Method for suppressing dephasing of an idle qubit in a quantum register comprising a plurality of qubits and quantum computer

Abstract

A method for suppressing dephasing of an idle qubit (qb1) in a quantum register comprising a plurality of qubits (qb1, qb2, qb3, qb4) is specified herein, comprising the step of applying an identity pulse (1) to the idle qubit (qb1), wherein the identity pulse (1) implements an identity operation on the idle qubit (qb1). Further, a quantum computer is specified herein.

Description

[0001] P2023,1435 WO N November13,2024 -1 - DescriptionMethod for suppressing dephasing of an idle qubit i n aquantum register comprising a plurality of qubits a nd quantumcomputerA method for suppressing dephasing of an idle qubit in aquantum register comprising a plurality of qubits a nd aquantum computerare specified herein.At least one object of certain embodiments is to sp ecify amethod for suppressing dephasing of an idle qubit i n aquantum register comprising a plurality of qubits o n a shorttimescale. This object is achieved by the method ac cording tothe independentclaim.Advantageous embodiments and further developments o f themethod and the quantum computer are specified in th edependentclaims.According to an embodiment, the method for suppress ingdephasing of an idle qubit in a quantum register co mprising aplurality of qubits comprises a step of applying an identitypulse to the idle qubit, wherein the identity pulseimplements an identity operation on the idle qubit. Inparticular, each qubit is a quantum mechanical two- statesystem comprising two linearly independent basis st ates,denoted by|0> and |1> in the following. Forexample,the quantum computerperformsquantumcomputations, such as gate operations, by manipulat ing statesofthe qubitsin the quantum register.The quantum computercan comprise one, two or more quantum registers tha t are P2023,1435 WO N November13,2024 -2 -physically separated by hardware elements. For exam ple, thebasis states of one qubit can be represented by two hyperfinestates of a trapped ion and multiple ions trapped i n one iontrap form the quantum register. For example, the ba sis statesof one qubit can be represented by different states of asuperconducting qubit and superconducting qubits co nnected toone quantum bus form the quantum register. For exam ple, theplurality of qubits in the quantum register interac t witheach other. For example, the interaction is an all- to-allinteraction, where each qubit in the quantum regist erinteracts with every other qubit in the quantum reg ister viaa pairwise interaction.In particular, the idle qubit is a qubit in the qua ntumregister that does not partake in quantum gate oper ations ofa quantum circuit during a specific idle time inter val. Forexample, during the idle time interval a quantum ga te isapplied to qubits in the quantum register other tha n the idlequbit. For example, the idle qubit is not an idle q ubitoutside the idle time interval. In particular, quan tum gateoperations of the quantum circuit are applied to th e idlequbit before and / or after the idle time interval. F orexample, different qubits in the quantum register c an be theidle qubitduring differentidle time intervals.In particular, here and in the following “dephasing ” refersto a loss of quantum coherence of the idle qubit du ring theidle time interval. For example, dephasing destroys a quantuminformation stored in the idle qubit.Forexample, dephasingis due to an unwanted coupling of the idle qubit to itsenvironment. For example, the dephasing of the idle qubit iscaused by external noise that couples to the idle q ubit, or P2023,1435 WO N November13,2024 -3 -it is caused by an unwanted interaction with the ot her qubitsin the quantum register during the idle time interv al.For example, the identity pulse comprises or consis ts of oneor more single qubit gates acting on the idle qubit duringthe idle time interval. For example, the single qub it gatesare rotation operators about the x-axis, the y-axis , and / orthe z-axis. For example, the single qubit gate rota tes astate of the idle qubit by a given angle around a g iven axisofitsBloch sphere.For example, the identity pulse comprises a predete rminednumber of sub-pulses, particularly at least two sub -pulses.Each of the sub-pulses are, for example, characteri stic ofone of the single qubit gates. Exemplarily, the sub -pulseshave a predetermined phase-trajectory for implement ing theidentityoperation on the idle qubit.In particular, the identity pulse implements an ide ntityoperation on the idle qubit, such that the state of the idlequbitremainsunchanged orapproximatelyunchanged after applying the identitypulse to the idle qubit.For example,the identity pulse maps the basis state |0> to itse lf, andmaps the basis state |1> to itself. For example, wh ile theidentity pulse is applied to the idle qubit, the ti meevolution ofthe state ofthe idle qubitdescribes a closedloop on the Bloch sphere. In particular, the initia l stateand the final state of the idle qubit before and af terapplying the identity pulse, respectively, are iden tical orapproximatelyidentical.The method described herein is based on the idea to suppressdephasing of the idle qubit on short timescales tha t are P2023,1435 WO N November13,2024 -4 - comparable to a period ofa Rabicycle ofa single qubitrotation or smaller. Here and in the following, the Rabicycle of a qubit corresponds to an oscillation of t he stateof the qubit between its two basis states |0> and | 1>, whenthe qubit is resonantly driven by an electromagneti c fieldthatcouplesthe two basisstates,forexample.Inparticular, the period of the Rabi cycle determines a speedofsingle qubitrotations.For example, periodic dynamical decoupling pulse se quencescan be used to suppressthe dephasing ofqubitsby atleastapproximately averaging an unwanted coupling betwee n thequbit and its environment to zero. For example, the dynamicaldecoupling pulse sequence is based on an iterated H ahn spin-echo scheme, wherein the state of the qubit is repe atedlyflipped back and forth at a high frequency. However , eachpulse of the dynamical decoupling pulse sequence th at flipsthe state ofthe qubitisa pi-pulse,forexample, that rotatesthe state ofthe qubitbyan angle of180° on theBloch sphere. Consequently, the pi-pulse takes a ti mecorresponding to half a Rabi cycle. Accordingly, us ingdynamical decoupling pulse sequences only works forsuppressing the dephasing ofqubitson time scales much longerthan a Rabicycle ofthe qubit.By contrast, the method described herein can be use d tosuppress dephasing on time scales smaller than a Ra bi cycleof the qubit. In particular, if the unwanted coupli ng of theidle qubit to the environment that causes the depha sing hasan energy scale that is smaller, e.g. at least five timessmaller, than an energy scale associated with the R abi cycleof the idle qubit, i.e. the Rabi frequency multipli ed byPlanck’s constant, the identity pulse approximately averages P2023,1435 WO N November13,2024 -5 -out the unwanted coupling between the idle qubit an d itsenvironment.According to a further embodiment of the method, th e identitypulse implements a single-qubit rotation on the idl e qubit.For example, the identity pulse time evolves the st ate of theidle qubit around a closed loop on the Bloch sphere .According to a further embodiment of the method, th e identitypulse suppresses dephasing due to interactions betw een theidle qubit and other qubits in the quantum register , and / orthe identity pulse suppresses dephasing due to ambi entelectromagnetic field fluctuations. For example, th e ambientelectromagnetic field fluctuations correspond to el ectricfield noise or magnetic field noise that couples to thequbit.According to a further embodiment of the method, th e identitypulse is applied to the idle qubit on a timescale t hat isshorter than or equal to half a Rabi cycle of the i dle qubit.In particular, the identity pulse has a duration th at isshorter than that of a pi-pulse that flips the stat e of theidle qubit,forexample.According to a further embodiment of the method, th e identitypulse comprisesa firstsub-pulse thatrotatesthe state of the idle qubitbyan angle θ and a second sub-pulse thatrotates the state of the idle qubit by an angle – θ back toits initial state. In particular, the first sub-pul se rotatesthe state ofthe idle qubitbyan angle θ around an axisofthe Bloch sphere and the second sub-pulse rotates t he stateof the idle qubit by an angle - θ around the same axis of theBloch sphere.Forexample,the angle θ isa polarangle of P2023,1435 WO N November13,2024 -6 - the Bloch sphere.Forexample,the angle θ islargerthan 0°. Forexample,the angle θ issmallerthan orequalto 180°,orsmaller than 90°. In particular, the second sub-pul se is aninverse of the first sub-pulse. For example, the se cond sub-pulse is configured to undo the time evolution of t he stateofthe idle qubitbythe firstsub-pulse.According to a further embodiment of the method, th eplurality of qubits in the quantum register interac t via apairwise Ising orXY interaction.Forexample,all qubitsinthe quantum register interact via an all-to-all pai rwiseIsing orXY interaction.For example, in a quantum register comprising N qub its theinteraction takesthe form In particular, all pairs of qubits in the quantum r egisterinteractvia Ising orXY interactions.In equation (1)aboveHint refers to an interaction term in a Hamiltonian, th eintegerindices i and j enumerate the N qubitsin the quantumregister, and with ^, ^ ∈ ^^, ^, ^^ denotes one of the three2×2 Paulimatrices acting on the basis states of qubit i with ! ∈ ^1, 2, … , %^. Here,products of Pauli matrices acting on different qubi ts are tobe understood astensorproducts.Further, Jijhasunitsofenergy and parametrizes the interaction strength be tweenqubits i and j.Forexample Jij = J isindependentofiand j. For α = β the interaction specified in equation (1)isdenoted as “Ising interaction” in the following, wh ereas for P2023,1435 WO N November13,2024 -7 - α β the interaction isdenoted as “XY interaction”in the following.Forthe case ofIsing interactionswith α = β,thebasis states |0> and |1> of the qubits are preferab lyeigenstatesofthe corresponding Paulimatrix and aredenoted as measurement basis states in the followin g.For example, pairwise Ising or XY interactions betw een qubitsarise for various physical qubit realizations, such assuperconducting qubits or trapped ion qubits. For e xample,the pairwise Ising or XY interaction between the qu bits canbe used to implement two-qubit gates and / or multi-q ubitgates,in particularentangling gates,between the respectivequbits. For example, a global entangling gate, such as ageneralized Mølmer-Sørensen gate or a magnetic grad ientinduced coupling gate, can be implemented by time e volvingthe qubits in the quantum register while the qubits interactvia the Hamiltonian specified in Equation (1).According to a further embodiment of the method, an energyscale of single qubit rotations is larger than an e nergyscale of the pairwise Ising or XY interaction betwe en theplurality of qubits in the quantum register. In par ticular,the Rabi frequency of the qubits multiplied by Plan ck’sconstant is larger, for example at least five times larger orat least ten times larger, than the interaction str ength J ij .Accordingly, the identity pulse can suppress the de phasing ofthe idle qubit due to its interaction with the othe r qubitsin the quantum register.According to a further embodiment of the method, th e idlequbit does not partake in gate operations of a quan tumcircuitacting on the pluralityofqubitsduring a specific P2023,1435 WO N November13,2024 -8 -idle time interval, during which the identity pulse isapplied to the idle qubit.According to a further embodiment of the method, ba sis statesof each qubit correspond to different hyperfine sta tes of acorresponding trapped ion. In particular, each qubi t isencoded in two different hyperfine states of a corr espondingtrapped ion. A system of two or more ions trapped i n the sameion trap formsthe quantum register,forexample.According to a further embodiment of the method, th eplurality of qubits in the quantum register interac t via amagneticgradientinduced coupling.Forexample,a magneticfield gradient along a chain of trapped ions induce s thepairwise Ising interaction between all pairs of qub its in theion trap. For example, this Ising interaction in th e presenceof the magnetic field gradient is mediated by a com monvibrationalmotion ofthe ionsin the ion trap. Furthera quantum computerisspecified herein.Inparticular, the quantum computer implements the met hod forsuppressing dephasing of an idle qubit in a quantum registercomprising a plurality of qubits described above. A llfeatures of the method are also disclosed for the q uantumcomputerand vice versa.According to an embodiment, the quantum computer ha s aquantum register comprising a plurality of qubits a ndimplements the method for suppressing the dephasing of anidle qubit in the quantum register as specified abo ve.Further advantageous embodiments and further embodi ments ofthe method and the quantum computer may become appa rent from P2023,1435 WO N November13,2024 -9 -the following exemplary embodiments described in co nnectionwith the figures.Figure 1 shows a schematic graph of an identity pul se appliedto an idle qubit according to an exemplary embodime nt of themethod for suppressing dephasing of an idle qubit i n aquantum registercomprising a pluralityofqubits.Figure 2 shows a schematic illustration of a time e volutionofthe state ofthe idle qubiton the Bloch sphere during anapplication of the identity pulse according to a fu rtherexemplaryembodimentofthe method forsuppressing dephasingof an idle qubit in a quantum register comprising a pluralityofqubits.Figure 3 shows a schematic illustration of a quantu m computeraccording to an exemplaryembodiment.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 .The identity pulse 1 according to the exemplary emb odiment ofthe method for suppressing dephasing of an idle qub it in aquantum register comprising a plurality of qubits s hown inFigure 1 is applied to an idle qubit qb1 in a quant umregister of a quantum computer 10 (c.f. Figure 3) d uring anidle time interval Ti. During the idle time interva l Ti, theidle qubit qb1 does not partake in quantum gate ope rations ofa quantum circuit that acts on the qubits qb1, qb2, qb3, qb4 P2023,1435 WO N November13,2024 -10 -in the quantum register. For example, during the id le timeinterval Ti, at least one gate operation of the qua ntumcircuit is only applied to the other qubits qb2, qb 3, qb4 inthe quantum register.Before and / orafterthe idle timeinterval Ti, the idle qubit qb1 does partake in qua ntum gateoperations of the quantum circuit, i.e. it is no id le qubitoutside the idle time intervalTi. In orderto suppressa dephasing ofthe idle qubit qb1 duringthe idle time interval Ti that is caused by an unwa ntedinteraction with the other qubits qb2, qb3, qb4 and / or by anunwanted coupling to environmental noise, an identi ty pulse 1is applied to the idle qubit qb1 during the idle ti meinterval Ti. The identity pulse 1 at least approxim atelyaverages the unwanted interaction or coupling of th e idlequbitqb1 with itsenvironmentto zero.Itisalso possibleto apply two or more identity pulses 1 subsequently to theidle qubit qb1, if the idle time interval Ti is lon ger thanan evolution time ofthe identitypulse 1.The identity pulse 1 performs a rotation of the sta te of theidle qubit qb1, such that the final state of the id le qubitqb1 after applying the identity pulse 1 to the idle qubit qb1is identical or approximately identical to the init ial stateof the idle qubit qb1 before the identity pulse 1 i s applied.In thisexemplaryembodiment,the identitypulse 1 comprisesa first sub-pulse 11 that rotates the initial state of theidle qubitqb1 byan angle θ between 0°and 180°around anaxis of the Bloch sphere, and a subsequent second s ub-pulse12 thatrotatesthe state ofthe idle qubitqb1 by an angle- θ around the same axis of the Bloch sphere back to t heinitial state, such that in total an identity opera tion is P2023,1435 WO N November13,2024 -11 -performed on the idle qubit qb1. For example, the s econd sub-pulse 12 directly follows the first sub-pulse 11 wi thout timedelay or pause in between the two sub-pulses 11, 12 .Alternatively, there can be a pause between the two sub-pulses 11, 12 as shown in Figure 1. It is also poss ible thatthe identity pulse 1 only consists of a single puls e, or itconsists of more than two sub-pulses with or withou t pausesin between.Figure 2 shows the state of the idle qubit qb1 at a specificinstant in time during the idle time interval Ti as a statevector 2 on the Bloch sphere 3. On the Bloch sphere 3, astate vector 2 pointing at the south pole correspon ds to thebasis state |0>, a state vector 2 pointing at the n orth polecorresponds to the basis state |1>, whereas a state vector 2pointing in other directions corresponds to a compl exsuperposition ofthe basisstates|0> and |1>,for example.The identity pulse 1 consists of single qubit rotat ions thatrotate the state of the idle qubit qb1 such that th e tip ofthe state vector 2 traces a closed loop 4 on the su rface ofthe Bloch sphere 3 during its time evolution. Accor dingly,the initial state of the idle qubit qb1 before appl ying theidentity pulse 1 and the final state of the idle qu bit qb1after applying the identity pulse 1 are identical o rapproximatelyidentical. The quantum computer10 according to the exemplary embodiment in Figure 3 comprisesa quantum registerwith four qubitsqb1, qb2, qb3, qb4. The two basis states |0> and |1 > of eachqubit qb1, qb2, qb3, qb4 are two hyperfine states o f acorresponding trapped ion. All ions belonging to th e quantumregisterare trapped in the same ion trap,such as a Paul P2023,1435 WO N November13,2024 -12 -trap or a Penning trap. A magnetic gradient along t he chainof trapped ions induces a pairwise Ising interactio n betweenall pairs of qubits qb1, qb2, qb3, qb4 in the quant umregister. Thispatentapplication claimsthe priorityofthe Germanpatent application 102023131673.7, 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 eexemplary embodiments, even if this feature or thiscombination itself is not explicitly specified in t he patentclaimsorexemplaryembodiments.

[0002] P2023,1435 WO N November13,2024 -13 - References 1 identitypulse 11 firstsub-pulse 12 second sub-pulse 10 quantum computer 2 state vector 3 Bloch sphere 4 closed loop qb1 idle qubit qb2…4 qubits t time Ti idle time interval θ angle

Claims

P2023,1435 WO N November13,2024 -14 - Claims1. A method for suppressing dephasing of an idle qu bit (qb1)in a quantum register comprising a plurality of qub its (qb1,qb2,qb3,qb4),comprising the step of: -applying an identitypulse (1)to the idle qubit (qb1),wherein the identity pulse (1) implements an identi tyoperation on the idle qubit(qb1),wherein- the identity pulse (1) is applied to the idle qub it (qb1)on a timescale that is shorter than or equal to hal f a Rabicycle ofthe idle qubit(qb1).

2. The method according to the previous claim, wher ein theidentity pulse (1) implements a single-qubit rotati on on theidle qubit(qb1).

3. The method according to any of the previous clai ms,wherein- the identity pulse (1) suppresses dephasing due t ointeractions between the idle qubit (qb1) and other qubits(qb2,qb3,qb4)in the quantum register,and / or- the identity pulse (1) suppresses dephasing due t o ambientelectromagneticfield fluctuations.

4. The method according to any of the previous clai ms,wherein the identity pulse (1) comprises a first su b-pulse(11) that rotates the state of the idle qubit (qb1) by anangle θ and a second sub-pulse (12) that rotates the state ofthe idle qubit (qb1) by an angle – θ back to its initialstate.

5. The method according to any of the previous clai ms,wherein the plurality of qubits (qb1, qb2, qb3, qb4 ) in theP2023,1435 WO N November13,2024 -15 -quantum register interact via a pairwise Ising or X Yinteraction.

6. The method according to the previous claim, wher ein anenergy scale of single qubit rotations is larger th an anenergy scale of the pairwise Ising or XY interactio n betweenthe plurality of qubits (qb1, qb2, qb3, qb4) in the quantumregister.

7. The method according to any of the previous clai ms,wherein the idle qubit (qb1) does not partake in ga teoperations of a quantum circuit acting on the plura lity ofqubits(qb1,qb2,qb3,qb4)during a specificidle time interval(Ti),during which the identitypulse (1) isapplied to the idle qubit(qb1).

8. The method according to any of the previous clai ms,wherein basisstatesofeach qubit(qb1,qb2,qb3, qb4)correspond to different hyperfine states of a corre spondingtrapped ion.

9. The method according to the previous claim, wher einthe plurality of qubits (qb1, qb2, qb3, qb4) in the quantumregister interact via a magnetic gradient induced c oupling.

10. A quantum computer (10), wherein a dephasing of an idlequbit (qb1) in a quantum register comprising a plur ality ofqubits (qb1, qb2, qb3, qb4) is suppressed using the methodaccording to anyofclaims1 to 9.

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