Method for providing control signals for an arbitrary waveform generator, system, computer program and computer-readable storage medium

Abstract

A method for providing control signals for an arbitrary waveform generator is provided which is configured to generate at least two signal sequences applied to at least one quantum particle, with - providing at least two predetermined pulse sequences (1, 2), - determining a first block (12), a second block (15) and a third block (16) dependent on the two predetermined pulse sequences (1, 2), - generating a first control signal corresponding to the first block (12), a second control signal corresponding to the second block (15) and a third control signal corresponding to the third block (16), and - providing the first control signal, the second control signal and the third control signal to the arbitrary waveform generator for generating the at least two signal sequences. Further a system, a computer program and a computer-readable storage medium are provided.

Description

[0001] Description

[0002] METHOD FOR PROVIDING CONTROL S IGNALS FOR AN ARBITRARY WAVEFORM GENERATOR, SYSTEM, COMPUTER PROGRAM AND COMPUTER- READABLE STORAGE MEDIUM

[0003] The present disclosure relates to a method, a system, a computer program and a computer-readable storage medium for providing control signals for an arbitrary waveform generator which is configured to generate at least two signal sequences applied to at least one quantum particle .

[0004] Generally, synthesi zing control signals for multiple qubits addressed by speci fic resonance frequencies requires either one oscillator per qubit or a device to generate arbitrary waveforms . In an arbitrary waveform generator the control signals are stored in a digital memory of the arbitrary waveform generator and are played by a digital to analog converter, DAC, of the arbitrary waveform generator . Data rates required are immense and therefore memory of an arbitrary waveform generator is always limited .

[0005] An obj ect to be solved is to provide a method, with which control signals are provided to the arbitrary waveform generator particularly ef ficient . Furthermore , a system, a computer program and a computer-readable storage medium for executing such a method are to be provided .

[0006] The obj ect is solved by the subj ect matter of the independent claims . Advantageous embodiments , implementations and further developments are the subj ect matter of the respective dependent claims . The method for providing control signals for an arbitrary waveform generator which is configured to generate at least two signal sequences applied to at least one quantum particle , is described . Exemplarily, the arbitrary waveform generator is configured to receive control signals , e . g . , from a computer device . Further, the arbitrary waveform is configured, for example , to generate signal sequences dependent on the control signals and is configured to provide the signal sequences to the quantum particle in order to confine , control and / or manipulate the quantum particle . In particular, the quantum particle is characteristic for a quantum bit , short qubit .

[0007] Exemplarily, the quantum particle is formed of an ion . The ion can be confined, i . e . trapped, controlled and / or manipulated by an ion trap . In particular, the ion trap is configured to confine at least one ion and / or to modi fy an electronic state of the at least one ion, in particular to perform a quantum calculation . The ion trap can be a Paul trap, a linear ion trap, a surface ion trap and / or a multilayer ion trap . Exemplarily, the ion trap comprises a set of electrodes . For example , a radio frequency, RE, voltage is applied to the electrodes such that a time-varying electric field is provided, configured to confine and / or to modi fy the ion .

[0008] According to at least one embodiment of the method, at least two predetermined pulse sequences are provided . In particular, the two predetermined pulse sequences are provided to the computer device . Each predetermined pulse sequence comprises at least two predetermined pulses , for example . Exemplarily, each predetermined pulse is characteristic for a signal , e . g . characteristic for the RE voltage to be applied to the electrodes , to be provided to the quantum particle , comprising a predetermined frequency, a predetermined amplitude , a predetermined duration and a predetermined phase .

[0009] Exemplarily, each predetermined pulse sequence is characteristic for at least one gate operation on the quantum particle . For example , the predetermined pulse sequences are configured to be provided to the quantum particle one after the other, i . e . successively, in time . In particular, each predetermined pulse is characteristic for one operation for controlling and / or changing a quantum state of the ion .

[0010] In particular, the predetermined pulses are predetermined in order to perform a quantum calculation .

[0011] According to at least one embodiment of the method, a first block, a second block and a third block are determined dependent on the two predetermined pulse sequences . In particular, the first block is characteristic for a predetermined first pulse with a predetermined first frequency, a predetermined first amplitude and a predetermined first phase . In particular, the second block is characteristic for a predetermined second pulse with a predetermined second frequency, a predetermined second amplitude and a predetermined second phase . In particular, the third block is characteristic for a predetermined third pulse with a predetermined third frequency, a predetermined third amplitude and a predetermined third phase .

[0012] According to at least one embodiment of the method, the first block is characteristic for a predetermined first pulse , which is present in both of the two predetermined pulse sequences . For example , each of the at least two predetermined pulse sequences comprise the predetermined first pulse such that the first block is determined . Each of the at least two predetermined pulse sequences can comprise a plurality of the predetermined pulses such that a plurality of blocks is determined accordingly .

[0013] Exemplarily, when determining the first block, all the predetermined pulses of the at least two predetermined pulse sequences are compared . I f one of the predetermined pulse sequences comprises at least one predetermined pulse which is the same being present in another predetermined pulse sequence , the first block is determined accordingly, being in particular characteristic for the predetermined first pulse .

[0014] According to at least one embodiment of the method, the second block is characteristic for a predetermined second pulse , which is di f ferent to the predetermined first pulse . For example , one of the at least two predetermined pulse sequences comprises the predetermined second pulse being di f ferent to the predetermined first pulse such that the second block is determined . Exemplarily, a single second block is determined which is characteristic for the predetermined second pulse .

[0015] Exemplarily, when determining the second block, the predetermined pulses of the at least two predetermined pulse sequences are compared . I f one of the predetermined pulse sequence comprises at least one predetermined pulse which is di f ferent from the predetermined first pulse , the second block is determined accordingly, being in particular characteristic for the predetermined second pulse . According to at least one embodiment of the method, the third block is characteristic for a predetermined third pulse , which is di f ferent to the predetermined first pulse and the predetermined second pulse . For example , one of the at least two predetermined pulse sequences comprises the predetermined third pulse being di f ferent to the predetermined first pulse and being di f ferent to the predetermined second pulse such that the third block is determined . Exemplarily, a single third block is determined, which is characteristic for the predetermined third pulse .

[0016] Exemplarily, when determining the third block, the predetermined pulses of the at least two predetermined pulse sequences are compared . I f one of the predetermined pulse sequence comprises at least one predetermined pulse which is di f ferent from the predetermined first pulse and the predetermined second pulse , the third block is determined accordingly, being in particular characteristic for the predetermined third pulse .

[0017] According to at least one embodiment of the method, a first control signal corresponding to the first block, a second control signal corresponding to the second block and a third control signal corresponding to the third block are generated . In particular, the first control signal , the second control signal and the third control signal are di f ferent from one another . Further, the first control signal , the second control signal and the third control signal are configured to be readable and / or processable from the arbitrary waveform generator . In particular, the computer device is configured to order the blocks according to the predetermined pulse sequences and subsequently generate the control signals .

[0018] According to at least one embodiment of the method, the first control signal , the second control signal and the third control signal are provided to the arbitrary waveform generator for generating the at least two signal sequences . For example , the at least two signal sequences are configured to be provided to the quantum particle one after the other, i . e . successively, in time .

[0019] Exemplarily, the arbitrary waveform generator comprises an internal processing device which is configured to receive the first control signal , the second control signal and the third control signal . Further, the internal processing device is configured to convert the first control signal , the second control signal and the third control to an analog voltage signal using the DAC . Subsequently, the arbitrary waveform generator, for example , generates the at least two signal sequences according to the analog voltage signal , wherein the at least two signal sequences are sent to an output connector of the arbitrary waveform generator, successively .

[0020] Exemplarily, output connector is connected to the ion trap such that the at least two signal sequences are provided to the ion trap, successively .

[0021] The method described herein above is , exemplarily, performed in the order indicated . The method described herein above is , exemplarily, a computer implemented method .

[0022] Typically, qubit signal sequences consisting of pulses can be stored either linearly in a memory of the arbitrary waveform generator, or be split into segments . Often, in an experiment and / or for a computation, phases of readout pulses or the initial state preparation pulses are varied to sample certain configurations . This is that generally, a maj ority of pulse signals during the experiment and / or during the computation therefore stays constant .

[0023] An idea of the method described herein is , inter alia, to segment the pulses of the at least two predetermined pulse sequences in blocks , wherein the first block is characteristic for pulses which are recurring in the at least two predetermined pulse sequences , in particular also recurring within one of the predetermined pulse sequences , and the second block and the third block are characteristic for pulses being di f ferent to the recurring pulses .

[0024] Advantageously, the predetermined pulse sequences are split into multiple blocks . The first block is characteristic for a signal that is the same for each experimental setting and the second and third block is characteristic for a signal that varies during the experiment and / or the computation . A selective replay of those blocks therefore allows to reduce the memory demand signi ficantly . Advantageously, the generation of the control signals is split into several converting steps to reduce computation time and memory .

[0025] According to at least one embodiment of the method, the two signal sequences are configured to be provided to a microwave antenna for producing a time varying electromagnetic field in a region of the at least one quantum particle . In particular, the set of electrodes of the ion trap comprises the microwave antenna . According to at least one embodiment of the method, each of the at least two predetermined pulse sequences comprises a predetermined subsequent pulse . In particular, each of the at least two predetermined pulse sequences comprises a predetermined the subsequent pulse or a plurality of predetermined subsequent pulses , wherein the plurality of predetermined subsequent pulses are di f ferent to one another, in particular with respect to a time stamp . Exemplarily, the number of predetermined subsequent pulses in each of the at least two predetermined pulse sequences is equal to one another .

[0026] According to least one embodiment of the method, a subsequent block is determined dependent on the two predetermined pulse sequences , wherein the subsequent block is characteristic for the predetermined subsequent pulse , which is present in both of the two predetermined pulse sequences .

[0027] According to at least one embodiment of the method, the first block and the subsequent block are combined to a first block sequence and a constant sequence signal is generated corresponding to the first block sequence . In particular, i f the predetermined subsequent pulse in one of the at least two predetermined pulse sequences are arranged directly after the first pulse , the first block and the subsequent block are combined accordingly, i . e . one after the other, in the first block sequence for generating the constant sequence signal .

[0028] According to at least one embodiment of the method, the constant sequence signal , the second control signal and the third control signal are provided to the arbitrary waveform generator for generating the at least two signal sequences . Advantageously, pulses corresponding to the second block and / or the third block can be replaced in particular ef ficiently thereby reducing computational and memory ef fort .

[0029] According to at least one embodiment of the method, a pause block is determined dependent on the two predetermined pulse sequences , wherein the pause block is characteristic for no pulse . Exemplarily, between the predetermined first pulse and the subsequent pulse , in particularly being adj acent to one another, and / or between a predetermined first pulse directly adj acent to the predetermined second pulse within the same predetermined pulse sequence , no signal is present . In particular, a region between the directly adj acent predetermined blocks within the same predetermined pulse sequence is characteristic for the pause block .

[0030] According to at least one embodiment of the method, the first block, the subsequent block and the pause blocks are combined . In particular, the first block, the subsequent block and the pause blocks being consecutively are combined to a first block pause block sequence and a further constant sequence signal is generated corresponding to the first block pause block sequence .

[0031] Advantageously, times in which no signal needs to be emitted are considered by including the pause block .

[0032] Exemplarily, the further constant sequence signal , the second control signal and the third control signal are provided to the arbitrary waveform generator for generating the at least two signal sequences . According to at least one embodiment of the method, each of the two predetermined pulse sequences are segmented in a predetermined number of segments , wherein each of the predetermined pulses comprises at least two segments . Exemplarily, the predetermined pulses in each of the at least two predetermined pulse sequences are consecutively arranged one after the other in time . Each of the at least two predetermined pulse sequences extends within a time interval . For example , a segment corresponds to a predetermined subset of each time interval , in particular dependent on the predetermined number . Exemplarily, the two predetermined pulse sequences are segmented into at least 5 or at least 10 segments .

[0033] For example , each the predetermined first pulse , the predetermined second pulse , the predetermined third pulse and particularly the region where no pulse is present comprise a number of segments . Exemplarily, a number of segments of the predetermined second pulse is di f ferent to a number of segments of the predetermined first pulse . For example , a number of segments of the predetermined third pulse is di f ferent to a number of segments of the predetermined first pulse .

[0034] According to at least one embodiment of the method, each of the two predetermined pulse sequences is characteristic for a gate sequence .

[0035] According to at least one embodiment of the method, each of the two predetermined pulse sequences comprise two predetermined pulse sub-sequences . Exemplarily, each predetermined pulse sub-sequence is configured to be provided to one quantum particle as a signal sequence . According to at least one embodiment of the method, the first block, the second block and the third block are determined dependent on the at least four predetermined pulse subsequences .

[0036] Exemplarily, the first block is determined, wherein the first block is characteristic for a predetermined first pulse , which is present in at least two of the four predetermined pulse sub-sequences . In particular, a further first block is determined, wherein the further first block is characteristic for a predetermined further first pulse , which is present in at least two of the four predetermined pulse sub-sequences , and wherein the predetermined first pulse is di f ferent to the predetermined further first pulse .

[0037] According to at least one embodiment of the method, the second block and / or the third block is provided to the arbitrary waveform generator dynamically during operation of the arbitrary waveform generator .

[0038] According to at least one embodiment of the method, the second block and the third block are di f ferent from one another with respect to a frequency, an amplitude and / or a phase .

[0039] Furthermore , a system for providing control signals for an arbitrary waveform generator which is configured to generate at least two signal sequences applied to at least one quantum particle 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 . According to at least one embodiment , the system comprises an arbitrary waveform generator, a computer device which is configured to generate the first control signal and the second control signal , and an ion trap . In particular, the computer device is configured to receive inputs such as the at least two predetermined pulse sequences . In particular, the arbitrary waveform generator is connected to the computer device and the ion trap .

[0040] In addition a computer program is speci fied comprising instruction which, when the computer program is executed by a computer, causes the computer program to execute the method described herein .

[0041] Further, a computer readable storage medium is speci fied on which the computer program described herein is stored .

[0042] In the following, the method and the ion trap are explained in more detail with reference to exemplary embodiments and the associated Figures .

[0043] Figure 1 shows predetermined pulse sequences for the method according to an exemplary embodiment .

[0044] Figure 2 shows a flowchart of the method according to an exemplary embodiment .

[0045] Elements that are identical , similar or have the same ef fect 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 .

[0046] Two predetermined pulse sequences of Figure 1 , being in particular used in the method of Figure 2 , namely a first predetermined pulse sequence 1 and a second predetermined pulse sequence 2 , each comprises two predetermined pulse subsequences , e . g . the first predetermined pulse sequence 1 comprises a first predetermined pulse sub-sequence 3 and a second predetermined pulse sub-sequence 4 and the second predetermined pulse sequence 2 comprises a third predetermined pulse sub-sequence 5 and a fourth predetermined pulse sub-sequence 6 .

[0047] Each predetermined pulse sub-sequence of one of the predetermined pulse sequences is configured to be applied to a respective ion . In particular, the first and the third predetermined pulse sub-sequences 3 , 5 are each configured to be applied to a first ion as well as the second and the fourth predetermined pulse sub-sequences 4 , 6 are each configured to be applied to a second ion . In particular, the predetermined pulse sequences are configured to be applied to the ions one after the other . In particular, the predetermined pulse sub-sequences of the same predetermined pulse sequence are configured to be applied to the ions simultaneously . A number of predetermined pulse sequences is dependent on an operation to be performed on the ions . A number of predetermined pulse sub-sequences is dependent on a number of ions involved in the operation to be performed .

[0048] The second and the fourth predetermined pulse sub-sequences

[0049] 4 , 6 both comprise a plurality of predetermined pulses 7 , 17 , being di f ferent to one another, e . g . a predetermined first pulse 7 and a plurality of predetermined subsequent pulses 17 , which are in particular di f ferent to one another . Further, the first and the third predetermined pulse subsequences 3 , 5 both comprise a plurality of predetermined further pulses 8 , being di f ferent to one another, e . g . a predetermined further first pulse and a plurality of predetermined further subsequent pulses , which are in particular di f ferent to one another, which are in particular di f ferent to the predetermined first pulse 7 and to each of the predetermined subsequent pulses 17 . The second predetermined pulse sub-sequence 4 comprises a predetermined second pulse 9 , being di f ferent to the predetermined first pulse 7 and to each of the predetermined subsequent pulses 17 as well as the predetermined further first pulse 8 and to each of the predetermined further subsequent pulses . Further, the fourth predetermined pulse sub-sequence 6 comprises a predetermined third pulse 10 , being di f ferent to the predetermined first pulse 7 , the predetermined further first pulse 8 , to each of the predetermined subsequent pulses 17 , and to each of the predetermined further subsequent pulses and the predetermined second pulse 9 . The pulses are spaced apart from one another in time by a spacing time interval , where no pulse 11 is present .

[0050] Each predetermined pulse sequence extends within a time interval along a time t . The time intervals of the predetermined pulse sequences is segmented into consecutive segments s , in particular equally .

[0051] Method stage S I according to the exemplary embodiment of Figure 2 comprises that at least two predetermined pulse sequences are provided, exemplarily shown in Figure 1 . Subsequently, in method stage S2, a first block 12, subsequent blocksl 18, and exemplarily a further first block 13 and further subsequent blocks 20 and / or a pause block, a second block 15 and a third block 16 are determined dependent on the two predetermined pulse sequences. The first block 12 is characteristic for the predetermined first pulse 7, which is present in both of the two predetermined pulse sequences, in particular in at least two of the predetermined pulse subsequences, e.g. marked in Figure 1. Exemplarily, the further first block 13 is characteristic for the predetermined further first pulse 8, which is present in both of the two predetermined pulse sequences, in particular in at least two of the predetermined pulse sub-sequences, e.g. marked in Figure 1. Exemplarily, the pause block is characteristic for no pulse 11, e.g. marked in Figure 1.

[0052] The second block 15 is characteristic for a predetermined second pulse 9, which is different to the predetermined first pulse 7, e.g. marked in Figure 1, and the third block 16 is characteristic for a predetermined third pulse 10, which is different to the predetermined first pulse 7 and the predetermined second pulse 9, e.g. marked in Figure 1.

[0053] In a method stage S3, a first control signal corresponding to the first block 12, and exemplarily a further first control signal corresponding to the further first block 13 and / or a pause control signal corresponding to the pause block, a second control signal corresponding to the second block 15 and a third control signal corresponding to the third block 16 are generated.

[0054] Exemplarily, the predetermined first pulse corresponding to the first block 12 and the predetermined further first pulse of the further first block 13 are combined accordingly . In particular, a sum of the first block 12 and the further first block 13 is produced . In particular, a summed control signal corresponding to the first block 12 and the further first block 13 is generated . Analogously, predetermined subsequent pulses 17 corresponding to the subsequent blocks 18 and predetermined further subsequent pulses 19 corresponding to the further subsequent blocks 20 are combined accordingly . This is a sum of the subsequent block 18 and the further subsequent block 20 , both corresponding to the same segments , is produced . In particular, a further summed control signal corresponding to the corresponding subsequent block 18 and the corresponding further subsequent block 20 is generated .

[0055] In particular, the first block 12 , the subsequent blocks 18 and the pause blocks 14 being consecutively arranged according to the respective pulses and no pulses are combined for the second and the fourth predetermined pulse subsequence 4 , 6 to a first block pause block sequence . Subsequently, a further constant sequence signal is generated corresponding to the first block pause block sequence .

[0056] Further, in particular, the further first block 13 , the further subsequent blocks 20 and the pause blocks 14 being consecutively arranged according to the respective pulses and no pulses are combined for the first and the third predetermined pulse sub-sequence 3 , 5 to a further first block pause block sequence . Subsequently, an additional further constant sequence signal is generated corresponding to the first block pause block sequence .

[0057] Subsequently, in a method step S4 the first control signal , and exemplarily the further first control signal and / or the pause control signal , in particular the further constant sequence signal and / or the additional further constant sequence , the second control signal and the third control signal are provided to the arbitrary waveform generator for generating the at least two signal sequences . In particular, the summed control signals are provided to the arbitrary waveform generator for generating the at least two signal sequences . 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 .

[0058] Reference signs

[0059] 1 first predetermined pulse sequence

[0060] 2 second predetermined pulse sequence

[0061] 3 first predetermined pulse sub-sequence

[0062] 4 second predetermined pulse sub-sequence

[0063] 5 third predetermined pulse sub-sequence

[0064] 6 fourth predetermined pulse sub-sequence

[0065] 7 predetermined first pulse

[0066] 8 predetermined further first pulse

[0067] 9 predetermined second pulse

[0068] 10 predetermined third pulse

[0069] 11 no pulse

[0070] 12 first block

[0071] 13 further first block

[0072] 14 pause block

[0073] 15 second block

[0074] 16 third block

[0075] 17 predetermined subsequent pulse

[0076] 18 subsequent block

[0077] 19 predetermined further subsequent pulse

[0078] 20 further subsequent block t time s segment

[0079] S 1 . . S 6 method stages

Claims

Claims1. Method for providing control signals for an arbitrary waveform generator which is configured to generate at least two signal sequences applied to at least one quantum particle, with- providing at least two predetermined pulse sequences (1, 2) ,- determining a first block (12) , a second block (15) and a third block (16) dependent on the two predetermined pulse sequences (1, 2) , wherein- the first block (12) is characteristic for a predetermined first pulse (7) , which is present in both of the two predetermined pulse sequences (1, 2) ,- the second block (15) is characteristic for a predetermined second pulse (9) , which is different to the predetermined first pulse (7) , and- the third block (16) is characteristic for a predetermined third pulse (10) , which is different to the predetermined first pulse (7) and the predetermined second pulse ( 9 ) ,- generating a first control signal corresponding to the first block (12) , a second control signal corresponding to the second block (15) and a third control signal corresponding to the third block (16) , and- providing the first control signal, the second control signal and the third control signal to the arbitrary waveform generator for generating the at least two signal sequences.

2. Method according to claim 1, wherein- the two signal sequences are configured to be provided to a microwave antenna for producing a time varyingelectromagnetic field in a region of the at least one quantum particle .

3. Method according to one of the claims 1 or 2, wherein- each of the at least two predetermined pulse sequences (1, 2) comprises a predetermined subsequent pulse (17) ,- a subsequent block (18) is determined dependent on the two predetermined pulse sequences (1, 2) , wherein the subsequent block (18) is characteristic for the predetermined subsequent pulse (17) , which is present in both of the two predetermined pulse sequences (1, 2) ,- the first block (12) and the subsequent block (18) are combined to a first block sequence and a constant sequence signal is generated corresponding to the first block sequence,- the constant sequence signal, the second control signal and the third control signal are provided to the arbitrary waveform generator for generating the at least two signal sequences .

4. Method according to claim 3, wherein- a pause block is determined dependent on the two predetermined pulse sequences (1, 2) ,- the pause block is characteristic for no pulse (11) , and- the first block (12) , the subsequent block (18) and pause blocks are combined.

5. Method according to one of the claims 1 to 4, wherein before determining the blocks,- segmenting each of the two predetermined pulse sequences (1, 2) in a predetermined number of segments, and- each of the predetermined pulses comprises at least two segments .

6. Method according to one of the claims 1 to 5, wherein- each of the two predetermined pulse sequences (1, 2) is characteristic for a gate sequence.

7. Method according to one of the claims 1 to 6, wherein- each of the two predetermined pulse sequences (1, 2) comprise two predetermined pulse sub-sequences (3, 4, 5, 6) , and- the first block (12) , the second block (15) and the third block (16) are determined dependent on the at least four predetermined pulse sub-sequences (3, 4, 5, 6) .

8. Method according to one of the claims 1 to 7, wherein- the second block (15) and / or third block (16) is provided to the arbitrary waveform generator dynamically during operation of the arbitrary waveform generator.

9. Method according to one of the claims 1 or 8, wherein- the second block (15) and the third block (16) are different from one another with respect to a frequency, an amplitude and / or a phase.

10. System for providing control signals for an arbitrary waveform generator which is configured to generate at least two signal sequences characteristic for at least two predetermined pulse sequences (1, 2) applied to at least one quantum particle, which is configured to perform the method according to one of the preceding claims.

11. System according to claim 10, comprising- an arbitrary waveform generator,- a computer device which is configured to generate the first control signal and the second control signal , and- an ion trap . 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 the claims 1 to 9 . 13 . Computer-readable storage medium on which the computer program according to claim 12 is stored .

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