Method for identifying a state of a dark ion in a chain of trapped IONS and quantum computer

Abstract

A method for identifying a state of a dark ion (11) in a chain of trapped ions (1) is specified herein, comprising the steps of : applying a magnetic field gradient (2) along the chain of trapped ions (1), - measuring a resonance frequency of a qubit transition (3) of at least one bright ion (12) in the chain of trapped ions (1), identifying the state of the dark ion (11) by determining a shift of the resonance frequency of the at least one bright ion (12) in the presence of the dark ion (11). Further, a quantum computer (10) is specified herein.

Description

[0001] P2023,1438 WO N November6,2024 -1 - DescriptionMETHOD FOR IDENTIFYING A STATE OF A DARK ION IN A C HAIN OFTRAPPED IONS AND QUANTUM COMPUTERA method for identifying a state of a dark ion in a chain oftrapped ions and a quantum computer are disclosed h erein.At least one object of certain embodiments is to sp ecify amethod for identifying a state of a dark ion in a c hain oftrapped ions that can detect the formation of a mol eculebetween a trapped ion and a background gas particle . Thisobject is achieved by the method according to the i ndependentclaim.Advantageous embodiments and further developments o f themethod are specified in the dependentclaims.According to an embodiment, the method for identify ing astate of a dark ion in a chain of trapped ions comp rises astep of applying a magnetic field gradient along th e chain oftrapped ions. For example, the trapped ions are tra pped usingelectric and / or magnetic fields. For example, the t rappedions are trapped in a Penning trap or in a Paul tra p. Inparticular, the chain of trapped ions comprises two , three,four,five ormore trapped ions.Forexample,each ion in thechain of trapped ions is an ion of the same chemica l element,such as Ytterbium. For example, the chain of trappe d ions inthe ion trap formsan ion crystalorispartofan ion crystal.For example, the magnetic field gradient is a linea r magneticfield gradientalong the chain oftrapped ions.In P2023,1438 WO N November6,2024 -2 -particular, a magnitude of the magnetic field incre ases, forexample linearly or approximately linearly increase s, fromone end of the chain of trapped ions to the other e nd of thechain oftrapped ions.Forexample,a direction of the magneticfield isparallelto the chain oftrapped ionsor perpendicularto the chain oftrapped ions.According to a further embodiment, the method compr ises astep ofmeasuring a resonance frequencyofa qubit transition ofatleastone brightion in the chain oftrapped ions.For example,two electronicstatesofeach trapped ion areselected as two linearly independent basis states o f a qubit,respectively. In particular, the qubit is the eleme ntaryinformation unit of a quantum computer. For example , the twoelectronic states are different hyperfine states of onetrapped ion. For example, a transition between thes e twoelectronic states can be driven by applying an osci llatingelectromagnetic field with a frequency correspondin g to anenergy difference between the two electronic states dividedbyPlanck’sconstant.In particular,the resonance frequencyof the qubit transition corresponds to the energy d ifferencebetween the two basis states of the qubit divided b y Planck’sconstant.For example, the resonance frequency of the qubit t ransitionof the at least one bright ion is measured spectros copically,in particular using a coherent spectroscopic techni que. Forexample, the resonance frequency of the qubit trans ition isin the optical spectral range or in the microwave s pectralrange.In particular,a brightion isan ion where the qubittransition can be resonantly driven. For example, t he brightion emits resonance fluorescence when the qubit tra nsition isdriven at the resonance frequency. By contrast, a d ark ion is P2023,1438 WO N November6,2024 -3 - in a differentelectronicstate otherthan the two qubitstates, for example, such that the qubit transition cannot beresonantly driven. Accordingly, the dark ion doesn’ t emitresonance fluorescence at the resonance frequency o f thequbittransition.In particular, the resonance frequency of the qubittransition is different for each qubit in the prese nce of themagneticfield gradient.Forexample,the magnetic fieldgradient induces a different energy shift to the hy perfinestates of each trapped ion along the ion chain. Acc ordingly,the resonance frequency of the qubit transition dep ends on aposition of the trapped ion in the ion trap, for ex ample.According to a further embodiment, the method compr ises astep of identifying the state of the dark ion by de termininga shiftofthe resonance frequencyofthe atleast one brightion in the presence of the dark ion. In particular, the shiftofthe resonance frequencyofthe qubittransition ofthebright ion is determined with respect to a referenc e statewhere no darkion ispresentin the ion chain.According to a preferred embodiment, the method foridentifying a state of a dark ion in a chain of tra pped ions,comprisesthe stepsof:- applying the magnetic field gradient along the ch ain oftrapped ions,- measuring the resonance frequency of the qubit tr ansitionofatleastone brightion in the chain oftrapped ions,- identifying the state of the dark ion by determin ing theshift of the resonance frequency of the at least on e brightion in the presence ofthe darkion. P2023,1438 WO N November6,2024 -4 -The method described herein is based on the idea th at thestate of a dark ion can be at least partially ident ified bymeasuring the resonance frequency of a qubit transi tion of abrightion in itsvicinity.Forexample,a trapped ion canbecome a dark ion by decaying into a metastable ele ctronicstate different from the two qubit basis states, or byforming a molecule with a background gasparticle. For example,the background gasparticle isan atom or a moleculeof the background gas. For example, the ion trap is operatedin ultra-high vacuum conditions, where a pressure o f thebackground gas is at most 10 -6 Pa. For example, the moleculecan form due to collisionsbetween the trapped ion and a background gasparticle.For example, the trapped ion changes its electronicconfiguration when forming the molecule with the ba ckgroundgas particle, such that it becomes dark, i.e. it no longeremits resonance fluorescence at the resonance frequ ency ofthe qubittransition.Furthermore,the trapped ion increases itsmasswhen forming the molecule.Accordingly,a masstocharge ratio of the trapped ion that forms the mole cule withthe background gas particle is changed. Consequentl y, due tothe altered mass to charge ratio, an effective radi altrapping potentialofthe trapped ion generated by aradiofrequency electric filed of the ion trap is ch anged, forexample. This in turn can change a resting position of thetrapped ion in the ion trap, such that due to a mut ualCoulomb repulsion between the trapped ions also the positionother ions in the ion trap, in particular bright io ns, ischanged.As the position of the bright ion is changed by the formationof the molecule, for example, the resonance frequen cy of the P2023,1438 WO N November6,2024 -5 -qubit transition of the bright ion changes due to t hemagnetic field gradient that is applied along the c hain oftrapped ions. Consequently, a shift of the resonanc efrequency of a bright ion indicates a change of mas s of thedark ion and thus indicates the formation of a mole cule bythe dark ion, for example. By contrast, no shift of theresonance frequency of the bright ion indicates tha t the darkion has decayed to a metastable state and can be re pumpedinto one ofthe qubitstates,forexample.According to a further embodiment of the method, tw odifferenthyperfine statesofeach ion are used as basisstates of the corresponding qubit and the qubit tra nsitioncorresponds to a microwave transition between the t wohyperfine states.According to a further embodiment of the method, th eresonance frequency of the bright ion is shifted du e to thedark ion forming a molecule with a background gas p article.In particular, the change in mass due to the molecu leformation of the dark ion changes its rest position andconsequentlyalso the restpositionsofthe bright ionsinthe ion trap. Due to the applied magnetic field gra dient, thepositionalchange causesa change in the resonance frequencyof the qubit transition of the bright ions. For exa mple, theshiftofthe resonance frequencyofthe brightion due to theformation of the molecule by the dark ion is larger than alinewidth ofthe resonance ofthe qubittransition ofthe brightion.According to a further embodiment, the method compr ises afurther step of selecting an error mitigation strat egydepending on the identified state ofthe darkion. For P2023,1438 WO N November6,2024 -6 -example, different operations are applied to the da rk iondepending on the determined shiftofthe resonance frequency ofthe brightion.According to a further embodiment, the method compr ises afurther step of removing the dark ion from the chai n oftrapped ions if the resonance frequency of the brig ht ion isshifted. For example, if the shift of the resonance frequencyof the bright ion is larger than a linewidth of the qubittransition, the dark ion has formed a molecule with abackground gasparticle.In thiscase the darkion cannotbefurther used as a qubit for quantum computations an d has tobe removed from the ion trap,forexample.According to a further embodiment, the method compr ises afurtherstep ofapplying a repumping scheme to the darkion,if the resonance frequency of the bright ion is not shifted.For example, if the resonance frequency of the brig ht ion isnot shifted, or the shift of the resonance frequenc y issmallerthan the linewidth ofthe qubittransition in thepresence of the dark ion, the dark ion is likely in ametastable electronic state other than the two qubi t states.Accordingly,the darkion can be repumped into one ofthequbit states and further used for quantum computati ons, forexample.According to a further embodiment, the method compr ises afurther step of waiting for a decay of the dark ion until thedark ion turns bright, if the resonance frequency o f thebright ion is not shifted, or if the shift of the r esonancefrequency is smaller than the linewidth of the qubi ttransition. P2023,1438 WO N November6,2024 -7 - Furthera quantum computerisspecified herein.Inparticular, the quantum computer implements the met hod foridentifying a state of a dark ion in a chain of tra pped ionsdescribed above. All features of the method are als odisclosed forthe quantum computerand vice versa.According to an embodiment, the quantum computer co mprises achain oftrapped ionsand a state ofa darkion is identified using the method described above.According to a further embodiment of the quantum co mputer,qubits interact via a magnetic gradient induced cou pling. Forexample, each qubit of the quantum computer is phys icallyrealized by choosing two hyperfine states of a corr espondingtrapped ion asthe basisstatesforthe respective qubit.For example,the magneticfield gradientalong a chain oftrappedions induces a pairwise Ising interaction between a ll pairsofqubitsin the ion trap.Forexample,thisIsinginteraction in the presence of the magnetic field g radient ismediated by a common vibrational motion of the ions in theion trap.Further advantageous embodiments and further embodi ments ofthe method and the quantum computer may become appa rent fromthe following exemplary embodiments described in co nnectionwith the figures.Figure 1 shows a schematic flow diagram of a method foridentifying a state of a dark ion in a chain of tra pped ionsaccording to an exemplaryembodiment.Figure 2 and 3 show schematic illustrations of a qu antumcomputeraccording to an exemplaryembodiment. P2023,1438 WO N November6,2024 -8 -Elements that are identical, similar or have the sa me effect,are denoted by the same reference signs in the figu res. Thefigures and the proportions of the elements shown i n thefigures are not to be regarded as true to scale. Ra ther,individual elements may be shown exaggeratedly larg e forbetter representability and / or better understanding .In a first step S1 of a method for identifying a st ate of adarkion 11 in a chain oftrapped ions1 according to the exemplaryembodimentin Figure 1 a linearmagnetic fieldgradient 2 is applied along a chain of trapped ions (c.f.Figures 2 for details). The chain of trapped ions 1 comprisestwo or more ions 11, 12 that are trapped using elec tricand / ormagneticfields.In a second step S2 of the method a resonance frequ ency of aqubittransition 3 ofa brightion 12 in the chain oftrappedions 1 is measured. In particular, the resonance fr equency ismeasured using spectroscopic methods. Specifically, twoelectronic hyperfine states of each trapped ion 11, 12 areselected as basis states |0>, |1> of a qubit qb1,…, qb4 of aquantum computer 10 (c.f. Figure 3). Each ion 11, 1 2 in thechain of trapped ions 1 represents one qubit qb1,…q b4,respectively.The resonance frequencyofthe qubit transition 3 ofone ofthe trapped ions11,12 correspondsto the energydifference between the two basis states |0>, |1> of the qubitqb1,…,qb4 divided by Planck’s constant. The qubit t ransition3 is driven by applying an oscillating electromagne tic field5 at the resonance frequency to the respective brig ht ion 12(c.f.Figure 3). P2023,1438 WO N November6,2024 -9 -By contrast, the dark ion 11 is in a metastable ele ctronicstate other than the two basis states |0>, |1> of t he qubitqb1,…,qb4, or forms a molecule 13 with a background gasparticle 4, for example, such that the qubit transi tion 3 ofthe dark ion 11 cannot be resonantly driven. Accord ingly, thedarkqubit11 doesnotemitresonance fluorescence atthe qubittransition 3.In a third step of the method the state of the dark ion 11 isidentified bydetermining a shiftofthe resonance frequencyof the at least one bright ion 12 in the presence o f the darkion 11. For example, if the dark ion 11 forms a mol ecule 13with a background gasparticle 4,itsmasschanges andtherefore its rest position in the ion trap changes . As theions in the chain of trapped ions 1 interact via re pulsiveCoulomb interactions, the rest positions of the bri ght ions12 change as well due to the shifted position of th e dark ion11. Due to the applied magnetic field gradient 2, t heresonance frequencies of the qubit transitions 3 of thebright ions 12 depend on the position of the bright ions 12in the ion trap. Accordingly, a shift of the positi on of thebright ion 12 can be determined by a shift of its r esonancefrequency, which in turn allows to determine if the dark ion13 has formed a molecule 13 with a background gas p article 4ornot.In an optional further step of the method, an errormitigation strategyforthe quantum computer10 is chosen depending on the state ofthe darkion 11 thatwas determined in step S3. Figures2 and 3 show a schematicillustration ofa quantumcomputer 10 with an ion trap (not shown) comprising a chain P2023,1438 WO N November6,2024 -10 -of trapped ions 1 with an applied magnetic field gr adient 2.Two hyperfine states |0>, |1> of each trapped ion 1 1, 12realize one qubitqb1,…qb4 ofthe quantum computer 10,respectively. The ion trap is arranged inside a vac uumchamber, where a pressure of a background gas is pa rticularlylow, e.g. smaller than 10 -6 Pa. Nonetheless, due tocollisions between background gas particles 4 and t rappedions 11, 12, a molecule 13 can form. Due to the mol eculeformation the corresponding trapped ion 11 changes itselectronic configuration and becomes dark. The dark ion 11 isno longer usable for quantum information processing , however.Accordingly, an error mitigation strategy is chosen dependingon the state ofthe darkion 11 thatisdetermined using themethod described in connection with Figure 1. For e xample,the dark ion 11 is removed from the trap, if the fo rmation ofa molecule 13 is detected via the shift of the reso nancefrequencyofthe brightion 12,while the darkion 11 isrepumped to a basis state |0> or |1> of the qubit q b1,…,qb4,if it does not form a molecule 13, i.e. if no shift of theresonance frequency of the bright ion 12 is detecte d. In thelattercase the darkion 11 turnsbrightagain and can be furtherused forquantum information processing. Thispatentapplication claimsthe priorityofthe Germanpatent application 102023131669.9, the disclosur e of whichisherebyincorporated byreference.The invention is not restricted to the exemplary em bodimentsbythe description on the basisofsaid exemplary embodiments.Rather,the invention encompassesany newfeature and also any combination of features, which inparticular comprises any combination of features in thepatent claims and any combination of features in th e P2023,1438 WO N November6,2024 -11 -exemplary embodiments, even if this feature or thiscombination itself is not explicitly specified in t he patentclaimsorexemplaryembodiments.

[0002] P2023,1438 WO N November6,2024 -12 - References 1 chain oftrapped ions 10 quantum computer 11 darkion 12 brightion 13 molecule 2 magneticfield gradient 3 qubittransition 4 background gasparticle 5 electromagneticradiation qb1…4 qubit |0>,|1> basisstatesofa qubit S1 firststep S2 second step S3 third step

Claims

P2023,1438 WO N November6,2024 -13 - Claims1. A method for identifying a state of a dark ion ( 11) in achain of trapped ions (1), comprising the steps of:-applying a magneticfield gradient(2)along the chain of trapped ions(1),- measuring a resonance frequency of a qubit transi tion (3)of at least one bright ion (12) in the chain of tra pped ions(1),- identifying the state of the dark ion (11) by det ermining ashift of the resonance frequency of the at least on e brightion (12)in the presence ofthe darkion (11).

2. The method according to the previous claim, wher ein twodifferent hyperfine states of each ion (11, 12) are used asbasis states of a corresponding qubit and the qubittransition (3) corresponds to a microwave transitio n betweenthe two hyperfine states.

3. The method according to any of the previous clai ms,wherein the resonance frequency of the bright ion ( 12) isshifted due to the dark ion (11) forming a molecule (13) witha background gasparticle (4).

4. The method according to any of the previous clai ms,comprising a further step of selecting an error mit igationstrategy depending on the identified state of the d ark ion(12).

5. The method according to any of the previous clai ms,comprising a furtherstep ofremoving the darkion (11)fromthe chain of trapped ions (1) if the resonance freq uency ofthe brightion (12)isshifted.P2023,1438 WO N November6,2024 -14 -6. The method according to any of the previous clai ms,comprising a further step of applying a repumping s cheme tothe dark ion (11), if the resonance frequency of th e brightion (12)isnotshifted.

7. The method according to any of the previous clai ms,comprising a further step of waiting for a decay of the darkion (11) until the dark ion (11) turns bright, if t heresonance frequency of the bright ion (12) is not s hifted.

8. A quantum computer (10) comprising a chain of tr apped ions(1), wherein the state of a dark ion (11) is identi fied usingthe method according to anyofclaims1 to 7.

9. The quantum computer (10) according to the previ ous claim,wherein qubits(qb1,qb2,qb3,qb4)interactvia a magnetic gradientinduced coupling.

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