Microwave circuit

Abstract

According to an embodiment, a microwave circuit for detecting electromagnetic power coupled to a second port of the microwave circuit via a first port of the microwave circuit comprises at least one Josephson junction having a non-linear mode of operation; wherein a first current and a second current is configured to flow through the at least one Josephson junction; the microwave circuit is configured to couple electromagnetic power from the first port to the first current and to couple electromagnetic power from the second port to the second current; and the at least one Josephson junction is configured to cause a coupling between the electromagnetic power coupled to the second current and a phase shift of the first current, wherein the phase shift is detectable via the first port.

Description

MICROWAVE CIRCUIT TECHNICAL FIELD

[0001] The present disclosure relates to a microwave circuit, and more particularly to a microwave circuit for detecting electromagnetic power coupled to a second port of the microwave circuit via a first port of the microwave circuit, a quantum computing arrangement, and method for reading a quantum state of a qubit. BACKGROUND

[0002] Various applications can utilise a microwave circuit that can detect electromagnetic power. Further, in many applications requiring high fidelity, such as quantum computing, it can be beneficial to be able to detect the electromagnetic power while disturbing the source of the electromagnetic power as little as possi- ble. This may be the case when, for example, reading the quantum state of a qubit. 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 a microwave cir- cuit for detecting electromagnetic power coupled to a second port of the microwave circuit via a first port of the microwave circuit. The foregoing and other ob- jectives 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, a microwave cir- cuit for detecting electromagnetic power coupled to a second port of the microwave circuit via a first port of the microwave circuit, the microwave circuit com- prising: the first port; the second port; and at least one Josephson junction having a non-linear mode of op- eration;, wherein a first current is configured to flow through the at least one Josephson junction and a second current is configured to flow through the at least one Josephson junction; the microwave circuit is configured to couple electromagnetic power from the first port to the first current and to couple electromagnetic power from the second port to the second current; and the at least one Josephson junction is configured to, when in the non-linear mode of operation, cause a coupling be- tween the electromagnetic power coupled to the second current from the second port and a phase shift of the first current, wherein the phase shift of the first current is detectable via the first port. The microwave circuit can, for example, detect electromagnetic power in the second port while minimizing electromagneticpower transfer between the first port and the second port.

[0006] In an implementation form of the first aspect, the first current comprises an asymmetric current and the second current comprises a symmetric current. The microwave circuit can, for example, reduce linear power transfer between the first port and the second port by reducing power transfer between the first current and the second current.

[0007] In another implementation form of the first aspect, the microwave circuit does not comprise a con- nection enabling linear power transfer between the sec- ond port and the first port. The microwave circuit can, for example, reduce linear power transfer between the first port and the second port while allowing the elec- tromagnetic power couple to the second port to be de- tected via the first port.

[0008] In another implementation form of the first aspect, the first current corresponds to a first reso- nance mode of the microwave circuit and the second cur- rent corresponds to a second resonance mode of the mi- crowave circuit.

[0009] In another implementation form of the first aspect, the phase shift of the first current is detect- able via the first port by transmitting a probing signal into the first port, measuring a response signal, and measuring a phase difference between the probing signal and the response signal. The microwave circuit can, for example, allow the electromagnetic power couple to thesecond port to be efficiently detected via the first port.

[0010] In another implementation form of the first aspect, the microwave circuit comprises a main loop and an electromagnetic coupling dividing the main loop into a first subloop and a second subloop, wherein the at least one Josephson junction comprises a plurality of Josephson junctions, the first subloop comprises at least one of the plurality of Josephson junctions, the second subloop comprises at least one of the plurality of Josephson junctions, the first current flows in a first rotational direction in the main loop, the second current flows in the first rotational direction in the first subloop, and the second current flows in a second rotational direction, opposite to the first rotational direction, in the second subloop. The microwave circuit can, for example, efficiently implement the first and second current while minimizing linear power transfer between the first port and the second port.

[0011] In another implementation form of the first aspect, the first port is inductively coupled to the first subloop and the second subloop, and the second port is capacitively coupled to the main loop. The mi- crowave circuit can, for example, efficiently couple the first and second port to the first and second current while minimizing linear power transfer between the first port and the second port.

[0012] In another implementation form of the first aspect, the electromagnetic coupling dividing the mainloop into the first subloop and the second subloop com- prises a capacitive coupling.

[0013] In another implementation form of the first aspect, the at least one Josephson junction functions as a non-linear inductance in the non-linear mode of operation. The microwave circuit can, for example, im- plement the coupling between the first current and the second current via the non-linear inductance.

[0014] In another implementation form of the first aspect, the non-linear inductance of the at least one Josephson junction is configured to cause the coupling between the electromagnetic power coupled to the second current from the second port and the phase shift of the first current due to the first current flowing through the at least one Josephson junction and the second cur- rent flowing through the at least one Josephson junc- tion. The microwave circuit can, for example, implement the coupling between the first current and the second current via the currents flowing through the at least one Josephson junction.

[0015] In another implementation form of the first aspect, the microwave circuit further comprises a first band-stop filter between the first port and a section of the microwave circuit comprising the first current and the second current and a second band-stop filter between the second port and the section of the microwave circuit comprising the first current and the second cur- rent. The microwave circuit can, for example, furtherreduce linear power coupling between the first port and the second port via the band-stop filters.

[0016] In another implementation form of the first aspect, an isolation between the second port and the first port is more than 40 decibels.

[0017] According to a second aspect, a quantum compu- ting arrangement comprising the microwave circuit ac- cording to any preceding claim, a qubit coupled to the second port of the microwave circuit, and a readout circuit coupled to the first port of the microwave cir- cuit for reading a quantum state of the qubit via the microwave circuit.

[0018] In an implementation form of the second aspect, the readout circuit is configured to transmit a probing signal to the first port, detect a response signal, and read the quantum state of the qubit based on a phase shift between the probing signal and the response sig- nal.

[0019] In another implementation form of the second aspect, in the readout circuit comprises a high-elec- tron-mobility transistor, HEMT, for detecting the re- sponse signal.

[0020] In another implementation form of the second aspect, the qubit comprises at least one Josephson junc- tion, a superconductive qubit, and / or a transmon qubit.

[0021] According to a third aspect, a method for read- ing a quantum state of a qubit using the microwave cir- cuit according to the first aspect comprises: coupling the qubit to the second port of the microwave circuit;transmitting a probing signal to the first port of the microwave circuit; detecting a response signal via the first port of the microwave circuit; and reading the quantum state of the qubit based on a phase shift between the probing signal and the response signal.

[0022] Many of the attendant features will be more readily 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

[0023] In the following, example embodiments are de- scribed in more detail with reference to the attached figures and drawings, in which:

[0024] Fig. 1 illustrates a schematic representation of a microwave circuit according to an embodiment;

[0025] Fig. 2 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to an embodiment;

[0026] Fig. 3 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0027] Fig. 4 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0028] Fig. 5 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0029] Fig. 6 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0030] Fig. 7 illustrates a schematic representation of a microwave circuit according to another embodiment;

[0031] Fig. 8 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0032] Fig. 9 illustrates a plot representation of simulation results according to an embodiment;

[0033] Fig. 10 illustrates a plot representation of simulation results according to another embodiment;

[0034] Fig. 11 illustrates a plot representation of simulation results according to another embodiment;

[0035] Fig. 12 illustrates a plot representation of simulation results according to another embodiment;

[0036] Fig. 13 illustrates a plot representation of simulation results according to another embodiment;

[0037] Fig. 14 illustrates a flow chart representation of a method according to an embodiment; and

[0038] Fig. 15 illustrates a schematic representation of a control unit according to an embodiment.

[0039] In the following, like reference numerals are used to designate like parts in the accompanying draw- ings. DETAILED DESCRIPTION

[0040] 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 illustra- tion, specific aspects in which the present disclosure may be placed. It is understood that other aspects may be utilised, 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 the scope of the present disclosure is defined by the ap- pended claims.

[0041] 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 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 oth- erwise.

[0042] Fig. 1 illustrates a schematic representation of microwave circuit for detecting electromagnetic powercoupled to a second port of the microwave circuit via a first port of the microwave circuit according to an embodiment.

[0043] According to an embodiment, a microwave circuit 100 for detecting electromagnetic power coupled to a second port 102 of the microwave circuit 100 via a first port 101 of the microwave circuit 101 comprises the first port 101, the second port 102, and at least one Josephson junction 103 having a non-linear mode of op- eration.

[0044] For example, in the embodiment of Fig. 1, the at least one Josephson junction 103 comprises two Jo- sephson junctions.

[0045] When the at least one Josephson junction 103 is in the non-linear mode of operation, the at least one Josephson junction 103 can function as at least one non- linear inductor.

[0046] The at least one Josephson junction 103 can comprise, for example, a superconductor – insulator - superconductor (SIS) junction or a superconductor - nor- mal metal – superconductor (SNS) junction.

[0047] The first port 101 may also be referred to as a probe port, a probing port, an output port, or similar.

[0048] The second port 102 may also be referred to as a signal port, a qubit port, an input port, or similar.

[0049] According to an embodiment, a first current 111 is configured to flow through the at least one Josephson junction 103 and a second current 112 is configured to flow through the at least one Josephson junction 103.

[0050] Thus, the first current 111 and the second cur- rent 112 may have overlapping current flows at the at least one Josephson junction 103.

[0051] The first current 111 can have a first reso- nance frequency and the second current 112 can have a second resonance frequency, different from the first resonance frequency.

[0052] The probing signal may comprise a frequency component at least at the first resonance frequency. The probing signal may not comprise a frequency component at the second resonance frequency.

[0053] The first current 111 and the second current 112 can substantially orthogonal and / or orthogonal. When the first current 111 and the second current 112 are substantially orthogonal, coupling electromagnetic power to the first current 111 does not cause substan- tially coupling of the electromagnetic power to the sec- ond current or vice versa. When the first current 111 and the second current 112 are orthogonal, coupling electromagnetic power to the first current 111 does not cause coupling of the electromagnetic power to the sec- ond current or vice versa.

[0054] According to an embodiment, the microwave cir- cuit 100 is configured to couple electromagnetic power from the first port 101 to the first current 111 and to couple electromagnetic power from the second port 102 to the second current 112.

[0055] For example, in the embodiments of Fig. 1, the first port 101 is inductively coupled to the first cur- rent 111 and the second port 102 is capacitively coupled to the second current 112.

[0056] The first port 101 may be configured to only substantially excite the first current 111 and / or to only excite the first current 111. The first port 101 may be configured to not substantially excite the second current 112 and / or to not excite the second current 112.

[0057] The second port 102 may be configured to only substantially excite the second current 112 and / or to only excite the second current 112. The second port 102 may be configured to not substantially excite the first current 111 and / or to not excite the first current 111.

[0058] According to an embodiment, the at least one Josephson junction 103 is configured to, when in the non-linear mode of operation, cause a coupling between the electromagnetic power coupled to the second current 112 from the second port 102 and a phase shift of the first current 111, wherein the phase shift of the first current 111 is detectable via the first port 101.

[0059] The coupling between the electromagnetic power coupled to the second current 112 and the phase shift of the first current 111 may cause the phase shift of the first current 111 to change in response to the elec- tromagnetic power being coupled to the second current 112. Thus, the phase shift of the first current 111 may be a function, such as a non-constant function, of the electromagnetic power coupled to the second current 112.For example, in some embodiments, the phase shift of the first current 111 can be linearly dependent or substan- tially linearly dependent on the electromagnetic power coupled to the second current 112.

[0060] According to an embodiment, the first current 101 corresponds to a first resonance mode of the micro- wave circuit 100 and the second current 102 corresponds to a second resonance mode of the microwave circuit 100. For example, the first current 101 may correspond to a mode current of the first resonance mode and the second current 102 may correspond to a mode current of the second resonance mode.

[0061] In other embodiments, the first current 101 and / or the second current 102 may be non-resonant.

[0062] For example, in the embodiment of Fig. 1, the phase shift of the first current 111 is detectable via the first port 101 by transmitting a probing signal to the first port 101, detecting a response signal via the first port 101 and detecting a phase shift between the probing signal and the response signal.

[0063] According to an embodiment, the first current 111 comprises an asymmetric current and the second cur- rent 112 comprises a symmetric current.

[0064] Herein, a symmetric current may refer to a cur- rent that has at least one axis of symmetry with respect to the circuit topology of a part of the microwave cir- cuit 100 comprising the current. For example, in the embodiment of Fig. 1, the second current 112 has re- flectional symmetry.

[0065] Herein, an asymmetric current may refer to a current that does not have any axis of symmetry with respect to the circuit topology of a part of the micro- wave circuit 100 comprising the current. For example, in the embodiment of Fig. 1, the first current 111 does not have any axis of symmetry.

[0066] According to an embodiment, the microwave cir- cuit does not comprise a connection enabling linear power transfer between the second port 102 and the first port 101.

[0067] For example, the microwave circuit 100 may be designed in such a way that there is no specific con- nection for enabling linear power transfer between the first port 101 and the second port 102. However, the linear power transfer may still be non-zero in practical implementations. Thus, in an ideal situation there may be no linear power transfer between the first port 101 and the second port 102.

[0068] There may only be a connection for detecting the electromagnetic power in the second port 102 via the first port 101 while there may be no coupling enabling linear power transfer between the second port 102 and the first port 101.

[0069] Linear power transfer between the second port 102 and the first port 101 may be considered to be a parasitic effect that should be minimized. This can in- fluence, for example, qubit coherence times if the mi- crowave circuit 100 is used for qubit readout. Thus, qubit decay caused by the linear power transfer needsto be at least much smaller than the natural qubit decay rate, which may for example be 100 microseconds.

[0070] According to an embodiment, the phase shift of the first current 111 is detectable via the first port 101 by transmitting a probing signal into the first port 101, measuring a response signal, and measuring a phase difference between the probing signal and the response signal.

[0071] The probing signal may also be referred to as a probe signal or similar.

[0072] The response signal may comprise any signal provided by the microwave circuit 100 in response to the probing signal. For example, the response signal may comprise a signal that is reflected from the microwave circuit 100 in response to the probing signal being inputted into the microwave circuit 100 via the first port 101. For example, the embodiment of Fig. 1 may provide a reflected probing signal.

[0073] According to an embodiment, the microwave cir- cuit 100 further comprises a main loop and an electro- magnetic coupling dividing the main loop into a first subloop and a second subloop, wherein the at least one Josephson junction comprises a plurality of Josephson junctions, the first subloop comprises at least one of the plurality of Josephson junctions, the second subloop comprises at least one of the plurality of Josephson junctions, the first current flows in a first rotational direction in the main loop, the second current flows in the first rotational direction in the first subloop, andthe second current flows in a second rotational direc- tion, opposite to the first rotational direction, in the second subloop.

[0074] For example, in the embodiment of Fig 1, the first subloop comprises one Josephson junction and the second subloop comprises one Josephson junction. The first current 111 flows counter clockwise in the main loop, the second current 112 flows counter clockwise in the first subloop, and the second current 112 flows clockwise in the second subloop.

[0075] According to an embodiment, the first port 101 is inductively coupled to the first subloop and the second subloop, and the second port 102 is capacitively coupled to the main loop.

[0076] For example, in the embodiment of Fig. 1, the first port 101 is inductively coupled to the first subloop via an inductive coupling between the inductive elements 121 and 122 and to the second subloop via an inductive coupling between the inductive elements 123 and 124. The second port 102 is capacitively coupled to the main loop via a capacitive coupling 131.

[0077] Herein, an inductive element may also be re- ferred to as an inductive coupling, an inductor, or similar. A capacitive element may also be referred to as a capacitive coupling, a capacitor, or similar.

[0078] According to an embodiment, the electromag- netic coupling dividing the main loop into the first subloop and the second subloop comprises a capacitive coupling 132.

[0079] For example, in the embodiment of Fig. 1, the main loop is divided into the first subloop and the second subloop by the capacitive element 132.

[0080] According to an embodiment, the at least one Josephson junction 103 functions as a non-linear in- ductance in the non-linear mode of operation.

[0081] According to an embodiment, the non-linear in- ductance of the at least one Josephson junction 103 is configured to cause the coupling between the electro- magnetic power coupled to the second current 112 from the second port 102 and the phase shift of the first current 111 due to the first current 111 flowing through the at least one Josephson junction 103 and the second current 112 flowing through the at least one Josephson junction 103.

[0082] For example, in the embodiment of Fig. 1, the first current 111 and the second current 112 flow through both of the two Josephson junctions 103.

[0083] The microwave circuit 100 may provide an infi- nite isolation between the first port 101 and the second port 102 in the limit of vanishing fabrication variance and ideal symmetric component values. In practical im- plementations, the isolation may be large but finite.

[0084] According to an embodiment, an isolation be- tween the second port 102 and the first port 101 is more than 40 decibels (dB).

[0085] Alternatively or additionally, the isolation between the second port 102 and the first port 101 maybe more than 35 dB, more than 30 dB, more than 20 dB, more than 15 dB, and / or more than 10dB.

[0086] The isolation between the second port 102 and the first port 101 may also be referred to as an s- parameter, a linear coupling, a linear power coupling, forward transmission loss, S21parameter, or similar.

[0087] I may be desirable to achieve a power coupling between the first port 101 and the second port 102 that is as low as possible. In an ideal implementation, the microwave circuit 100 may not have any power coupling from the first port 101 to the second port 102 or from the second port 102 to the first port 101.

[0088] It may be desirable that the electromagnetic power reflected from second port 102 affects the phase of the electromagnetic power reflected from the first port 101. This can be quantified using, for example, a phase shift of the response signal per a unit of elec- tromagnetic power at the second port 102. This may be referred to as sensitivity.

[0089] The sensitivity may be considered high enough when noise equivalent power (NEP) and response time al- lows one to reach the target qubit readout time, for example 100 ns, and readout fidelity, for example 99%, at a given qubit frequency, for example 5 GHz.

[0090] The first port 101 and the second port 102 may function as an output port and as an input port, re- spectively, in the sense that the first port 101 has a different response that depends on the state of the second port 102, but no net power flow occurs from thesecond port 102 to the first port 101. Thus, the micro- wave circuit 100 can function as a detector of the state of the second port 102.

[0091] Frequencies of the probing signal, of the re- sponse signal, and of the first / second current 111, 112 can be configured by choosing the capacitance values of the capacitive elements 132, 133, 134 of the microwave circuit 100.

[0092] While it may be of most interest typically to prevent power flow from the first port 101 to the second port 102, in some scenarios it may also be desirable to prevent power flow from the second port 102 to the first port 101. This can be beneficial in, for example, pre- venting a qubit coupled to the second port 102 from decaying through the microwave circuit 100. The micro- wave circuit 100 can accomplish preventing flow from in either direction.

[0093] The microwave circuit 100 may present a sub- stantially zero impedance to the second port 102. Thus, the electromagnetic power from the second port 102 may not be absorbed by the microwave circuit 100.

[0094] The second port 102 can be impedance matched to, for example, a typical 50-ohm impedance by placing a 50-ohm resistor in series with the second port 102. This may, however, double the NEP.

[0095] The microwave circuit 100 may be referred to as a pseudo-bolometer. The microwave circuit 100 may comprise Josephson junctions and linear components and can implement a similar electrical response as a thermalbolometer. Compared to thermal bolometers, the microwave circuit 100 can have similar NEP and response times, and can be realized with, for example, SIS junctions.

[0096] The microwave circuit 100 can be directly in- tegrated into, for example, a qubit readout circuitry.

[0097] Fig. 2 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to an embodiment.

[0098] In some embodiments disclosed herein, the mi- crowave circuit 100 is illustrated as a part of a quantum computing arrangement 200. The microwave circuit 100 illustrated in any of such embodiments can also be used in various other applications and arrangements, and the quantum computing arrangement 200 is only one example. Thus, any disclosure herein in relation to the microwave circuit 100 may apply even when the microwave circuit is not part of a quantum computing arrangement 200. Thus, features of the microwave circuit 100 are not inextricably linked to other features of the quantum computing arrangement 200.

[0099] According to an embodiment, a quantum computing arrangement 200 comprises the microwave circuit 100, a qubit 201 coupled to the second port 102 of the microwave circuit 100, and a readout circuit 202 coupled to the first port 101 of the microwave circuit 100 for reading a quantum state of the qubit 201 via the microwave cir- cuit 100.

[0100] The second resonance frequency may be substan- tially equal to a qubit frequency of the qubit 201.

[0101] The qubit 201 and the readout circuit 202 may be, for example, electromagnetically coupled to the mi- crowave circuit 100 in various ways. For example, in the embodiment of Fig. 2, the qubit 201 is galvanically coupled to the second port 102 and the readout circuit 202 is galvanically coupled to the first port 101.

[0102] In the embodiment of Fig. 2, the first port 101 is galvanically coupled to the first current and the second port 102 is inductively coupled to the second current.

[0103] According to an embodiment, the readout circuit 202 is configured to transmit a probing signal to the first port 101, detect a response signal, and read the quantum state of the qubit 201 based on a phase shift between the probing signal and the response signal.

[0104] For example, as illustrated in the embodiment of Fig. 2, the probing signal can be transmitted via a capacitive coupling 203 to the first port 101. The ca- pacitive coupling 203 can be a weak capacitive coupling implemented using, for example, a weak coupling capac- itor in order to direct most of the reflected power of the response signal to an amplifier 204.

[0105] Although the amplifier 204 is illustrated as galvanically coupled to the readout circuit 202 in the embodiment of Fig. 2, the amplifier 204 may be coupled to the readout circuit 202 in various other ways also. For example, the amplifier 204 may be coupled to the readout circuit 202 capacitively, inductively, or via any other electromagnetic coupling.

[0106] In some embodiments, most of the power of the probing signal before the capacitive coupling 203 can be terminated if, for example, the probing signal is fed from a 50-ohm environment and attenuators. This can min- imize signal-to-noise ratio (SNR) loss in the detection of the response signal.

[0107] According to an embodiment, the readout circuit comprises a high-electron-mobility transistor (HEMT) for detecting the response signal.

[0108] The HEMT may comprise a cryogenic HEMT.

[0109] For example, the amplifier 204 illustrated in the embodiment of Fig. 2 may comprise a HEMT.

[0110] Fig. 3 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment;

[0111] According to an embodiment, the qubit 201 com- prises at least one Josephson junction 301, a supercon- ductive qubit, and / or a transmon qubit.

[0112] Although some embodiments may be disclosed herein with reference to a certain type of qubit, these qubit types are only exemplarily. In any embodiment dis- closed herein, the qubits may be implemented in various ways and using various technologies.

[0113] For example, in the embodiment of Fig. 3, the qubit 201 is illustrated as a qubit comprising a Jo- sephson junction 201 and a capacitive element 302. In other embodiments, the qubit 201 may comprise any type of qubit such as any type of superconducting qubit, aflux qubit, a phase qubit, a charge qubit, and / or a transmon qubit.

[0114] In the embodiment of Fig. 3, the readout cir- cuit 202 is implemented using a signal source 311 for providing the probing signal, a resistive element 312, a circulator 313, such as a parametric circulator, and an amplifier 204. The circulator 313 can direct the probing signal into the microwave circuit 100 via the first port 101 and direct the resulting response signal to the amplifier 204.

[0115] In any embodiment disclosed herein, the readout circuit 202 may be implemented with or without a circu- lator 313. For example, the readout circuit 202 illus- trated in the embodiment of Fig. 2 can direct most of the reflected power of the response signal to an ampli- fier 204 due to the weak coupling capacitor without needing a circulator.

[0116] The microwave circuit 100 of the embodiment of Fig. 3 can achieve approximately a 0.2-degree phase shift between the probing signal and the response signal in response to a single photon in the qubit 201 with the following parameters: capacitive element 321 capaci- tance of 10 fF, inductive element 221 – 224 inductance of 20 nH and transformer k-factor of K=0.9, Josephson junction 103 critical current of 10 nA, probing signal current of 20 nA.

[0117] In the embodiment of Fig. 3, the Josephson junctions 103 may be considered to form a superconduct-ing quantum interference device (SQUID) that is induc- tively coupled to the first port 101 and galvanically coupled to the second port 102. A SQUID may comprise two Josephson junctions connected in a loop. Such a loop may also be referred to as a SQUID loop. Thus, the embodiment of Fig. 3 can function as a large bandwidth SQUID-like readout arrangement with similar or better phase shifts in response to single photon in the qubit 201 as other embodiments. In the embodiment of Fig. 3, the qubit is integrated with the SQUID in a configuration that may not provide a direct decay channel due to orthogonality and operating below critical current in the phase readout manner.

[0118] In the embodiment of Fig. 3, transformer com- ponent values and symmetric parameter values can be challenging for fabrication. Further, bandwidth of the probing signal may need to be limited to prevent HEMT input noise from saturating the junctions and from in- troducing qubit dephasing.

[0119] Fig. 4 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment.

[0120] In the embodiment of Fig. 4, the inductive cou- pling between the second port 102 and the second current illustrated in the embodiments of Figs. 1 – 3 has been replaced with an alternative implementation comprising inductive elements 402.

[0121] In the embodiment of Fig. 4, the first port 101 is galvanically coupled to the first current, the secondport 102 is galvanically coupled to the second current, and the qubit 201 is capacitively coupled via capacitive elements 401 to the second port 102. Alternatively, the second port 102 may be considered capacitively coupled to the second current and the qubit 201 is galvanically coupled to the second port 102.

[0122] Fig. 5 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment.

[0123] In the embodiment of Fig. 5, the inductive el- ements 402 illustrated in the embodiment of Fig. 4 have been replaced with Josephson junctions 501.

[0124] In the embodiment of Fig. 5, the first port 101 is galvanically coupled to the first current, the second port 102 is galvanically coupled to the second current, and the qubit 201 is galvanically coupled to the second port 102. Alternatively, the second port 102 may be considered capacitively coupled to the second current and the qubit 201 is galvanically coupled to the second port 102.

[0125] The embodiment of Fig. 5 can allow a smaller circuit footprint as large geometric inductors are typ- ically physically larger than if the same amount of inductance is provided by Josephson junctions.

[0126] Fig. 6 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment.

[0127] In the embodiment of Fig. 6, the first port 101 is galvanically coupled to the first current, the secondport 102 is galvanically coupled to the second current, and the qubit 201 is galvanically coupled to the second port 102.

[0128] The capacitors 601 can allow implementing an inductive loop with the qubit 201 in order to flux bias of the qubit 201 for tuning purposes without flux bias- ing the readout SQUID.

[0129] In the embodiments of Figs. 4 – 6, a single photon in the qubit 201 can cause, for example, a phase shift of approximately 0.3 degrees between the probing signal and the response signal when 28 nA probing signal current is used.

[0130] Fig. 7 illustrates a schematic representation of a microwave circuit according to another embodiment.

[0131] In the embodiment of Fig. 7, the first current and the second current are coupled via a parametric coupling due to the currents flowing over the same Jo- sephson junctions 103 similarly to the embodiments of Figs. 1 - 6. Parametric coupling may refer to a circuit parameter, such as an inductance, a capacitance, a speed of light, a length of a resonator, an impedance, being modulated by a signal. The interaction of two or more signals can thus occur through this type of indirect process, typically facilitated by some nonlinearity, rather than direct transmission or absorption of energy.

[0132] In the embodiment of Fig. 7, the Josephson junctions 103 form a superconducting loop. An external flux through the superconducting loop can be set to zero.

[0133] A critical current of the Josephson junction can be, for example, 10 nA.

[0134] Fig. 8 illustrates a schematic representation of a microwave circuit and of a quantum computing ar- rangement according to another embodiment.

[0135] According to an embodiment, the microwave cir- cuit 100 further comprises a first band-stop filter 801 between the first port 101 and a section of the microwave circuit 101 comprising the first current and the second current and a second band-stop filter 802 between the second port 102 and the section of the microwave circuit 100 comprising the first current and the second current.

[0136] In the embodiment of Fig. 8, the microwave cir- cuit 100 comprises a first resonator 803 and a second resonator 804 sharing a common Josephson junction 103. The Josephson junction 103 can function as a common non- linearity of the first resonator 803 and the second resonator 804.

[0137] The first resonator 803 can be tuned to the frequency of the probing signal and the second resonator 804 can be tuned to the frequency of the qubit 201. The frequency of the probing signal and the frequency of the qubit 201 can have a large frequency separation. Elec- tromagnetic power at the second port 102 will introduce a phase shift on the response signal.

[0138] Transmission from the second port 102 to the first port 101 can be further prevented by additional band-stop and / or band-pass filters at the respective ports.

[0139] For example, the embodiment of Fig. 8 further comprises a first band-stop filter 801 capacitively cou- pled 805 to the first resonator 803 and a second band- stop filter 802 capacitively coupled 806 to the second resonator 804.

[0140] Fig. 9 illustrates a plot representation of simulation results according to an embodiment.

[0141] Embodiments of Figs. 9 – 12 illustrate simula- tion results for the microwave circuit of Fig. 1 for the following parameters and conditions: - Probing signal: 0.8032 GHz, -151 dBm - Second port signal: 5.0006 GHz, -170 dBm (10 zW) - The response signal is read out with a cryogenic HEMT o State-of-the-art HEMT has a noise temperature ^^= 1.2 K at 1 GHz o Equivalent noise power spectral density (PSD) is -197.8 dBm / Hz - Steady-state NEP analysis: o ^^= ^2^^^^^= 41 ^^⁄√^^- Response time from decay of sideband vs. modulation o ^^^^= 1.166^^^, ^ = 1⁄ (2^^) = 137^^ o Photon number resolution at signal frequency

[0142] The embodiment of Fig. 9 illustrates the phase shift between the probing signal and the response signalas a function of the frequency of the probing signal for a probing signal sweep from -172 dBm to -142 dBm in 3 dB steps.

[0143] Fig. 10 illustrates a plot representation of simulation results according to another embodiment.

[0144] The embodiment of Fig. 10 illustrates the phase shift between the probing signal and the response signal as a function of electromagnetic power coupled to the second port. The line of Fig. 10 follows a linear rela- tion 5.8×1017rad / W.

[0145] Fig. 11 illustrates a plot representation of simulation results according to another embodiment. Curve 1101 corresponds to an envelope plot of the power coupled to the second port 102. Curve 1102 corresponds to probing signal power.

[0146] Fig. 12 illustrates a plot representation of simulation results according to another embodiment.

[0147] The sideband power illustrated in the embodi- ment of Fig. 12 is associated with the detector band- width which is a relevant figure of merit. The detector bandwidth can quantify how quickly the device responds to changes in the input and as such how quickly readout can be performed with particular circuit parameters.

[0148] Fig. 13 illustrates a plot representation of simulation results according to another embodiment.

[0149] The embodiment of Fig. 13 illustratesand ^^^parameters as functions of frequency when a signal is fed into the second port of the microwave circuit 100 of the embodiment of Fig. 8. Curve 1301 corresponds tothe ^^^parameter and curve 1302 corresponds to the ^^^parameter. The first band-stop filter 801 comprises a 1.02 pF capacitive element and a 2.75 nH inductive el- ement. The second band-stop filter 802 comprises a 2 pF capacitive element and a 13.5 nH inductive element. The first resonator 803 comprises a 0.23 pF capacitive el- ement and a 0.5 nH inductive element. The second reso- nator 804 comprises a 0.23 pF capacitive element and a 19 nH inductive element. The capacitively couplings 805, 806 are 67.454 fF and 200 fF, respectively. The critical current of the Josephson junction 103 is 11 nA.

[0150] Fig. 14 illustrates a flow chart representation of a method according to an embodiment.

[0151] According to an embodiment, a method 1400 for reading a quantum state of a qubit using the microwave circuit 100 comprises coupling 1401 the qubit to the second port of the microwave circuit.

[0152] The method 1400 may further comprise transmit- ting 1402 a probing signal to the first port of the microwave circuit.

[0153] The method 1400 may further comprise detecting 1403 a response signal via the first port of the micro- wave circuit.

[0154] The method 1400 may further comprise reading 1404 the quantum state of the qubit based on a phase shift between the probing signal and the response sig- nal.

[0155] Fig. 15 illustrates a schematic representation of a control unit according to an embodiment.

[0156] According to an embodiment, a quantum computing system comprises a plurality of the quantum computing arrangements 200.

[0157] According to an embodiment, the quantum compu- ting system further comprises a control unit 1500 cou- pled to each quantum computing arrangement in the plu- rality of the quantum computing arrangements 200.

[0158] When the quantum computing system is opera- tional, each quantum computing arrangement 200 may be physically located in a cryostat or similar. The cryo- stat may cool each quantum computing arrangement 200 to cryogenic temperatures. This may be required if the qubit 201 in each quantum computing arrangement 200 is, for example, a superconducting qubit. The control unit 1500 may be located outside the cryostat.

[0159] The control unit 1500 may be configured to per- form the method 1400. For example, the control unit 1500 may perform the method 1400 for each quantum computing arrangement 200 in the plurality of quantum computing arrangements. The control unit 1500 may be coupled to the first port 101 of each quantum computing arrangement 200 and to the second port 102 of each quantum computing arrangement 200 via the readout circuit 202. For exam- ple, the control unit 1500 may be configured to control a signal source 311 in order to provide the probing signal to the first port 101. The control unit 1500 may be further configured to detect the response signal us- ing the amplifier 204, such as a HEMT. The control unit 1500 may be further configured to read the quantum stateof the qubit 201 based on a phase shift between the probing signal and the response signal.

[0160] The control unit 1500 may comprise at least one processor 1501. The at least one processor 1501 may comprise, for example, one or more of various processing devices, such as a co-processor, a microprocessor, a control unit 1500, a digital signal processor (DSP), a processing circuitry with or without an accompanying DSP, or various other processing devices including in- tegrated circuits such as, for example, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a microprocessor unit (MCU), a hard- ware accelerator, a special-purpose computer chip, or the like.

[0161] The control unit 1500 may further comprise a memory 1502. The memory 1502 may be configured to store, for example, computer programs and the like. The memory 1502 may comprise one or more volatile memory devices, one or more non-volatile memory devices, and / or a com- bination of one or more volatile memory devices and non- volatile memory devices. For example, the memory 1502 may be embodied as magnetic storage devices (such as hard disk drives, floppy disks, magnetic tapes, etc.), optical magnetic storage devices, and semiconductor mem- ories (such as mask ROM, PROM (programmable ROM), EPROM (erasable PROM), flash ROM, RAM (random access memory), etc.).

[0162] The control unit 1500 may further comprise other components not illustrated in the embodiment ofFig. 15. The control unit 1500 may comprise, for exam- ple, an input / output bus for connecting the control unit 1500 to the arrangement 100. Further, a user may control the control unit 1500 via the input / output bus. The control unit 1500 may further comprise means for provid- ing the first / second pulse to the signal lines. For example, the control unit 1500 may comprise a DC source, such as a DC current source.

[0163] When the control unit 1500 is configured to implement some functionality, some component and / or com- ponents of the control unit 1500, such as the at least one processor 1501 and / or the memory 1502, may be con- figured to implement this functionality. Furthermore, when the at least one processor 1501 is configured to implement some functionality, this functionality may be implemented using program code comprised, for example, in the memory 1502.

[0164] The control unit 1500 may be implemented using, for example, a computer, some other computing device, or similar.

[0165] 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 embod- iment unless explicitly disallowed.

[0166] Although the subject matter has been described in 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, thespecific 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.

[0167] 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 benefits and advantages. It will further be un- derstood that reference to 'an' item may refer to one or more of those items.

[0168] The steps of the methods described herein may be 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 the other embodiments described to form further embodiments without losing the effect sought.

[0169] 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 exclu- sive list and a method or apparatus may contain addi- tional blocks or elements.

[0170] 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. A microwave circuit (100) for detecting electro- magnetic power coupled to a second port (102) of the microwave circuit (100) via a first port (101) of the microwave circuit (100), the microwave circuit (100) comprising: the first port (101); the second port (102); and at least one Josephson junction (103) having a non- linear mode of operation; wherein a first current (111) is configured to flow through the at least one Josephson junction (103) and a second current (112) is configured to flow through the at least one Josephson junction (103); the microwave circuit (100) is configured to couple electromagnetic power from the first port (101) to the first current (111) and to couple electromagnetic power from the second port (102) to the second current (112); and the at least one Josephson junction (103) is con- figured to, when in the non-linear mode of operation, cause a coupling between the electromagnetic power cou- pled to the second current (112) from the second port (102) and a phase shift of the first current (111), wherein the phase shift of the first current (111) is detectable via the first port (101).

2. The microwave circuit (100) according to claim 1, wherein the first current (111) comprises anasymmetric current and the second current (112) com- prises a symmetric current.

3. The microwave circuit (100) according to claim 1 or claim 2, wherein the microwave circuit (100) does not comprise a connection enabling linear power transfer between the second port (102) and the first port (101).

4. The microwave circuit (100) according to any preceding claim, wherein the first current (101) corresponds to a first resonance mode of the microwave circuit (100) and the second current (102) corresponds to a second resonance mode of the microwave circuit (100).

5. The microwave circuit (100) according to any preceding claim, wherein the phase shift of the first current (111) is detectable via the first port (101) by transmitting a probing signal into the first port (101), measuring a response signal, and measuring a phase difference between the probing signal and the response signal.

6. The microwave circuit (100) according to any preceding claim, further comprising a main loop and an electromagnetic coupling dividing the main loop into a first subloop and a second subloop, wherein the at least one Josephson junction (103) comprises a plurality of Josephson junctions, the first subloop comprises atleast one of the plurality of Josephson junctions, the second subloop comprises at least one of the plurality of Josephson junctions, the first current (111) flows in a first rotational direction in the main loop, the second current (112) flows in the first rotational di- rection in the first subloop, and the second current (112) flows in a second rotational direction, opposite to the first rotational direction, in the second subloop.

7. The microwave circuit (100) according to claim 6, wherein the first port (101) is inductively coupled to the first subloop and the second subloop, and the second port (102) is capacitively coupled to the main loop.

8. The microwave circuit (100) according to claim 6 or claim 7, wherein the electromagnetic coupling dividing the main loop into the first subloop and the second subloop comprises a capacitive coupling (132).

9. The microwave circuit (100) according to any preceding claim, wherein the at least one Josephson junction (103) functions as a non-linear inductance in the non-linear mode of operation.

10. The microwave circuit (100) according to claim 9, wherein the non-linear inductance of the at least one Josephson junction (103) is configured to cause the coupling between the electromagnetic powercoupled to the second current (112) from the second port (102) and the phase shift of the first current (111) due to the first current (111) flowing through the at least one Josephson junction (103) and the second current (112) flowing through the at least one Josephson junc- tion (103).

11. The microwave circuit (100) according to any preceding claim, further comprising a first band- stop filter (801) between the first port (101) and a section of the microwave circuit comprising the first current and the second current and a second band-stop filter (802) between the second port (102) and the sec- tion of the microwave circuit comprising the first cur- rent and the second current.

12. The microwave circuit (100) according to any preceding claim, wherein an isolation between the second port (102) and the first port (101) is more than 40 decibels.

13. A quantum computing arrangement (200) com- prising the microwave circuit (100) according to any preceding claim, a qubit (201) coupled to the second port (102) of the microwave circuit (100), and a readout circuit (202) coupled to the first port (101) of the microwave circuit (100) for reading a quantum state of the qubit (201) via the microwave circuit (100).

14. The quantum computing arrangement (200) according to claim 13, wherein the readout circuit (202) is configured to transmit a probing signal to the first port (101), detect a response signal, and read the quan- tum state of the qubit based on a phase shift between the probing signal and the response signal.

15. The quantum computing arrangement (200) according to claim 14, wherein the readout circuit (202) comprises a high-electron-mobility transistor, HEMT, for detecting the response signal.

16. The quantum computing arrangement (200) according to any of claims 13 – 15, wherein the qubit (202) comprises at least one Josephson junction (301), a superconductive qubit, and / or a transmon qubit.

17. A method (1400) for reading a quantum state of a qubit using the microwave circuit according to any of claims 1 - 12, the method comprising: coupling (1401) the qubit to the second port of the microwave circuit; transmitting (1402) a probing signal to the first port of the microwave circuit; detecting (1403) a response signal via the first port of the microwave circuit; and reading (1404) the quantum state of the qubit based on a phase shift between the probing signal and the response signal.

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