Arrangement for quantum computing

Abstract

According to an embodiment, an arrangement for quantum computing comprises: a first qubit; a second qubit, wherein a frequency of the second qubit is tunable via a magnetic flux applied to the second qubit; a tunable coupling element for coupling the first qubit and the second qubit, wherein a frequency of the tunable coupling element is tunable via a magnetic flux applied to the tunable coupling element and a coupling between the first qubit and the second qubit is tunable at least via the frequency of the second qubit and the frequency of the tunable coupling element; wherein the second qubit has a lower sweet spot corresponding to a lower stationary point of the frequency of the second qubit with respect to the magnetic flux applied to the second qubit; the tunable coupling element has a lower sweet spot corresponding to a lower stationary point of the frequency of the tunable coupling element with respect to the magnetic flux applied to the tunable coupling element; and a frequency of the lower sweet spot of the tunable coupling element is lower than a frequency of the lower sweet spot of the second qubit.

Description

ARRANGEMENT FOR QUANTUM COMPUTINGTECHNICAL FIELD

[0001] The present disclosure relates to a quantum computing, and more particularly to an arrangement for quantum computing, a use of the arrangement , and a quantum computing system .BACKGROUND

[0002] In current implementations quantum computing, qubits need to be cooled to cryogenic temperatures in order to minimi ze errors in the computation caused by heat . Therefore , it is typically desirable to minimi ze any heat sources in a quantum computing arrangement .SUMMARY

[0003] This summary is provided to introduce a selection of concepts in a s implif ied form that are further described below in the detailed description . This summary is not intended to identify key features or essential features of the claimed subj ect matter, nor is it intended to be used to limit the scope of the claimed subj ect matter .

[0004] It is an obj ective to provide an arrangement for quantum computing, a use of the arrangement , and a quantum computing system . The foregoing and other obj ectives are achieved by the features of the independent claims . Further implementation forms are apparent from the dependent claims , the description and the figures .

[0005] According to a first aspect , an arrangement for quantum computing comprises : a first qubit ; a second qubit , wherein a frequency of the second qubit is tunable via a magnetic flux applied to the second qubit ; a tunable coupling element for coupling the first qubit and the second qubit , wherein a frequency of the tunable coupling element is tunable via a magnetic flux applied to the tunable coupl ing element and a coupling between the first qubit and the second qubit is tunable at least via the frequency of the second qubit and the frequency of the tunable coupl ing element ; wherein the second qubit has a lower sweet spot corresponding to a lower stationary point of the frequency of the second qubit with respect to the magnetic flux applied to the second qubit ; the tunable coupling element has a lower sweet spot corresponding to a lower stationary point of the frequency of the tunable coupling element with respect to the magnetic flux applied to the tunable coupling element ; and a frequency of the lower sweet spot of the tunable coupling element is lower than a frequency of the lower sweet spot of the second qubit .

[0006] In an implementation form of the first aspect , the tunable coupling element further has a higher sweet spot corresponding to a higher stationary point of the frequency of the tunable coupling element with respect to the magnetic flux applied to the tunable coupling element , a frequency of the higher sweet spot of the tunable coupling element is higher that the frequency of the lower sweet spot of the tunable coupling element , and the frequency of the higher sweet spot of the tunablecoupling element is higher or equal to the frequency of the lower sweet spot of the second qubit .

[0007] In another implementation form of the first aspect , a magnetic flux appl ied to the second qubit at the lower sweep spot of the second qubit is substantially equal to a magnetic flux appl ied to the tunable coupling element at the lower sweep spot of the tunable coupling element .

[0008] In another implementation form of the first aspect , the f irst qubit comprises a data qubit and the second qubit comprise an anci lla qubit or the first qubit comprises an ancilla qubit and the second qubit comprise a data qubit .

[0009] In another implementation form of the first aspect , the tunable coupling element comprises a superconducting quantum interference device , SQUID, loop comprising a first Josephson j unction and a second Josephson j unction, wherein a critical current of the first Josephson j unction is different from a critical current of the second Josephson j unction .

[0010] In another implementation form of the first aspect , the second qubit comprises a superconducting quantum interference device , SQUID, loop comprising a third Josephson j unction and a fourth Josephson j unction, wherein a critical current of the third Josephson j unction is different from a critical current of the fourth Josephson j unction .

[0011] In another implementation form of the first aspect , the arrangement further comprises a readout resonator, wherein a frequency of the readout resonator ishigher that the frequency of the lower sweet spot of the second qubit .

[0012] In another implementation form of the first aspect , the tunable coupling element comprises a splitisland coupler .

[0013] In another implementation form of the first aspect , the first qubit comprises a transmon qubit and / or the second qubit comprises a transmon qubit .

[0014] In another implementation form of the first aspect , the arrangement further comprises a global magnetic flux source configured to provide a global magnetic flux at least to the second qubit and to the tunable coupling element wherein the global magnetic flux is configured to cause the second qubit to idle substantially at the lower sweet spot of the second qubit .

[0015] In another implementation form of the first aspect , the global magnetic flux is configured to cause the tunable coupling element to idle substantially at the lower sweet spot of the tunable coupling element .

[0016] In another implementation form of the first aspect , the arrangement further comprises a first local magnetic flux source configured to provide a local magnetic flux to the tunable coupling element .

[0017] In another implementation form of the first aspect , the arrangement further comprise a second local magnetic flux source configured to provide a local magnetic flux to the second qubit .

[0018] In another implementation form of the first aspect , the arrangement further comprises a control unit configured to : apply a global magnetic flux to at leastto the second qubit and to the tunable coupling element , wherein the global magnetic flux is configured to cause the tunable coupling element to idle substantially at the lower sweet spot of the tunable coupling element and cause the second qubit to idle substantially at the lower sweet spot of the second qubit ; and perform a two- qubit gate by applying a local magnetic flux at least to the tunable coupling element , wherein the local magnetic flux is configured to cause coupl ing between the first qubit and the second qubit by shifting the frequency of the tunable coupling element .

[0019] According to a second aspect , the arrangement according to the first aspect is used for quantum error correction .

[0020] According to a third aspect , a quantum computing system comprises the arrangement according to the first aspect .

[0021] Many of the attendant features wil l be more readily appreciated as they become better understood by reference to the following detailed description considered in connection with the accompanying drawings .DESCRIPTION OF THE DRAWINGS

[0022] In the following, example embodiments are described in more detail with reference to the attached figures and drawings , in which :

[0023] Fig . 1 illustrates a schematic representation of an arrangement for quantum computing according to an embodiment ;

[0024] Fig . 2 illustrates a plot representation of frequencies as functions of a magnetic flux bias according to an embodiment ;

[0025] Fig . 3 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment ;

[0026] Fig . 4 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment ;

[0027] Fig . 5 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment ;

[0028] Fig . 6 illustrates a schematic representation of a control unit according to another embodiment ;

[0029] Fig . 7 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment ; and

[0030] Fig . 8 illustrates a plot representation of simulation results according to an embodiment .

[0031] In the following, like reference numerals are used to designate like parts in the accompanying draw- rngs .DETAILED DESCRIPTION

[0032] In the following description, reference is made to the accompanying drawings , which form part of the disclosure , and in which are shown, by way of illustration, specific aspects in which the present disclosure may be placed . It is understood that other aspects may be utili zed, and structural or logical changes may bemade without departing from the scope of the present disclosure . The following detailed description, therefore , is not to be taken in a limiting sense , as the scope of the present disclosure is defined by the appended claims .

[0033] For instance , it is understood that a disclosure 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 device may include a unit to perform the described method step, even if such unit is not explicitly described or il lustrated in the f igures . On the other hand, for example , if a specific apparatus is described based on functional units , a corresponding method may include a step performing the described functionality, even if such 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 otherwise .

[0034] Fig . 1 illustrates a schematic representation of an arrangement for quantum computing according to an embodiment .

[0035] According to an embodiment , an arrangement 100 for quantum computing comprises a first qubit 101 and a second qubit 102 , wherein a frequency of the second qubit is tunable via a magnetic flux applied to the second qubit 102 .

[0036] Herein a frequency of a qubit may also be referred to as a qubit frequency, a qubit resonance frequency, or similar .

[0037] In some embodiments , a frequency of the first qubit 101 may be tunable via a magnetic flux applied to the first qubit 101 .

[0038] When a frequency of a qubit is tunable via a magnetic flux applied to qubit , the frequency of the qubit can shift based on the applied magnetic flux .

[0039] The arrangement 100 may further comprise a tunable coupling element 103 for coupling the first qubit101 and the second qubit 102 .

[0040] The tunable coupling element 103 may be elec- tromagnetically coupled to the f irst qubit 101 and the second qubit 102 . The electromagnetic coupling may comprise , for example , a capacitive coupling, an inductive coupling, a galvanic coupling, or any combination thereof .

[0041] When the tunable coupling element 103 couples the first qubit 101 and the second qubit 102 , the first qubit 101 and the second qubit 102 can be used to perform quantum gates , such as two-qubit quantum gates .

[0042] A frequency of the tunable coupling element 103 may be tunable via a magnetic flux applied to the tunable coupling element 103 and a coupling between the first qubit 101 and the second qubit 102 may be tunable at least via the frequency of the second qubit 102 and the frequency of the tunable coupling element 103 .

[0043] For example , the first qubit 101 and the qubit102 can be coupled by tuning the frequencies of thetunable coupling element 103 and of the second qubit 102 close to the frequency of the first qubit 101 .

[0044] The second qubit 102 may have a lower sweet spot corresponding to a lower stationary point of the frequency of the second qubit 102 with respect to the magnetic flux applied to the second qubit .

[0045] Herein, a stationary point of a frequency with respect to a magnetic flux may refer to a point at which a derivative of the frequency with respect to the magnetic flux is zero .

[0046] Herein, a sweet spot may refer to a range around stationary point . For example , if the stationary point corresponds to a magnetic flux Q, the sweet spot may comprise the range 0.9Q — 1.1Q, the range 0.95Q — 1.05Q, or the range 0.99Q — 1.01Q . Correspondingly, if the stationary point corresponds to a frequency f , the sweet spot may comprise the range 0.9 / — 1.1 / , the range 0.95 / — 1.05 / , or the range 0.99 / — 1.01 / .

[0047] Herein, a lower stationary point may correspond to a local minimum of a frequency with respect to a magnetic flux .

[0048] The tunable coupling element 103 may have a lower sweet spot corresponding to a lower stationary point of the frequency of the tunable coupling element 103 with respect to the magnetic flux applied to the tunable coupling element 103 .

[0049] A frequency of the lower sweet spot of the tunable coupling element 103 may be lower than a frequency of the lower sweet spot of the second qubit 102 .

[0050] The arrangement 100 may be reali zed, for example , in a superconducting circuit architecture .

[0051] Fig . 2 illustrates a plot representation of frequencies as functions of a magnetic flux bias according to an embodiment .

[0052] In the embodiment of Fig . 2 , the x axis is referred to as a global flux bias measured in volts . This refers to the voltage that generates a global magnetic flux applied to the first qubit 101 , the second qubit 102 , and the tunable coupling element 103 .

[0053] In the embodiment of Fig . 2 , curve 211 correspond to the frequency of the first qubit 101 , curve 212 corresponds to the frequency of the second qubit 102 , curve 213 corresponds to the frequency of the tunable coupling element 103 , and curve 214 corresponds to the transition frequency between the first excited state and the second excited state of the second qubit 102 . This transition can be used for making a conditional phase gate used as a two-qubit gate . The second qubit 102 has a lower sweet spot 201 corresponding to a lower stationary point of the frequency of the second qubit 102 with respect to the magnetic flux applied to the second qubit 102 . The tunable coupling element 103 has a lower sweet spot 202 corresponding to a lower stationary point of the frequency of the tunable coupling element 103 with respect to the magnetic flux appl ied to the tunable coupling element 103 .

[0054] According to an embodiment , a magnetic flux applied to the second qubit 102 at the lower sweep spot 201 of the second qubit 102 is substantially equal to a magnetic flux applied to the tunable coupling element103 at the lower sweep spot 202 of the tunable coupling element 103 .

[0055] For example , in the embodiment of Fig . 2 , a magnetic flux applied to the second qubit 102 at the lower sweep spot 201 of the second qubit 102 is substantially equal to a magnetic flux applied to the tunable coupling element 103 at the lower sweep spot 202 of the tunable coupling element 103 .

[0056] Herein when two magnetic fluxes are substantially equal , a difference between the magnetic fluxes may be , for example , less than 15% , less than 10 % , less than 5% , or less than 1 % .

[0057] According to an embodiment , the tunable coupling element 103 further has a higher sweet spot 203 corresponding to a higher stationary point of the frequency of the tunable coupling element 103 with respect to the magnetic flux applied to the tunable coupling element 103 , a frequency of the higher sweet spot 203 of the tunable coupling element 103 is higher that the frequency of the lower sweet spot 202 of the tunable coupling element 103 , and the frequency of the higher sweet spot 203 of the tunable coupl ing element 103 is higher or equal to the frequency of the lower sweet spot 201 of the second qubit 102 .

[0058] Herein, a higher stationary point may correspond to a local maximum of a frequency with respect to a magnetic flux .

[0059] Herein when two frequencies are substantially equal , a difference between the frequencies may be , for example, less than 15% , less than 10 % , less than 5% , or less than 1 % .

[0060] For example , in the embodiment of Fig . 2 , the tunable coupling element 103 has a higher sweet spot 203 corresponding to a higher stationary point of the frequency of the tunable coupling element 103 with respect to the magnetic flux applied to the tunable coupling element 103 . A frequency of the higher sweet spot 203 of the tunable coupl ing element 103 is higher that the frequency of the lower sweet spot 202 of the tunable coupling element 103 and the frequency of the higher sweet spot 203 of the tunable coupl ing element 103 is substantially equal to the frequency of the lower sweet spot 201 of the second qubit 102 .

[0061] By having the higher sweet spot 203 of the tunable coupling element 103 higher or equal to the frequency of the lower sweet spot 201 of the second qubit 102 , the frequency of the tunable coupling element 103 can be tuned to be substantially equal to the frequency of the second qubit 201 by applying an appropriate magnetic flux to the tunable coupling element 103 and / or to the second qubit 102 . For example , the tunable coupling element 103 can be tuned to point 206 , the second qubit 102 can be tuned to point 207 , and the first qubit 101 can be tuned to point 208 for performing quantum gates , such as two-qubit gates , using the first qubit 101 and the second qubit 102 . In some embodiments , the first qubit 101 may not be tunable or may be only weakly tunable .

[0062] Since the derivative of the frequency with respect to the magnetic flux is zero at the stationary points , the frequency is not sensitive to changes in the magnetic flux at the sweet spots .

[0063] By performing quantum gates close to the sweet spot 201 of the second qubit 102 , fidelity of the quantum gates may be improved .

[0064] In some embodiments , the first qubit 101 may not be strongly tunable via a magnetic flux appl ied to the f irst qubit 101 . For example , in the embodiment of Fig . 2 , the first qubit 101 is not strongly tunable , since the frequency of the first qubit 101 does not strongly change as a function of the magnetic flux applies to the first qubit 101 . In other embodiments , the first qubit 101 may be tunable via a magnetic f lux appl ied to the first qubit 101 . In some embodiments , the first qubit 101 may be weakly tunable via a magnetic flux applied to the first qubit 101 . In such embodiments , the magnetic flux may be used to , for example , tune the frequency of the first qubit 101 to an appropriate frequency to compensate for manufacturing variance .

[0065] According to an embodiment , the arrangement further comprises a readout resonator, wherein a frequency of the readout resonator is higher that the frequency of the lower sweet spot of the second qubit .

[0066] For example , in the embodiment of Fig . 2 , curve 215 corresponds to a frequency of a f irst readout res onator and curve 216 corresponds to a frequency of a second readout resonator .

[0067] A readout can be performed on the second qubit 102 using the second readout resonator by tuning the frequency of the second qubit closer to the frequency of the second readout resonator . With a reduced frequency difference between the frequency of the secondreadout resonator and the second qubit 102 , the readout rate of the qubit readout can be increased .

[0068] For example , in the embodiment of Fig . 2 , the second qubit 102 further has a higher sweet spot 205 corresponding to a higher stationary point of the frequency of the second qubit 102 with respect to the magnetic flux applied to the second qubit 102 . The frequency of the second qubit 102 can be tuned to be close to the higher sweet spot 205 , such as to point 209 , for qubit readout .

[0069] Although in the embodiment of Fig . 2 , the frequency of the higher sweet spot 205 of the second qubit 102 is less than the frequency of the second readout resonator, in other embodiments , the frequency of the higher sweet spot 205 of the second qubit 102 may be equal to or greater than the frequency of the second readout resonator . In such embodiments , the frequency of the second qubit 102 may be tuned to substantially match with the frequency of the second readout resonator in order to perform, for example , qubit reset and readout on the second qubit 102 .

[0070] Any disclosure herein in relation to the second readout resonator and the second qubit 102 may also apply to the first readout resonator and the first qubit 101 when the frequency of the first qubit 101 is tunable .

[0071] In some embodiments , the first qubit 101 may be insensitive to magnetic flux and used as a data qubit The second qubit 102 may be used as an ancilla qubit . The ancilla qubit may be read out quickly by tuning the frequency of the ancilla qubit close to the frequency of the corresponding readout resonator .

[0072] Fig . 3 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment .

[0073] According to an embodiment , the tunable coupling element 103 comprises a superconducting quantum interference device ( SQUID) loop 301 comprising a first Josephson j unction 302 and a second Josephson j unction 303 , wherein a critical current of the f irst Josephson j unction 302 is different from a critical current of the second Josephson j unction 303 .

[0074] According to an embodiment , the tunable coupling element 103 comprises a split-island coupler .

[0075] For example , in the embodiment of Fig . 3 , the tunable coupling element 103 comprises a split-island coupler comprising a SQUID loop 301 comprising a first Josephson j unction 302 and a second Josephson j unction 303 .

[0076] An asymmetric tunable coupling element 103 with different critical currents for the Josephson j unctions can be used to configure the tunable coupling element 103 to have two sweet spots . This may also be referred to as an asymmetric SQUID or as an asymmetric SQUID loop . One sweet spot can be configured to be near the idling point of the tunable coupling element 103 , such as the lower sweet spot 202 , and one sweet spot can be configured to be near the quantum gate operation point , such as the higher sweet spot 203 .

[0077] Herein, a SQUID loop may also be referred to as a SQUID or similar .

[0078] Although some embodiments disclose herein may illustrate SQUID loops comprising two Josephson junctions, a SQUID loop may also comprise a different number of Josephson junctions.

[0079] According to an embodiment, the second qubit102 comprises a SQUID loop 420 comprising a third Josephson 412 junction and a fourth Josephson junction 422, wherein a critical current of the third Josephson junction 421 is different from a critical current of the fourth Josephson junction 422.

[0080] According to an embodiment, the first qubit 101 comprises a SQUID loop 410 comprising a fifth Josephson junction 411 and a sixth Josephson junction 412, wherein a critical current of the fifth Josephson junction 411 is different from a critical current of the sixth Josephson junction 412.

[0081] According to an embodiment, the first qubit 101 comprises a transmon qubit and / or the second qubit 102 comprises a transmon qubit.

[0082] In some embodiments, a magnetic flux, such as a local magnetic flux and / or a global magnetic flux may be configured to control the Josephson inductance of the SQUID loop 301, 410, 420 of the first qubit 101, of the second qubit 102, and / or of the tunable coupling element103 via controlling a magnetic flux through the SQUID loop. By controlling the Josephson inductance of the SQUID loop, a frequency of the corresponding component can be tuned. This may be referred to as flux tuning.

[0083] The sweet spots of the qubits 101, 102 and of the tunable coupling element 103 can be tuned by tuning the area of the corresponding SQUID loop 301, 410, 420.

[0084] In the embodiment of Fig . 3 , the first qubit 101 comprises a first transmon qubit and the second qubit 102 comprise a second transmon qubit . The tunable coupling element 103 comprises a split-island coupler .

[0085] The first qubit 101 and the second qubit 102 are coupled to each other via a capacitor C12501 and indirectly coupled to each other via the tunable coupling element 103 .

[0086] The tunable coupling element 103 comprises a first superconducting island 511 and a second superconducting island 512 which are both ungrounded . The first superconducting island 511 and the second superconducting island 512 are arranged such that each of them is directly coupled only to one of the first qubit 101 and the second qubit 102 . More specifically, there is a first non-galvanic coupling between the first qubit 101 and the first superconducting island 511 and a second non-galvanic coupling between the second qubit 102 and the second superconducting island 512 . The first and second non-galvanic couplings are both capacitive implemented via capacitors Clc502 and C2c503 , respectively . However, in some other embodiments , at least one of the first non-galvanic coupling, the second non-galvanic coupling, and the direct coupling between the first and second qubits 101 and 102 may be inductive , if required and depending on the particular application . Moreover, in some other embodiments , 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 .

[0087] The first superconducting island 511 and the second superconducting island 512 are coupled to each other via Josephson j unctions 302 , 303 . Thus , the indirect coupling between the first qubit 101 and the second qubit 102 comprises the above-mentioned first non-gal- vanic coupling, Josephson coupling, and second non-gal- vanic coupling .

[0088] As can be seen in FIG . 3 , the arrangement area of the first superconducting is land 511 is confined by one plate of the capacitor Clc502 , one plate of a capacitor Cc504 , and the two Josephson j unction 302 , 303 . As for the second superconducting island 512 , its arrangement area is confined by one plate of the capacitor C2c503 , another plate of the capacitor Cc504 , and the two Josephson j unctions 302 , 303 . Such arrangements of the first superconducting island 511 and the second superconducting island 512 are given by way of example only . In some other embodiments , the first superconducting island 511 and the second superconducting island 512 may be arranged such that the indirect coupl ing between the first and second qubit 101 , 102 comprises an additional third (galvanic or non-galvanic) coupling between the second qubit 102 and the first superconducting island 511 and an additional fourth (galvanic or non-galvanic) coupling between the first qubit 101 and the second superconducting island 512 . Again, the third and fourth couplings may be capacitive or inductive , if required and depending on particular applications . By using these additional couplings , it is possible to increase the applicability and flexibility of the arrangement 100 . Additionally, one or both of thesuperconducting islands 511 and 512 may also have a coupling to the ground via additional capacitors .

[0089] In some embodiments , the arrangement 100 may further comprise a first readout resonator and a second readout resonator (which are not shown in the figures ) . The first readout resonator may be configured to readout the first qubit 101 and have a first operating frequency . The second readout resonator may be configured to readout the second qubit 102 and have a second operating frequency . Each of the first operating frequency and the second operating frequency may be set a value higher than the value of the operating frequency of the tunable coupling element 103 . In this case , during the operation of the arrangement 100 , there may be no resonance between the tunable coupling element 103 and the readout resonators , which could otherwise adversely affect the operation of the arrangement 100 .

[0090] Fig . 4 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment .

[0091] According to an embodiment , the arrangement further comprises a global magnetic flux source 601 configured to provide a global magnetic flux 602 at least to the second qubit 102 and to the tunable coupling element 103 , wherein the global magnetic flux 602 is configured to cause the second qubit 102 to idle substantial ly at the lower sweet spot of the second qubit 102 .

[0092] The global magnetic flux source 601 may comprise , for example , one or more current loops configured to provide the global magnetic flux 602 . For example ,the global magnetic flux source 601 may comprise at least one persistent current loop .

[0093] Herein, a global magnetic flux 602 may refer to a magnetic flux that is arranged to be provided to multiple components , such as the second qubit 102 and to the tunable coupling element 103 . In some embodiments , the arrangement 100 may comprise any number of qubits and / or tunable coupling elements and the global magnetic flux may be applied to all of the qubits and / or tunable coupling elements .

[0094] Since the global magnetic flux 602 is conf igured to cause the second qubit 102 to idle substantially at the lower sweet spot 201 of the second qubit 102 , local magnetic flux does not need to be applied to the second qubit 102 . Therefore , heat caused by applying a local magnetic flux can be reduced and heat load of the second qubit 102 can be reduced . For example , the global magnetic flux 602 may be provided by a single external coil as the global magnetic flux source 601 or any other type of external global magnetic flux source . The external global magnetic flux source may be , for example , arranged onto a different circuit from the qubits 101 , 102 and to the tunable coupling element 103 . Thus , minimal heating may be introduced to the qubits 101 , 102 and to the tunable coupling element 103 . Typically, the arrangement 100 and the external global magnetic flux source are placed inside a cryostat since magnetic shielding of the cryostat can strongly attenuate magnetic fields from sources outside the cryostat .

[0095] According to an embodiment , the global magnetic flux 602 is configured to cause the tunable couplingelement 103 to idle substantially at the lower sweet spot 202 of the tunable coupling element 103 .

[0096] According to an embodiment , the global magnetic flux 602 is configured to cause the second qubit 102 to idle substantially at the lower sweet spot 201 of the second qubit 102 and cause the tunable coupling element 103 to idle substantially at the lower sweet spot 202 of the tunable coupling element 103 .

[0097] According to an embodiment , the global magnetic flux 602 is configured to remove the coupling between the first qubit 101 and the second qubit 102 when the tunable coupling element 103 is idling .

[0098] In many applications , the first 101 and / or second qubit 102 may be idling for a significant portion of time . Thus , reducing heat load during idling can be important .

[0099] The global magnetic flux 602 may also be able to provide more stable bias ing with less noise than a local magnetic flux provided via, for example , a flux line that supports fast flux pulsing .

[0100] Fig . 5 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment .

[0101] According to an embodiment , arrangement 100 further comprise a first local magnetic flux source 701 configured to provide a local magnetic flux 702 to the tunable coupling element 103 .

[0102] Herein, a local magnetic flux may refer to a magnetic flux that is arranged to be mainly provided to a specific component of the arrangement 100 , such as the second qubit 102 or the tunable coupling element 103 .

[0103] According to an embodiment , the arrangement further comprises a second local magnetic flux source 703 configured to provide a local magnetic flux 704 to the second qubit 102 .

[0104] The first / second magnetic flux source 701 , 703 may comprise , for example , one or more current loops configured to provide the local magnetic flux 702 , 704 . For example , the first / second local magnetic flux source 701 , 703 may comprise at least one persistent current loop .

[0105] According to an embodiment , the arrangement further comprises a control unit 705 configured to : apply a global magnetic flux 602 to at least to the second qubit 102 and to the tunable coupl ing element 103 , wherein the global magnetic flux 602 is configured to cause the tunable coupling element 103 to idle substantially at the lower sweet spot 202 of the tunable coupling element 103 and cause the second qubit 102 to idle substantially at the lower sweet spot 201 of the second qubit 102 ; and perform a two-qubit gate by applying a local magnetic flux 702 at least to the tunable coupl ing element 103 , wherein the local magnetic flux 702 i s configured to cause coupling between the first qubit 101 and the second qubit 102 by shifting the frequency of the tunable coupling element 103 .

[0106] According to an embodiment , the control unit 705 is configured to : perform a two-qubit gate by applying a local magnetic flux 702 to the tunable coupl ing element 103 and applying a local magnetic flux 704 to the second qubit 102 , wherein the local magnetic flux 702 applied to the tunable coupling element 103 and thelocal magnetic flux 704 applied to the second qubit 102 are configured to cause coupling between the first qubit 101 and the second qubit 102 by shifting the frequency of the tunable coupling element 103 and the frequency of the second qubit 102 .

[0107] For example , the control unit 705 may be elec- tromagnetically coupled to the global magnetic flux source 601 , to the first local magnetic flux source 701 , and to the second local magnetic flux source 703 .

[0108] Herein, idl ing of a qubit may refer to a mode of 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 the tunable coupling element 103 may refer to a mode of operation of the tunable coupling element 103 does not cause coupling between the first qubit 101 and the second qubit 102 .

[0109] The global magnetic flux may be utili zed for idling of the qubits 101 , 102 and of the tunable coupling element 103 . Thus , heat load of the components of the arrangement 100 during idling can be reduced .

[0110] The local magnetic fluxes can be used when the first 101 and second qubit 102 need to be coupled for performing quantum computing .[01 1 1 ] Fig . 6 illustrates a schematic representation of a control unit according to another embodiment .

[0112] The control unit 705 may comprise at least one processor 801 . The at least one proces sor 801 may comprise , for example , one or more of various processing devices , such as a co-processor, a microprocessor, a digital signal processor ( DSP) , a processing circuitrywith or without an accompanying DSP, or various other processing devices including integrated circuits such as, for example, an application specific integrated circuit (ASIC) , a field programmable gate array (FPGA) , a microprocessor unit (MCU) , a hardware accelerator, a special-purpose computer chip, or the like.

[0113] The control unit 705 may further comprise a memory 802. The memory 802 may be configured to store, for example, computer programs and the like. The memory 802 may comprise one or more volatile memory devices, one or more non-volatile memory devices, and / or a combination of one or more volatile memory devices and nonvolatile memory devices. For example, the memory 802 may be embodied as magnetic storage devices (such as hard disk drives, floppy disks, magnetic tapes, etc.) , optical magnetic storage devices, and semiconductor memories (such as mask ROM, PROM (programmable ROM) , EPROM (erasable PROM) , flash ROM, RAM (random access memory) , etc . ) .

[0114] The control unit 705 may further comprise other components. The control unit 705 may comprise, for example, an input / output bus for connecting the control unit 705 to other units / devices . Further, a user may control the control unit 705 via the input / output bus. The user may, for example, control quantum computation operations performed by the arrangement 100 via the control unit 705 and the input / output bus.

[0115] When the control unit 705 is configured to implement some functionality, some component and / or components of the control unit 705, such as the at leastone processor 801 and / or the memory 802, may be configured to implement this functionality. Furthermore, when the at least one processor 801 is configured to implement some functionality, this functionality may be implemented using program code comprised, for example, in the memory 802.

[0116] The control unit 705 may be implemented using, for example, a computer, an ASIC, a microcontroller, some other computing device, or similar.

[0117] Fig. 7 illustrates a schematic representation of an arrangement for quantum computing according to another embodiment.

[0118] The embodiment of Fig. 7 illustrates how an arrangement 100 comprising a plurality of qubits 101, 102 and a plurality of tunable coupling elements 103 can be arranged. The embodiment of Fig. 7 only illustrates an exemplary number of qubits 101, 102 and tunable coupling elements 103. In practical implementations, the arrangement 100 may comprise any number of qubits 101, 102 and tunable coupling elements 103.

[0119] According to an embodiment, the arrangement 100 comprises a plurality of first qubits 101, a plurality of second qubits 102, and a plurality of tunable coupling elements 103, wherein each qubit in the plurality of first qubits 101 is coupled to at least one qubit in the plurality of second qubits 102 via a tunable coupling element in the plurality of tunable coupling elements 103.

[0120] According to an embodiment, the first qubit 101 comprises a data qubit and the second qubit 102 comprise an ancilla qubit or the first qubit 101 comprises anancil la qubit and the second qubit 102 compri se a data qubit .

[0121] The frequency of the data qubits may need to be only slightly tunable since it may not be necessary to tune the frequency of the data qubits for qubit readout . It may be beneficial to implement the data qubits with a high SQUID asymmetry in order to minimi ze dephasing errors .

[0122] According to an embodiment , the arrangement 100 is used for quantum error correction .

[0123] For example, the plurality of first qubits 101 may be configured as data qubits for quantum error correction and the plurality of second qubits 102 may be configured as ancilla qubits for quantum error correction or the plurality of first qubits 101 may be configured as ancilla qubits for quantum error correction and the plurality of second qubits 102 may be configured as data qubits for quantum error correction .

[0124] According to an embodiment , a quantum computing system comprises the arrangement 100 .

[0125] For example , a quantum computing system may comprise any number of qubits 101 , 102 and tunable coupling elements 103 , and the first qubits 101 may be coupled to the second qubits 102 via the tunable coupling element 103 according to the arrangement 100 .

[0126] Fig . 8 illustrates a plot representation of simulation results according to an embodiment .

[0127] Curve 1001 corresponds to heating power as a function of detuning without global magnetic flux biasing and curve 1002 corresponds to heating power as a function of detuning with global magnetic flux biasing .

[0128] The detuning illustrated in Fig . 8 is defined as the difference in the qubit frequency from the frequency at the sweet spot . At zero magnetic flux bias offset in the flux dispersion curve of the qubit , the sweet spot of the qubit is reached at zero magnetic flux bias in the embodiment of Fig . 8 . A magnetic flux bias , such as the global magnetic flux, detunes the qubit away from this sweet spot and examples from the relation are given in the embodiment of Fig . 2 .

[0129] The embodiment of Fig . 8 considers a case where the heat load is given by the ohmic losses arising from the local magnetic flux, provided by an electric current , while the global magnetic flux does not cause any heat load . Therefore , with the global magnetic flux, the position on the flux dispersion of the qubit can be adj usted and around which the local magnetic flux adj ustments can be made . In the embodiment of Fig . 8 , the global magnetic flux results in a zero flux offset in the case of curve 1001 , while for curve 1002 , the qubit is detuned to close to 500 MHz away from the sweet spot . Fig . 8 illustrates how the heat load can be mitigated in such a case by the use of the global magnetic flux when there is some knowledge of the desired operation regimes for the qubits . In Fig . 8 , the flux offset , such as the one controlled by the global magnetic flux, enables a lower heat load in the regime where curve 1002 is below curve 1001 . The shape of curve 1002 is governed by the flux offset , which is controlled by the global magnetic flux .

[0130] To achieve a reduced heating power, the qubits 101 , 102 and / or the tunable coupling element 103 do notneed to idle exactly at the center of the corresponding sweet spot . For example , in the simulation illustrated in Fig . 8 the global magnetic flux biasing can introduce a benefit when curve 1002 is below curve 1001 . However, the simulation of Fig . 8 is only one example and the behavior of the heating power may change depending on the exact configuration of the arrangement 100 .

[0131] Any range or device value given herein may be extended or altered without losing the effect sought . Also any embodiment may be combined with another embodiment unless explicitly disallowed .

[0132] Although the subj ect matter has been described in language specific to structural features and / or acts , it is to be understood that the subj ect 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 equivalent features and acts are intended to be within the scope of the claims .

[0133] It will be understood that the benefits and advantages 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 benef its and advantages . It wi ll further be understood that reference to ' an ' item may refer to one or more of those items .

[0134] The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate . Additionally, individual blocks maybe deleted from any of the methods without departing from the spirit and scope of the subj ect matter described herein . Aspects of any of the embodiments described above may be combined with aspects of any of the other embodiments described to form further embodiments without losing the effect sought .

[0135] The term ' comprising ' is used herein to mean including the method, blocks or elements identified, but that such blocks or elements do not comprise an exclusive list and a method or apparatus may contain additional blocks or elements .

[0136] It will be understood that the above description is given by way of example only and that various modif ications may be made by those s kil led in the art . The above specification, examples and data provide a complete description of the structure and use of exemplary embodiments . Although various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments , those skilled in the art could make numerous alterations to the disclosed embodiments without departing from the spirit or scope of this specification .

Claims

CLAIMS :

1. An arrangement (100) for quantum computing, the arrangement (100) comprising: a first qubit (101) ; a second qubit (102) , wherein a frequency of the second qubit is tunable via a magnetic flux applied to the second qubit (102) ; a tunable coupling element (103) for coupling the first qubit (101) and the second qubit (102) , wherein a frequency of the tunable coupling element (103) is tunable via a magnetic flux applied to the tunable coupling element and a coupling between the first qubit (101) and the second qubit (102) is tunable at least via the frequency of the second qubit (102) and the frequency of the tunable coupling element (103) ; wherein the second qubit (102) has a lower sweet spot (201) corresponding to a lower stationary point of the frequency of the second qubit (102) with respect to the magnetic flux applied to the second qub i t ; the tunable coupling element (103) has a lower sweet spot (202) corresponding to a lower stationary point of the frequency of the tunable coupling element (103) with respect to the magnetic flux applied to the tunable coupling element (103) ; and a frequency of the lower sweet spot (202) of the tunable coupling element (103) is lower than a frequency of the lower sweet spot (201) of the second qubit (102) .

2. The arrangement (100) according to claim 1, wherein the tunable coupling element (103) further has a higher sweet (203) spot corresponding to a higher stationary point of the frequency of the tunable coupling element (103) with respect to the magnetic flux applied to the tunable coupling element (103) , a frequency of the higher sweet spot (203) of the tunable coupling element (103) is higher that the frequency of the lower sweet spot (202) of the tunable coupling element (103) , and the frequency of the higher sweet spot (203) of the tunable coupling element (103) is higher or equal to the frequency of the lower sweet spot (201) of the second qubit (102) .

3. The arrangement (100) according to claim 1 or claim 2, wherein a magnetic flux applied to the second qubit (102) at the lower sweep spot (201) of the second qubit (102) is substantially equal to a magnetic flux applied to the tunable coupling element (103) at the lower sweep spot (202) of the tunable coupling element (103) .

4. The arrangement (100) according to any preceding claim, wherein the first qubit (101) comprises a data qubit and the second qubit (102) comprise an an- cilla qubit or the first qubit (101) comprises an an- cilla qubit and the second qubit (102) comprise a data qubit .

5. The arrangement (100) according to any preceding claim, wherein the tunable coupling element (103)comprises a superconducting quantum interference device, SQUID, loop (301) comprising a first Josephson junction (302 and a second Josephson junction (303) , wherein a critical current of the first Josephson junction (302) is different from a critical current of the second Josephson junction (303) .

6. The arrangement (100) according to any preceding claim, wherein the second qubit (102) comprises a superconducting quantum interference device, SQUID, loop (420) comprising a third Josephson junction (421) and a fourth Josephson junction (422) , wherein a critical current of the third Josephson junction (421) is different from a critical current of the fourth Josephson junction (422) .

7. The arrangement (100) according to any preceding claim, the arrangement further comprising a readout resonator, wherein a frequency of the readout resonator is higher that the frequency of the lower sweet spot (201) of the second qubit (102) .

8. The arrangement (100) according to any preceding claim, wherein the tunable coupling element (103) comprises a split-island coupler.

9. The arrangement (100) according to any preceding claim, further comprising a global magnetic flux source (601) configured to provide a global magnetic flux (602) at least to the second qubit (102) and to thetunable coupling element (103) wherein the global magnetic flux (602) is configured to cause the second qubit(102) to idle substantially at the lower sweet spot (201) of the second qubit (102) .

10. The arrangement (100) according to claim 9, wherein the global magnetic flux (602) is configured to cause the tunable coupling element (103) to idle substantially at the lower sweet spot (202) of the tunable coupling element (103) .

11. The arrangement (100) according to any preceding claim, further comprising a first local magnetic flux source (701) configured to provide a local magnetic flux (702) to the tunable coupling element(103) .

12. The arrangement (100) according to any preceding claim, further comprising a second local magnetic flux source (703) configured to provide a local magnetic flux (704) to the second qubit (102) .

13. The arrangement (100) according to any preceding claim, further comprising a control unit (705) configured to: apply a global magnetic flux (601) to at least to the second qubit (102) and to the tunable coupling element (103) , wherein the global magnetic flux (601) is configured to cause the tunable coupling element (103) to idle substantially at the lower sweet spot (202) of the tunable coupling element (103) and causethe second qubit (102) to idle substantially at the lower sweet spot (201) of the second qubit (102) ; and perform a two-qubit gate by applying a local magnetic flux (702) at least to the tunable coupling element (103) , wherein the local magnetic flux (702) is configured to cause coupling between the first qubit (101) and the second qubit (102) by shifting the frequency of the tunable coupling element (103) .

14. Use of the arrangement (100) according to any preceding claim for quantum error correction.

15. A quantum computing system comprising the arrangement (100) according to any of claims 1 - 13.

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