via coupling element 103. Logical qubit 101 is also coupled to auxiliary qubit 104. Energy source 105 can be operated by controller 106 to direct energy to auxiliary qubit 104, coupling element 103, and / or readout resonator 107.

[0033] According to some embodiments, logical qubit 101 and logical qubit 102 each include a cavity that supports quantum states of microwave photons. For example, in some embodiments, first logical qubit 101 and second logical qubit 102 may be transmission line resonators or three-dimensional cavities formed of superconducting materials such as aluminum.

[0034] In some embodiments, coupling element 103 may be a superconducting transport sub-qubit that is dispersion coupled to both first logical qubit 101 and second logical qubit 102. Coupling element 103 mediates the coupling between the quantum states of the two logical qubits, allowing interaction between first logical qubit 101 and second logical qubit 102. In some embodiments, coupling element 103 may be a superconducting nonlinear asymmetric inductor element (SNAIL), a superconducting quantum interference device (SQUID), or some other nonlinear element. In some embodiments, auxiliary qubit 104 may be a superconducting transport sub-qubit, a SNAIL, a SQUID, or some other nonlinear element.

[0035] An illustrative implementation of system 100 is shown as Figure 2A In the system 200 of FIG. 1 , logical qubits are implemented as bosonic modes stored in cavities 201 and 202 (eg, microwave cavities). The microwave source ( Figure 2A 204, the coupling element 203, and / or the readout resonator 207. Such a microwave source can be coupled to the auxiliary qubit and the coupling element. The coupling between the microwave source and these components provides a way for the microwave source to apply microwave radiation to the components. In some embodiments, the energy source 105 can be capacitively coupled to each of the auxiliary qubit 204, the coupling element 203, and the readout resonator 207.

[0036] exist Figure 2A In an example of , a microwave source (not shown) can be operated to read out the state of the auxiliary qubit 204. For example, the readout resonator 207 can be arranged so that its resonant frequency (e.g., ~ GHz) is away from the transition frequency of the auxiliary qubit 204 (e.g., dispersion coupling). The coupling between the auxiliary qubit and the readout resonator means that the offset of the resonator frequency depends on the state of the qubit. The offset is small compared to the resonant frequency of the resonator (e.g., ~ MHz). Therefore, a tone near the resonant frequency sent to the readout resonator 207 will be reflected by the resonator, and the form of the reflected tone (also referred to herein as a "readout signal") can be analyzed to determine the state of the auxiliary qubit. In this way, the state of the auxiliary qubit 204 can be non-destructively detected by sending a probe tone to the readout resonator 207 that is dispersion coupled to the qubit.

[0037] Including Figure 2A In the example system described herein, the entanglement gate is based on a Hamiltonian that implements the bosonic mode (e.g., Figure 1logical qubits 101 and 102 in, or Figure 2A The beam splitter interaction between the cavities 201 and 202 in FIG. 1 and the auxiliary qubits (e.g., Figure 1 The auxiliary quantum bit 104 or Figure 2A The auxiliary qubit 204 in the embodiment of FIG. 1 is connected to one of the bosonic modes (e.g., Figure 1 Bosonic patterns in logical qubits 101 or Figure 2A The Hamiltonian can be written as:

[0038]

[0039] in,

[0040]

[0041] and is the Pauli Z operator in a two-level subspace defined by the auxiliary |g> and |f> levels. In this example, three levels of assistance are utilized, which may have the benefit of allowing the use of the |e> level to detect a single auxiliary decay event.

[0042] In the following, for the purpose of illustration, reference will be made to Figure 2A The illustrative implementation of the system 100 shown is used to describe the interaction between Bosonic systems, but it should be understood that the technology described herein is not limited to Figure 2A Therefore, in the following description, references to logical qubits may refer to logical information stored in each of the two cavities 201 and 202.

[0043] exist Figure 2A In the example, the term represents the beam splitter coupling between cavities 201 and 202 as generated by coupling element 203, and the term represents the dispersion coupling between cavity 201 and auxiliary qubit 204. These couplings are Figure 2B In the Hamiltonian In the annihilation operator and The Bosonic modes acting on cavities 201 and 202, g BS (t) is the complex amplitude of the beam splitter interaction between cavities 201 and 202, Δ(t) is the effective detuning between the two modes, and χ is the mode of the auxiliary qubit 204 (in the gf manifold) with cavity 201 The Hamiltonian Written in the dispersion interaction symmetry system, according to the auxiliary state The frequency shift is ±χ / 2.

[0044] By appropriately selecting the microwave drive signal applied to the coupling element 203 and the auxiliary qubit 204, the Hamiltonian can be controlled and changed. For example, the coupling strength g BS (t), its phase and detuning Δ(t) can be changed rapidly via microwave drive techniques. As described below, in this system, operations including two-qubit gates can be designed by actuating microwave drive while designing time-dependent control of these parameters, where different parameter values ​​correspond to different operations / gates. Although auxiliary qubit 204 is only coupled to one of the two bosonic modes of cavities 201 and 202, in the presence of beam splitter interactions, both modes interact with the auxiliary qubit, thereby achieving a variety of non-trivial dual-mode operations.

[0045] To further explain the The resulting dynamics introduces an “operator Bloch sphere” that uses the conventional description of single-qubit control on a Bloch sphere to illustrate the design of two-qubit gates for bosonic qubits.

[0046] Inspired by Schwinger's angular momentum formalism for bosonic operators, We can use the angular momentum operator and Rewrite, which allows Rewritten as:

[0047]

[0048] For parameter g BS , When Δ is a constant, the Heisenberg representation of the mode operator can be obtained by using the unitary operator Transform the mode operator to obtain,

[0049]

[0050] in is a matrix in SU(2), which can be interpreted as the precession vector At rate The polar angle of the precession vector is given by the coupling strength g BS The ratio of the detuning Δ is determined so that and

[0051] Analogous to the state evolution on the qubit Bloch sphere, the mode transformation can be plotted at each time point to form a trajectory on the operator Bloch sphere, e.g. Figure 2C As shown. Figure 2CIn the example, the North Pole represents the initial mode operator And the solid arrows represent the transformed mode operators Similarly, the South Pole represents the initial mode operator And the dotted arrows represent the transformed mode operators The trajectory can be completely controlled by modulating the complex amplitude of the beam splitter interaction, which can be achieved in a cQED system such as system 200 by sending a microwave pulse to coupling element 203 and by adjusting the complex amplitude of the pulse g BS The amplitude, duration and phase of the oscillation are set to the desired values. The trajectories from the north and south poles are antipodal to each other, and therefore only the transformation. Figure 2C The endpoints of the trajectory shown indicate the original Final mode transformation of the operator.

[0052] The impact of auxiliary interactions Shows detuning that depends on the auxiliary state where Δ′ now represents the detuning of the beam splitter drive from resonance. The dispersive beam splitter Hamiltonian can now be rewritten as:

[0053]

[0054] Since the total detuning of the beam splitter becomes dependent on the auxiliary state, there are now two different "conditional" precession vectors with different z components, allowing one to construct a mode trajectory for auxiliary control that is unitary, where if the auxiliary qubit is in its ground state |g>, the identity operation is performed on the bosonic mode, and where if the auxiliary is in its second excited state |f>, a unitary gate is performed on the bosonic mode. An illustrative mode trajectory for auxiliary control is given in Figure 2D and are respectively represented as and

[0055] Detuned beam splitter Hamiltonian All possible dynamics generated can be represented on the operator Bloch sphere. The dispersive beam splitter Hamiltonian g BS (t) The three degrees of freedom in Δ(t) and Δ(t) determine the axis and rate of precession. This is true even when these parameters are time-dependent, which results in a time-varying precession axis and precession rate. The operator Bloch sphere picture is necessary to visualize the temporal dynamics generated by the continuous beamsplitter interaction, over which we have fine control over the Hamiltonian parameters. This is different from the discrete beamsplitter transformations found in linear optics, for example.

[0056] The operator Bloch sphere image is used to find The resulting new and interesting unitary operations are powerful tools for auxiliary control. Figure 2A The illustrative hardware implementation shown is used to describe the implementation of cZZ L and cSWAP L Both methods (the subscript L is used to remind that these gates are performed on logical qubits).

[0057] At the end of the unitary operation of the auxiliary control, the bosonic state is returned to the logic code space, which restricts the analysis to trajectories starting and ending at the poles of the operator Bloch sphere, corresponding to the SWAP or identity operation. However, the important feature is that the solid angle enclosed by these trajectories determines the geometric phase assigned to the bosonic mode and can be used as a resource for formulating logic operations. This effect is the ZZ of the designed auxiliary control L 、cZZ L , and the basis of auxiliary control SWAP, cSWAP ​​gates, such as FIG. 3A to FIG. 3B Furthermore, by combining these unitary operations with arbitrary auxiliary rotations, we can construct families of excitation-preserving gates, such as ZZ L (θ), iSWAP(θ), and fSim(θ1, θ2) gates to be executed on the logic subspace.

[0058] Designing trajectories that encompass a particular geometric phase can be used to create useful unitary operations. The geometric phase is determined by the The terms in the above equation are To set. Completely enclosing the solid angle φ corresponds to performing a unitary operation on the Bosonic mode For many bosonic codes, And therefore This is true, for example, for binomial and quadruple codes. Thus, by varying the relative strengths of the microwave-controlled Hamiltonian parameters, the enveloping geometric phase can be chosen to match the ZZ of a particular bosonic code. L Furthermore, the ability to map the system dynamics onto trajectories on the Bloch sphere also allows us to introduce noise suppression and gate optimization techniques developed for qubits that exploit geometric phase control.

[0059] The trajectories that depend on the states of the auxiliary qubits |g> and |f> generate three types of auxiliary controlled unitary operations back into the code space:

[0060] (1) Both trajectories return to the starting pole;

[0061] (2) one trajectory returns to the starting pole and the other trajectory returns to the opposite pole; or

[0062] (3) Both trajectories return to the opposite pole.

[0063] Although these trajectories are a small subset of all possible trajectories that can be designed, each case represents a different, useful logic operation for auxiliary control.

[0064] To consider this further, consider the evolution of trajectories of type (1), where two trajectories conditioned on the state of the auxiliary qubit return to their starting poles (see Figure 3A ). The geometric phase accumulation φ means performing the following unitary operation of auxiliary control:

[0065]

[0066] Geometric phase accumulation can be used to perform logical operations on the bosonic modes of cavities 201 and 202. For many bosonic codes, for codes with n-fold rotational symmetry, Z L use of the form, and therefore when or This is equivalent to cZZ L Unitary Operation

[0067]

[0068] Until the rotation operator It can be tracked by the operating system's controller.

[0069] The required Hamiltonian parameters are found from the general formula for the solid angle φ. For an orbit about a fixed precession vector, this is given by For Boson codes, cZZ is shown in Table 1 below L The parameters of the gate, where or Since the interaction strength g BS = / 2π and χ / 2π can both be several MHz, so all these gates on the multiphoton encoded qubit can be executed in ~1 μs, which is 3 orders of magnitude faster than the typical microwave cavity decay rate (1 ms) and 2 orders of magnitude faster than the superconducting transport decoherence rate (100 μs), which yields p phys ∝τ gate / T coh Coherence confinement infidelity at the level of ∼1-10%, similar scaling to previously achieved bosonic entanglement gates.

[0070]

[0071] Table 1 - Pump operating conditions

[0072] The above binomial code and four-cat code represent alternative logical encodings to the Fock 01 encoding or dual-rail encoding described herein and are defined as follows. The logical codewords defined for the lowest order binomial code are:

[0073]

[0074] | 1 L >=| 2>

[0075] The (even photon number) quadruple code is based on the superposition of coherent states and is defined as:

[0076]

[0077] Where N0 and N1 are normalization factors. Both codes share a similar photon number structure, where |0> L Status and |1> L The states contain the same average number of photons in the large-α limit. Codewords contain only an even number of photons, allowing detection of photon loss via photon number parity measurement after application of a two-qubit gate.

[0078] Returning to the required Hamiltonian parameters to formulate the desired gate, using a different set of Hamiltonian parameters, Figure 3B The cSWAP ​​(controlled SWAP) gate shown can be defined as:

[0079]

[0080] In this case, the trajectory conditioned on |f> ends at the opposite pole, while the trajectory conditioned on |g> completes an orbit around a different precession vector to return to the initial pole (trajectory type (2) above). For the parameters of the cSWAP ​​gate presented in Table 1, this achieves the unitary operation

[0081]

[0082] Undesirable geometric phase accumulation may be mitigated by performing a series of operations that include this unitary operation in addition to one or more delays to achieve a cSWAP ​​unitary operation.

[0083] Finally, when both trajectories end at opposite poles (trajectory type (3) above), a SWAP can be performed between the bosonic modes of cavities 201 and 202 that is independent of the auxiliary state (until geometric phase accumulation), which is referred to herein as an "unconditional SWAP" gate. Due to the static nature of the dispersive interactions, this operation is difficult to implement using conventional frameworks when the auxiliary is in a superposition of states. Unconditional SWAP is a useful operation that allows the extension of unitary operations for auxiliary control to more than two bosonic modes.

[0084] An example of an unconditional SWAP (or uSWAP) gate with the described trajectory is given in Figure 3C These trajectories can be obtained by detuning the parametric beam splitter χ gf / 2 and g BS ≥χ gf / 2. Once the trajectory reaches the equator of the operator Bloch sphere, a π pulse can be performed in the gf manifold to effectively reverse the detuning. This does not implement a true unconditional SWAP unitary operation, but a unitary operation.

[0085]

[0086] With this approach, either by performing delays before and after the above unitary operation and using the dispersion interaction, or by finding such that trajectories to reverse the undesired conditional rotation.

[0087] An alternative to the above method for implementing the uSWAP gate is to detune the beam splitter coupling by χ / 2 and set g BS =|χ| / 2 makes the polar angles of the two precession vectors both 45°. After applying this Hamiltonian, both trajectories reach the equator and are antipodal. If the sign of the beam splitter drive then flips so that g BS = -|χ| / 2, then after the same duration, both trajectories will reach the South Pole at the same time. The area between these trajectories on the operator Bloch sphere is 2π steradians. Figure 3D Shown in.

[0088] cZZ above L The 'building block' operations of cSWAP ​​can be combined with arbitrary rotations on the auxiliary qubits to perform a continuous family of entanglement gates on the bosonic logic subspace. L The operation itself generates entanglement only between the auxiliary qubit 204 and the bosonic modes of cavities 201 and 202. However, with this circuit, it is possible to perform an entanglement gate that acts only on the bosonic modes, leaving the auxiliary disentangled at the end of the circuit. Therefore, the auxiliary should start and end in its initial state |g>. As described above, the advantage of this method is that an auxiliary error that occurs during the gate can be detected by checking whether the auxiliary returns to |g>. That is, if the auxiliary returns to |g>, no such error has occurred, otherwise, if the auxiliary is in |e> or |f>, an error is detected.

[0089] Figure 4A Depicts a general case of an error detection circuit for a bosonic entanglement gate according to some embodiments. Figure 4A in (and in Figure 4B and Figure 4C In the first line |ψ a >, the operation performed on cavity 201, and in the second line |ψ b >, the operation performed on cavity 202, and in the third line |g> represents the operation performed on the ancillary qubit which is initially in its ground state |g>. Figure 4A The gates shown can be implemented by operating on a system such as the one described above Figure 1 or Figure 2A by operating on the energy source 105 in the system of Figure 1 , or by operating on a microwave source to supply microwave energy to the components of the system of Figure 2A .

[0090] In Figure 4A the example, the operations performed on the bosonic modes of cavities 201 and 202 (operations 402 and 404) are the following exponentiation circuits:

[0091]

[0092] The operation is derived from an ancilla-controlled unitary operation where is any "Pauli-like" operator acting on a two-qubit logical subspace satisfying (in other words, is Hermitian and unitary). The full unitary operation implemented by the circuit of Figure 4A on the qubit-ancilla system is:

[0093]

[0094] The exponentiation circuit provides an elegant way to control multiple logical qubits and also has desirable error-detection properties. By changing the angle of the intermediate ancilla rotation X θ , any one of the multiple parameterized entanglement gates in can be implemented on the logical qubits. The construction of the remaining gates remains the same, allowing the logical gates to be calibrated for many different values of θ. In Figure 4A the example, operations 401 and 405 are Hadamard gates H which each create an equal superposition of the two ground states (e.g., mapping |0> to |+> and |1> to |->).

[0095] In Figure 4AThe circuit depicted in the example of allows detection of single auxiliary dephasing errors in addition to auxiliary decay events by measuring the state of the auxiliary qubit in operation 406. The state of the auxiliary qubit acts as a flag to indicate whether the gate represented by operations 401, 402, 403, 404, and 405 is executed without auxiliary dephasing or auxiliary decay errors. In particular, if after performing operations 401, 402, 403, 404, and 405, the state of the auxiliary qubit is the ground state |g>, this indicates that no such error has occurred. Otherwise, if the state of the auxiliary qubit is the first excited state |e> or the second excited state |f>, this indicates that at least one such error has occurred while performing operations 401, 402, 403, 404, and 405. This error detection method provides for the use of auxiliary qubits that may be much noisier than logical qubits, because the propagation of auxiliary errors to logical qubits is first-order error detectable.

[0096] When an error is detected, the system can operate in various ways. For example, in cases where the circuit is relatively short and many gates are executed, the results produced when the error occurs can be filtered out. In the use case where gates are at least partially executed to prepare resource states (e.g., entangled states) for larger computations, or in short depth circuits used in quantum algorithms, the presence or absence of errors can be used to indicate the quality of the resource states.

[0097] As Figure 4A An illustrative implementation of the circuit using cZZ L Unitary Operation Settings Produced ZZ L The construction of the (θ) gate, such as Figure 4B Here, the initial rotation operation 411 is performed as Also known as Y + , rather than a Hadamard gate, since it also causes the |0> state to be mapped to |+>, but is easier to implement in practice. Similarly, the final operation 415 is performed as Also known as Y - The cZZ applied in each of operations 412 and 414 is L Unitary operation:

[0098]

[0099] As described above, the g shown in Table 1 BS Appropriate values ​​of , Δ and T are used to operate the energy source.

[0100] as Figure 4A For example, Figure 4BThe circuit depicted in the example of allows detecting a single auxiliary dephasing error in addition to an auxiliary decay event during a ZZ gate by measuring the state of the auxiliary qubit in operation 416. The state of the auxiliary qubit acts as a flag to indicate whether the gate represented by operations 411, 412, 413, 414, and 415 is executed without an auxiliary dephasing or auxiliary decay error. In particular, if after performing operations 411, 412, 413, 414, and 415, the state of the auxiliary qubit is the ground state |g>, this indicates that no such error has occurred. Otherwise, if the state of the auxiliary qubit is the first excited state |e> or the second excited state |f>, this indicates that at least one such error has occurred while performing operations 411, 412, 413, 414, and 415.

[0101] As Figure 4A Another illustrative implementation of the circuit of , using cSWAP ​​unitary operation to set This results in the construction of exponential SWAP (eSWAP) gates, such as Figure 4C As shown. The cSWAP ​​unitary operation applied in each of operation 422 and operation 424 is:

[0102]

[0103] As described above, the g shown in Table 1 BS Appropriate values ​​of , Δ and T are used to operate the energy source.

[0104] as Figure 4A For example, Figure 4C The circuit depicted in the example of allows detecting a single auxiliary dephasing error in addition to an auxiliary decay event during an eSWAP gate by measuring the state of the auxiliary qubit in operation 426. The state of the auxiliary qubit acts as a flag to indicate whether the gate represented by operations 421, 422, 423, 424, and 425 is executed without an auxiliary dephasing or auxiliary decay error. In particular, if after performing operations 421, 422, 423, 424, and 425, the state of the auxiliary qubit is the ground state |g>, this indicates that no such error has occurred. Otherwise, if the state of the auxiliary qubit is the first excited state |e> or the second excited state |f>, this indicates that at least one such error has occurred while performing operations 421, 422, 423, 424, and 425.

[0105] exist FIG. 4A to FIG. 4C In each of the examples, X θThe angle θ of operation 403, 413 or 423 can be varied, which is controlled by changing the angle of the intermediate auxiliary rotation. For all values ​​of θ except 0 and integer multiples of π, the choice of θ value produces entanglement from separable input states. For θ = π / 2, the gate is maximally entangled, and Equivalent to CNOT gates, up to single-qubit gates.

[0106] By combining eSWAP(θ) and ZZ L (θ) and single quantum bit Z L (θ) gate combination, it is possible to perform any desired excitation-preserving logical two-qubit gate on two bosonic qubits. L The (θ) gate can be Figure 4A The same construction is achieved, except that the rotation is controlled by the auxiliary control of a single bosonic mode, such as Figure 4D The auxiliary qubit rotations 441, 443 and 445 and the single bosonic mode rotations 442 and 444 are shown. L The (θ) gates may be implemented using fault-tolerant Selective Digitally Associated Arbitrary Phase (SNAP) gates, such as those described in U.S. Pat. No. 10,540,602, entitled “Techniques of Oscillator Control for Quantum Information Processing and Related Systems and Methods,” the entire contents of which are incorporated herein by reference.

[0107] The above construction can also be used when using GKP codewords to encode the bosonic state of logical qubits. Using the conditional shift Hamiltonian, the unitary operation cZ that assists control can be designed L 、cZZ L 、cX L 、cXX L etc., which in turn allows the realization of gate Z L (θ), ZZ L (θ), X L (θ), XX L (θ). In other words, the construction allows the implementation of parameterized entanglement gates and arbitrary single-qubit rotations in GKP codes while being able to detect auxiliary errors during the gate. cQED allows the direct implementation of unitary manipulations of desired auxiliary control by stringing together conditional shifts acting on different bosonic modes coupled to the same auxiliary to construct a joint conditional shift.

[0108] Another powerful application of logic gates for auxiliary control is to operate Perform QND logic measurements. This is done by Preparation assistance, application and then in |±> gf This is done with the help of measurements in the foundation. For cSWAP, this is equivalent to the SWAP test. Similarly, cZZ L Convert to ZZ L QND logical measurement of operators. This operation can be used as a measurement-based alternative to entanglement gates and can form part of a Bell measurement. Unlike the gate construction, these measurements can, in principle, correct for single auxiliary attenuation errors and auxiliary dephasing of all orders.

[0109] Using the above parameterized eSWAP(θ) and ZZ L (θ) gates, we can construct any desired two-qubit gate that conserves the total number of excitations in the encoding subspace. A general excitation-preserving two-qubit gate can be written as Figure 5A The circuit parameterization shown consists of a single qubit Z executed on the Bosonic mode of each logical qubit. L (θ) gate (as above Figure 4D described), ZZ L (θ) gate (as above Figure 4B described above) and the cSWAP(θ) gate (described above with respect to Figure 4C described).

[0110] By making specific choices for θ1, θ2, θ3, and θ4, useful gate families can be generated. Figure 5B , Figure 5C and Figure 5D The CPHASE(θ), iSWAP(θ), and fSim(θ, φ) gates shown in FIG. 5 can be formed from appropriate choices of θ1, θ2, θ3, and θ4.

[0111] As mentioned above, one way to implement the above technique for performing an error-detecting two-qubit gate is to Figure 2A However, these techniques can be applied to any other suitable system in which two logical qubits are connected by The beam splitter couplings described are coupled to each other, and one of the logical qubits is coupled to an auxiliary qubit. Another example of such a system is one in which each logical qubit is implemented as a dual-rail qubit.

[0112] As mentioned above, in a dual-rail qubit, photons are stored in one of the two oscillators; the photons in the first oscillator are considered logical 0, and the photons in the other oscillator are considered logical 1. Therefore, the two oscillators together form a single logical dual-rail qubit. In other words, a dual-rail qubit is a qubit that occupies two bosonic modes. logical qubits, where the codeword is |0> L =|01> and |1> L =|10〉 L .

[0113] exist Fig. 6A A system suitable for practicing the above-described two-qubit gate with two dual-rail qubits as logical qubits is depicted in accordance with some embodiments. Fig. 6A In the example of FIG. 6 , a pair of dual-rail logic qubits 601 and 602 are depicted as being coupled to each other via a coupler 603. Dual-rail qubit 601 includes cavities 611 and 612 (e.g., microwave cavities) coupled together via a coupling element 613; and dual-rail qubit 602 includes cavities 621 and 622 (e.g., microwave cavities) coupled together via a coupling element 623. Each of cavities 612 and 622 is coupled to a respective ancillary qubit 614 or 624 (e.g., each of which can be a superconducting transporter qubit), which is coupled to a respective readout resonator. Each of coupling elements 603, 613, and 623 can be a superconducting nonlinear asymmetric inductor element (SNAIL), a superconducting quantum interference device (SQUID), or some other nonlinear element.

[0114] By adding a coupler 603 between the two-track qubits (rather than, for example, Figure 2A In the example of FIG. 4 , by guiding energy through a coupler 203 between two logical qubits implemented by cavities 201 and 202, a two-qubit gate as described above can be performed on two dual-track logical qubits. When a two-qubit gate is performed on a pair of dual-track qubits, an auxiliary qubit 624 coupled to cavity 622 (cavity 622 is coupled to cavity 611 of another dual-track qubit via coupler 603) can be operated as an auxiliary qubit in the above two-qubit gate scheme. Therefore, operations such as operations 411, 413, and 415 can be applied to auxiliary qubit 624, and any errors that occur during the execution of the two-qubit gate can be detected by measuring the state of auxiliary qubit 624 and determining whether the auxiliary qubit is in state |g>, |e>, or |f>. Fig. 6A The coupling depicted in Figure 6B As further shown in FIG. 1 , the indication mode including a logical quantum bit 601, and Includes logical quantum bits 602.

[0115] A single-qubit logic Z gate can be Fig. 6A In a system of , the Z gate is performed by physically interacting with one of the bosonic modes in the two-rail qubit. In particular, the Z gate can be operated via the unitary or equivalently via This means that even though the two two-rail qubits consist of four physical modes, only two of them need to interact to perform a logical two-qubit gate and measurement. is defined as a mode in the second two-rail qubit, then it can be coupled to the mode by using The auxiliary qubits and set (which is the joint parity operator) to perform the logic ZZ L (θ) gate. Figure 7 An illustrative ZZ for a dual-rail qubit according to some embodiments is depicted in L (θ) gate. Figure 7 In the example, ZZ L The (θ) gates include Hadamard gates 711 and 715 (each creating an equal superposition of two two-orbit ground states (e.g., mapping |0〉 to |+〉, and mapping |1〉 to |->)), a joint parity operation 712 and 714, and auxiliary rotation operation X θ 713.

[0116] as Figure 4A For example, Figure 7 The circuit depicted in the example of allows the detection of the state of the auxiliary qubit in ZZ by measuring the state of the auxiliary qubit in operation 716. L (θ) Single auxiliary dephasing error other than auxiliary decay event during the gate. The state of the auxiliary qubit acts as a flag to indicate whether the gate represented by operations 711, 712, 713, 714, and 715 is executed without auxiliary dephasing or auxiliary decay errors. In particular, if after performing operations 711, 712, 713, 714, and 715, the state of the auxiliary qubit is the ground state |g〉, this indicates that no such error occurred. Otherwise, if the state of the auxiliary qubit is the first excited state |e〉 or the second excited state |f〉, this indicates that at least one such error occurred while performing operations 711, 712, 713, 714, and 715.

[0117] All logic gates in the dual-rail code conserve the total number of excitations in the system and can be obtained by the pattern and The beam splitter interaction between the two can realize the rotation of any single quantum bit in the dual-track quantum bit. L When combined with (θ) gates, this forms a universal gate set. In contrast, any bosonic code that uses only one bosonic mode per logical qubit necessarily requires gates that do not conserve the total number of excitations. For example, the X gate in the Fock 01 code is It involves transitions between states with different photon numbers, however Not involved.

[0118] For the above gate and measurement construction to be applied to dual-rail codes, the desired modes are bosonic, with the ability to support up to two excitations per mode. This is because when we start with the state Initially, the construction relies on Hong-Ou-Mandel type interference. The dual-rail code also has the ability to detect photon loss errors after a gate or measurement. One or both of the dual-rail qubits can be in the state Finish.

[0119] Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art.

[0120] Such changes, modifications and improvements are intended to be part of the present disclosure and are intended to be within the spirit and scope of the present invention. In addition, although the advantages of the present invention are pointed out, it should be understood that not every embodiment of the technology described herein will include every described advantage. Some embodiments may not implement any feature described as advantageous herein, and in some cases, one or more of the described features may be implemented to implement further embodiments. Therefore, the foregoing description and drawings are provided only as examples.

[0121] Aspects of the present disclosure may include, but are not limited to:

[0122] Aspect 1. A system for implementing an entanglement gate that operates on two logical quantum bits, the system comprising: a first quantum oscillator; a second quantum oscillator; a coupling element coupled to the first quantum oscillator and the second quantum oscillator; an auxiliary quantum bit coupled to the first quantum oscillator; at least one energy source; a readout resonator coupled to the auxiliary quantum bit; and at least one controller, the at least one controller being configured to: perform an entanglement gate between logical states of the first quantum oscillator and the second quantum oscillator by operating the at least one energy source one or more times to direct energy to the coupling element and / or to the auxiliary quantum bit; measure the state of the auxiliary quantum bit measured after performing the entanglement gate; and determine whether the entanglement gate has generated an error based on the measured state of the auxiliary quantum bit.

[0123] Aspect 2. The system according to aspect 1, wherein: the coupling element is dispersively coupled to the first quantum oscillator and the second quantum oscillator; and the auxiliary quantum bit is dispersively coupled to the first quantum oscillator.

[0124] Aspect 3. A system according to any one of aspects 1 to 2, wherein the coupling element is a superconducting transporter qubit, a superconducting nonlinear asymmetric inductor element (SNAIL), or a superconducting quantum interference device (SQUID).

[0125] Aspect 4. A system according to any one of Aspects 1 to 3, wherein operating the at least one energy source one or more times to direct energy to the coupling element and / or to the auxiliary quantum bit includes operating the at least one energy source one or more times to direct a microwave tone to the coupling element and / or to the auxiliary quantum bit.

[0126] Aspect 5. A system according to any one of aspects 1 to 4, wherein the auxiliary quantum bit is not coupled to the second quantum oscillator.

[0127] Aspect 6. A system according to any one of Aspects 1 to 5, wherein the at least one controller is configured to measure the state of the auxiliary quantum bit after executing the entanglement gate by operating the at least one energy source to direct energy to the readout resonator.

[0128] Aspect 7. A system according to any one of Aspects 1 to 6, wherein the at least one controller is further configured to operate the at least one energy source to place the auxiliary quantum bit in a ground state before executing the entanglement gate.

[0129] Aspect 8. A system according to any one of Aspects 1 to 7, wherein performing the entanglement gate between the logic states of the first quantum oscillator and the second quantum oscillator includes operating the at least one energy source: directing energy to the auxiliary quantum bit to perform a first rotation of the state of the auxiliary quantum bit; directing energy to the coupling element to perform a beam splitter operation on the first quantum oscillator and the second quantum oscillator; and directing energy to the auxiliary quantum bit to perform a second rotation of the state of the auxiliary quantum bit.

[0130] Aspect 9. A system according to Aspect 8, wherein the auxiliary quantum bit exhibits a ground state |g>, a first excited state |e> and a second excited state |f>, and wherein the first rotation and the second rotation of the state of the auxiliary quantum bit are rotations between the ground state |g> and the second excited state |f> of the auxiliary quantum bit.

[0131] Aspect 10. A system according to any one of aspects 1 to 9, wherein performing the entanglement gate between the logic states of the first quantum oscillator and the second quantum oscillator also includes operating the at least one energy source to direct energy to the coupling element for a certain time length, and the time length is half of the time length required to exchange the excitations of the first quantum oscillator and the second quantum oscillator.

[0132] Aspect 11. A system according to any one of aspects 1 to 10, wherein the auxiliary qubit is a superconducting transporter qubit.

[0133] Aspect 12. A system for implementing an entanglement gate that operates on two dual-rail quantum bits, the system comprising: a first dual-rail quantum bit, comprising: a first quantum oscillator; a second quantum oscillator; a first coupling element coupled to the first quantum oscillator and the second quantum oscillator; and an auxiliary quantum bit coupled to the second quantum oscillator; a second dual-rail quantum bit, comprising: a third quantum oscillator; a fourth quantum oscillator; and a second coupling element coupled to the third quantum oscillator and the fourth quantum oscillator; a third coupling element coupled to the second quantum oscillator and the third quantum oscillator; at least one energy source; and at least one controller, the at least one controller being configured to: perform an entanglement gate between a dual-rail state of the first dual-rail quantum bit and a dual-rail state of the second dual-rail quantum bit by operating the at least one energy source one or more times to direct energy to the third coupling element and / or to the auxiliary quantum bit; measure the state of the auxiliary quantum bit measured after performing the entanglement gate; and determine whether the entanglement gate has generated an error based on the measured state of the auxiliary quantum bit.

[0134] Aspect 13. A system according to Aspect 12, wherein the at least one controller is further configured to operate the at least one energy source to place the first dual-rail quantum bit in a 0 logic state or a 1 logic state in the following manner: when the first dual-rail quantum bit is to be initialized to the 0 logic state, operate the at least one energy source to place the first quantum oscillator in a single-photon state and place the second quantum oscillator in its ground state; or when the first dual-rail quantum bit is to be initialized to the 1 logic state, operate the at least one energy source to place the first quantum oscillator in its ground state and place the second quantum oscillator in a single-photon state.

[0135] Aspect 14. A system according to Aspect 13, wherein the at least one controller is further configured to operate the at least one energy source to place the second dual-rail quantum bit in a 0 logic state or a 1 logic state in the following manner: when the second dual-rail quantum bit is to be initialized to the 0 logic state, operate the at least one energy source to place the third quantum oscillator in a single-photon state and place the fourth quantum oscillator in its ground state; or when the second dual-rail quantum bit is to be initialized to the 1 logic state, operate the at least one energy source to place the third quantum oscillator in its ground state and place the fourth quantum oscillator in a single-photon state.

[0136] Aspect 15. A system according to any one of Aspects 12 to 14, wherein each of the first coupling element, the second coupling element and the third coupling element is one of the following: a superconducting transporter qubit, a superconducting nonlinear asymmetric inductor element (SNAIL) or a superconducting quantum interference device (SQUID).

[0137] Aspect 16. A system according to any one of Aspects 12 to 15, wherein operating the at least one energy source one or more times to direct energy to the third coupling element and / or to the auxiliary quantum bit includes operating the at least one energy source one or more times to direct a microwave tone to the third coupling element and / or to the auxiliary quantum bit.

[0138] Aspect 17. A system according to any one of aspects 12 to 16, wherein the auxiliary qubit is not coupled to the first quantum oscillator.

[0139] Aspect 18. A system according to any one of Aspects 12 to 17, wherein the at least one controller is configured to measure the state of the auxiliary quantum bit after executing the entanglement gate by operating the at least one energy source to direct energy to a readout resonator coupled to the auxiliary quantum bit.

[0140] Aspect 19. A system according to any one of aspects 12 to 18, wherein the auxiliary qubit is a superconducting transporter qubit.

[0141] The above embodiments of the technology described herein can be implemented in any of many ways. For example, a controller (including Figure 1Controller 106 shown) can be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or processor set, whether the processor is set in a single computer or distributed in multiple computers. Such a processor can be implemented as an integrated circuit, with one or more processors in the integrated circuit component, including commercially available integrated circuit components named such as CPU chips, GPU chips, microprocessors, microcontrollers or coprocessors known in the art. Alternatively, the processor can be implemented in a customized circuit system such as ASIC or in a semi-custom circuit system generated by configuring a programmable logic device. As another alternative, the processor can be part of a larger circuit or semiconductor device (whether commercially available, semi-custom or customized). As a specific example, some commercially available microprocessors have multiple cores, so that one or a subset of those cores can constitute a processor. However, the circuit system of any suitable format can be used to implement the processor.

[0142] The various aspects of the present invention can be used alone, in combination, or in various arrangements not specifically described in the embodiments described in the foregoing, and therefore its application is not limited to the arrangement and details of the components described in the foregoing description or shown in the drawings. For example, an aspect described in one embodiment can be combined with an aspect described in other embodiments in any way.

[0143] In addition, the present invention can be implemented as a method, and examples of such methods have been provided. The actions performed as part of the method can be ordered in any suitable manner. Therefore, embodiments can be constructed that perform actions in an order different from the order shown, and even if shown as sequential actions in illustrative embodiments, the embodiments can still include performing some actions simultaneously.

[0144] The use of ordinal terms such as "first", "second", "third", etc. to modify claim elements in the claims does not itself imply any priority, precedence or order of one claim element relative to another claim element, or the temporal order in which the actions of the method are performed, but is merely used as a mark to distinguish one claim element with a certain name from another element with the same name (whereas ordinal terms are used) to distinguish the claim elements.

[0145] The terms "approximately" and "about" can be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and also within ±2% of a target value in some embodiments. The terms "approximately" and "about" can include target values. The term "substantially equal" can be used to refer to values ​​that are within ±20% of each other in some embodiments, within ±10% of each other in some embodiments, within ±5% of each other in some embodiments, and also within ±2% of each other in some embodiments.

[0146] The term "substantially" may be used to refer to values ​​within ±20% of a comparison measurement in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and also within ±2% in some embodiments. For example, a first direction that is "substantially" perpendicular to a second direction may refer to a first direction that is within ±20% of a 90° angle with the second direction in some embodiments, within ±10% of a 90° angle with the second direction in some embodiments, within ±5% of a 90° angle with the second direction in some embodiments, and also within ±2% of a 90° angle with the second direction in some embodiments.

[0147] In addition, the phraseology and terminology used herein are for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," or "having," "containing," "involving," and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

Claims

1. A system for implementing an entanglement gate operating on two logical qubits, the system comprising: The first quantum oscillator; The second quantum oscillator; a coupling element coupled to the first quantum oscillator and the second quantum oscillator; an auxiliary qubit coupled to the first quantum oscillator; at least one energy source; a readout resonator coupled to the auxiliary qubit; as well as at least one controller, the at least one controller being configured to: performing an entanglement gate between logic states of the first quantum oscillator and the second quantum oscillator by operating the at least one energy source one or more times to direct energy to the coupling element and / or to the auxiliary qubit; measuring the state of the auxiliary qubit measured after executing the entanglement gate; as well as Whether an error occurs in the entanglement gate is determined based on the measured state of the auxiliary qubit.

2. The system of claim 1, wherein: The coupling element is dispersively coupled to the first quantum oscillator and the second quantum oscillator; and The auxiliary quantum bit is coupled to the first quantum oscillator in a divergent manner.

3. The system according to any one of claims 1 to 2, wherein: The coupling element is a superconducting transport quantum bit, a superconducting nonlinear asymmetric inductor element (SNAIL) or a superconducting quantum interference device (SQUID).

4. The system according to any one of claims 1 to 3, wherein: Operating the at least one energy source one or more times to direct energy toward the coupling element and / or toward the auxiliary qubit includes operating the at least one energy source one or more times to direct a microwave tone toward the coupling element and / or toward the auxiliary qubit.

5. The system according to any one of claims 1 to 4, wherein: The auxiliary qubit is not coupled to the second quantum oscillator.

6. The system according to any one of claims 1 to 5, wherein: The at least one controller is configured to measure a state of the auxiliary qubit after executing the entanglement gate by operating the at least one energy source to direct energy to the readout resonator.

7. The system according to any one of claims 1 to 6, wherein: The at least one controller is further configured to operate the at least one energy source to place the auxiliary qubit in a ground state prior to executing the entanglement gate.

8. The system according to any one of claims 1 to 7, wherein: Performing the entanglement gate between logic states of the first quantum oscillator and the second quantum oscillator comprises operating the at least one energy source: directing energy to the auxiliary qubit to perform a first rotation of a state of the auxiliary qubit; directing energy to the coupling element to perform a beam splitter operation on the first quantum oscillator and the second quantum oscillator; as well as Energy is directed toward the auxiliary qubit to perform a second rotation of the state of the auxiliary qubit.

9. The system according to claim 8, wherein: The auxiliary qubit exhibits a ground state |g>, a first excited state |e>, and a second excited state |f>, and wherein the first rotation and the second rotation of the state of the auxiliary qubit are rotations between the ground state |g> and the second excited state |f> of the auxiliary qubit.

10. The system according to any one of claims 1 to 9, wherein: Executing the entanglement gate between logic states of the first quantum oscillator and the second quantum oscillator further comprises operating the at least one energy source to direct energy to the coupling element for a length of time that is half of a length of time required to exchange excitations of the first quantum oscillator and the second quantum oscillator.

11. The system according to any one of claims 1 to 10, wherein: The auxiliary qubit is a superconducting transporter qubit.

12. A system for implementing an entanglement gate operating on two dual-rail qubits, the system comprising: The first dual-track qubit, including: The first quantum oscillator; The second quantum oscillator; a first coupling element coupled to the first quantum oscillator and the second quantum oscillator; and an auxiliary qubit coupled to the second quantum oscillator; The second dual-track quantum bit includes: The third quantum oscillator; a fourth quantum oscillator; and a second coupling element coupled to the third quantum oscillator and the fourth quantum oscillator; a third coupling element coupled to the second quantum oscillator and the third quantum oscillator; at least one energy source; and at least one controller, the at least one controller being configured to: performing an entanglement gate between a dual-rail state of the first dual-rail qubit and a dual-rail state of the second dual-rail qubit by operating the at least one energy source one or more times to direct energy to the third coupling element and / or to the auxiliary qubit; measuring the state of the auxiliary qubit measured after executing the entanglement gate; and Whether an error occurs in the entanglement gate is determined based on the measured state of the auxiliary qubit.

13. The system according to claim 12, wherein: The at least one controller is further configured to operate the at least one energy source to place the first dual-rail qubit in a 0 logic state or a 1 logic state by: When the first dual-rail qubit is to be initialized to the 0 logic state, operating the at least one energy source to place the first quantum oscillator in a single-photon state and the second quantum oscillator in its ground state; or When the first dual-rail qubit is to be initialized to the 1 logic state, operating the at least one energy source places the first quantum oscillator in its ground state and places the second quantum oscillator in a single photon state.

14. The system according to claim 13, wherein: The at least one controller is further configured to operate the at least one energy source to place the second dual-rail qubit in a 0 logic state or a 1 logic state by: When the second dual-rail qubit is to be initialized to the 0 logic state, operating the at least one energy source to place the third quantum oscillator in a single photon state and to place the fourth quantum oscillator in its ground state; or When the second dual-rail qubit is to be initialized to the 1 logic state, operating the at least one energy source places the third quantum oscillator in its ground state and places the fourth quantum oscillator in a single photon state.

15. The system according to any one of claims 12 to 14, wherein: Each of the first coupling element, the second coupling element and the third coupling element is one of the following: a superconducting transporter qubit, a superconducting nonlinear asymmetric inductor element (SNAIL) or a superconducting quantum interference device (SQUID).

16. A system according to any one of claims 12 to 15, wherein: Operating the at least one energy source one or more times to direct energy toward the third coupling-element and / or toward the auxiliary qubit includes operating the at least one energy source one or more times to direct a microwave tone toward the third coupling-element and / or toward the auxiliary qubit.

17. A system according to any one of claims 12 to 16, wherein: The auxiliary qubit is not coupled to the first quantum oscillator.

18. A system according to any one of claims 12 to 17, wherein: The at least one controller is configured to measure a state of the auxiliary qubit after executing the entanglement gate by operating the at least one energy source to direct energy to a readout resonator coupled to the auxiliary qubit.

19. A system according to any one of claims 12 to 18, wherein: The auxiliary qubit is a superconducting transporter qubit.

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