Arrangement for quantum computing

Abstract

According to an embodiment, an arrangement for quantum computing comprises: a first plurality of qubits, wherein a qubit frequency of each qubit in the first plurality of qubits is configured according to a first mean frequency; a second plurality of qubits, wherein a qubit frequency of each qubit in the second plurality of qubits is configured according to a second mean frequency, different from the first mean frequency; and a plurality of couplers, wherein each coupler in the plurality of couplers is configured to couple a qubit in the first plurality of qubits to a qubit in the second plurality of qubits; wherein at least one operational parameter of the arrangement is configured to vary around a mean value over the arrangement according to a designed disorder, wherein the at least one operational parameter affects at least one of: the first plurality of qubits, the second plurality of qubits, and / or the plurality of couplers.

Description

ARRANGEMENT FOR QUANTUM COMPUTING TECHNICAL FIELD

[0001] The present disclosure relates to a quantumcomputing, and more particularly to an arrangement forquantum computing, a quantum computing system, and amethod for designing an arrangement for quantum compu- ting. BACKGROUND

[0002] In current implementations quantum computing,it is typically desirable to minimize unwanted interac-tions between qubits and between couplers. Such unwantedinteractions may arise, for example, when qubits and / or couplers are in resonance with each other even whenquantum gates are not performed. This can cause thequbits to hybridize with each other and the eigenstates of the qubits to extend over the lattice of qubits. Such non-local states can be difficult to control using local operations. SUMMARY

[0003] This summary is provided to introduce a selec-tion of concepts in a simplified form that are further described below in the detailed description. This sum- mary is not intended to identify key features or essen- tial features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

[0004] It is an objective to provide an arrangementfor quantum computing, a quantum computing system, and a method for designing an arrangement for quantum com- puting. The foregoing and other objectives are achieved by the features of the independent claims. Further im- plementation forms are apparent from the dependent claims, the description and the figures.

[0005] According to a first aspect, an arrangement forquantum computing comprises: a first plurality ofqubits, wherein a qubit frequency of each qubit in thefirst plurality of qubits is configured according to afirst mean frequency; a second plurality of qubits, wherein a qubit frequency of each qubit in the secondplurality of qubits is configured according to a secondmean frequency, different from the first mean frequency;and a plurality of couplers, wherein each coupler in theplurality of couplers is configured to couple a qubitin the first plurality of qubits to a qubit in the secondplurality of qubits; wherein at least one operationalparameter of the arrangement is configured to varyaround a mean value over the arrangement according to adesigned disorder, wherein the at least one operational parameter affects at least one of: the first pluralityof qubits, the second plurality of qubits, and / or theplurality of couplers.

[0006] In an implementation form of the first aspect,the at least one operational parameter comprises at least one of: the qubit frequency of each qubit in the first plurality of qubits; the qubit frequency of each qubit in the second plurality of qubits; a coupler fre- quency of each coupler in the plurality of couplers; aqubit anharmonicity of each qubit in the first plurality of qubits; a qubit anharmonicity of each qubit in the second plurality of qubits; and / or a qubit coupling strength of each coupler in the plurality of couplers.

[0007] In another implementation form of the firstaspect, the designed disorder follows a distribution.

[0008] In another implementation form of the firstaspect, the distribution is configured to prevent col- lisions of the at least one operational parameter be- tween different parts of the arrangement.

[0009] In another implementation form of the firstaspect, the designed disorder follows a quasiperiodic distribution.

[0010] In another implementation form of the firstaspect, the at least one operational parameter of the arrangement is configured to vary over the arrangement according to the quasiperiodic distribution based at least on a location in the arrangement, an irrational number, and at least one periodic function.

[0011] In another implementation form of the firstaspect, the designed disorder follows a preconfigured probability distribution.

[0012] In another implementation form of the firstaspect, the designed disorder over the arrangement fol- lows a preconfigured probability distribution with col- liding values of the at least one operational parameter removed.

[0013] In another implementation form of the firstaspect, the plurality of couplers comprises a plurality of couplers of a first type and a plurality of couplers of a second type.

[0014] In another implementation form of the firstaspect, an idling frequency of the plurality of couplers of the first type is configured to be greater than the first mean frequency and an idling frequency of the plurality of couplers of the second type is configured to be less than the first mean frequency.

[0015] In another implementation form of the firstaspect, the first plurality of qubits comprises transmon qubits and / or the second plurality of qubits comprises transmon qubits.

[0016] According to a second aspect, a quantum compu-ting system comprises the arrangement according to the first aspect.

[0017] According to a third aspect, a method for de-signing an arrangement for quantum computing, wherein the arrangement comprises a first plurality of qubits, wherein a qubit frequency of each qubit in the first plurality of qubits is configured according to a first mean frequency, a second plurality of qubits, wherein a qubit frequency of each qubit in the second plurality of qubits is configured according to a second mean fre- quency, different from the first mean frequency, and a plurality of couplers, wherein each coupler in the plu- rality of couplers is configured to couple a qubit in the first plurality of qubits to a qubit in the second plurality of qubits, comprises varying at least one op- erational parameter of the arrangement around a mean value over the arrangement according to a designed dis- order, wherein the at least one operational parameter affects at least one of: the first plurality of qubits,the second plurality of qubits, and / or the plurality of couplers.

[0018] Many of the attendant features will be morereadily appreciated as they become better understood by reference to the following detailed description consid- ered in connection with the accompanying drawings. DESCRIPTION OF THE DRAWINGS

[0019] In the following, example embodiments are de-scribed in more detail with reference to the attached figures and drawings, in which:

[0020] Fig. 1 illustrates a schematic representationof an arrangement for quantum computing according to an embodiment;

[0021] Fig. 2 illustrates a schematic representationof qubit and coupler frequencies according to an embod- iment;

[0022] Fig. 3 illustrates a schematic representationof couplings according to an embodiment;

[0023] Fig. 4 illustrates a schematic representationof qubit and coupler frequencies according to a compar- ative example;

[0024] Fig. 5 illustrates a schematic representationof qubit and coupler frequencies according to an embod- iment;

[0025] Fig. 6 illustrates a schematic representationof qubit eigenstates according to an embodiment;

[0026] Fig. 7 illustrates a schematic representationof coupler eigenstates according to an embodiment;

[0027] Fig. 8 illustrates a schematic representationof qubit coupling according to an embodiment; and

[0028] Fig. 9 illustrates a flow chart representationof a method according to an embodiment.

[0029] In the following, like reference numerals areused to designate like parts in the accompanying draw- ings. DETAILED DESCRIPTION

[0030] In the following description, reference is madeto the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustra- tion, specific aspects in which the present disclosure may be placed. It is understood that other aspects may be utilized, and structural or logical changes may be made without departing from the scope of the present disclosure. The following detailed description, there- fore, is not to be taken in a limiting sense, as thescope of the present disclosure is defined by the ap-pended claims.

[0031] For instance, it is understood that a disclo-sure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding de- vice may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. On the other hand, for ex- ample, if a specific apparatus is described based on functional units, a corresponding method may include a step performing the described functionality, even ifsuch step is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various example aspects described herein may be combined with each other, unless specifically noted oth- erwise.

[0032] Fig. 1 illustrates a schematic representationof an arrangement for quantum computing according to an embodiment.

[0033] According to an embodiment, an arrangement 100for quantum computing comprises a first plurality ofqubits 101, wherein a qubit frequency of each qubit inthe first plurality of qubits 101 is configured accord- ing to a first mean frequency.

[0034] The arrangement 100 may further comprise a sec-ond plurality of qubits 102, wherein a qubit frequencyof each qubit in the second plurality of qubits 102 is configured according to a second mean frequency, dif- ferent from the first mean frequency.

[0035] Herein a qubit frequency may also be referredto as a qubit resonance frequency, a qubit idling fre-quency, or similar.

[0036] The arrangement may further comprise a plural-ity of couplers 103, wherein each coupler in the plu-rality of couplers is configured to couple a qubit in the first plurality of qubits 101 to a qubit in thesecond plurality of qubits 102.

[0037] Each coupler 103 may be electromagneticallycoupled to a qubit in the first plurality of qubits 101and a qubit in the second plurality of qubits 102. Theelectromagnetic coupling may comprise, for example, acapacitive coupling, an inductive coupling, a galvanic coupling, or any combination thereof.

[0038] When coupler 103 couples a qubit in the firstplurality of qubits 101 and a qubit in the second plu-rality of qubits 102, the coupled qubits can be used toperform quantum gates, such as two-qubit quantum gates.

[0039] Herein, a coupler may also be referred to as acoupling element, a tunable coupler, a tunable couplingelement, or similar.

[0040] At least one operational parameter of the ar-rangement 100 may be configured to vary around a mean value over the arrangement 100 according to a designed disorder, wherein the at least one operational parameter affects at least one of: the first plurality of qubits101, the second plurality of qubits 102, and / or theplurality of couplers 103.

[0041] Herein, the designed disorder may also be re-ferred to as an engineered disorder or similar.

[0042] The at least one operation parameter may com-prise any parameter affecting the operation of the first plurality of qubits 101, the second plurality of qubits 102, and / or the plurality of couplers 103.

[0043] In the embodiment of Fig. 1, the arrangement100 is illustrated in a lattice configuration where each qubit, that is not at the edges of the lattice, in the first plurality of qubits 101 is coupled to four qubitsin the second plurality of qubits 102 via couplers inthe plurality of couplers 103. This is only an exemplaryconfiguration and the arrangement 100 may be arranged in various other ways and comprise any number of qubits and / or couplers.

[0044] On the scale of a quantum processing unit(QPU), resonances between qubits can lead to stronger hybridization of the qubits. This can be difficult to control with local operations and can thus lead to worse one-qubit gates and two-qubits gates due to errors like population leakage.

[0045] Typically, parameters of a QPU are designedsuch that qubits and couplers are almost identical in terms of frequencies, anharmonicities, and couplings.Imperfect fabrication method can lead to random devia-tions in these parameters, but improvements in fabrica-tion methods can mitigate this disorder. However, asfabrication method improve and if the system parametersare designed to be identical, these random deviationscan be removed, which can result into worse performingdevices. Moreover, the calibration of qubit and couplerfrequencies can be very accurately using, for example, magnetic flux.

[0046] The designed disorder in the arrangement 100can remove resonances and localize the eigenstates ofthe qubits and / or of the couplers of the arrangement 100by reducing unwanted hybridization between qubits and / orbetween couplers.

[0047] According to an embodiment, the at least oneoperational parameter comprises at least one of: the qubit frequency of each qubit in the first plurality ofqubits 101; the qubit frequency of each qubit in thesecond plurality of qubits 102; a coupler frequency ofeach coupler in the plurality of couplers 103; a qubitanharmonicity of each qubit in the first plurality ofqubits 101; a qubit anharmonicity of each qubit in thesecond plurality of qubits 102; and / or a qubit couplingstrength of each coupler in the plurality of couplers 103.

[0048] Anharmonicity can affect operating frequencyin of qubits when performing two-qubit gates. Thus, dis- order in anharmonicity can also result in disorder in operating frequencies.

[0049] The qubit coupling strength of a coupler candetermine the coupling strength between the qubits and the coupler. Disorder in the coupling strengths can re-duce coupler hybridization.

[0050] For example, the qubit frequency of each qubitin the first plurality of qubits 101 may vary around the first mean frequency according to a disorder parameter. The disorder parameter may define, for example, a var- iance or a standard deviation according to which the qubit frequency of each qubit in the first plurality of qubits 101 can vary around the first mean frequency. Alternatively, the disorder parameter may define the range in which the qubit frequency of each qubit in the first plurality of qubits 101 can vary in some othermanner. The disorder parameter may also be referred toas a disorder window or similar.

[0051] The arrangement 100 may be realized, for exam-ple, in a superconducting circuit architecture. Thefirst plurality of qubits 101 may comprise supercon- ducting qubits and / or the second plurality of qubits 102 may comprise superconducting qubits.

[0052] Contrary to variance due to fabrication, var-ious aspects, such as the strength and distribution, ofthe designed disorder can be controller. Thus, the de- signed disorder can be optimized according to the re-quirements of each application. Moreover, the uncon-trolled nature of variance due to fabrication can also introduce unwanted resonances and / or hybridization.

[0053] According to an embodiment, a quantum computingsystem comprises the arrangement 100.

[0054] Fig. 2 illustrates a schematic representationof qubit and coupler frequencies according to an embod- iment.

[0055] Herein the first plurality of qubits 101 maybe referred to as qubits of group A and the second plurality of qubits 102 may be referred to as qubits of group B or vice versa.

[0056] In the embodiment of Fig. 2, the first meanfrequency 201, the second mean frequency 202, and a meancoupler frequency 203 are illustrated. Further, a firstdisorder parameter ^^211, a second disorder parameter ^^212, and a third disorder parameter ^^213 are il- lustrated. The qubit frequency of each qubit in the first plurality of qubits 101 may vary around the first mean frequency 201 according to the first disorder pa- rameter ^^211. The qubit frequency of each qubit in the second plurality of qubits 102 may vary around the sec- ond mean frequency 202 according to the second disorder parameter ^^212. The coupler frequency of each coupler in the plurality of couplers 103 may vary around the mean coupler frequency 203 according to the third dis- order parameter ^^213.

[0057] Herein, a detuning can refer to a differencebetween two frequencies. For example, the distance be- tween the first mean frequency 201 and the second meanfrequency 202 may be referred to as the detuning betweenthe first plurality of qubits 101 and the second plu- rality of qubits 102.

[0058] The detuning between the first plurality ofqubits 101 and the second plurality of qubits 102 can be, for example, approximately 200 megahertz (MHz). The anharmonicity of the of the first plurality of qubits 101 and / or the second plurality of qubits 102 can also be approximately 200 MHz.

[0059] The detuning between the first plurality ofqubits 101 and the second plurality of qubits 102 canbe, for example, in the range 100 – 800 MHz, 100 – 500MHz, 100 – 400 MHz, 100 – 300 MHz, or 150 – 250 MHz.

[0060] The first mean frequency 201 and the first dis-order parameter ^^211 can, for example, define the idling frequency of each qubit in the first plurality of qubits 101. Similarly, the second mean frequency 202 and the second disorder parameter ^^212 can define the idling frequency of each qubit in the second plurality of qubits 102.

[0061] The mean coupler frequency 203 and the thirddisorder parameter ^^213 can, for example, define the idling frequency of each coupler in the plurality of couplers 103. During idling, the detuning between the coupler and qubit frequencies can be, for example, of the order of 1 GHz. Depending on the type of the coupler, its frequency can be either higher or lower than the qubit frequencies.

[0062] During idling, the detuning between the couplerand qubit frequencies can be, for example, 0.5 GHz – 5,0.5 GHz – 3 GHz, GHz, 0.5 GHz – 2 GHz, or 0.5 GHz – 1.5GHz.

[0063] Herein, idling of a qubit may refer to a modeof operation of the qubit where the qubit is not being used for performing quantum computation, i.e. no quantum gates are being performed on the qubit. Similarly,idling of a coupler may refer to a mode of operationwhere the coupler does not cause coupling betweenqubits.

[0064] For performing quantum gates, the frequency ofa qubit in the first plurality of qubits 101 and a qubit in the second plurality of qubits 102 can be tuned to a substantially matching frequency by tuning the frequency of the qubit in the first plurality of qubits 101 and / or a qubit in the second plurality of qubits 102. Further, the frequency of the coupler between the qubits can be tuned to be closer to the frequency of the qubits.

[0065] In some embodiments, a frequency of the firstplurality of qubits 101 may be tunable via a magneticflux applied to the first plurality of qubits 101 and / ora frequency of the second plurality of qubits 102 may be tunable via a magnetic flux applied to the second plurality of qubits 102.

[0066] When a frequency of a qubit is tunable via amagnetic flux applied to the qubit, the frequency of the qubit can shift based on the applied magnetic flux.

[0067] In some embodiments, a frequency of the plu-rality of couplers 103 may be tunable via a magnetic flux applied to the plurality of couplers 103.

[0068] Fig. 3 illustrates a schematic representationof couplings according to an embodiment.

[0069] In the embodiment of Fig. 3, three qubits andtwo couplers are illustrated. Qubits Q1 and Q3 may com-prise qubits from the first plurality of qubits 101 andqubit Q2 may comprise a qubit from the second pluralityof qubits 102 or vice versa. Parameters ^ illustratedin Fig. 3 are related to the coupling strength betweenthe qubits and between the qubits and couplers. In ad-dition to couplings between qubits coupled to each other via couplers, there can also exist longer-distance cou- plings such as the one drawn between qubit Q1 and qubitQ3 in Fig. 3, which can cause problems if these qubitsare in resonance.

[0070] According to an embodiment, the first pluralityof qubits 101 comprises transmon qubits and / or the sec- ond plurality of qubits 102 comprises transmon qubits.

[0071] Although some disclosure herein may refer totransmon qubits, various other types of qubits can also be used instead.

[0072] For example, in any embodiment, the first plu-rality of qubits 101 and / or the second plurality of qubits 102 may comprise charge qubits, flux qubits, split-Cooper-pair-box charge qubits, and / or unimon qubits.

[0073] The arrangement 100 can be described by theHamiltonian operator, ^^ − ^^^where ^^ are the annihilation operators, ^^ = ^^^^^is the number operator, and ^^and ^^are the angular frequency and the anharmonicity of the ^th transmon, respectively.Parameter ^^^ =describes the coupling between^th and ^th transmon in the arrangement 100, and is de-termined by the dimensionless coupling strength ^^^which can depend linearly on the coupling capacitancebetween the two transmons. These parameters can be se- lected during the design of the arrangement 100.

[0074] According to an embodiment, the first pluralityof qubits 101 comprises transmon qubits, the second plu- rality of qubits 102 comprises transmon qubits, and the plurality of couplers 103 comprises transmon couplers.

[0075] Without the designed disorder, a typical designchoice has been to make the qubit frequencies into A-B-A-B pattern, i.e. qubits are in resonance with theirnext-nearest neighbors but not with their nearest neigh-bors. Further, the coupling strengths between the qubitsand the couplers, as well as the direct couplings be-tween the nearest-neighbor qubits have typically beendesigned to be equal. This can cause the couplers toidle in resonance with each other. According to thecurrent understanding, the computational states are theeigenstates of the system. However, this can be prob-lematic in such a symmetric system, since due to theresonances, the eigenstates can be extended. Thus, thequbits of type A and B can hybridize amongst themselves. Such eigenstates can be difficult to use as computa- tional states, since their control locally, with for example local pulses, can be challenging. Further, the couplers can hybridize with each other even morestrongly than the qubits. This can occur because thereis only a single qubit between the resonant couplers,whereas there is one qubit and two couplers between theresonant qubits.

[0076] As illustrated in Fig. 3, in addition to directcoupling only between qubits via the couplers, there canalso exist weak direct couplings between more distant qubits. Thus, the couplers can also be directly coupled to each other, as well as qubits of the same type.Accordingly, there can be direct couplings between res-onant objects, which can result in even more hybridiza-tion of the eigenstates than shown here. Despite beingweak, these couplings can hinder quantum gate fidelities especially when four nines, i.e. quantum gate fidelitiesof 0.9999, are desired. These unwanted couplings can inprinciple be mitigated by increasing the spacing betweenthe qubits and the couplers, but this may not be prac-tical in a larger QPU.

[0077] Fig. 4 illustrates a schematic representationof qubit and coupler frequencies according to a compar- ative example.

[0078] The comparative example of Fig. 4 illustratesa 9 x 9 QPU lattice. Qubits are illustrated by circles and couplers by rectangles. Angular frequencies ^^of the qubits are set in the A-B-A-B pattern, all of thecouplers idle in resonance at an angular frequency ^^,and coupling strengths are all equal. This kind of con-figuration can cause unwanted resonances and hybridiza- tion as discussed above.

[0079] Fig. 5 illustrates a schematic representationof qubit and coupler frequencies according to an embod- iment.

[0080] According to an embodiment, the designed dis-order follows a distribution.

[0081] The distribution may comprise, for example, arandom distribution, a probability distribution, or a non-random distribution.

[0082] According to an embodiment, the distributionis configured to prevent collisions of the at least one operational parameter between different parts of thearrangement 100.

[0083] Herein, a collision may mean that two compo-nents / parts of the arrangement 100 have the same value of an operational parameter.

[0084] In some embodiments, the distribution may beconfigured to prevent collisions of the at least one operational parameter between two components of the ar- rangement 100 that are closer to each other than a pre-configured threshold distance. For example, the distri-bution may be configured to prevent collisions of the at least one operational parameter, such as a qubitfrequency, between two qubits that are closer to eachother than the preconfigured threshold distance. Forexample, the distribution may be configured to prevent collisions of the at least one operational parameter, such as a coupler frequency, between two couplers that are closer to each other than the preconfigured thresh- old distance.

[0085] According to an embodiment, the designed dis-order follows a quasiperiodic distribution.

[0086] The quasiperiodic distribution may also be re-ferred to as a quasiperiodic function or similar.

[0087] According to an embodiment, the at least oneoperational parameter of the arrangement is configured to vary over the arrangement according to the quasiperi- odic distribution based at least on a location in the arrangement, an irrational number, and at least one pe- riodic function.

[0088] For example, the quasiperiodic distributionmay be a function of a location in the arrangement 100. For example, the quasiperiodic distribution may be used to calculate the at least one operational parameter for a component, such as qubit or a coupler, of the arrange- ment 100 based on the location of the component in the arrangement 100.

[0089] In order to avoid random frequency collisionsin the arrangement 100, it may be advantageous to have a deterministic way of generating distributed frequen- cies around a mean value. An example of such distribu- tion is the quasiperiodic distribution where the fre- quency is given bywhere ^^and ^^are integers giving the location of the^th qubit of type A in the arrangement 100, ^ is thedisorder parameter, ^ is an irrational number, and ^^is the mean frequency of the qubits of type A, such as the first mean frequency or the second mean frequency.The irrational number ^ may comprise, for example, thegolden ratio, ^ = . Disorder for any other opera-tional parameter, such as the coupling strengths and / orqubit anharmonicities, can be obtained in a similarfashion. For example, an operational parameter Ω for acomponent ^ may be obtained asΩ^ = Ω^^^^^cos^2^^^^ + ^^^^^ + cos^4^^^^^^,where Ω^^^^is the mean value of the operational param- eter, ^^is the disorder parameter of the operation pa- rameter and other parameters are as discussed above.

[0090] The coupling strengths can depend on both thequbit frequencies and capacitances. Thus, the disorderin the qubit frequencies can also introduce disorderalso to the coupling strengths. This can be furtherenhanced by making also the capacitances disordered.Quasiperiodicity can ensure that there is no repeating patterns in the parameters, which could in large scale result in symmetry and thus delocalization in the ei- genstates.

[0091] According to an embodiment, the designed dis-order follows a preconfigured probability distribution.

[0092] According to an embodiment, the designed dis-order over the arrangement follows a preconfigured prob- ability distribution with colliding values of the at least one operational parameter removed.

[0093] For example, the preconfigured probabilitydistribution may comprise a Gaussian distribution.

[0094] Removal of the colliding values can be achievedby, for example, when generating an operational param-eter value for a component, generating the operationalparameter value for the component using the probabilitydistribution, checking whether the generated value col- lides with a previously generated value, and in responseto the generated value colliding with a previously gen- erated value, generating a new operational parametervalue for the component using the probability distribu-tion. If the generated value does not collide with anypreviously generated value, the generated value can be kept and operational parameter values can be generated for remaining components in a similar fashion.

[0095] In some embodiments, different distributionscan be used for different components of the arrangement100. For example, in some embodiments, a different qua-siperiodic distribution may be used for each component type. Furthermore, in some embodiments, a probability distribution may be used for some components, such as qubits, or subsets of components, such as the firstplurality of qubits 101 and / or the second plurality ofqubits 102, and a quasiperiodic distribution can be used for other components, such as couplers, or vice versa.

[0096] For example, the coupling strengths can bedrawn from a Gaussian distribution with a standard de-viation of 10% from the mean coupling strength. Thecouplers may still couple to their neighboring qubitswith an equal magnitude. Similarly, the qubit frequen-cies can be distributed randomly around the first / secondmean frequency.

[0097] Fig. 5 illustrates an embodiment in which cou-pling strengths follow a Gaussian distribution. Qubitangular frequencies ^^are disordered around the first and second mean frequency by using the quasiperiodic pattern from the equation above. As a result, also the idling angular frequencies ^^of the couplers becomedisordered. The disorder window of the disorder param- eter used here is 25 megahertz.

[0098] Fig. 6 illustrates a schematic representationof qubit eigenstates according to an embodiment.

[0099] Fig. 6 illustrates the qubit eigenstates whenthe qubit frequencies and the coupling strengths com-prise designed disorder in a manner disclosed above. Thequbit eigenstates now become well localized, mostly hy- bridizing with their neighboring tunable couplers. This hybridization between qubits and couplers can be reduced further by increasing the idling detuning of the qubits and the couplers. Such states can be easier to control with local operations.

[0100] Fig. 7 illustrates a schematic representationof coupler eigenstates according to an embodiment.

[0101] Fig. 7 illustrates the coupler eigenstates whenthe qubit frequencies and the coupling strengths are distributed according to Gaussian distributions as dis- cussed above. The coupler states are still somewhat ex- tended. Since these states are not used in quantumgates, they may not affect quantum computation, but theycan become temporarily excited during two-qubit gates.

[0102] According to an embodiment, the plurality ofcouplers 103 comprises a plurality of couplers of a first type and a plurality of couplers of a second type.

[0103] Using different types of couplers can furtherreduce the hybridization between the couplers. For ex-ample, in some embodiments, every other coupler can com-prise a coupler of the first type and every other couplercan comprise a coupler of the second type.

[0104] According to an embodiment, an idling frequencyof the plurality of couplers of the first type is con- figured to be greater than the first mean frequency and an idling frequency of the plurality of couplers of the second type is configured to be less than the first mean frequency.

[0105] For example, the plurality of couplers of thefirst type can idle at a frequency above the frequencies of the qubits and the plurality of couplers of the second type can idle at a frequency below the frequencies of the qubits.

[0106] For example, in some embodiments, the pluralityof couplers of the first type may comprise single-island couplers and the plurality of couplers of the second type may comprise two-island couplers or vice versa. In other embodiments, the couplers may be implemented using some other coupler type.

[0107] According to an embodiment, the plurality ofcouplers of the first type and the plurality of couplers of the second type are alternated between adjacent cou- plers in the arrangement 100.

[0108] Fig. 8 illustrates a schematic representationof qubit coupling according to an embodiment.

[0109] In the embodiment of Fig. 8, the coupler 103comprises a two-island coupler comprising a supercon-ducting quantum interference device (SQUID) loop 301comprising a first Josephson junction 302 and a second Josephson junction 303.

[0110] Herein, a SQUID loop may also be referred toas a SQUID or similar.

[0111] Although some embodiments disclose herein mayillustrate SQUID loops comprising two Josephson junc- tions, a SQUID loop may also comprise a different number of Josephson junctions.

[0112] Although the embodiment of Fig. 8 illustratesa two-island coupler as the coupler, the coupler can also be implemented in various other ways, such as those disclosed herein.

[0113] In the embodiment of Fig. 8, a first qubit 101comprises a first transmon qubit and a second qubit 102comprise a second transmon qubit. The second qubit 102comprises a SQUID loop 420 comprising a third Josephson 412 junction and a fourth Josephson junction 422. The first qubit 101 comprises a SQUID loop 410 comprising a fifth Josephson junction 411 and a sixth Josephson junction 412.

[0114] The first qubit 101 and the second qubit 102are coupled to each other via a capacitor ^^^501 andindirectly coupled to each other via the coupler 103.

[0115] The coupler 103 comprises a first supercon-ducting island 511 and a second superconducting island512 which are both ungrounded. The first superconductingisland 511 and the second superconducting island 512 arearranged such that each of them is directly coupled onlyto one of the first qubit 101 and the second qubit 102.More specifically, there is a first non-galvanic cou-pling between the first qubit 101 and the first super-conducting island 511 and a second non-galvanic couplingbetween the second qubit 102 and the second supercon-ducting island 512. The first and second non-galvaniccouplings are both capacitive implemented via capacitors^^^502 and ^^^503, respectively. However, in some other embodiments, at least one of the first non-galvanic cou- pling, the second non-galvanic coupling, and the directcoupling between the first and second qubits 101 and 102may be inductive, if required and depending on the par- ticular application. Moreover, in some other embodi- ments, the direct coupling itself may be implemented as a galvanic coupling, and at least one of the first non- galvanic coupling and the second non-galvanic coupling may be replaced with a galvanic coupling.

[0116] The first superconducting island 511 and thesecond superconducting island 512 are coupled to eachother via Josephson junctions 302, 303. Thus, the indi-rect coupling between the first qubit 101 and the secondqubit 102 comprises the above-mentioned first non-gal-vanic coupling, Josephson coupling, and second non-gal- vanic coupling.

[0117] As can be seen in FIG. 8, the arrangement areaof the first superconducting island 511 is confined byone plate of the capacitor ^^^502, one plate of a ca-pacitor ^^ 504, and the two Josephson junction 302, 303.As for the second superconducting island 512, its ar- rangement area is confined by one plate of the capacitor ^^^503, another plate of the capacitor ^^504, and thetwo Josephson junctions 302, 303. Such arrangements ofthe first superconducting island 511 and the second su-perconducting island 512 are given by way of exampleonly. In some other embodiments, the first supercon-ducting island 511 and the second superconducting island512 may be arranged such that the indirect couplingbetween the first and second qubit 101, 102 comprisesan additional third (galvanic or non-galvanic) couplingbetween the second qubit 102 and the first supercon-ducting island 511 and an additional fourth (galvanicor non-galvanic) coupling between the first qubit 101and the second superconducting island 512. Again, the third and fourth couplings may be capacitive or induc- tive, if required and depending on particular applica- tions. By using these additional couplings, it is pos- sible to increase the applicability and flexibility ofthe arrangement 100. Additionally, one or both of thesuperconducting islands 511 and 512 may also have acoupling to the ground via additional capacitors.

[0118] Fig. 9 illustrates a flow chart representationof a method according to an embodiment.

[0119] According to an embodiment, a method 900 fordesigning an arrangement for quantum computing, wherein the arrangement comprises a first plurality of qubits, wherein a qubit frequency of each qubit in the first plurality of qubits is configured according to a firstmean frequency, a second plurality of qubits, wherein aqubit frequency of each qubit in the second plurality of qubits is configured according to a second mean fre- quency, different from the first mean frequency, and a plurality of couplers, wherein each coupler in the plu- rality of couplers is configured to couple a qubit in the first plurality of qubits to a qubit in the second plurality of qubits, comprises: varying 901 at least one operational parameter of the arrangement around a mean value over the arrangement according to a designed dis- order, wherein the at least one operational parameter affects at least one of: the first plurality of qubits,the second plurality of qubits, and / or the plurality of couplers.

[0120] The method 900 may comprise any feature of thearrangement 100 disclosed herein.

[0121] According to an embodiment, the varying 901 theat least one operational parameter of the arrangement around a mean value over the arrangement according to a designed disorder comprises varying 901 the at least one operational parameter according to a distribution.

[0122] According to an embodiment, the distributionis configured to prevent collisions of the at least one operational parameter between different parts of the arrangement.

[0123] According to an embodiment, the designed dis-order follows a quasiperiodic distribution.

[0124] According to an embodiment, the varying 901 theat least one operational parameter of the arrangementaround the mean value over the arrangement according tothe designed disorder comprises varying the at least oneoperational parameter of the arrangement over the ar- rangement according to the quasiperiodic distribution based at least on a location in the arrangement, an irrational number, and at least one periodic function.

[0125] According to an embodiment, the designed dis-order follows a preconfigured probability distribution.

[0126] According to an embodiment, the varying 901 atleast one operational parameter of the arrangementaround the mean value over the arrangement according tothe designed disorder comprises the varying the at least one operational parameter of the arrangement around themean value over the arrangement according to the pre- configured probability distribution and removing col- liding values of the at least one operational parameter.

[0127] Any range or device value given herein may beextended or altered without losing the effect sought. Also any embodiment may be combined with another embod- iment unless explicitly disallowed.

[0128] Although the subject matter has been describedin language specific to structural features and / or acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as examples of implementing the claims and other equiv- alent features and acts are intended to be within the scope of the claims.

[0129] It will be understood that the benefits andadvantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will further be un- derstood that reference to 'an' item may refer to one or more of those items.

[0130] The steps of the methods described herein maybe carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter de- scribed herein. Aspects of any of the embodiments de- scribed above may be combined with aspects of any of theother embodiments described to form further embodiments without losing the effect sought.

[0131] The term 'comprising' is used herein to meanincluding the method, blocks or elements identified, but that such blocks or elements do not comprise an exclu- sive list and a method or apparatus may contain addi- tional blocks or elements.

[0132] It will be understood that the above descrip-tion is given by way of example only and that various modifications may be made by those skilled in the art. The above specification, examples and data provide a complete description of the structure and use of exem- plary embodiments. Although various embodiments have been described above with a certain degree of particu- larity, or with reference to one or more individual embodiments, those skilled in the art could make numer- ous alterations to the disclosed embodiments without departing from the spirit or scope of this specifica- tion.

Claims

CLAIMS:

1. An arrangement (100) for quantum compu-ting, the arrangement (100) comprising: afirst plurality of qubits (101), wherein aqubit frequency of each qubit in the first plurality ofqubits (101) is configured according to a first meanfrequency; asecond plurality of qubits (102), wherein aqubit frequency of each qubit in the second pluralityof qubits (102) is configured according to a second meanfrequency, different from the first mean frequency; and aplurality of couplers (103), wherein eachcoupler in the plurality of couplers (103) is configuredto couple a qubit in the first plurality of qubits (101)to a qubit in the second plurality of qubits (102);wherein at least one operational parameter of the arrangement (100) is configured to vary around amean value over the arrangement (100) according to adesigned disorder, wherein the at least one operational parameter affects at least one of: the first pluralityof qubits (101), the second plurality of qubits (102),and / or the plurality of couplers (103).

2. The arrangement (100) according to claim 1,wherein the at least one operational parameter comprises at least one of: the qubit frequency of each qubit in the first plurality of qubits; the qubit frequency of each qubit in the sec- ond plurality of qubits;a coupler frequency of each coupler in the plurality of couplers; a qubit anharmonicity of each qubit in the first plurality of qubits; a qubit anharmonicity of each qubit in the second plurality of qubits; and / or a qubit coupling strength of each coupler in the plurality of couplers.

3. The arrangement (100) according to claim 1or claim 2, wherein the designed disorder follows a distribution.

4. The arrangement (100) according to claim 3,wherein the distribution is configured to prevent col- lisions of the at least one operational parameter be- tween different parts of the arrangement.

5. The arrangement (100) according to any pre-ceding claim, wherein the designed disorder follows a quasiperiodic distribution.

6. The arrangement (100) according to claim 5,wherein the at least one operational parameter of the arrangement (100) is configured to vary over the ar- rangement (100) according to the quasiperiodic distri- bution based at least on a location in the arrangement, an irrational number, and at least one periodic func- tion.

7. The arrangement (100) according to any ofclaims 1 - 4, wherein the designed disorder follows apreconfigured probability distribution.

8. The arrangement (100) according to any ofclaims 1 - 4, wherein the designed disorder over thearrangement (100) follows a preconfigured probability distribution with colliding values of the at least one operational parameter removed.

9. The arrangement (100) according to any pre-ceding claim, wherein the plurality of couplers (103) comprises a plurality of couplers of a first type and a plurality of couplers of a second type.

10. The arrangement (100) according to claim9, wherein an idling frequency of the plurality of cou- plers of the first type is configured to be greater than the first mean frequency and an idling frequency of the plurality of couplers of the second type is configured to be less than the first mean frequency.

11. The arrangement (100) according to anypreceding claim, wherein the first plurality of qubits (101) comprises transmon qubits and / or the second plu- rality of qubits (102) comprises transmon qubits.

12. A quantum computing system comprising thearrangement (100) according to any preceding claim.

13. A method (900) for designing an arrange-ment for quantum computing, wherein the arrangement com- prises a first plurality of qubits, wherein a qubit frequency of each qubit in the first plurality of qubits is configured according to a first mean frequency, a second plurality of qubits, wherein a qubit frequency of each qubit in the second plurality of qubits is con- figured according to a second mean frequency, different from the first mean frequency, and a plurality of cou- plers, wherein each coupler in the plurality of couplers is configured to couple a qubit in the first plurality of qubits to a qubit in the second plurality of qubits, wherein the method comprises varying (901) at least one operational parameter of the arrangement around a mean value over the arrangement according to a designed dis- order, wherein the at least one operational parameter affects at least one of: the first plurality of qubits, the second plurality of qubits, and / or the plurality of couplers.

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