Method and system for high-fidelity ZZ rotation of qubits

Abstract

This provides a method for executing a ZZ rotation quantum gate acting on two qubits having XX coupling and corresponding resonant frequencies. [Solution] A method comprising applying a rotation pulse and an echo pulse twice, wherein in each pulse application, a corresponding rotation pulse is applied to each of the two qubits. The rotation pulse has a corresponding phase and amplitude and a drive frequency ω different from each of the resonant frequencies. (i) It has such that each of the two qubits has the corresponding detuning Δ_0,1 (i) The echo pulse is commutative with the Pauli ZZ operator associated with the two qubits. The echo pulse is XX+θ(Δ_0y (i) Δ_1 (i) )YY rotation and XY-θ(Δ_0 (i) Δ_1 (i) The pulses are applied to control the magnitude of either the Y or X rotation. In each pulse application, the echo pulse is applied after the rotation pulse.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims priority to U.S. Provisional Patent Application No. 63 / 701,005, filed on 30 September 2024, which is incorporated herein by reference in its entirety.

[0002] This disclosure relates to the field of quantum computing, and more specifically, to the field of quantum error suppression. [Background technology]

[0003] The development of useful quantum computers critically depends on reducing execution errors (the difference between the actual execution of quantum logic operations and their ideal execution).

[0004] Certain types of errors, namely coherent errors (including stochastic coherent errors and associated subcorrelation-time coherent interactions with the environment), can be significantly reduced through quantum error suppression (QES). A key feature of QES is that it does not require significant overhead in terms of the number of qubits, circuit depth, or circuit iterations needed to obtain a result up to a given statistical error (total number of "shots"). A prototypical example of QES is "dynamic decoupling," where a non-idle quantum circuit implements better quantum memory than an idle circuit. Another important example is given by "Pauli-Twiling," where a single noisy circuit is replaced by an average across noisy circuits obtained by randomly adding specific Pauli layers. While several separate circuits must be used, the total number of shots required is similar to that of the original circuit.

[0005] Further background to the subject matter of this disclosure is as follows: [Nguyenet al.,2024] Nguyen, LB, et.al. (2024), Programmable Heisenberg interactions between Floquet qubits, Nature Physics, 20(2):240-246

[0006] Furthermore, the references to the above publications in this specification should not be inferred to mean that they are in any way related to the patentability of the currently disclosed subject matter. In particular, the references to the above publications in this specification should not be inferred to mean that the above publications do not in any way negate the patentability of the currently claimed subject matter. [Overview of the project]

[0007] Quantum gates typically suffer from significant coherent errors in multiple rotational directions. Some errors are not necessarily errors from a hardware perspective. In other words, errors may not be an effect of the gate's non-ideal execution, but rather may be rotations that are desirable to eliminate in order to execute a particular gate. For example, a single-qubit gate implemented on a particular two-level system ideally has a π / 4 Pauli X rotational action and a π / 16 Pauli Y rotational action simultaneously. The Pauli X or Pauli Y rotation may be undesirable. Sometimes these rotations are small relative to the gate's primary rotational action. Sometimes these errors can be non-Markov (i.e., have time-dependent effects). These errors are sometimes referred to as “oscillation errors” in this disclosure. Oscillation errors may include single-qubit rotations and two-qubit rotations. The effects of oscillation errors depend on the resonant frequencies of the qubits involved in the gate's execution, the frequency of the driving field, crosstalk with neighboring qubits, and the anharmonic properties of the qubits (if applicable).

[0008] A concrete example is superconducting qubits. Cross-resonance (CR) gates may be the most abundant two-qubit gates for fixed-frequency transmon architectures. In [Nguyen et al., 2024], the authors demonstrated an alternative gate in which both qubits are driven using frequencies far from their resonances, generating ZZ rotation, oscillating terms XX and YY. XX and YY can also be prevented from oscillating to generate a Heisenberg gate. When applying this method to the generation of a ZZCZ gate, the authors relied on oscillating these extraneous terms (XX and YY) at high frequencies to minimize their influence.

[0009] The complex nature of oscillation errors complicates and therefore inefficient protocols for eliminating (suppressing) these errors (e.g., new errors are introduced into the computation). Simple, robust, and efficient protocols for suppressing oscillation errors are crucial for the functionality of current and future quantum computers.

[0010] This disclosure provides a method for generating an optimal gate along with an error suppression protocol, which can reduce, and preferably eliminate, oscillation execution errors.

[0011] Generally, qubits are driven using a single frequency (or a similar frequency), and dynamic decoupling (echo) can be incorporated as part of the pulse that generates the gate. This approach has several key advantages. 1. Most importantly, this approach allows for working within an optimal parameter range, and the XX and YY terms do not oscillate. Primarily, the frequency can be exactly midway between the two-qubit resonant frequencies. Thus, the quantum gates applied by the methods according to this disclosure are sometimes called “intermediate-resonance” (MR) gates. 2. The echo gate automatically eliminates single-qubit Z rotations, which include slowly changing fluctuations and are the main cause of decoherence. 3. All removed errors (XX, YY, ZI, IZ) are replaced by the (ideal) ZZ gate, there are no residual BCH terms, and the MR gate is noisier than the CR gate, even for parameters far from the optimal range.

[0012] According to a second aspect of the subject matter of this disclosure, a method for performing a ZZ rotation quantum gate is provided. The ZZ rotation quantum gate is a two-qubit Q having XX coupling. 0,1 It is acting on the corresponding resonant frequency ω. 0,1 The method comprises applying the following pulses twice: a rotation pulse and an echo pulse. With each pulse application, a corresponding rotation pulse is applied to each of the two qubits. The rotation pulse has a resonant frequency ω 0,1 Each of them has a different drive frequency ω (i) Because it has, each of the two qubits has the corresponding detuning

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[0013] In addition to the features described above, the methods for performing the ZZ rotation quantum gate according to this embodiment of the subject matter of this disclosure may optionally include one or more of the following features (i) to (xvi) in technically possible combinations or permutations.

[0014] i. Echo pulses are,

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[0015] ii. Echo pulses are,

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[0016] iii. The corresponding echo pulse has an effect.

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[0017] iv. (a) The sum of the phases associated with the first application of the rotation pulse [Number] (b) The sum of the phases associated with the second application of the rotation pulse [Number] (c) Either of the sums of phases ψ = ψ0 + ψ1 is configured for either (I) [Number] controlling the magnitude of one of them and eliminating the other, and (II) [Number] eliminating both of them.

[0018] v. Either of the corresponding echo pulses has either the action XY or YX.

[0019] vi. The corresponding phase [Number] The difference of is equal to an integer multiple of π.

[0020] vii. The drive frequency ω associated with the first application of the rotation pulse (1) is equal to the drive frequency ω associated with the second application of the rotation pulse (2) and the amplitude Ω associated with the first application of the rotation pulse (1) is equal to the amplitude Ω associated with the second application of the rotation pulse (2) .

[0021] viii. The two-qubit Q 0,1 is executed based on two energy levels included in the multi-level quantum system.

[0022] ix. The echo pulse is configured to eliminate IZ noise and ZI noise.

[0023] x. Drive frequency ω (i) However, it lies between the lower resonant frequency ω0 and the higher resonant frequency ω1.

[0024] xi. Drive frequency ω (i) but,

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[0025] xii. Driving frequency ω (i) However, the resonant frequency ω 0,1 This is the average.

[0026] xiii. Drive frequency ω (i) However, it is lower than the lower resonant frequency ω0, or higher than the higher resonant frequency ω1.

[0027] xiv. 2-qubit Q 0,1 One qubit q of the neighboring qubit Q n It communicates with the sum of phases associated with the first application of the rotation pulse.

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[0028] xv. Phase sum

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[0029] xvi. The ZZ rotation angle α1 associated with the first application of the rotation pulse is equal to the ZZ rotation angle α2 associated with the second application of the rotation pulse.

[0030] According to a second aspect of the subject matter of this disclosure, a method for performing a two-qubit Pauli rotational quantum gate is provided. The Pauli rotational quantum gate is a two-qubit Q 0,1 It is acting on the 2-qubit Q. 0,1 However, it has XX coupling. This method uses two qubits Q 0,1 At least one of them contains a 2-qubit Q 0,1 This method involves applying a single-qubit rotation to shift the basis of at least one qubit from a measurement basis to a rotation basis. 0,1 This method involves applying a ZZ rotation quantum gate to a 2-qubit Q. The ZZ rotation quantum gate is according to a first aspect of the subject matter of this disclosure. 0,1 At least one of them contains a 2-qubit Q 0,1 This involves applying a single-qubit rotation to shift at least one of the bases from a rotation base to a measurement base.

[0031] A third aspect of the subject matter of this disclosure provides a method for performing a two-qubit quantum gate. The quantum gate is a two-qubit Q 0,1 It acts on the 2-qubit Q. 0,1 However, it has XX coupling. The method includes performing the method according to a second embodiment to perform at least one of XX rotation, YY rotation, and ZZ rotation. The corresponding rotation angles of the rotations follow the KAK decomposition of a 2-qubit quantum gate.

[0032] According to a fourth aspect of the subject matter of this disclosure, a quantum processing unit is provided. The quantum processing unit includes at least two qubits. The at least two qubits (i.e., the aforementioned two qubits included in a plurality of qubits) have an XX interaction. The quantum processing unit includes at least one pulse generator coupled to the at least two qubits to apply pulses to the at least two qubits. The quantum processing unit includes a controller. The controller communicates with the at least one pulse generator to provide commands to the at least one pulse generator. The quantum processing unit is configured to perform methods according to the first to third aspects of the subject matter of this disclosure.

[0033] In addition to the features described above, the quantum processing units according to these embodiments of the subject matter of this disclosure may optionally include one or more of the following features (i) to (iii) in any technically possible combination or permutation: i. At least one pulse generator is configured to apply high-frequency pulses. ii.2 The qubit is a superconducting qubit. iii. At least one pulse generator is configured to apply either an infrared pulse, a visible light pulse, or an ultraviolet pulse.

[0034] According to a fifth aspect of the subject matter of this disclosure, a system is provided comprising a computer and a quantum processing unit. The computer has pulse-level access to the quantum processing unit. The computer system is configured to perform the methods according to the first to third aspects of the subject matter of this disclosure.

[0035] According to some embodiments, the quantum processing unit is in accordance with a fourth aspect of the subject matter of this disclosure.

[0036] According to a sixth aspect of the subject matter of this disclosure, a non-temporary computer-readable storage medium is provided. The non-temporary computer-readable storage medium stores computer instructions. The computer instructions are used to cause a computer communicating with a quantum processing unit to perform a method according to any one of the first to third aspects of the subject matter of this disclosure.

[0037] According to the seventh aspect of the subject matter of this disclosure, a computer execution method is provided. This method includes simulating a method according to any one of the first to third aspects of the subject matter of this disclosure.

[0038] According to an eighth aspect of the subject matter of this disclosure, a non-temporary computer-readable storage medium is provided. The non-temporary computer-readable storage medium, which stores computer instructions, is used to cause a computer to perform a method according to a seventh aspect of the subject matter of this disclosure.

[0039] Furthermore, the error suppression protocol can be modified to have a controlled rotation term to calibrate the quantum gate. The error suppression protocol can be executed such that the calibrated gate has a desired rotation term, according to the results of the characterization protocol. Thus, this disclosure also provides a gate calibration protocol, which can be used, for example, when recompiling a quantum circuit. The action of an oscillating execution error can rather be considered a desired quantum gate that assists the main (ideal) action of the quantum gate being applied. This can be beneficial, for example, by eliminating native gates that may be applied by the quantum processing unit, reducing memory requirements, execution time, and / or reducing errors.

[0040] For the sake of brevity of this disclosure, non-coherent execution errors are ignored. In other words, execution errors are assumed to be coherent. Note that the methods, systems, and quantum circuits disclosed herein are applicable without this assumption.

[0041] In this disclosure, the following terms and their derivatives should be understood in accordance with the following commentary.

[0042] The terms "gate" and "quantum gate" can be synonymous.

[0043] The term "term" may refer to an element of a generator or an augment in a series expansion when it relates to a generator or execution error in a quantum logic operation. For example, a matrix element in a matrix representation, an augment in a perturbation expansion, or a Pauli matrix in a Pauli matrix expansion.

[0044] The term "Pauli term" can refer to a matrix included in a Pauli group P. A Pauli group is defined as a subgroup of unitary groups containing the tensor product of Pauli matrices. In the formula:

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[0045] The term "horizontal term" refers to each term included in the tensor product of its respective relation.

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[0046] The term "Pauli gate" can refer to any quantum gate that can be represented by a matrix included in the Pauli group P.

[0047]

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[0048]

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[0049] The term "direction" is,

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[0050] The term "based on" can indicate that the first mentioned quantity may have a dependence on the second mentioned quantity. In other words, the first mentioned quantity may be a function of the second mentioned quantity, and the function is non-constant.

[0051] The quantum gates performed by the methods described herein are sometimes referred to as "EMR gates." [Brief explanation of the drawing]

[0052] Embodiments are described herein, only as non-limiting examples, with reference to the accompanying drawings, in order to better understand the subject matter disclosed herein and to illustrate how it may actually be carried out. [Figure 1A] A flowchart of the method according to the embodiments of this disclosure is shown. [Figure 1B] A schematic diagram of a system that implements the method outlined in Figure 1A is shown. [Figure 2] A flowchart illustrating the method described herein is provided. [Figure 3] A flowchart illustrating the method described herein is provided. [Figure 4A] A scatter plot showing the simulated fidelity of a bare ZZ rotation is presented. [Figure 4B] A scatter plot showing the simulated non-fidelity of a ZZ rotation performed using the method according to the embodiments of this disclosure is presented. [Figure 5] A scatter plot showing the simulated normalized magnitude of the ZZ rotation performed by the method disclosed herein is presented. [Figure 6A] A bar graph illustrating the performance of the error suppression method according to the embodiments of this disclosure is presented. [Figure 6B] A bar graph illustrating the performance of the error suppression method according to the embodiments of this disclosure is presented. [Figure 7] A schematic representation of a computer performing the method according to the embodiments of this disclosure is shown. [Figure 8] A schematic diagram of a system for performing the method according to the embodiments of this disclosure is provided. [Modes for carrying out the invention]

[0053] This specification describes several examples of systems and methods useful for high-fidelity ZZ rotation of qubits.

[0054] The following detailed description includes numerous specific details to ensure a complete understanding of the subject matter. However, it will be understood by those skilled in the art that some examples of the subject matter can be carried out without these specific details. In other examples, well-known methods, procedures, components, and circuits are not described in detail so as not to obscure the subject matter of this disclosure.

[0055] As used herein, phrases such as “for example,” “etc.,” and “as an example,” and variations thereof, describe non-limiting embodiments of the subject matter of this disclosure.

[0056] In this specification, references to “one example,” “several examples,” “another example,” “other examples,” “one instance,” “several examples,” “another example,” “another example,” “one case,” “several cases,” “another case,” “other cases,” or variations thereof, mean that a particular feature, structure, or characteristic described is included in at least one example of the subject matter, but the appearance of the same term does not necessarily refer to the same example.

[0057] For clarity, certain features, structures, and / or properties disclosed herein, described in the context of separate examples, may be provided in combination in a single example. Conversely, various features, structures, and / or properties disclosed herein, described in the context of a single example for brevity, may be provided separately or in any appropriate partial combination.

[0058] Unless otherwise specified, as will be apparent from the following descriptions, any use of terms such as “calculate,” “determine,” and “execute” throughout this specification may refer to actions and / or processes of any combination of software, hardware, and / or firmware. For example, these terms may, in some cases, refer to actions and / or processes of a programmable machine that manipulate and / or convert data, which is represented as a physical quantity such as an electronic quantity in the registers and / or memory of the programmable machine, into other data, which is similarly represented as a physical quantity in the memory, registers, and / or other such information storage, transmission, and / or display elements of the programmable machine.

[0059] Refer to Figures 1A and 1B. Figure 1A shows a schematic flowchart illustrating Method 100 according to the present disclosure. Figure 1B shows a schematic system 1100 that performs Method 100.

[0060] Method 100 may be for performing the ZZ rotation quantum gate. In other words, Method 100 transforms the quantum state |ψ〉 into the quantum state e iαZZ It may be for converting to |ψ〉. The ZZ rotating quantum gate is a 2-qubit Q 0,1 It can act on (i.e., the first qubit can be represented by Q0, and the second qubit can be represented by Q1). 2-qubit Q 0,1 It may have XX coupling 110. Each of the two qubits has a corresponding resonant frequency ω 0,1 It may have the following characteristics: That is, the first qubit Q0 may have a first resonant frequency ω0, and the second qubit Q1 may have a second resonant frequency ω1.

[0061] A two-qubit Hamiltonian without a driving field is:

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[0062] By moving from the experimental frame to a frame that rotates according to the drive pulse term and ignoring the high-speed rotation term (i.e., applying a rotation wave approximation), the following is provided:

[0063]

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[0064] When a coordinate transformation is applied,

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[0065] definition

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[0066] Therefore, the Hamiltonian includes a (non-oscillating) ZZ term and an oscillating XX-YY term. The XX-YY term is,

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[0067] In some embodiments, two qubit Q 0,1 This can be performed based on two energy levels contained in a multi-level quantum system. In other words, a qubit can be performed by a two-level subspace (e.g., a qubit implemented by a superconducting circuit). When a qubit is performed by a two-level subspace, the ZZ term can be shifted (i.e., the coefficient of the ZZ term can change). The shift can be large,

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[0068] The phase of the driving field can be considered. The Hamiltonian (in the experimental frame) is:

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[0069]

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[0070] The sum of two phases is sometimes called the "MR phase," and φ MR , in other words, φ MR It can be expressed as =φ1+φ0. Several special cases are worth noting. The condition φ1=φ0 gives a ZZ gate with an oscillation term YY-XX (equivalently, XY+YX).

[0071]

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[0074] The ZZ term (or its coefficient) is suppressed by the cos(φ1-φ0) coefficient, and therefore phase calibration may be required. Since the damping coefficient is cosine, it is not sensitive to small phase mismatches. For example, to lose 1% of the value of the ZZ Hamiltonian term, an error of 0.14 radians (8 degrees) in φ1-φ0 is an unlikely large calibration error (e.g., calibration errors are typically in the range of a few milliradians on current superconducting hardware). MR This defines the direction of oscillation error in a plane perpendicular to the XY axes. That is, φ MR This rotates YY-XX and XY+YX around the XY axes.

[0075] When performing method 100, it may be desirable to utilize the MR ZZ generator (i.e., using the ZZ term in the MR Hamiltonian). However, as described above, an XX,YY,ZI,IZ generator (rotation) may also be present. Undesirable rotations can be eliminated by applying an echo pulse that can be inversely exchanged with the XX,YY,ZI,IZ generator.

[0076] Method 100 may include step 130 of applying a first rotation pulse. Step 130 is a 2-qubit Q 0,1 This may include applying a corresponding rotational pulse (indicated as pulses 133, 136) to each of them (for example, via pulse generator 120).

[0077] Each rotational pulse corresponds to the phase

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[0078] Method 100 may include step 140 of applying a first dynamic decoupling pulse, i.e., applying a first echo pulse. Step 140 is a 2-qubit Q 0,1 This may include applying a corresponding echo pulse (indicated as pulses 143, 146) to each of them (for example, via pulse generator 120).

[0079] The first echo pulse corresponds to a 2-qubit Q 0,1It can be exchanged with the Pauli ZZ operator associated with it. In other words, the Hamiltonian term associated with the first echo pulse is a 2-qubit Q 0,1 It can be replaced with the Pauli ZZ operator associated with it. The first echo pulse is

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[0080] Method 100 may include step 150 of applying a second rotation pulse. Step 150 is a 2-qubit Q 0,1 This may include applying a corresponding rotational pulse (indicated as pulses 153, 156) to each of them (for example, via pulse generator 120).

[0081] Each rotational pulse corresponds to the phase

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[0082] Method 100 may include step 160 of applying a second dynamic decoupling pulse. In other words, applying a second echo pulse. Step 160 is a 2-qubit Q 0,1 This may include applying a corresponding rotational pulse (indicated as pulses 163, 166) to each of them (for example, via pulse generator 120).

[0083] The second echo pulse corresponds to the 2-qubit Q 0,1 It can be exchanged with the Pauli ZZ operator associated with it. In other words, the Hamiltonian term associated with the second echo pulse is a 2-qubit Q 0,1 This is the Pauli ZZ operator associated with it. The second echo pulse is

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[0084] In other words, steps 130 and 150 involve two qubits Q 0,1 This can be described as applying two rotation pulses corresponding to each of the following. The application of rotation pulses can be indexed by index i. Each rotation pulse corresponds to the resonant frequency ω 0,1 Each of them has a different drive frequency ω (i) It may have, and thereby, 2 qubit Q 0,1 Each of them corresponds to a different detune.

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[0085] Furthermore, steps 140 and 160 involve 2 qubit Q 0,1 This can be described as applying two echo pulses corresponding to each of the following:

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[0086] Each application of a rotation pulse (i.e., each of steps 130 and 150) may provide a ZZ rotation corresponding to a corresponding angle. The sum of the corresponding rotation angles may be the total rotation angle α. In some embodiments, the corresponding rotation angles may be equal, i.e., each of steps 130 and 150 may provide a ZZ rotation corresponding to an angle α / 2. That is, the ZZ rotation angle α1 associated with the first application of a rotation pulse may be equal to the ZZ rotation angle α2 associated with the second application of a rotation pulse.

[0087] In some embodiments, the parameters of the rotation pulse associated with the first application of the rotation pulse (i.e., the drive frequency ω) (i) ,

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[0088] In some embodiments, all parameters of the rotation pulse associated with the first application of the rotation pulse may be equal to the corresponding parameters associated with the second application of the rotation pulse. In other words, the rotation pulse of the first application may be identical to the rotation pulse of the second application.

[0089] In some embodiments, the echo pulse is

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[0090] An example of an echo pulse is detailed below. A convenient choice of echo pulse may be an XY echo, i.e., a pulse having the action of a Pauli XY gate. In this choice, the ZZ rotation quantum gate is performed according to method 100, and steps 130 and 150 corresponding to the rotation angle may be equal, in the following form

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[0091] XY echo has a driving frequency that is the MR frequency, and the phase can be such that φ MR This can be applied when = 0. In some embodiments, the echo pulse is in the following form

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[0092]

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[0093] In some embodiments, the phase [Number] can be configured to control the magnitude of either one and eliminate the rotation of the other, and / or [Number] can be configured to eliminate both. In some embodiments, the sum of the phases associated with the first application of the rotation pulse [Number] is the sum of the phases associated with the second application of the rotation pulse [Number] and / or the sum of the phases ψ = ψ0 + ψ1 is [Number] can be configured to control the magnitude of either one and eliminate the rotation, and / or [Number] can be configured to eliminate both. In some embodiments, the difference between the corresponding phases [Number] can be an integer multiple of π. [Number]

[0094] ​In some embodiments, the phases ψ0, ψ1 can be determined according to the formula.

[0095]

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[0096] In some embodiments, the phases can be predetermined. In some other embodiments, method 100 can include calculating the phases ψ0, ψ1.

[0097] The XY echo is a special case of the general case

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[0098] Since the XX, YY, ZI, and IZ terms all commute with the ZZ term, these echo pulses may not leave residual Baker-Campbell-Hausdorff (BCH) terms. This offers an advantage over echo CR. In a CR gate, the control echo pulse cannot isolate the Z noise on the target qubit. Furthermore, CR generates residual BCH terms arising from the reverse flow of the ZX and IZ terms (terms that do not change with the echo pulse) and the ZZ and IX terms (terms whose sign is reversed with the echo pulse).

[0099] Generally, method 100 uses the resonant frequency ω 0,1 It can be performed at any drive frequency which may differ from each of the others. In some embodiments, the drive frequency ω (i) It can be between the lower resonant frequency (i.e., ω0) and the higher resonant frequency (i.e., ω1). That is, the condition ω0 < ω (i) <ω1 may hold true. In some embodiments, the driving frequency ω (i) It may be lower than the lower resonant frequency (i.e., ω0) or higher than the higher resonant frequency (i.e., ω1). In other words, the condition ω (i) <ω0, ω1<ω (i) One of the following may be true.

[0100] A particular frequency range may be especially advantageous. In some embodiments, the drive frequency ω (i) teeth,

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[0101] In an EMR gate, the drive frequency is 2 qubits Q 0,1Unlike the resonance frequency, the drive frequency can be the same as that of an adjacent qubit Q 0,1 that communicates with one of the two qubits Q n . That is, the adjacent qubit Q n may have crosstalk with a qubit q that is a single qubit included in the two qubits Q 0,1 . In such a case, the EMR gate drives the cross resonance between the qubit q and the adjacent qubit Q n , which can thereby be a source of infidelity to the EMR gate. In other words, an unwanted cross-resonance rotation gate may act on the qubit q and the adjacent qubit Q n .

[0102] (The detuning between the drive field (of the rotation pulse) and the adjacent qubit Q n ) can be expressed as

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[0103]

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[0105] GT g The first-order qubit q and adjacent qubit Q in this case. n The effect of MR pulses in a subspace:

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[0106] When the effect of echo pulses is added,

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[0107] Finally, the action of the EMR gate is,

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[0108] In general, the parameters of the rotation pulse can be set to reduce the effects of crosstalk. In some embodiments, the phase

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[0109]

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[0110] If there are two or more neighboring qubits and the neighboring qubits may have different resonant frequencies that are close to the MR frequency, a more complex application of Method 100 may be required to eliminate the effects of crosstalk with all neighboring qubits. For example, a ZZ rotation may be divided into multiple sub-rotations (some sub-rotations or each sub-rotation may be performed according to Method 100), and the drive fields and echo pulses of the sub-rotations may be configured such that the overall effect is the elimination of the effects of crosstalk with all neighboring qubits.

[0111] Refer to Figure 2, which shows a flowchart illustrating Method 200 according to this disclosure. Method 200 may be for performing Pauli rotational quantum gates. In other words, Method 200 is a quantum state |ψ〉

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[0112] Method 200 may include a base shift step 220. Step 220 involves two qubits Q 0,1 At least one of the two qubits Q 0,1 This may involve applying a single-qubit rotation to shift the basis. The basis can be shifted from a measurement basis to a rotation basis. For example, the basis of the first qubit Q0 can be shifted to the X basis. In another example, the basis of the first qubit Q0 can be shifted to the Y basis, and the basis of the second qubit Q1 can be shifted to the X basis.

[0113] Method 200 involves two qubits Q 0,1 This may include applying a ZZ rotation quantum gate. The ZZ rotation quantum gate may be performed as described above in this disclosure. In other words, method 200 may include a step 230 of applying a first rotation pulse. Step 230 may correspond to step 130 of method 100 described above and may include performing its described action. Method 200 may include a step 240 of applying a first echo pulse. Step 240 may correspond to step 140 of method 100 described above and may include performing its described action. Method 200 may include a step 250 of applying a second rotation pulse. Step 250 may correspond to step 150 of method 100 described above and may include performing its described action. Method 200 may include a step 260 of applying a second rotation pulse. Step 260 may correspond to step 160 of method 100 described above and may include performing its described action.

[0114] Method 200 may include a shift-back step 270. Step 270 involves two qubits Q 0,1 Shift back at least one of the basis sets, 2-qubit Q 0,1 This may include applying a single-qubit rotation to at least one of the following: The basis can be shifted from a rotation basis to a measurement basis. For example, the basis for the first qubit Q0 can be shifted back from the X basis. In another example, the basis for the first qubit Q0 can be shifted back from the Y basis, and the basis for the second qubit Q1 can be shifted back from the X basis.

[0115] Refer to Figure 3, which shows a flowchart illustrating Method 300 according to this disclosure. Method 300 may be for performing a general quantum gate. In other words, Method 300 is a quantum state |ψ〉

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[0116] Generally, method 300 may involve performing method 200 to perform at least one of XX rotation, YY rotation, and / or ZZ rotation. The corresponding rotation angles of the rotations may follow the KAK decomposition of a two-qubit quantum gate.

[0117] More specifically, method 300 may include step 310 of applying a preceding single-qubit gate. The aforementioned single-qubit gate may follow the KAK decomposition of a two-qubit quantum gate.

[0118] Method 300 may include step 320 of applying XX rotations, where XX rotations may be by an angle α. Step 320 is performed on both qubits Q 0,1 Step 320 may include a step 323 of shifting the basis to the X basis. Step 320 may include a step 325 of performing a ZZ rotation as described herein.

[0119] Method 300 may include step 330 of applying a YY rotation. The YY rotation may be by angle β. Step 330 is performed on both qubits Q 0,1 Step 330 may include a step 333 to shift the basis to the Y basis. Step 330 may include a step 335 to perform the ZZ rotation as described herein.

[0120] Method 300 may include step 340 of applying a ZZ rotation. The ZZ rotation may be by angle γ. Step 340 is performed on both qubits Q 0,1 Step 343 may include shifting the basis to the Z basis. Step 340 may include step 345 performing the ZZ rotation as described herein.

[0121] Furthermore, the specific order in which the XX, YY, and ZZ rotations are performed may not be necessary, as these rotations are interchangeable. In some embodiments, a specific order may be required, for example, due to the non-ideal nature of the available gates.

[0122] In some embodiments, the ZZ rotation may be omitted (i.e., step 340 may be omitted), or the ZZ rotation may not be performed last (i.e., steps 320 and / or 330 may be performed after step 340), and method 300 may include a step of shifting back to the Z basis.

[0123] Method 300 may include step 350 of applying a subsequent single-qubit gate, which may follow the KAK decomposition of a two-qubit quantum gate.

[0124] In some embodiments, adjacent single-qubit quantum gates applied to perform different steps may be recompiled to reduce the total number of quantum gates applied. For example, single-qubit quantum gates applied to perform the first steps of steps 310 and 323, 333, and 343 may be recompiled into a single single-qubit gate layer.

[0125] Experimental results Echo gates (i.e., gates performed by the method according to the present invention) and non-echo gates (known in the art) are directly related and can therefore be easily compared through simulation and execution on quantum computing devices. The method according to this disclosure was simulated according to the error model of the publicly accessible "Brisbane" (also known as "ibm_brisbane") quantum computing device operated by IBM. Furthermore, echo gates were also executed on the "ibm_brisbane" quantum computing device. The simulations and executions were performed in a layered context according to IBM's ELPG scheme (see McKay, DC, et al., (2023), Benchmarking quantum processor performance at scale, arXiv:2311.05933), but the non-fidelity characterization protocols were different.

[0126] Refer to Figures 4A-4B. Figure 4A presents a scatter plot showing the simulated non-fidelity of a bare ZZ rotation. Figure 4B presents a scatter plot showing the simulated non-fidelity of a ZZ rotation performed using the error suppression method according to an embodiment of the present disclosure. Each data point represents the application of a ZZ rotation to one pair of qubits out of the device's 144 qubit pairs, having a specific detuning from the MR frequency (a two-qubit gate may be applied thereon). The drive frequency is given as detuning from the MR frequency,

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[0127] Near the MR frequency, non-echo gates have very low fidelity because the XX-YY components oscillate slowly, generating very large coherent errors. For echo gates, this is the optimal region. At about a quarter of the resonant frequency, the XX-YY components rotate fast enough that the echo is no longer an advantage. Therefore, the echo pulse is almost

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[0128] Refer to Figure 5, which presents a scatter plot showing the simulated normalized magnitude of the ZZ rotation performed by the method of this disclosure.

[0129] The above simulation (with the results described above for Figures 4A-4B) does not include coherence time and only simulates the intrinsic nonfiction arising from the 3-level system Hamiltonian with the presented drive (and therefore, in some cases, the nonfiction value is very low). Figure 5 shows the ZZ Hamiltonian terms of different frequencies for the same qubit pairs as in the previous figure (i.e., each qubit pair out of 144 qubit pairs in a device to which a 2-qubit gate can be applied). The Hamiltonian ZZ term is given normalized to its optimal (maximum) value. The drive frequency is given as detuning from the MR frequency,

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[0130] Here too, the optimal value is usually,

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[0131] Refer to Figures 6A and 6B, which show bar graphs demonstrating the performance of the gates and error suppression methods according to embodiments of this disclosure. Figure 6A shows the fidelity of EMR gates (brightly shaded dataset) versus native CR gates (darkly shaded dataset) for 25 qubit pairs. The x-axis labels are qubit pairs ordered according to the enumeration of the qubit devices. The average non-fidelity value for CR gates is 1.82%, and the average non-fidelity value for EMR gates is 0.64%. Figure 6B shows the fidelity of EMR gates for 13 qubit pairs. The x-axis labels are qubit pairs ordered according to the enumeration of the qubit devices. Some of the EMR gates are executed with phase shifts to compensate for crosstalk (darkly shaded dataset), and some are executed without phase shifts (lightly shaded dataset). The 13 qubit pairs associated with Figure 6B are the qubit pairs with the strongest crosstalk with neighboring qubits in the "Brisbane" quantum computing device. For all 13 qubit pairs, the resonant frequencies of neighboring qubits are less than 5 MHz away from the MR frequency. In some cases (such as qubit pairs (12, 13) and (58, 59)), the resonant frequencies of neighboring qubits are only about 1 MHz away from the MR frequency. Applying a phase shift has a significant impact on these pairs, often reducing fidelity from the O(10%) range to the O(1%) range.

[0132] The experimental results showed an average improvement in non-fidelity of nearly three times compared to the CR gate, with a consistent improvement—all qubit pairs showed improved fidelity. In conclusion, the EMR gate was demonstrated to be superior to both the non-echo gate demonstrated in [Nguyen et al., 2024] and the widely used CR gate.

[0133] Figure 7 and the following discussion are intended to provide a brief and general description of exemplary computing environments in which the disclosed technology may be implemented. While not required, the disclosed technology is described in the general context of computer executable instructions, such as program modules, executed by a personal computer (PC). Generally, a program module includes routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. Furthermore, the disclosed technology may be implemented in other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, and mainframe computers. The disclosed technology may also be practiced in a distributed computing environment where tasks are performed by remote processing devices linked via a communication network. In a distributed computing environment, program modules may reside in both local and remote memory storage devices.

[0134] Referring to Figure 7, an exemplary system for implementing the disclosed technology includes a general-purpose (typical) computing device in the form of an exemplary conventional PC 700, comprising one or more processing units 710, a system memory 720, and a system bus 730 that connects various system components, including the system memory 720, to one or more processing units 710. The system bus 730 may be one of several types of bus structures, including a memory bus or a memory controller, a peripheral bus, and / or a local bus using any of various bus architectures. The exemplary system memory 720 includes read-only memory (ROM) 722 and random-access memory (RAM) 727. A basic input / output system (BIOS) 725, which contains basic routines useful for transferring information between elements within the PC 700, is stored in the ROM 722. As shown in Figure 7, the system memory 720 may store computer-executable instructions for performing any of the disclosed techniques (e.g., sending instructions to a quantum computer to apply a characterization gate sequence and an adjacent gate sequence to a subset of qubits, measuring the results, collecting frequencies, and calculating model parameters) in their respective memory portions (generally indicated as executable software 729 for performing any embodiment of the disclosed synthesis technique).

[0135] An exemplary PC700 further includes one or more storage devices 740, such as a hard disk drive for reading and writing to a hard disk, a magnetic disk drive for reading and writing to a removable magnetic disk, and / or an optical disk drive for reading and writing to a removable optical disk (such as a CD-ROM or other optical medium). Such storage devices can each be connected to the system bus 730 by a hard disk drive interface, a magnetic disk drive interface, and / or an optical drive interface. The drives and their associated computer-readable media provide non-volatile storage for computer-readable instructions, data structures, program modules, and other data for the PC700. In the exemplary operating environment, other types of computer-readable media that can store data accessible by the PC may also be used, such as magnetic cassettes, flash memory, digital video discs, CDs, DVDs, RAM, NVRAM, and ROM. As used herein, the terms storage, memory, and computer-readable media may not include or encompass the propagating carrier or signal itself.

[0136] The operating system, one or more application programs, other program modules, and several program modules including program data may be stored in the storage device 740. The storage of quantum measurement results and instructions for obtaining such measurements (and / or instructions for carrying out any embodiment of the disclosed technology) may also be stored in the storage device 740. The user may input commands and information to the PC 700 via one or more input devices 750, such as a keyboard and a pointing device such as a mouse. Other input devices may include a digital camera, microphone, joystick, gamepad, satellite receiver, scanner, etc. These and other input devices are often connected to one or more processing units 710 via a serial port interface coupled to the system bus 730, but may be connected by other interfaces such as a parallel port, game port, or universal serial bus (USB). A monitor 780 or other type of display device is also connected to the system bus 730 via an interface such as a video adapter. Other peripheral output devices 760 may include speakers and a printer (not shown). In some cases, a user interface is displayed so that the user can input the circuit for synthesis and verify the success of the synthesis.

[0137] The PC700 may operate in a networked environment using logical connections to one or more remote computers, such as remote computers 790. In some examples, this may include one or more network or communication connections 770. The remote computer 790 may be another PC, server, router, network PC, or peer device or other common network node, and typically includes many or all of the elements described above with respect to the PC700, although Figure 7 illustrates only the memory storage device 795. The personal computer 700 and / or remote computer 790 may be connected to a local area network (LAN) and a wide area network (WAN). Such networking environments are common in offices, enterprise-wide computer networks, intranets, and the internet.

[0138] When used in a LAN networking environment, the PC700 connects to the LAN via a network interface. When used in a WAN networking environment, the PC700 typically includes a modem or other means for establishing communication over a WAN such as the Internet. In a networked environment, program modules or parts thereof described in relation to the personal computer 700 may be stored in a remote memory storage device or other location on the LAN or WAN. The illustrated network connection is illustrative, and other means may be used to establish communication links between computers.

[0139] Referring to Figure 8, an exemplary system for implementing the disclosed technology includes a computing environment 800, the environment including one or more quantum processing units 810, each including one or more monitoring / measurement devices. The quantum processing units execute quantum circuits provided by a typical processing unit 820. The quantum circuits are downloaded to the quantum processing units 810 or used (e.g., via control lines (quantum buses) 870) to program or configure the quantum processing units. Procedures according to any of the disclosed embodiments (e.g., high-level descriptions of qubit patches and sets of quantum circuits applied to neighboring qubits) may be stored in memory 830.

[0140] Referring to Figure 8, a high-level description of quantum software can be translated into a quantum circuit (e.g., a sequence of quantum gates, or a layer of gates acting in parallel on different qubits). Such a high-level description may optionally be stored on one or more external computers 860 outside the computing environment 800 using one or more memory and / or storage devices 865, and then, if necessary, can be downloaded to the computing environment 800 via one or more communication connections 840. The quantum circuit (according to any of the disclosed embodiments) is coupled to a quantum processor 810.

[0141] The quantum processing unit may be, but is not limited to, one or more of the following: (a) a superconducting quantum computer, (b) an ion-trap quantum computer, (c) a topological quantum computer using, for example, a Majorana zero-mode, (d) a photon quantum computer, or (e) a neutral-atom quantum computer. A set of gates (e.g., using any of the disclosed embodiments) can be transmitted to the quantum processing unit via control lines 870 in the controller 850 (or may be otherwise applied). In the illustrated example, the desired quantum computing process is carried out using one or more controllers 850, each specifically adapted to control one of the corresponding quantum processors 810. The classical processor 820 can further interact with a measurement / monitoring device (e.g., a readout device) 880 to help control and implement the desired quantum computing process (e.g., by reading or measuring data results from the quantum processing unit when available).

[0142] The foregoing description of embodiments of the present invention is presented for illustrative and explanatory purposes only and is not intended to be exhaustive or to limit the invention to the exact form disclosed. Numerous modifications and adaptations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. For example, techniques from any example can be combined with techniques described in any one or more of the other examples.

[0143] Therefore, applying the wording of the clause, this disclosure provides methods, systems, and circuits subject to the following clauses, but not limited to these: Clause 1: Two qubit Q with XX coupling 0,1 A method for executing a ZZ rotation quantum gate acting on a qubit, wherein each of the two qubits has a corresponding resonant frequency ω 0,1 The method has (a) Each of the two qubits is given a corresponding rotational pulse, i) The resonant frequency ω 0,1Unlike each of the others, each of the two qubits corresponds to the detuning.

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[0144] Clause 2: The echo pulse,

number

[0145] Clause 3: The echo pulse,

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[0146] Clause 4: The corresponding echo pulse acts

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[0147] Article 5: (a) The sum of phases associated with the first application of the rotation pulse.

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[0148] Clause 6: The method according to any one of Clauses 4 to 5, wherein any of the corresponding echo pulses has either action XY or YX.

[0149] Clause 7: The corresponding phase

number

[0150] Clause 8: The drive frequency ω associated with the first application of the rotation pulse. (1) The driving frequency ω associated with the second application of the rotation pulse is (2) The amplitude Ω is equal to the first application of the rotation pulse. (1) However, the amplitude Ω associated with the second application of the rotation pulse is (2) The method described in any one of the clauses 1 to 7, which is equivalent to the method described in any one of the clauses 1 to 7.

[0151] Clause 9: The two qubits Q 0,1 However, the method described in any one of the clauses 1 to 8 is performed based on two energy levels contained in a multi-level quantum system.

[0152] Clause 10: The method according to any one of Clauses 1 to 9, wherein the echo pulse is configured to eliminate IZ noise and ZI noise.

[0153] Clause 11: The drive frequency ω (i) The method according to any one of the clauses 1 to 10, wherein the resonant frequency is between the lower resonant frequency ω0 and the higher resonant frequency ω1.

[0154] Clause 12: The drive frequency ω (i) but,

[0155]

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[0156] Clause 13: The drive frequency ω (i) However, the resonant frequency ω 0,1 The method described in Clause 12, which is the average of [the specified value].

[0157] Clause 14: The drive frequency ω (i) However, the method described in any one of the clauses 1 to 10, wherein the resonant frequency is lower than the lower resonant frequency ω0, or higher than the higher resonant frequency ω1.

[0158] Clause 15: The two qubits Q 0,1 One qubit q of the neighboring qubit Q n It is communicating with, (a) The sum of phases associated with the first application of the rotation pulse.

number

number

[0159] Clause 16: The sum of the phases

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[0160] Clause 17: The method according to any one of Clauses 1 to 16, wherein the ZZ rotation angle α1 associated with the first application of the rotation pulse is equal to the ZZ rotation angle α2 associated with the second application of the rotation pulse.

[0161] Clause 18: Two-qubit Q having XX coupling 0,1 A method for performing a 2-qubit Pauli rotational quantum gate that acts on, (a) the two qubits Q 0,1 At least one of them is the two qubit Q 0,1 Applying a single-qubit rotation to shift at least one of the basis bases from the measurement basis to the rotation basis, (b) the two qubits Q 0,1 The application of a ZZ rotation quantum gate to the given object, wherein the said ZZ rotation quantum gate is one of those described in any one of clauses 1 to 17, (c) the two qubits Q 0,1 At least one of them is the two qubit Q 0,1 A method comprising: applying a single-qubit rotation to shift at least one basis of from a rotation basis to a measurement basis.

[0162] Clause 19: Two-qubit Q with XX coupling 0,1 A method for performing a two-qubit quantum gate acting on a two-qubit quantum gate, the method comprising performing the method described in clause 18 to perform at least one of XX rotation, YY rotation, and ZZ rotation, wherein the corresponding rotation angles of the rotation conform to the KAK decomposition of the two-qubit quantum gate.

[0163] Clause 20: A quantum processing unit, (a) at least two qubits having XX coupling, (b) at least one pulse generator coupled to the at least two qubits, so as to apply pulses to the at least two qubits, (c) A controller that communicates with the at least one pulse generator and provides commands to the at least one pulse generator, The quantum processing unit is configured to perform the method described in any one of the clauses 1 to 19.

[0164] Clause 21: The quantum processing unit according to Clause 20, wherein the at least one pulse generator is configured to apply radio frequency pulses.

[0165] Clause 22: The two qubits Q 0,1 The quantum processing unit described in Clause 21 is a superconducting qubit.

[0166] Clause 23: The quantum processing unit according to Clause 22, wherein at least one pulse generator is configured to apply an infrared pulse, a visible light pulse, or an ultraviolet pulse.

[0167] Clause 24: A system comprising a computer and a quantum processing unit, wherein the computer has pulse-level access to the quantum processing unit, and the system is configured to perform the method described in any one of Clauses 1 to 19.

[0168] Clause 25: The quantum processing unit is one of the systems described in Clause 24, which is one of the systems described in any one of Clauses 20 to 23.

[0169] Clause 26: A non-temporary computer-readable storage medium for storing computer instructions, wherein the computer instructions are used to cause a computer to communicate with a quantum processing unit to perform the actions described in any one of Clauses 1 to 19.

[0170] Clause 27: A computer implementation method comprising simulating the application of a ZZ rotation quantum gate as described in any one of Clauses 1 to 19.

[0171] Clause 28: A non-temporary computer-readable storage medium for storing computer instructions, wherein the computer instructions are used to cause a computer to perform the actions described in Clause 28.

Claims

1. Two qubit Q with XX coupling ０，１ A method for executing a ZZ rotation quantum gate acting on a corresponding resonant frequency ω ０，１ The method has, (a) A rotational pulse corresponding to each of the two qubits, i) the resonant frequency ω ０，１ Unlike each of the others, each of the two qubits corresponds to the detuning [Math 1] Having a drive frequency ω （ｉ） and, ii) Each of the two qubits is [Math 2] The corresponding effective frequency [Math 3] The corresponding amplitude has such that θ(x) is the sign function. [Math 4] and, iii) Corresponding phase [Math 5] and, As a result, each rotational pulse is determined by the Hamiltonian [Math 6] It has, [Number 7] However, the corresponding Pauli X operator is the rotational pulse, (b) [Number 8] An echo pulse that exchanges with the Pauli ZZ operator associated with the two qubits to control the magnitude of either of the following, the echo pulse being applied after the rotation pulse, and the application of the echo pulse twice. Each application (i) of the rotation pulse corresponds to the drive frequency ω （ｉ） ,amplitude [Number 9] and phase [Number 10] A method associated with a set of methods.

2. The echo pulse, [Math 11] and the above [Math 12] The method according to claim 1, configured to exclude any of the following.

3. The echo pulse, [Number 13] and the above [Number 14] The method according to claim 2, configured to eliminate both of the following.

4. The corresponding echo pulse acts [Number 15] It has ψ ０ ψ １ However, the two qubits Q ０，１ The method according to any one of claims 1 to 3, wherein the phase is a predetermined phase corresponding to the specified phase.

5. (a) The sum of phases associated with the first application of the rotation pulse [Number 16] (b) The sum of phases associated with the second application of the rotation pulse [Number 17] And, (c) Sum of phases ψ = ψ ０ + ψ １ , One of the following iii. The aforementioned [Number 18] and the above [Number 19] Control the size of one of them and eliminate the other, and iv. The aforementioned [Number 20] and the above [Math 21] The method according to claim 4, configured to eliminate either of the following.

6. The method according to claim 4 or 5, wherein any of the corresponding echo pulses has either action XY or YX.

7. The corresponding phase [Number 22] The method according to any one of claims 1 to 6, wherein the difference is equal to an integer multiple of π.

8. The drive frequency ω associated with the first application of the rotation pulse （１） However, the drive frequency ω associated with the second application of the rotation pulse is （２） The amplitude Ω is equal to the first application of the rotation pulse. （１） However, the amplitude Ω associated with the second application of the rotation pulse is （２） The method according to any one of claims 1 to 7, which is equivalent to the method according to any one of claims 1 to 7.

9. The two qubits Q ０，１ The method according to any one of claims 1 to 8, wherein the method is performed based on two energy levels contained in a multi-level quantum system.

10. The method according to any one of claims 1 to 9, wherein the echo pulse is configured to eliminate IZ noise and ZI noise.

11. The aforementioned drive frequency ω （ｉ） However, the lower resonant frequency ω ０ and the higher resonant frequency ω １ The method according to any one of claims 1 to 10, wherein the method is between the above.

12. The aforementioned drive frequency ω （ｉ） but, [Number 23] The method according to claim 11, which is within the range.

13. The aforementioned drive frequency ω （ｉ） is the resonant frequency ω ０，１ The method according to claim 12, which is the average of [the specified values].

14. The aforementioned drive frequency ω （ｉ） However, the lower resonant frequency ω ０ The resonant frequency ω that is lower or higher than ω １ The method according to any one of claims 1 to 10, which is higher than the method described in any one of claims 1 to 10.

15. The two qubits Q ０，１ One qubit q corresponds to the adjacent qubit Q ｎ It is communicating with, (a) The sum of phases associated with the first application of the rotation pulse [Number 24] and, (b) The sum of phases associated with the second application of the rotation pulse [Number 25] The difference between the two is the difference between the one qubit q and the adjacent qubit Q. ｎ The method according to any one of claims 1 to 14, configured to suppress the above cross-resonance rotation.

16. The sum of the phases mentioned above [Number 26] However, the one qubit q and the adjacent qubit Q ｎ The method according to claim 15, configured to eliminate the above cross-resonance rotation.

17. The ZZ rotation angle α associated with the first application of the rotation pulse. １ However, the ZZ rotation angle α associated with the second application of the rotation pulse is ２ The method according to any one of claims 1 to 16, which is equivalent to the method according to any one of claims 1 to 16.

18. Two qubit Q with XX coupling ０，１ A method for performing a two-qubit Pauli rotational quantum gate that acts on, (a) The two qubits Q ０，１ At least one of them is the two qubit Q ０，１ Applying a single-qubit rotation to shift at least one of the aforementioned bases from the measurement base to the rotation base, (b) the two qubits Q ０，１ The method involves applying a ZZ rotation quantum gate, wherein the ZZ rotation quantum gate is one of the claims described in any one of claims 1 to 17. (c) The two qubits Q ０，１ At least one of them is the two qubit Q ０，１ A method comprising applying a single-qubit rotation to shift at least one basis of from a rotation basis to a measurement basis.

19. Two qubit Q with XX coupling ０，１ A method for performing a two-qubit quantum gate acting on a two-qubit quantum gate, the method comprising performing the method according to claim 18 to perform at least one of XX rotation, YY rotation, and ZZ rotation, wherein the corresponding rotation angles of the rotation conform to the KAK decomposition of the two-qubit quantum gate.

20. A quantum processing unit, (a) at least two qubits having XX coupling, (b) At least one pulse generator coupled to the at least two qubits to apply pulses to the at least two qubits, (c) A controller that communicates with the at least one pulse generator to provide commands to the at least one pulse generator, A quantum processing unit configured to perform the method according to any one of claims 1 to 19.

21. The quantum processing unit according to claim 20, wherein the at least one pulse generator is configured to apply radio frequency pulses.

22. The two qubits Q ０，１ The quantum processing unit according to claim 21, wherein the quantum bit is a superconducting qubit.

23. The quantum processing unit according to claim 22, wherein the at least one pulse generator is configured to apply an infrared pulse, a visible light pulse, or an ultraviolet pulse.

24. A system comprising a computer and a quantum processing unit, wherein the computer has pulse-level access to the quantum processing unit, and the system is configured to perform the method according to any one of claims 1 to 19.

25. The system according to claim 24, wherein the quantum processing unit is one of those described in any one of claims 20 to 23.

26. A non-temporary computer-readable storage medium for storing computer instructions, wherein the computer instructions are used to cause a computer communicating with a quantum processing unit to execute the method according to any one of claims 1 to 19.

27. A computer execution method comprising simulating the application of a ZZ rotation quantum gate as described in any one of claims 1 to 19.

28. A non-temporary computer-readable storage medium for storing computer instructions, wherein the computer instructions are used to cause a computer to execute the method according to claim 28.

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