Ion trap, quantum computing arrangement and method for operating an ion trap and / or a quantum computing arrangement

Abstract

An ion trap (1) for a quantum computing arrangement (10), comprises an arrangement (9) of permanent magnets ( 2, 3) generating a magnetic field at an ion trap axis (T) and a solenoid (4) for modifying a gradient and / or a field strength of the magnetic field at a position along the ion trap axis (T) at least during one stage of a quantum computing algorithm.

Description

[0001] P2024,0043 DE E August7,2025 -1 - ION TRAP,QUANTUM COMPUTING ARRANGEMENT AND METHOFDOR OPERATING AN ION TRAP AND / OR A QUANTUM COMPUTING ARRANGEMENTThe present disclosure relates to an ion trap, a qu antumcomputing arrangement and a method for operating an ion trap.A typical repetition of a quantum algorithm with tr apped ionsstartswith initialization,which includescooling andoptical pumping, continues with carrying out a gate sequenceand ends with state detection. While for the gate s equence alarge magnetic field gradient is of advantage, init ializationand state detection requires no gradient or a low g radient.For generating the required field gradient, a perma nentmagnetcan be employed,which hasthe advantage of lowdissipation. Publication DE 102022124674 B4 disclos es an iontrap for a quantum computing arrangement with a Hal bacharrangement of permanent magnets. Alternatively, ti medependent magnetic fields can be generated by using solenoidsbut at the expense of substantial dissipation. This isparticularly critical when implemented in cryogenic setups.An object to be solved is to provide an improved io n trap fora quantum computing arrangement.The object is solved by the subject matter of indep endentclaim 1.Advantageousembodiments,implementations and furtherdevelopmentsare the subjectmatterofthe respective dependentclaims.According to a first aspect, an ion trap for a quan tumcomputing arrangement comprises an arrangement of p ermanentmagnetsgenerating a magneticfield atan ion trap axis.The P2024,0043 DE E August7,2025 -2 -ion trap further comprises a solenoid for modifying agradient and / or a field strength of the magnetic fi eld at aposition along the ion trap axisatleastduring a stage ofa quantum computing algorithm.By the permanent magnet arrangement, a basic gradie nt and / ormagnetic field strength can be generated. The gener ation ofthe magnetic field by permanent magnets has the adv antage ofa low dissipation when compared to the generation b y coils.The gradientand / ormagneticfield can be modified bythesolenoid. For example, in stages where a gradient a nd / or amagnetic field strength is not required or detrimen tal, thegradient and / or magnetic field strength can be redu ced by thesolenoid.The arrangement of permanent magnets may comprise a firstpermanent magnet and a second permanent magnet. Mag netizationdirections may run in the direction of a connection line ofthe magnets.The connection line maycoincide with the iontrap axis. In one embodiment, corresponding poles o f thepermanent magnets point to each other. In this case , thepermanentmagnetsmaybe arranged mirrorsymmetric relativeto a mirror plane perpendicular to the axis. In suc h anarrangement, a large magnetic gradient can be gener ated alongthe axis.The arrangement of permanent magnets may be a Halba charrangement. The arrangement may generate a quadrup ole field.A Halbach arrangement is a special arrangement of p ermanentmagnetsthatstrengthensthe magneticfield on one side ofthe arrangement and almost cancels it out on the ot her side.This can be achieved by a spatially rotating patter n of the P2024,0043 DE E August7,2025 -3 - magnetization directionsofpermanentmagnets.The permanentmagnets may be segments of the Halbach arrangement.In a further embodiment, opposite poles of the perm anentmagnets point to each other. In this case, the seco ndpermanentmagnetmaybe shifted along the ion trap axisrelative to the first permanent magnet. The permane nt magnetarrangement generates a uniform field along the ion trapaxis.A homogenous magnetic field, i.e., a field with low or nogradient may be useful for initialization (e.g. Dop plercooling,sub-Dopplercooling,opticalpumping)and for detection.According to some embodiments, the solenoid compris es ananti-Helmholtz coil. An anti-Helmholtz coil compris es a firstcoil and a second coil, wherein current flows in op positedirections in the first coil and second coils. Each of thecoils may have a single turn, for example. It is al sopossible that one or each of the coils have multipl e turns.By such a coil a magnetic field can be generated al ong theconnection line of the permanent magnets with field strengthincreasing from a central point towards opposite di rectionsalong the connection line. Thereby, a magnetic fiel d gradientgenerated by the permanent magnet arrangement can b ecompensated at least at a central point of the conn ectionline. It is also possible to compensate the field g radient ina region along the axis. The region may be the rele vantregion asoccupied bythe ion register. P2024,0043 DE E August7,2025 -4 -According to other embodiments, the solenoid is con figured asa helicalcoil.Thereby,a homogenousfield,i.e., a fieldwith parallel field lines and a homogenous field st rength canbe generated.With such an arrangement,a magnetic field strength can be reduced orsetto zero atleastat a centralpoint of the axis. It is also possible to compensat e thefield gradient in a region along the axis. The regi on may bethe relevant region as occupied by the ion register .As an example, the solenoid is configured for reduc ing agradient / and or a field strength in an initializati on phaseand / or a state detection phase of a quantum computi ngalgorithm. The solenoid may be configured for enhan cing ormaintaining a gradient and / or a field strength of a magneticfield in a gate sequence of the quantum computing a lgorithm.As a further example, the solenoid is configured fo rgenerating a sinusoidally modulated gradient of the magneticfield.Thereby,the coupling ofionsparticipating in thesame mode can be enhanced. It is also possible that thesolenoid generates a field for reducing and or canc elling amagneticfield strength and / ora field gradientin additionto a sinusoidally modulated gradient. As an example , asinusoidally modulated gradient may be generated du ring agate sequence and a different field may be generate d duringinitialization and / ordetection.The ion trap may comprise electrodes for trapping o ne or moreions along the ion trap axis. The ion trap may comp rise firstelectrodes configured to provide a time-varying ele ctricfield and second electrodes configured to provide a staticelectric field. The one or more ions may be arrange d alongthe trap axisand / oroscillate around the trapping axis. The P2024,0043 DE E August7,2025 -5 -one or more ions may intersect with the trapping ax is and / oroscillate around the trapping axis. Exemplarily, th e ions arearranged in an ion chain along the trapping axis.The ion trap axismaycoincide with the connection line ofthe permanent magnets. It is also possible that the ion trapaxisdoesnotcoincide with the connection line of the permanentmagnets. According to a furtheraspect,a quantum computingarrangement is specified, wherein the quantum compu tingarrangement comprises the ion trap as described abo ve. Thequantum computing arrangement further comprises a d evice formanipulating the trapped ions.The device maybe a laser device.According to a further aspect, a method for operati ng an iontrap and / or a quantum computing arrangement is disc losed. Themethod maybe carried outwith the ion trap and / or thequantum computing arrangement as disclosed in the f oregoing.The method comprises the steps of generating a curr ent flowthrough the solenoid such thata gradientand / ora field strength ofthe magneticfield ata position along the ion trap axisismodified atleastduring a stage ofa quantum computing algorithm.The method may comprise the steps of initializing t he quantumalgorithm, carrying out a gate sequence and carryin g outstate detection.In some embodiments,currentflow in thesolenoid may be such that the magnetic field gradie nt and / orthe magnetic field strength at a position along the ion trapaxis is smaller during initialization and / or detect ion thanduring the gate sequence. P2024,0043 DE E August7,2025 -6 - Asan example,currentflow maybe shutoffduring a gatesequence wherein current flows through the solenoid duringinitialization and / or state detection. As a further example,the direction of current flow may be reversed durin g a gatesequence when compared to initialization and / or sta tedetection.It is also possible that, at least during a gate se quence,current flow in the solenoid is such that a sinusoi dallymodulated gradient of the magnetic field is generat ed.The present disclosure comprises several aspects an dembodiments. Every feature described with respect t o one ofthe aspects and embodiments is also disclosed herei n withrespectto the otheraspectsand embodiments,even iftherespective feature is not explicitly mentioned in t hiscontext.Further features, refinements and expediencies beco meapparent from the following description of the exem plaryembodimentsin connection with the figures.In the figures,elements of the same structure and / or functionality may bereferenced by the same reference signs. It is to beunderstood that the embodiments shown in the figure s areillustrative representations and are not necessaril y drawn toscale.Figure 1 shows an embodiment of an ion trap in a sc hematicview,Figure 2 shows an embodiment of the ion trap of Fig . 1 withelectrodesin a schematicview, P2024,0043 DE E August7,2025 -7 -Figure 3 shows an embodiment of a quantum computingarrangement, Figure 4 showsa furtherembodimentofan ion trap in a schematicview, Figure 5 showsa furtherembodimentofan ion trap in a schematicview, Figure 6 showsa furtherembodimentofan ion trap in a schematicview,Figure 7 shows an embodiment of a method for quantu mcomputing in a schematicprocessdiagram,Figure 8 shows an embodiment of a method for quantu mcomputing in a schematic diagram of current flowingthrough a solenoid overtime,Figure 9 shows an ion trap with a Halbach arrangeme nt.Figure 1 shows an embodiment of an ion trap 1 compr ising apermanent magnet arrangement 9. The permanent magne tarrangement9 comprisesa firstpermanentmagnet2 and asecond permanent magnet 3. The permanent magnets 2, 3generate a magnetic field with a field gradient alo ng aconnection line A of the permanent magnets 2, 3. Th e axis Amay coincide with the ion trapping axis T, along wh ich theionsare confined.In the shown embodiment, the permanent magnets 2, 3 arearranged such thatlike polespointto each other. Asan P2024,0043 DE E August7,2025 -8 - example,the like polespointing to each othercan be the south polesS.The permanent magnet arrangement 9 may be a Halbacharrangement. An example of a Halbach arrangement fo r the iontrap 1 isshown in Fig.9.The Halbach arrangement comprisesthe permanent magnets 2, 3 as shown in Fig. 1 and f urtherpermanent magnets not shown in Fig. 1 but which areadditionally present when using a Halbach arrangeme nt.The permanent magnets 2, 3 generate a permanent gra dient ofthe magnetic field along the connection line A with low orzero dissipation. Such a magnetic gradient is of ad vantage incertain sequences of a quantum computing scheme. Ho wever, forothersequences,a large magneticgradientcan bedetrimental. In particular, a large gradient can pr ovideidealconditionsto carryouta gate sequence.The fieldstrength is different for different positions along thetrapping axisT.Thereby,a resonance frequencyof each ofthe ions at the trapping axis T, on which the magne tic fieldgradient acts, can be unique for each trapped ion d ue to themagneticfield gradient.For certain stages, such as initialization and stat edetection, a low or a vanishing gradient is benefic ial. Forcancelling orreducing the magneticfield gradient along the ion trapping axisT in certain stagesofa quantum algorithm,the ion trap 1 comprises a solenoid 4 for generatin g asuperimposed gradient to cancel or reduce the magne tic fieldgradient along the ion trapping axis T. In particul ar, themagnetic field gradient may be reduced or cancelled duringinitialization and state detection and may be not r educed P2024,0043 DE E August7,2025 -9 -during a gate sequence. Thereby, cooling and detect ion can besimplified.The solenoid 4 is configured as an anti-Helmholtz c oilcomprising a first coil 5 and a second coil 6, wher eincurrent flows in opposite directions in the first c oil 5 andsecond coils 6 around the common axis C of the coil s 5, 6. Itis also possible that the first coil 5 and / or the s econd coil6 comprises multiple turns. By the coils 5, 6, a su perimposedmagnetic field is generated which is zero in the ce ntrebetween the coils 5, 6 and increases in both direct ions alongthe coil axis. The coil axis C coincides with the c onnectionline A of the permanent magnets 2, 3 and with the t rappingaxisT.Thereby,the magneticfield gradientalong the trapping axisT can be reduced orcancelled out.Alternatively, the magnetic field gradient can be i ncreasedby inverting the direction of the current or by mod ulationwith an AC current.Different structures for the ion trap 1 are possibl e. As anexample, the solenoid 4 and / or the permanent magnet s 2, 3 maybe created asplanarstructuresin ion trap chips.Figure 2 shows an ion trap 1 comprising the permane nt magnetarrangement 9, the solenoid 4 and electrodes 7, 8 f orconfining the ions. The electrodes7,8 comprise firstelectrodes7 in the formof blade electrodes for a radial confinement and se condelectrodes 8 for an axial confinement. The first el ectrodes 7may provide a time-varying electric field and the s econdelectrodes 8 may provide a static electric field. O ne or moreionsare thusconfined along the trapping axisT. For P2024,0043 DE E August7,2025 -10 -example, the ion 11, in particular each of the ions ,intersects with the trapping axis T and / or there ma y be anoscillation along the trapping axis T and a furtheroscillation perpendicular to the trap axis T. Exem plarily,the ions11 are arranged in an ion chain along the trap axis. The ion trap 1 maybe a Paultrap.Figure 3 shows a schematic view of a quantum comput ingarrangement 10 comprising an ion trap 1, a device 1 2 formanipulating trapped ions and a detector 13. The de vice 12may be a laserdevice and the detector13 maybe a singlephoton detector. The ion trap 1 may be the ion trap 1 ofFigures 1 and 2. The device 12 is configured to pro vide laserlight to the trapped ions for manipulating the ions in a gatesequence. The detector 13 serves to detect the ions ’ state.Figure 4 showsa furtherembodimentofan ion trap 1comprising an arrangement 9 of permanent magnets 2, 3 and asolenoid 4. Also here, the permanent magnets 2, 3 a rearranged along a connection line A, which can be th e trappingaxisT.In this case, opposite poles of the permanent magne ts 2, 3point to each other. The solenoid 4 is configured a s a helixcoil. When current flows through the solenoid 4, an offsetfield is generated along the connection line A. The reby, theelectric field along the connection line A can be r educed orcancelled.The electricfield can be alternatively increasedby inverting the direction of the current or by mod ulationwith an AC current.Figures 5 and 6 show further embodiments of ion tra ps 1. Inthese embodiments, the solenoid 4 generates an offs et field P2024,0043 DE E August7,2025 -11 -for an ion 11 which is displaced from the connectio n line Aof the permanent magnet arrangement 9. The magnetic fieldgenerated by the solenoid 4 serves to compensate th edisplacementand cancelsthe magneticfield ofthe permanent magnetarrangement9 atthe location ofthe ion 11 and / orin a region along the trapping axisT.The region may be the relevantregion asoccupied bythe ion register.In Figure 5, the ion 11 is displaced along the axia ldirection ofthe connection line A.The solenoid 4 isconfigured as a helical coil and generates a magnet ic fieldperpendicular to the connection line A of the perma nentmagnetarrangement9 along the trapping axisT.In Figure 6, the ion 11 is displaced in a perpendic ulardirection from the connection line A.The solenoid 4 isconfigured as a helical coil and generates a magnet ic fieldperpendicular to the connection line A of the perma nentmagnet arrangement 9 along the trapping axis T. The windingaxis C of the solenoid 4 is perpendicular to the tr appingaxis T. In the embodiments of Figs. 1, 2 and 4, the windingaxis C of the solenoid 4 is parallel to the trappin g axis T.The embodiments of Figs. 5 and 6 can be modified su ch thattwo solenoidsare provided in the same ion trap 1, whereinone solenoid 4 is arranged as in Fig. 5 and a secon d solenoid4 is arranged as in Fig. 6. Additionally or alterna tively, inthe embodiments of Figs. 4 and 6, a further solenoi d may beprovided along a third direction. In particular, th e furthersolenoid may have an axis C pointing in the directi on of thepicture plane. P2024,0043 DE E August7,2025 -12 - The solenoids4 ofFigs.5 and 6 maybe configured forgenerating a magnetic field during a gate sequence. Themagneticfield maybe generated onlyduring a gate sequence.As a variant, the magnetic field may be generated o nly duringtwo qubit gate sequences.Figure 7 shows steps in a quantum algorithm in a sc hematicview. A repetition ofthe quantum algorithm startswithinitialization in step A. In the initialization sta ge, thetrapped ions are subjected to cooling and optical p umping. Ina following step B, a gate sequence is carried out, whereinthe trapped ions are manipulated, e.g., by laser be ams. Inthe following step C, state detection of the trappe d ions iscarried out,e.g.,bya detector.The quantum algorithm can be carried out with the i on trap 1and the quantum computing arrangement 10 of the for egoingfigures, in particular with a permanent magnet arra ngement 9and a solenoid 4.Figure 8 shows a schematic diagram of current flowi ng througha solenoid 4 in the quantum computing steps of Figu re 7according to an embodiment of a quantum computing m ethod.At time t 0, initialization starts and current I c = I init , with|I init |>0 A, flows through the solenoid 4 such that themagnetic field gradient of the permanent magnet arr angement 9iscancelled outorreduced along the ion trapping axis.Attime t 1, a gate sequence starts and the current through th esolenoid 4 is shut off (I gate =0 A). At time t 2, statedetection starts and current I c = I detect , with |I detect |>0 A, P2024,0043 DE E August7,2025 -13 -flows again through the solenoid 4 such that the ma gneticfield gradientofthe permanentmagnetarrangement 9 iscancelled out or reduced along the ion trapping axi s. Thelevel of the current I init , I detect flowing through the solenoid4 during initialization and state detection maybe different.Compared to an ion trap where a magnetic field grad ient isonly generated by coils instead of permanent magnet s 2, 3,the dissipation averaged over one repetition is red uced by afactor (t init (=t 1-t 0)denotes the time used for initialization, t gate (=t 2-t 1) is thetime to carry out the gate sequence and t detect (=t 3-t 2) is thetime for state detection. The reduction in dissipat ion isparticularly large in the case of t gate >> t init , t detect .It is also possible that during the gate sequence t he currentflowing through the solenoid 4 is reversed compared to theinitialization (I gate = - I init ). In this case, the gradient isincreased during the gate sequence by a factor of t wo suchthatthe gate sequence can be speed up bya factor offour.It is also possible that a sinusoidally modulated g radient isgenerated by the solenoid 4 on top of a gradient ge nerated bythe permanent magnet arrangement 9. This gradient i s providedby a current modulation in the solenoid 4. This can be usedto enhance the coupling of ions participating in th e samemode while saving a large fraction of the dissipati on whichwould occur with a larger, constant gradient. Due t o thegradientbythe solenoid 4,the gradientgenerated bythepermanent magnet arrangement 9 can be smaller. Ther eby,dissipation during initialization and detection can bereduced. It is further possible that the solenoid 4 provides P2024,0043 DE E August7,2025 -14 -a sinusoidally modulated gradient and a field for r educing orcancelling the gradientand / orfield strength. The solenoids4 maybe configured forgenerating a magneticfield during a gate sequence. The magnetic field ma y begenerated only during a gate sequence. As a variant , themagnetic field may be generated only during two qub it gatesequences.Figure 9 showsan ion trap 1 with an arrangement9 ofsegments 14 of permanent magnets in the form of a H albacharrangement.The arrangement9 and furtherdetails ofthe iontrap 1 may be provided in any of the embodiments di sclosed inthe foregoing. The permanent magnets 2, 3 of the fo regoingembodiments are, in this case, segments 14 of the H albacharrangement. The ion trap 1 comprises a planar Paul trap 16.The planar Paul trap 16 is configured to trap an io n crystalwith a pluralityofionslined up along a trapping axisT. The Paultrap 16 isarranged in a chamber17 which issurrounded by the permanent magnet arrangement 9. T hepermanentmagnetarrangement9 isarranged between an innerradius R i and an outer radius R 0. The ion trap 1 may insteadbe configured non-planar as shown in Fig. 2, for ex ample.The arrangement 9 has the shape of a ring, in the c enter ofwhich the ions are trapped. The magnetization direc tions 15of the segments 14 which are arranged at opposite a reas inrelation to a center of the permanent magnet arrang ement 9are directed in opposite directions. The trapping a xis T runsthrough the center of the permanent magnet arrangem ent 9 andintersects with two opposing segments 14, which cor respond tothe permanent magnets 2, 3 of the embodiments descr ibed in P2024,0043 DE E August7,2025 -15 -the foregoing. The magnetization directions 15 of t hese twosegments14 run parallelto the trapping axisT.The Halbach arrangement generates a magnetic quadru polefield,wherebythe magnitude ofthe magneticfield changesalong the trapping axis T. Thereby, each of the tra pped ionsarranged along the trapping axis T sees a different magneticfield.

[0002] P2024,0043 DE E August7,2025 -16 - Reference signs 1 ion trap 2 firstpermanentmagnet 3 second permanentmagnet 4 solenoid 5 firstcoil 6 second coil 7 firstelectrodes 8 second electrodes 9 permanentmagnetarrangement 11 ion 10 quantum computing arrangement 12 device 13 detector 14 segment 15 magnetizing direction 16 Paultrap A connection line ofpermanentmagnets T ion trapping axis C winding axisofsolenoidRi inner radiusR0outerradiusI c current through solenoidI init current during initializationI gate current during gate sequenceI detect current during detectiont 0, t 1, t 2, t 3 points in time in quantum algorithm

Claims

P2024,0043 DE E August7,2025 -17 - Claims1. An ion trap (1) for a quantum computing arrangem ent (10),comprising- an arrangement (9) of permanent magnets (2, 3) ge nerating amagneticfield atan ion trap axis(T)and -a solenoid (4)formodifying a gradientand / ora field strength ofthe magneticfield ata position along the ion trap axis(T)atleastduring a stage ofa quantum computing algorithm, wherein a currentflow in the solenoid (4)issuch thatthemagnetic field gradient and / or the magnetic field s trength ata position along the ion trap axis (T) is smaller i n aninitialization and / or state detection phase than in a gatesequence and / orwherein a sinusoidally modulated gradient of the ma gneticfield isgenerated during the gate sequence. 2.The ion trap (1)ofclaim 1,wherein the solenoid (4) is configured for reducing agradient / and or a field strength in an initializati on phaseand / or a state detection phase of a quantum computi ngalgorithm. 3.The ion trap (1)ofanyofclaims1 and 2,wherein the solenoid (4) is configured for enhancin g ormaintaining a gradient and / or a field strength of a magneticfield in a gate sequence of a quantum computing alg orithm.

4. The ion trap (1) of any of the preceding claims,wherein the arrangement (9) of permanent magnets (2 , 3)comprises a first permanent magnet (2) and a second permanentP2024,0043 DE E August7,2025 -18 -magnet (3) with magnetizations (15) in the directio n of aconnection line ofthe magnets(3).

5. The ion trap (1) of any of the preceding claims,wherein the solenoid (4) comprises an anti-Helmholt z coil.

6. The ion trap (1) of any of the preceding claims,wherein the solenoid (4)comprisesa helicalcoil.

7. The ion trap (1) of any of the preceding claims,wherein the solenoid (4)isconfigured to generate a magneticfield with field lines parallel to an ion trap axis (T).8.The ion trap (1)ofanyofclaims1 to 6, wherein the solenoid (4)isconfigured to generate a magneticfield with field lines perpendicular to an ion trap axis (T).

9. The ion trap (1) of any of the preceding claims,comprising several solenoids (4) for generating mag neticfield linesin differentdirectionsrelative to an ion trap axis(T).

10. A quantum computing arrangement (10), comprisin g- the ion trap (1) according to any of the precedin g claims,and- a device (12) for manipulating trapped ions (11).11.A method foroperating the ion trap (1)and / or thequantum computing arrangement (10) of any of the pr ecedingclaims,comprising the stepsof generating a currentflow through the solenoid (4) such that a gradientand / ora field strength ofthe magnetic field ataP2024,0043 DE E August7,2025 -19 -position along the ion trap axis (A) is modified at leastduring a stage ofa quantum computing algorithm, and comprising the stepsof A)initializing the quantum algorithm, B)carrying outa gate sequence, C)carrying outstate detection,wherein current flow in the solenoid (4) is such th at themagnetic field gradient and / or the magnetic field s trength ata position along the ion trap axis (T) is smaller i n step Aand / orC than in step B and / orwherein at least in step B a sinusoidally modulated gradientofthe magneticfield isgenerated bythe solenoid (4). 12.The method ofclaim 11, wherein in step B currentflow in the solenoid (4) isshut off. 13.The method ofclaim 12, wherein in step B the direction ofcurrentflow in the solenoid (4)isreversed compared to step A and / or step C.

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