Method, system, computer program, and computer-readable storage medium for applying a quantum gate operation to a qubit register with a plurality of qubits

Abstract

A method for applying a quantum gate operation to a qubit register with a plurality of qubits (q1, q2, q3, q4) is specified, wherein each qubit (q1, q2, q3, q4) is represented by an ion confined in a processing region of an ion trap (2), and wherein a magnetic field gradient is applied along the processing region, comprising: - preparing the qubits (q1, q2, q3, q4) in a first manifold, wherein a transition within the first manifold is not dependent on the magnetic field gradient, and - recoding at least one qubit (q1, q2, q3, q4) with a recoding signal to at least one operational qubit in a second manifold different to the first manifold, wherein a transition within the second manifold is dependent on the magnetic field gradient, and - applying the quantum gate operation to the qubit register, wherein the at least one operational qubit performs the applied quantum gate operation. Additionally, a system (1), a computer program and a computer-readable storge medium are specified.

Description

[0001] Description

[0002] METHOD, SYSTEM, COMPUTER PROGRAM, AND COMPUTER-READABLE STORAGE MEDIUM FOR APPLYING A QUANTUM GATE OPERATION TO A QUBIT REGISTER WITH A PLURALITY OF QUBITS

[0003] The present disclosure relates to a method, a system, a computer program, and a computer-readable storage medium for applying a quantum gate operation to a qubit register with a plurality of qubits .

[0004] Typically, i f there is a magnetic field gradient along a trapping axis of qubits , there are always-on interactions between qubits within a qubit register, allowing multi qubit gate operations .

[0005] An obj ect to be achieved is to provide a method where qubits of a qubit register can be coupled or decoupled from one another for ef ficiently performing at least one quantum gate operation . Furthermore , a system, a computer program, and a computer-readable storage medium for applying a quantum gate operation to a qubit register with a plurality of qubits are to be provided .

[0006] The method for applying a quantum gate operation to a qubit register with a plurality of qubits is described . In particular, each qubit is represented by an ion confined in a processing region of an ion trap, and a magnetic field gradient is applied along the processing region . Exemplarily, each qubit is formed of an ion .

[0007] For example , the ion trap can be a Penning trap or a Paul trap, a linear ion trap, a surface ion trap and / or a multi- layer ion trap . Exemplarily, the ion trap comprises a set of electrodes . For example , a radio frequency, RE, voltage is applied to at least some electrodes of the set of electrodes such that a time-varying electric field is provided in the processing region configured to confine and / or to manipulate the qubits . For example , the qubits intersect with a trapping axis and / or oscillate around a trapping axis within the processing region . The processing region comprises , for example , at least one quantum register .

[0008] The processing region is in particular configured to confine at least one qubit , exemplarily a plurality of qubits . Exemplarily, at most 100 qubits or at most 60 qubits are provided in the processing region . Exemplarily, the confined qubits form the quantum register .

[0009] Exemplarily, the ion trap comprises and / or is provided with a microwave antenna . The microwave antenna is in particular configured to emit electromagnetic radiation, e . g . a microwave field, provided to qubits for performing a quantum gate operation .

[0010] The microwave field is , for example , configured to induce a transition between the energy levels of at least one or at least some of the qubits in the processing region . Exemplarily, by providing the microwave field, an operation on the quantum states of the ions , such as a qubit rotation and / or a state preparation, is performed .

[0011] The microwave field is in particular characteristic of electromagnetic radiation with a frequency of at least 0 . 1 GHz and at most 500 GHz , in particular at least 0 . 3 GHz and at most 300 GHz . The ion trap is , exemplarily, a processing unit of a quantum computer device .

[0012] The ion trap comprises or is provided with, for example , at least one magnet arrangement configured to establish a magnetic field, in particular the magnetic field gradient . Exemplarily, the ion trap comprises or is provided with at least one magnet arrangement for the processing region . The at least one magnet arrangement can comprise at least one permanent magnet arrangement and / or at least one coil . The at least one magnet arrangement is , for example , spaced apart from the processing region in lateral directions and / or in a vertical direction .

[0013] In particular, the at least one magnet arrangement is configured to establish the magnetic field gradient in the processing region, e . g . along the trapping axis . This means that the magnetic field of the magnet arrangement has di f ferent magnitudes for di f ferent positions in the processing region and in particular for di f ferent positions on the respective trapping axis , forming the magnetic field gradient .

[0014] Particularly, magnitudes of the magnetic field being characteristic of the magnetic field gradient in the processing region established by the magnet arrangement change by at least 0 . 5 T / m and at most 500 T / m . In particular, the magnitudes of the magnetic field in the processing region change by at least 50 T / m and at most 250 T / m, exemplarily 150 T / m . Advantageously, if there is a plurality of qubits in the processing region, the resonance frequency of each of the qubits on which the magnetic field gradient of the magnet arrangement acts, is different, i.e. unique, for each qubit in the processing region.

[0015] According to at least one embodiment of the method, the qubits are prepared in a first manifold, wherein a transition within the first manifold is not dependent on the magnetic field gradient. That the qubits are prepared in the first manifold means here and in the following, for example, that the qubits are initialized in the first manifold. The first manifold exemplarily comprises a first set of states of a corresponding qubit.

[0016] For example, each qubit is represented by an n-level quantum system, wherein n is an integer bigger than 2. If no magnetic field is applied to the n-level quantum system, the n-level quantum system comprises at least one first level and at least one second level, wherein both levels correspond to a respective eigenstate of the qubit. Exemplarily, the first level and the second level can be any level of the n-level quantum system. For example, the first level represents a low energy state of the qubit and the second level represents a high energy state of the qubit. The low energy state is, for example, characteristic of a ground state and the high energy state is, for example, characteristic of an excited state.

[0017] If the magnetic field is applied to the n-level quantum system, a degeneracy of at least the second level is lifted such that at least two, in particular at least three, sublevels are generated. This results in two, in particular three, possible transitions from each of the two, in particular three , sub-levels to the first level . In particular, a strength of a splitting of the sub-levels is dependent on the applied magnetic field .

[0018] I f the qubits are represented by the n-level quantum system with three sub-levels , two of the three possible transitions are dependent on the magnetic field gradient , exemplarily called o+-transition . One of the three possible transitions is not dependent on the magnetic field gradient , exemplarily called n-transition . The sub-level being not dependent on the magnetic field gradient is arranged energetically between the two transitions being dependent on the magnetic field gradient .

[0019] In particular, the first mani fold comprises a set of states corresponding to the n-transition . This means that the first mani fold comprises the low energy state and the high energy state , which corresponds to the one sub-level being not dependent on the magnetic field gradient .

[0020] "Not dependent on the magnetic field gradient" and "dependent on the magnetic field gradient" means herein above and in the following that an energy di f ference of the first level and the second level , in particular the first level and the respective sub-level , of neighbouring qubits is smaller by at least one magnitude for the qubits in the first mani fold compared to the qubits in the second mani fold . In particular, that the qubits in the first mani fold are not dependent on the magnetic field gradient means that crosstalk is prevented between neighbouring qubits , in particular to a large extent . Exemplarily, the qubits in the processing region being prepared in the first mani fold are not coupled to one another .

[0021] According to at least one embodiment of the method, the qubits are prepared in a first mani fold, and at least one qubit is recoded with a recoding signal to at least one operational qubit in a second mani fold di f ferent to the first mani fold, wherein a transition within the second mani fold is dependent on the magnetic field gradient .

[0022] The second mani fold exemplarily comprises a second set of states of a corresponding qubit , di f ferent to the first set of states . In particular, the second mani fold comprises a set of states corresponding to the o+-transition . This means that the second mani fold comprises the low energy state and the high energy state , which corresponds to the two sub-levels being dependent on the magnetic field gradient .

[0023] Exemplarily, the recoding signal is characteristic of the microwave field . The recoding signal is particularly provided to the at least one qubit such that the at least one qubit is recoded to the at least one operational qubit . For example , the operational qubit is configured to undergo the quantum gate operation . In particular, the operational qubit in the second mani fold is configured to undergo the quantum gate operation, whereas the rest of the qubits in the first mani fold are not configured to undergo the quantum gate operation .

[0024] According to at least one embodiment of the method, the quantum gate operation is applied to the qubit register, wherein the at least one operational qubit performs the applied quantum gate operation.

[0025] Exemplarily, the quantum gate operation is characteristic of a basic building block of a quantum circuit, in particular analogous to classical logic gates in conventional computing. The quantum gate operation is in particular characteristic of a mathematical operation that changes the state of the operational qubit. The quantum gate operation is represented, for example, by at least one unitary matrix that acts on a state vector of the operational qubit.

[0026] If the quantum gate operation is applied to one operational qubit, the quantum gate operation is characteristic of a single quantum gate, e.g. a Pauli gate, a Hadamard gate, a phase gate, a rotation gate and / or an identity gate.

[0027] If the quantum gate operation is applied to at least two operational qubits, the quantum gate operation is characteristic of a multi quantum gate, e.g. a controlled NOT gate, an Toffoli gate, a swap gate, and / or a Fredkin gate.

[0028] The method described herein above is, exemplarily, performed in the order indicated. The method described herein above is, exemplarily, a computer implemented method.

[0029] An idea of the method described herein is, inter alia, that the qubits in the quantum register are initialized to qubits in the first manifold.

[0030] Exemplarily, a coupling of the qubits is dependent on the magnitudes of the magnetic field, i.e. the magnetic field gradient. As the corresponding transitions are not dependent on the magnetic field gradient , there is advantageously no coupling between the qubits in the first mani fold, such that crosstalk is prevented .

[0031] I f a single gate or two- or multi-qubit gates are to be performed, the respective qubits are advantageously recoded in respective operational qubits in the second mani fold .

[0032] Thus , crosstalk is advantageously prevented induced by the always-on interaction characteristic of the magnetic field gradient , for the qubits not used for the quantum gate operation .

[0033] According to at least one embodiment of the method, the first mani fold is characteristic of a first transition in which a magnetic quantum number does not change . In particular, the first transition is a transition between the first level and the second level , which is characteristic of the sub-level not being dependent on the magnetic field gradient . In particular, the transition within the first mani fold not dependent on the magnetic field is the first transition in which a magnetic quantum number does not change .

[0034] Exemplarily, the first transition is characteristic of a first energy di f ference . This means that the first energy di f ference corresponds particularly to an energetic di f ference of the first level and the second level , which is characteristic of the sub-level not being dependent on the magnetic field gradient .

[0035] According to at least one embodiment of the method, the second mani fold is characteristic of a second transition in which a magnetic quantum number changes . In particular, the second transition is a transition between the first level and the second level , which second level is characteristic of one of the sub-levels being dependent on the magnetic field gradient . In particular, the transition within the second mani fold being dependent on the magnetic field is the second transition, in which a magnetic quantum number does change .

[0036] Exemplarily, the second transition is characteristic of a second energy di f ference . In particular, a change of the first energy di f ferences of neighbouring qubits in the first mani fold is smaller by at least one order of magnitude compared to a change of the second energy di f ferences of neighbouring qubits in the second mani fold .

[0037] In particular, the second transition is a o+-transition and the first transition is a n-transition .

[0038] According to at least one embodiment of the method, the recoding signal is characteristic of a qubit recode pulse sequence . In particular, the qubit recode pulse sequence comprises more than one pulse , wherein at least two pulses are di f ferent from one another .

[0039] Exemplarily, each pulse is characteristic of a predetermined time duration and a predetermined frequency . The predetermined time duration defines how long the respective predetermined frequency is applied . In particular, the predetermined frequency is directly proportional to an energy .

[0040] According to at least one embodiment of the method, the qubit recode pulse sequence comprises an unhide pulse sequence and a hide pulse sequence . For example , the unhide pulse and the hide pulse are applied in the order indicated . The unhide pulse sequence is exemplarily configured to trans form at least one of the qubits in the first mani fold to an operational qubit in the second mani fold . The hide pulse sequence is exemplarily configured to trans form the operational qubit in the second mani fold to a qubit in the first mani fold .

[0041] Advantageously, the unhide pulse sequence is configured to decouple the respective qubits from the first mani fold for performing the quantum gate operation .

[0042] According to at least one embodiment of the method, between the unhide pulse sequence and the hide pulse sequence , an operational pulse sequence is applied . The operational pulse sequence exemplarily comprises at least one or more pulses each being characteristic of at least a part of the quantum gate operation . It is , for example , possible that the operational pulse sequence exclusively comprises one pulse being characteristic of the quantum gate operation .

[0043] According to at least one embodiment of the method, the unhide pulse sequence and the hide pulse sequence are each characteristic of the first mani fold and the second mani fold . Exemplarily, the unhide pulse sequence and the hide pulse sequence each comprise at least one pulse characteristic of the first mani fold and at least one pulse characteristic of the second mani fold . "At least one pulse characteristic of the first mani fold" means here , for example , that the respective pulse has a predetermined frequency corresponding to the first energy di f ference . "At least one pulse characteristic of the second mani fold" means here , for example , that the respective pulse has a predetermined frequency corresponding to the second energy di f ference . According to at least one embodiment of the method, the operational pulse sequence is characteristic of the second mani fold . Exemplarily, the operational pulse sequence exclusively comprises at least one pulse or pulses characteristic of the second mani fold .

[0044] According to at least one embodiment of the method, the unhide pulse sequence and / or the hide pulse sequence comprise ( s ) a first n-pulse in the first mani fold, a second n-pulse in the second mani fold, and a third n-pulse in the first mani fold . In particular, the unhide pulse sequence and the hide pulse sequence are equal to one another . The first n-pulse in the first mani fold, the second n-pulse in the second mani fold, and the third n-pulse in the first mani fold are applied particularly in the order indicated .

[0045] The respective n-pulse is in particular characteristic of the predetermined time duration . The predetermined time duration is determined to achieve a 180 ° rotation of a Bloch sphere of a corresponding qubit .

[0046] With such an unhide pulse sequence as well as hide pulse sequence , the corresponding qubit can be advantageously ef fectively trans formed to the second mani fold and after the quantum gate operation can be advantageously ef fectively trans formed back to the second mani fold .

[0047] According to at least one embodiment of the method, at least two qubits from the qubit register are recoded with the recoding signal to at least two operational qubits in the second mani fold . According to at least one embodiment of the method, the at least two operational qubits perform the applied quantum gate operation .

[0048] Thus , advantageously, also multi qubit gate operations can advantageously be performed - with the qubits involved being in the second mani fold, where they are ef ficiently coupled dependent on the magnetic field gradient .

[0049] According to at least one embodiment of the method, a frequency di f ference of the first transition between neighbouring qubits is at least 2n * 30 Hz and at most 2n * 620 kHz .

[0050] According to at least one embodiment of the method, a frequency di f ference of the second transition between neighbouring qubits is at least 2n * 27 kHz and at most 2n * 120 MHz .

[0051] Furthermore , a system for applying a quantum gate operation to a qubit register with a plurality of qubits is described . The system is configured to perform the method described herein . Therefore , all features and embodiments disclosed in connection with the method are also disclosed in connection with the system and vice versa .

[0052] According to at least one embodiment , the system is configured to perform the method described herein before .

[0053] According to at least one embodiment , the system comprises an ion trap configured for confining the qubit register, wherein each qubit is represented by an ion confined in a processing region of the ion trap . According to at least one embodiment , the system comprises a magnet arrangement configured for producing a magnetic field gradient applied along the processing region .

[0054] According to at least one embodiment , the system comprises a laser system configured for preparing the qubits in an initial state .

[0055] According to at least one embodiment , the system comprises a microwave antenna configured for providing the qubits in the first mani fold, in the second mani fold and for providing the quantum gate operation .

[0056] In addition, a computer program is speci fied, comprising instructions which, when the computer program is executed by a computer, cause the computer program to execute the method described herein .

[0057] Further, a computer-readable storage medium is speci fied, on which the computer program described herein is stored .

[0058] In the following, the method and the system are explained in more detail with reference to exemplary embodiments and the associated Figures .

[0059] Figure 1 shows a flowchart of the method for applying a quantum gate operation to a qubit register with a plurality of qubits according to an exemplary embodiment .

[0060] Figures 2 and 3 each schematically show quantum gate operations applied to a qubit register according to an exemplary embodiment . Figure 4 schematically shows a pulse sequence used in the method according to an exemplary embodiment.

[0061] Figure 5 schematically shows a two-level system of each qubit used in the method according to an exemplary embodiment.

[0062] Figure 6 shows a system which is configured to perform the method according to an exemplary embodiment.

[0063] Elements that are identical, similar or have the same effect are given the same reference signs in the Figures. The Figures and the proportions of the elements shown in the figures are not to be regarded as true to scale. Rather, individual elements may be shown exaggeratedly large for better representability and / or for better comprehensibility.

[0064] Method stage SI according to the exemplary embodiment of Figure 1 comprises that qubits ql, q2, q3, q4, e.g. as shown in Figure 2, are prepared in a first manifold, wherein a transition within the first manifold is not dependent on a magnetic field gradient. The qubits ql, q2, q3, q4 are comprised of a qubit register, wherein each qubit ql, q2, q3, q4 is represented by an ion confined in a processing region of an ion trap 2, and wherein a magnetic field gradient is applied along the processing region.

[0065] That the first manifold is not dependent on a magnetic field gradient means that the first manifold is characteristic of a first transition in which a magnetic quantum number does not change. In particular, the first transition is characteristic of a n-transition . In particular, all qubits ql, q2, q3, q4 of the quantum register in the processing region are prepared, i . e . initiali zed, in the first mani fold .

[0066] Subsequently, in method stage S2 , at least one qubit is recoded with a recoding signal to at least one operational qubit in a second mani fold di f ferent to the first mani fold, wherein a transition within the second mani fold is dependent on the magnetic field gradient . The operational qubit in the second mani fold is configured to undergo the quantum gate operation, which is particularly predetermined, whereas the rest of the qubits in the first mani fold are not configured to undergo the quantum gate operation .

[0067] That the second mani fold is dependent on a magnetic field gradient means that the second mani fold is characteristic of a second transition in which a magnetic quantum number does change . In particular, the second transition is characteristic of a o+-transition . In particular, solely the qubit with which the quantum gate operation is to be performed is recoded to be in the second mani fold .

[0068] The recoding signal is characteristic of a qubit recode pulse sequence , particularly comprising an unhide pulse sequence 7 and a hide pulse sequence 8 . In method stage S2 , before the quantum gate operation is applied, the unhide pulse sequence 7 is applied to the qubit which is to be recoded . The unhide pulse sequence 7 is characteristic of a trans formation of the respective qubit in the first mani fold to the operational qubit in the second mani fold .

[0069] In a next method stage S3 , the quantum gate operation is applied to the qubit register, wherein the at least one operational qubit performs the applied quantum gate operation. In particular, the quantum gate operation is applied to the qubit in the second manifold.

[0070] Optionally, in method stage S3, after the quantum gate operation is applied, the hide pulse sequence 8 is applied to the operational qubit. The hide pulse sequence 8 is characteristic of a transformation of the operational qubit in the second manifold to a qubit in the second manifold. In particular, between the unhide pulse sequence 7 and the hide pulse sequence 8, an operational pulse sequence is applied, which is particularly characteristic of the quantum gate operation .

[0071] The unhide pulse sequence 7 and the hide pulse sequence 8 are described in more detail in connection with the embodiment of Figure 4.

[0072] The qubit register in connection with the exemplary embodiment of Figure 2 comprises four qubits ql, q2, q3 and q4, for example. The four qubits ql, q2, q3, q4 are prepared in the first manifold, marked with n as a dotted region. If a quantum gate operation is to be applied to the respective qubits, the qubits involved are transformed to the second manifold, marked with o as a dashed region.

[0073] The first qubit ql is transformed from the first manifold to an operational qubit in the second manifold according to the method according to Figure 1. This is followed by applying an Hadamard gate marked with H as the quantum gate operation to the operational qubit. After the quantum gate operation is applied to the operational qubit, the first qubit ql being the operational qubit in the second manifold is transformed back to the first manifold. Subsequently, the third qubit q3 is transformed from the first manifold to an operational qubit in the second manifold according to the method according to Figure 1. This is followed by applying a Pauli gate, e.g. a NOT gate marked with X, as the quantum gate operation to the operational qubit. After the quantum gate operation is applied to the operational qubit, the third qubit q3 being the operational qubit in the second manifold is transformed back to the first manifold.

[0074] Subsequently, the first and the second qubit ql, q2 are each transformed from the first manifold to operational qubits in the second manifold according to the method according to Figure 1. This is followed by applying a multi quantum gate, particularly a two-qubit gate, as the quantum gate operation to the operational qubits. After the quantum gate operation is applied to the operational qubits, the first and the second qubit ql, q2 being the operational qubits in the second manifold are each transformed back to the first manifold.

[0075] Subsequently, the second, the third and the fourth qubits q2, q3, q4 are each transformed from the first manifold to operational qubits in the second manifold according to the method according to Figure 1. This is followed by applying a single quantum gate to each of the second, the third and the fourth qubit q2, q3, q4. After the quantum gate operations are applied to the respective operational qubits, the second, the third and the fourth qubits q2, q3, q4 being the operational qubits in the second manifold are each transformed back to the first manifold. Subsequently, the third and the fourth qubit q3, q4 are each transformed from the first manifold to operational qubits in the second manifold according to the method according to Figure 1. This is followed by applying a multi quantum gate, particularly a two-qubit gate, as the quantum gate operation to the operational qubits. After the quantum gate operation is applied to the operational qubits, the third and the fourth qubit q3, q4 being the operational qubits in the second manifold are each transformed back to the first manifold.

[0076] In connection with the exemplary embodiment of Figure 3, the transformation of the respective qubit, e.g. as shown in Figure 2, is performed by an unhide pulse sequence 7 and a hide pulse sequence 8, as shown in connection with Figure 4. In particular, the unhide pulse sequence 7 and the hide pulse sequence 8 are equal to one another, and each of them comprises a first n-pulse in the first manifold, a second impulse in the second manifold, and a third n-pulse in the first manifold.

[0077] For example, each qubit ql, q2, q3, q4 is represented by a two-level quantum system, as schematically shown in Figure 5, comprising a fist level indicated with F=0 and a second level indicated with F=l, which splits up in three sub-levels indicated with mFdependent on the magnetic field gradient. The first manifold corresponds to a first transition between the first level and the sub-level corresponding to mF=0. The second manifold corresponds to a second transition between the first level and the sub-level corresponding to mF=±l, here +1. The system 1 being particularly a quantum computing system according to the exemplary embodiment of Figure 6 comprises a quantum processor comprising the ion trap 2 which is arranged in a chamber 3 , providing a vacuum environment and / or a cryogenic environment . The quantum processor and a possible laser system are connected by means of connections 4 to a control electronics system 5 , which is connected to a computer device 6 being a classical computer device . The invention is not limited to the exemplary embodiments by their description . Rather, the invention encompasses any new feature as well as any combination of features , which in particular includes any combination of features in the claims , even i f this feature or combination itsel f is not explicitly indicated in the claims or exemplary embodiments .

[0078] Reference signs

[0079] 1 system

[0080] 2 ion trap 3 chamber

[0081] 4 connections

[0082] 5 control electronics system

[0083] 6 computer device 7 unhide pulse

[0084] 8 hide pulse

[0085] S I . . S3 method stages ql . . q4 qubits

Claims

Claims1. Method for applying a quantum gate operation to a qubit register with a plurality of qubits (ql, q2, q3, q4 ) , wherein each qubit (ql, q2, q3, q4 ) is represented by an ion confined in a processing region of an ion trap (2) , and wherein a magnetic field gradient is applied along the processing region, comprising:- preparing the qubits (ql, q2, q3, q4 ) in a first manifold, wherein a transition within the first manifold is not dependent on the magnetic field gradient, and- recoding at least one qubit (ql, q2, q3, q4 ) with a recoding signal to at least one operational qubit in a second manifold different to the first manifold, wherein a transition within the second manifold is dependent on the magnetic field gradient, and- applying the quantum gate operation to the qubit register, wherein the at least one operational qubit performs the applied quantum gate operation.

2. Method according to claim 1, wherein- the first manifold is characteristic of a first transition in which a magnetic quantum number does not change, and- the second manifold is characteristic of a second transition in which a magnetic quantum number changes.

3. Method according to one of claims 1 or 2, wherein- the recoding signal is characteristic of a qubit recode pulse sequence,- the qubit recode pulse sequence comprises an unhide pulse sequence (7) and a hide pulse sequence (8) , and- between the unhide pulse sequence (7) and the hide pulse sequence (8) , an operational pulse sequence is applied.

4. Method according to claim 3, wherein- the unhide pulse sequence (7) and the hide pulse sequence(8) are each characteristic of the first manifold and the second manifold, and- the operational pulse sequence is characteristic of the second manifold.

5. Method according to one of claims 1 to 4, wherein- the unhide pulse sequence (7) and / or the hide pulse sequence (8) comprise (s) a first n-pulse in the first manifold, a second n-pulse in the second manifold, and a third n-pulse in the first manifold.

6. Method according to one of claims 1 to 5, wherein- at least two qubits (ql, q2, q3, q4 ) from the qubit register are recoded with the recoding signal to at least two operational qubits in the second manifold, and- the at least two operational qubits perform the applied quantum gate operation.

7. Method according to one of claims 1 to 6, wherein- a frequency difference of the first transition between neighbouring qubits (ql, q2, q3, q4 ) is at least 2n * 30 Hz and at most 2n * 620 kHz.

8. Method according to one of claims 1 to 7, wherein- a frequency difference of the second transition between neighbouring qubits (ql, q2, q3, q4 ) is at least 2n * 27 kHz and at most 2n * 120 MHz.

9. System (1) for applying a quantum gate operation to a qubit register with a plurality of qubits (ql, q2, q3, q4 ) ,wherein the system (1) is configured to perform the method according to one of the preceding claims.

10. System (1) according to claim 9, comprising- an ion trap (2) configured for confining the qubit register, wherein each qubit (ql, q2, q3, q4 ) is represented by an ion confined in a processing region of the ion trap( 2 ) , and- a magnet arrangement configured for producing a magnetic field gradient applied along the processing region.

11. System (1) according to one of claims 9 or 10, comprising- a laser system (1) configured for preparing the qubits (ql, q2, q3, q4 ) in an initial state, and / or- a microwave antenna configured for providing the qubits (ql, q2, q3, q4 ) in the first manifold, in the second manifold, and for providing the quantum gate operation.

12. Computer program comprising instructions which, when the computer program is executed by a computer, cause the computer program to execute the method according to one of claims 1 to 8.

13. Computer-readable storage medium on which the computer program according to claim 12 is stored.

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