Method, device, computer program and computer-readable storage medium for determining a pulse sequence for a quantum processor for solving a QUBO problem

Abstract

A method for determining a pulse sequence for a quantum processor (2) is specified for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem, comprising: - providing an initial coupling matrix characteristic of a coupling of at least some qubits of the quantum processor (2) and an initial cost matrix characteristic of the QUBO problem, - determining a rearranged cost matrix by rearranging at least some elements of the initial cost matrix dependent on a distance to the initial coupling matrix, - determining an adjusted coupling matrix by adjusting at least some elements of the initial coupling matrix dependent on a further distance of the initial coupling matrix to the rearranged cost matrix, - determining several sub-coupling matrices dependent on the adjusted coupling matrix, and - determining the pulse sequence dependent on the sub-coupling matrices. Further, a device (6), a computer program and a computer-readable storage medium are specified.

Description

[0001] P2024,0239 WO N / QSW-67 March 14, 2025 - 1 - Description METHOD, DEVICE, COMPUTER PROGRAM AND COMPUTER-READABLE STORAGE MEDIUM FOR DETERMINING A PULSE SEQUENCE FOR A QUANTUM PROCESSOR FOR SOLVING A QUBO PROBLEM The present disclosure relates to a method, a device, a computer program and a computer-readable storage medium for determining a pulse sequence for a quantum processor for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem. Typically, quadratic unconstrained binary optimization, QUBO, problems form a subset of NP-hard optimization problems and enable a mathematical modelling of various classical optimization problems applied to several technical applications. However, QUBOs cannot be reliably implemented, exemplarily to quantum computing systems. An object to be achieved is to provide a method for implementing any QUBO on a quantum processor. Furthermore, a device, a computer program and a computer-readable storage medium for determining such a pulse sequence for implementing the QUBO are to be provided. The method for determining a pulse sequence for a quantum processor for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem is described. The quantum processor can be a superconducting qubit processor, wherein the qubits are formed in a superconducting material system, a topological qubit processor, wherein the qubits are formed of anyons, a quantum dot processor, wherein P2024,0239 WO N / QSW-67 March 14, 2025 - 2 - the qubits are formed of respective quantum dots in a semiconductor material system, a neutral atom processor, wherein qubits are formed of neutral atoms provided by optical tweezers or magnetic traps, a photonic qubit processor, wherein qubits are formed of photons, a vacancy center processor, wherein qubits are formed of vacancy centers in e.g. diamond, and / or a trapped ion processor, wherein qubits are formed of trapped ions provided by at least one ion trap. The quantum processor is, for example, part of a quantum computer which is configured to perform a predetermined quantum computing process by using at least some qubits of the quantum processor. The quantum processor can comprise several segments, wherein each segment is configured to host at least one or several qubits. Exemplarily, the quantum processor comprises or is the ion trap. The ion trap exemplarily comprises several segments. The ion trap is, for example, a segmented Paul trap, particularly configured to trap a plurality of ions. Exemplarily, the segments are arranged linearly along a trapping axis next to one another. Each section is configured for hosting at least one ion and / or at least one ion crystal. The at least one ion crystal comprises, for example, at least some of the trapped ions, wherein the at least some of the trapped ions are arranged along the trapping axis. One ion crystal can comprise or consist of more than two, e.g. at least 8, at least 20 or at least 100 and / or at most 1000, trapped ions. Each trapped ion is a quantum bit, qubit for short. P2024,0239 WO N / QSW-67 March 14, 2025 - 3 - Exemplarily, the ion trap, in particular each segment, comprises a set of electrodes. The electrodes are particularly configured to generate electric fields configured to trap, confine and modify the at least one ion. In particular, the electrodes can be provided with a radio frequency, RF, voltage and / or a direct current, DC, voltage. The voltages are exemplarily applied to the electrodes such that a time-varying electric field is provided, configured to trap, confine and / or modify at least some of the trapped ions. Exemplarily, with the electrodes to which the DC voltage is applied, a position of the ions in an axial direction along the trapping axis is predetermined. In particular, a DC potential applied to the trapped ions is predetermined by the applied DC voltage. For example, a coupling of the trapped ions is dependent on the DC potential. In particular, changing a shape of the DC potential in the axial direction changes the coupling between the trapped ions. For example, a magnetic gradient is provided to at least some of the qubits, in particular the trapped ions, or all qubits, in particular all trapped ions, along the trapping axis. Exemplarily, the magnetic gradient is provided by a permanent magnet arrangement. The qubits, in particular the trapped ions, subjected to the magnetic gradient are individually addressable due to the magnetic gradient. If the quantum processor is an ion trap, each of at least some sections is provided with at least one magnet arrangement, and / or at least some sections are provided with at least one magnet arrangement, or all sections are provided with at least one magnet arrangement. This means that at P2024,0239 WO N / QSW-67 March 14, 2025 - 4 - least some of the trapped ions or all trapped ions are individually addressable due to the magnetic gradient. The magnet arrangement can comprise a permanent magnet arrangement and / or at least one electromagnetic arrangement such as a coil. Exemplarily, a microwave radiation is applied to at least some trapped ions, in particular by at least some of the electrodes and / or at least one external microwave antenna. The microwave radiation is, for example, configured to induce a transition between an energy level of at least some of the trapped ions. Exemplarily, by applying the microwave radiation, an operation on the quantum states of the trapped ions, such as qubit rotations or state preparations, is performed. The QUBO problem is characteristic of an optimization problem, wherein a minimum value of a quadratic objective function f(x) of binary variables x is determined. The QUBO problem is defined, for example, for minimizing f(x) = xTQx, wherein x is characteristic of a binary vector representative of the binary variables, and Q is characteristic of a matrix representative of coefficients of the quadratic terms. Particularly, the coefficients are characteristic of a strength of an interaction between the binary variables. Exemplarily, Q is a matrix which is characteristic of a cost matrix of the QUBO problem. In particular, for solving the QUBO problem the binary vector x is determined that minimizes the quadratic function f(x). The QUBO problem is in particular used in the fields of optimization, computer science, and engineering. In particular, solving QUBO problems is particularly useful for P2024,0239 WO N / QSW-67 March 14, 2025 - 5 - solving combinatorial optimization problems. This can be used for solving technical optimization problems such as a maximum cut, a graph colouring and / or a partition problem. Solving such problems in particular has a practical application in various technical fields such as network design, logistics, scheduling, and resource allocation. Solving the maximum cut problem is particularly used in network design, where a communication flow is maximized and / or interference is minimized. Solving the graph colouring problem is particularly used in scheduling, register allocation in compilers, and resource allocation in timetabling problems. Solving the partition problem is particularly used in load balancing, for distributing computational tasks or resources evenly across multiple servers or processors. Further, images can be analyzed as well as features can be extracted from such images by implementing a respective QUBO problem. According to at least one embodiment of the method, an initial coupling matrix characteristic of a coupling of at least some qubits of the quantum processor and an initial cost matrix characteristic of the QUBO problem are provided. The initial coupling matrix is exemplarily characteristic of a coupling of at least some qubits in an initial state, e.g. an initial state of the quantum processor. If the quantum processor is an ion trap, each segment or at least some of the segments are configured to provide a harmonic potential to the respective trapped ions. The initial coupling matrix is in particular characteristic of a strength between the trapped ions. Exemplarily, the strength is characteristic of a Coulombic repulsion or attraction between the trapped ions dependent on a position of the P2024,0239 WO N / QSW-67 March 14, 2025 - 6 - trapped ions relative to each other and particularly a curvature of the corresponding DC potential. The initial cost matrix characteristic of the QUBO problem is initially determined and provided for reflecting the specific problem to be solved. In particular, the initial cost matrix is determined dependent on the specific problem to be solved. According to at least one embodiment of the method, a rearranged cost matrix is determined by rearranging at least some elements of the initial cost matrix dependent on a distance to the initial coupling matrix. Exemplarily, the distance is characteristic of a measure of dissimilarity or difference between the initial cost matrix and the initial coupling matrix. In particular, the initial cost matrix and the initial coupling matrix are compared, and the distance is determined. Dependent on the determined distance, the elements of the initial cost matrix are rearranged. For example, at least some elements of the initial cost matrix are rearranged for reducing the distance to the initial coupling matrix. The rearranging is performed such that the initial cost matrix is adapted to initial coupling matrix. Therefore, the initial cost matrix is rearranged in particular to be adapted to a design of the quantum processor. The rearranged cost matrix is determined, for example, by an optimization process. According to at least one embodiment of the method, an adjusted coupling matrix is determined by adjusting at least some elements of the initial coupling matrix dependent on a P2024,0239 WO N / QSW-67 March 14, 2025 - 7 - further distance of the initial coupling matrix to the rearranged cost matrix. Exemplarily, the further distance is characteristic of a further measure of dissimilarity or difference between the initial coupling matrix and the rearranged cost matrix. In particular, the initial coupling matrix and the rearranged cost matrix are compared and the further distance is determined. Dependent on the determined further distance, the elements of the initial coupling matrix are adjusted. In particular, values of the elements of the initial coupling matrix are changed for adjustment. For example, at least some elements of the initial coupling matrix are adjusted for reducing the further distance to the rearranged cost matrix. The adjusting is performed such that the initial coupling matrix is adapted to the rearranged cost matrix. In particular, the rearranged coupling matrix can be realized approximately by adjusting the initial coupling matrix. The adjusted coupling matrix is determined, for example, dependent on a minimization process. According to at least one embodiment of the method, several sub-coupling matrices are determined dependent on the adjusted coupling matrix. Exemplarily, the adjusted coupling matrix is split in a series of the sub-coupling matrices. Exemplarily, a predetermined length in time is determined for every sub-coupling matrix when determining the sub-coupling matrices. In particular, each of the sub-coupling matrices is assigned to one of the predetermined lengths in time. For example, the series of sub-coupling matrices and the corresponding predetermined lengths in time are characteristic of the rearranged cost matrix. P2024,0239 WO N / QSW-67 March 14, 2025 - 8 - For example, the sub-coupling matrices are characteristic of a recoding of the qubits, in particular the trapped ions. The recoding of the qubits, in particular the trapped ions, is in particular characteristic of a change of the quantum state of at least some of the qubits, in particular the trapped ions. According to at least one embodiment of the method, the pulse sequence is determined dependent on the sub-coupling matrices. In particular, the method is used to translate the QUBO problem into a set of parameters for implementing the QUBO problem with the qubits of the quantum processor, particularly for solving the QUBO problem. The parameters comprise particularly the pulse sequence. If the quantum processor is an ion trap, the pulse sequence is characteristic of voltage pulses for producing the microwave radiation configured to be applied to the trapped ions, in particular for recoding the trapped ions. With such a pulse sequence provided to the quantum processor, the QUBO problem is advantageously implemented and particularly solved. The method described herein above is, exemplarily, performed in the order indicated. The method described herein above is, exemplarily, a computer implemented method. In particular, the method described herein is performed automatically. An idea of the method described herein is, inter alia, that arbitrary QUBOs can be transferred and implemented on a quantum computer comprising a quantum processor, particularly an ion trap. Advantageously, with the method described herein QUBO problems can be implemented quickly and efficiently on a P2024,0239 WO N / QSW-67 March 14, 2025 - 9 - quantum computer comprising the quantum processor. Thus, a plurality of optimization problems each reflected by a respective QUBO problem, can be solved and improve the respective technical application. According to at least one embodiment of the method, for determining the rearranged cost matrix, at least some rows and / or at least some columns of the initial cost matrix are permutated. In particular, the rows and columns of the initial cost matrix are rearranged such that the rearranged cost matrix is configured to reflect the design of the respective quantum processor. The permutations are determined in particular dependent on an optimization algorithm of the optimization process particularly dependent on the distance of the initial cost matrix and the initial coupling matrix. For example, the optimization algorithm is adapted to a structure of the QUBO problem. Exemplarily, the optimization algorithm is configured to efficiently approximate the permutations to be performed dependent on the distance. Exemplarily, the optimization algorithm comprises a random permutation. For example, the optimization algorithm comprises an iteratively swapping of two indices of the corresponding matrix, such that a set of rearranged cost matrices is determined. For example, the optimization algorithm comprises a minimization of the distance by permutation of rows and columns of the initial cost matrix. According to at least one embodiment of the method, for determining the rearranged cost matrix, the rearranging is performed dependent on a first threshold. Exemplarily, the first threshold is characteristic for a predetermined P2024,0239 WO N / QSW-67 March 14, 2025 - 10 - runtime. Since the optimal solution is not known, the rearranging is performed in particular until the first threshold is reached. For example, the permutation which results in a smallest distance between one of the rearranged cost matrices of the set of rearranged cost matrices and the initial coupling matrix, forms the rearranged cost matrix. Alternatively, the first threshold is characteristic for a predetermined distance. If the distance of the rearranged cost matrix and the initial coupling matrix is above the first threshold, the optimization process is terminated. If the distance of the rearranged cost matrix and the initial coupling matrix is below the first threshold, the optimization process is performed again on the rearranged cost matrix. In particular, the first threshold is predetermined such that a computing time of the optimization process is less than a computing time for solving the QUBO problem on the quantum processor. According to at least one embodiment of the method, for determining the adjusted coupling matrix, the elements are characteristic of direct current, DC, voltages configured to be provided to at least some segments. Particularly, when changing a value of an element, the respective DC voltage changes accordingly. Exemplarily, by adjusting an element, the respective DC voltage of the segment is adjusted such that a respective DC potential is adjusted accordingly. If the quantum processor is an ion trap, the DC voltages are provided to at least some electrodes of the segments. Exemplarily, the elements are characteristic of the coupling P2024,0239 WO N / QSW-67 March 14, 2025 - 11 - of the trapped ions, and the coupling is dependent on a spacing of the ions between one another. In particular, the coupling of the trapped ions is dependent on the spacing of the trapped ions and a curvature of the DC potential, exemplarily in an equilibrium position of the respective trapped ion. Exemplarily, the spacing of the trapped ions and the curvature of the DC potential are adjusted by adjusting the elements. Further, the coupling of the trapped ions is particularly further dependent on a size of the segments and a distance of the trapped ions from the segments. According to at least one embodiment of the method, for determining the adjusted coupling matrix, the adjusting is dependent on a minimization process. Exemplarily, the minimization process is dependent on an element of the initial coupling matrix, e.g. dependent on the DC potential of a respective qubit, and the minimization process is dependent on a respective element of the rearranged cost matrix. Particularly, a solution of the minimization process is used to adjust the respective element in the adjusted coupling matrix. If the quantum processor is the ion trap, the minimization process is characteristic of minimizing a sum of square distances of the first and second derivatives of the DC potential at the trapped ion position with respect to a respective element of the rearranged cost matrix. Exemplarily, according to an embodiment, adjusted DC voltages are determined dependent on the adjusted coupling matrix. By determining the adjusted DC voltages of individual segments, the rearranged cost matrix can advantageously be realized approximately precisely. In particular, by the combination of P2024,0239 WO N / QSW-67 March 14, 2025 - 12 - the pulse sequence and the adjusted DC voltages provided to the quantum processor, particularly to the ion trap, the QUBO problem is advantageously precisely implemented and can be solved. According to at least one embodiment of the method, the adjusting is performed dependent on a second threshold. Exemplarily, if the further distance of the rearranged cost matrix and the adjusted coupling matrix is above the second threshold, the minimization process is terminated. If the distance of the rearranged cost matrix and the adjusted coupling matrix is below the first threshold, the minimization process is performed again on the adjusted cost matrix. In particular, the second threshold is predetermined such that a computing time of the minimization process is less than a computing time for solving the QUBO problem on the quantum processor. According to at least one embodiment of the method, at least some of the sub-coupling matrices have at least one row and / or column which is set to zero. Advantageously, by using such sub-coupling matrices, any matrix can be realized sequentially. According to at least one embodiment of the method, for a quantum processor being an ion trap a row and / or a column set to zero is characteristic of at least one ion not coupled to the other ions, and a row and / or a column not set to zero is characteristic of at least one ion coupled to the other ions. Particularly, for an ion trap with the permanent magnet arrangement a row and / or a column set to zero is P2024,0239 WO N / QSW-67 March 14, 2025 - 13 - characteristic of at least one magnetically insensitive ion, and a row and / or a column not set to zero is characteristic of at least one magnetically sensitive ion. For example, each trapped ion is represented by a two-level quantum system. If no magnetic field is applied to a two- level quantum system, the two-level quantum system comprises a first level and a second level, wherein both levels correspond to a respective eigenstate of the respective trapped ion. For example, the first level represents a ground state of the respective trapped ion and the second level represents an excited state of the respective trapped ion. Exemplarily, if a magnetic field, in particular the magnetic gradient, is applied to the two-level quantum system, a degeneracy of the second level is lifted such that in particular at least three sub-levels -1, 0 and 1 are generated. This results in three possible transitions from each of the three sub-levels -1, 0 and 1 to the first level. A magnetically sensitive ion is characteristic of an excited trapped ion, where the sub-level -1 or 1 is occupied. In particular, the magnetically sensitive ion has electrons occupying orbitals with m values of -1 and 1. Thus, these electrons are sensitive to the magnetic field due to the interaction between the magnetic moment of the electrons and the magnetic field, e.g. the magnetic gradient. A magnetically insensitive ion is characteristic of an excited trapped ion, where the sub-level 0 is occupied. In particular, the magnetically insensitive ion has electrons occupying an orbital with an m value of 0. Thus, these electrons remain unchanged by the magnetic field, e.g. the magnetic gradient. P2024,0239 WO N / QSW-67 March 14, 2025 - 14 - According to at least one embodiment of the method, each of the sub-coupling matrices is representative of a predetermined length in time. Exemplarily, the pulse sequence is characteristic of recoding of the qubits, and the predetermined length in time is characteristic of a time between the different recodings. Exemplarily, each pulse sequence comprises several blocks of pulses, wherein each block is characteristic to one of the sub-coupling matrices, and wherein each predetermined length in time is characteristic of the time between applying the blocks. In particular, the sub-coupling matrices are each characteristic of the DC voltages and thus the DC potentials configured to be provided to the quantum processor and thus the qubits, particularly to the ion trap and thus the ions. The combination of the sub-coupling matrices and the corresponding predetermined lengths in time is in particular characteristic of the rearranged cost matrix. Since an accuracy of the DC potential is limited, inter alia, by the size of the segments, the rearranged cost matrix indicative of the QUBO problem is indicated by the sub- coupling matrices and the corresponding predetermined lengths in time. Advantageously, the adjusted coupling matrix and thus rearranged cost matrix of the QUBO problem is precisely realized by trotterizing the rearranged cost matrix indicative of the coupling of the qubits in order to implement the QUBO problem with maximum accuracy. P2024,0239 WO N / QSW-67 March 14, 2025 - 15 - According to at least one embodiment of the method, the first threshold and the second threshold are predetermined such that the rearranging and the adjusting are characteristic of a combined computational effort which is less than a computational effort for solving the QUBO problem by the quantum processor. According to at least one embodiment of the method, the determined pulse sequence is provided to the quantum processor. According to at least one embodiment of the method, the quantum processor is operated with the determined pulse sequence. Exemplarily, the determined pulse sequence and the adjusted DC voltages are provided to the quantum processor. Further, the quantum processor is operated with the determined pulse sequence and the adjusted DC voltages. According to at least one embodiment of the method, the quantum processor is a processing unit of the quantum computer system. Furthermore, a device for determining a pulse sequence for a quantum processor for solving a QUBO problem is described. The device 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 device and vice versa. In particular, the device is part of the quantum computer system. P2024,0239 WO N / QSW-67 March 14, 2025 - 16 - In addition, a computer program is specified, comprising instructions which, when the computer program is executed by a computer, cause the computer program to execute the method described herein. Further, a computer-readable storage medium is specified, on which the computer program described herein is stored. In the following, the method and the system are explained in more detail with reference to exemplary embodiments and the associated Figures. Figure 1 shows a flowchart of the method for determining a pulse sequence for a quantum processor for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem according to an exemplary embodiment. Figure 2 shows a quantum computer system which is configured to perform the method according to an exemplary embodiment. 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. Method stage S1 according to the exemplary embodiment of Figure 1 comprises a provision of an initial coupling matrix characteristic of a coupling of at least some qubits of the quantum processor 2 and an initial cost matrix characteristic of a QUBO problem. P2024,0239 WO N / QSW-67 March 14, 2025 - 17 - Subsequently, in a method stage S2, a rearranged cost matrix is determined by rearranging at least some elements of the initial cost matrix dependent on a distance to the initial coupling matrix. The distance is indicative of a difference of the initial cost matrix dependent and the initial coupling matrix. The elements of the initial cost matrix are rearranged by a permutation of several rows and columns. The permutations are determined in particular dependent on an optimization algorithm of an optimization process particularly dependent on the distance of the initial cost matrix and the initial coupling matrix. In method stage S3, an adjusted coupling matrix is determined by adjusting at least some elements of the initial coupling matrix dependent on a further distance of the initial coupling matrix to the rearranged cost matrix. The distance is indicative of a difference of the initial coupling matrix to the rearranged cost matrix. The elements are adjusted dependent on a minimization process. Subsequently, in a method stage S4, several sub-coupling matrices are determined dependent on the adjusted coupling matrix, wherein each of the sub-coupling matrices is representative of a predetermined length in time. Particularly, the predetermined length in time is determined when determining the sub-coupling matrices. Dependent on the sub-coupling matrices, and in particular the respective predetermined lengths in time, the pulse sequence is determined. The predetermined lengths in time are each characteristic of a time between several blocks of pulses of the pulse sequence. P2024,0239 WO N / QSW-67 March 14, 2025 - 18 - Advantageously, the pulse sequence is characteristic of the QUBO problem which is implemented on the quantum processor 2 based on the pulse sequence and is in particular advantageously solved by the quantum processor 2. The quantum computer system 1 according to the exemplary embodiment of Figure 2 comprises a quantum processor 2 which is arranged in a chamber 3, providing a vacuum environment and / or a cryogenic environment. The quantum processor 2 and a possible laser system are connected by means of connections 4 to a control electronics system 5, which is connected to a device 6 being a classical computer device. Exemplarily, the method described herein can be performed on the device 6. 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 if this feature or combination itself is not explicitly indicated in the claims or exemplary embodiments.

[0002] P2024,0239 WO N / QSW-67 March 14, 2025 - 19 - Reference signs 1 quantum computer system 2 quantum processor 3 chamber 4 connections 5 control electronics system 6 device S1..S5 method stages

Claims

P2024,0239 WO N / QSW-67 March 14, 2025 - 20 - Claims 1. Method for determining a pulse sequence for a quantum processor (2) for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem, comprising: - providing an initial coupling matrix characteristic of a coupling of at least some qubits of the quantum processor (2) and an initial cost matrix characteristic of the QUBO problem, - determining a rearranged cost matrix by rearranging at least some elements of the initial cost matrix dependent on a distance to the initial coupling matrix, - determining an adjusted coupling matrix by adjusting at least some elements of the initial coupling matrix dependent on a further distance of the initial coupling matrix to the rearranged cost matrix, - determining several sub-coupling matrices dependent on the adjusted coupling matrix, and - determining the pulse sequence dependent on the sub- coupling matrices.

2. Method according to claim 1, wherein - for determining the rearranged cost matrix, at least some rows and / or at least some columns of the initial cost matrix are permutated.

3. Method according to claim 2, wherein - the rearranging is performed dependent on a first threshold.

4. Method according to one of claims 1 to 3, whereinP2024,0239 WO N / QSW-67 March 14, 2025 - 21 - - for determining the adjusted coupling matrix, the elements are characteristic of direct current, DC, voltages configured to be provided to at least some segments, and - for determining the adjusted coupling matrix, the adjusting is dependent on a minimization process.

5. Method according to claim 4, wherein - the adjusting is performed dependent on a second threshold.

6. Method according to one of claims 1 to 5, wherein - at least some of the sub-coupling matrices have at least one row and / or column which is set to zero.

7. Method according to claim 6, wherein for a quantum processor (2) being an ion trap - a row and / or a column set to zero is characteristic of at least one ion not coupled to the other ions, and - a row and / or a column not set to zero is characteristic of at least one ion coupled to the other ions.

8. Method according to one of claims 6 or 7, wherein - each of the sub-coupling matrices is representative of a predetermined length in time.

9. Method according to claims 3 and 5, wherein - the first threshold and the second threshold are predetermined such that the rearranging and the adjusting are characteristic of a combined computational effort which is less than a computational effort for solving the QUBO problem by the ion trap.

10. Method according to one of claims 1 to 9, whereinP2024,0239 WO N / QSW-67 March 14, 2025 - 22 - - the determined pulse sequence is provided to the quantum processor (2), and / or - the quantum processor (2) is operated with the determined pulse sequence.

11. Method according to one of claims 1 to 10, wherein - the quantum processor (2) is a processing unit of the quantum computer system.

12. Device (6) for determining a pulse sequence for a quantum processor (2) for solving a Quadratic Unconstrained Binary Optimization, QUBO, problem, wherein the device (6) is configured to perform the method according to one of the preceding claims.

13. 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 11.

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