TECHNICAL FIELD

[0001] The present disclosure relates to a quantum electronic device and more particularly to multiplexed readout of qubits.

BACKGROUND

[0002] In quantum computing, it has become common to use the term "qubit" to specify not only a basic unit of information but also an information storage element for storing one qubit of information. As an example, a superconductive memory circuit may comprise one or more qubits (i.e. qubit-sized information storage elements). In such an example the qubit is an anharmonic oscillator, such as a transmon, and it may be coupled to an associated, or nearby, readout resonator for facilitating the readout of the state of the qubit stored therein.

[0003] The readout fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is also known as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency.

[0004] Each qubit can have its own filter, whereby the number of filters needed for a quantum electronic device will scale with the number of qubits, which also increase the size of the device.

SUMMARY

[0005] The scope of protection sought for various embodiments of the invention is set out by the independent claims. The embodiments, examples and features, if any, described in this specification that do not fall under the scope of the independent claims are to be interpreted as examples useful for understanding various embodiments of the invention.

[0006] It is an objective to overcome at least some of the problems identified above related to quantum computing. [0007] According to a first aspect there is provided an apparatus for multiplexed readout of qubits, comprising:

- readout resonators coupled to the qubits connected in series to a probe line for multiplexed readout of the qubits, wherein the probe line is configured to have a pass band at a readout band of the qubits.

[0008] According to a second aspect there is provided a quantum computing system comprising an apparatus according to an aspect.

[0009] According to a third aspect there is provided method for multiplexed readout of qubits by the apparatus of according to the first aspect, comprising:

- feeding, by a control device operatively coupled to a probe line of an apparatus according to an aspect, a probe signal to the probe line for multiplexed readout of qubits at a readout band;

- reading, by the control device, a readout signal from the probe line;

- determining, by the control device, one or more states of the qubits based on the readout signal.

[0010] According to a fourth aspect there is provided a computer program product comprising program code configured to perform the method according to the third aspect when the program code is executed by a control device operatively coupled to a probe line of an apparatus according to an aspect.

[0011] At least some embodiments provide a scalable solution for filtering qubits.

DESCRIPTION OF THE DRAWINGS

[0012] Other features and advantages of the invention will become apparent from the following description of a non-limiting example embodiment, with reference to the appended drawings, in which:

Fig.1 illustrates a schematic example of apparatus for multiplexed readout of qubits in accordance with at least some embodiments;

Fig. 2 illustrates a schematic example of apparatus for multiplexed readout of qubits in accordance with at least some embodiments; Fig. 3 illustrates a schematic exampie of apparatus for multiplexed readout of qubits in accordance with at least some embodiments;

Fig. 4 illustrates a schematic example of a quantum computing system in accordance with at least some embodiments;

Fig. 5 illustrates an example of performance of a probe line configured to perform bandpass filtering in accordance with at least some embodiments;

Fig. 6 illustrates an example of performance of a probe line configured to perform bandpass filtering in accordance with at least some embodiments; and

Fig. 7 illustrates an example of a method in accordance with at least some embodiments.

DETAILED DESCRIPTION

[0013] 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 utilized, and structural or logical changes may be made 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 be the appended claims.

[0014] 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 illustrated in the figures. 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.

[0015] Figs. 1-3 illustrate schematic examples of circuits 100, 200, 300, for a quantum electronic device. The circuits may be for example superconductive quantum processor circuits. The circuits comprise qubits 114, 116, 118, 120, 214, 216, 218, 220, 314, 316, 318, 320 and associated readout resonators 106, 206, 306 connected in series to a probe line 101 , 201 , 301 for multiplexed readout of the qubits at a readout band. The probe line is configured to have a pass band isolated from a qubit band. In an example, the pass band is preferably aligned with the readout band, whereby the qubits coupled to the readout band may be read at a relatively high magnitude while being isolated from the resonators at the resonator band. The pass band may for example extend over the whole readout band. In an example, the readout band comprises multiplexed resonator frequencies which are dispersively coupled to qubits at a qubit band, i.e. a frequency band that corresponds with operational frequencies of the qubits. Total bandwidth of the multiplexed resonators coincides with the pass band. Therefore, the pass band, and the readout band, includes the resonator frequencies and may be referred to a resonator band. It should be noted that the qubit band and the readout band, or a resonator band, are chosen differently which facilitates read out of the qubits by using a dispersive coupling technique. The dispersive coupling technique includes that a qubit frequency and a resonator frequency are detuned. Detuning between the qubit frequency and the resonator frequency facilitates limiting decay of the qubits because of the Purcell effect, i.e. the Purcell decay.

[0016] In an example, a pass band, or a low attenuation band, of the probe line may be at the readout band of the probe line, whereby the qubits at the readout band may have high magnitudes and isolated from a qubit band. In an example, during operation, the qubits can be excited by excitation waveforms brought to excitation ports of the qubits and the excited qubits may be coupled by respective readout connections to the probe line. A probe signal, or a readout waveform, may be fed, or coupled, to the probe line at an input terminal 108, 208, 308, or port, arranged at one end of the probe line for obtaining a readout signal. Each of the resonators of the qubits may have a different resonant frequency, such that frequencies of the probe signal may determine which qubits are actually read. The resulting readout signal comprises the determined qubit states at the readout band. The values of the qubits may be detected based on a phase of the readout signal. It should be noted that depending on implementation of the bandpass filtering, the probe line may be measured in transmission and/or in reflection of the probe signal for reading the values of the qubits.

[0017] In an example in accordance with at least some embodiments, the probe line 101 , 201 301 comprises at least one bandpass filter 102, 202, 204, 302 arranged to at least one end of the probe line for bandpass filtering of the qubits at the readout band. In this way, multiplexed readout of the qubits may be supported.

[0018] In an example in accordance with at least some embodiments, a pass band of the probe line 101 , 201 , 301 is at the readout band.

[0019] In the example illustrated in Fig. 1 , a bandpass filter 102 is arranged between an output terminal 110 of the probe line 101 and a readout connection of the qubit 114 that is closest to the output terminal 110 along the probe line. In this way the bandpass filter may perform filtering in transmission of the probe signal from input terminal 108 to the output terminal 1 10.

[0020] In the example illustrated in Fig. 2, a bandpass filter 202 is arranged between an input terminal 208 of the probe line 201 and a readout connection of the qubit 214 that is closest to the input terminal 208 along the probe line, and a further bandpass filter 204 is arranged between an output terminal 210 of the probe line and a readout connection of the qubit 220 that is closest to the output terminal 210 along the probe line. In this way the bandpass filter may perform filtering of the probe signal in transmission at input to the probe line and in transmission at output from the probe line.

[0021] In the example illustrated in Fig. 3, a bandpass filter 302 may be arranged between an input terminal 308 of the probe line 301 and a readout connection of the qubit 314 that is closest to the input terminal 308 along the probe line. In this way the probe signal is filtered in transmission to the probe line by the bandpass filter 302. The input terminal 308 may be a combined input and output terminal 308, whereby the input terminal serves both for feeding a probe signal to the probe line and for reading a readout signal from the probe line. In this way the probe signal is filtered by the bandpass filter 302 twice, i.e. in transmission to the probe line and in reflection from the probe line.

[0022] It should be noted that in the examples, the closest readout connection to the input terminal or the output terminal is the first readout connection of the qubits connected to the probe line in series.

[0023] In an example in accordance with at least some embodiments, the bandpass filter 102, 202, 204, 302, comprises consecutive sections of the probe line and the consecutive sections have a stepped impedance profile. The stepped impedance profile provides a frequency response for multiplexed readout of the qubits. In an example, the bandpass filter has a pass band at the readout band. In an example the probe line may comprise five consecutive sections, where impedances of the sections decrease from impedance of a first section, Zi, to impedance of a second section, Z2, and to an impedance of a third section, Z3. Then impedances of the sections increase from the third section to an impedance of a fourth section, Z4, and to an impedance of a fifth section, Z5. The impedances may be designed e.g. such that Z1 = Z5, Z2 = Z4 and Z1 > Z2, Z2 > Z3. Accordingly, the impedance of the third section, Z3, is the lowest in the series of sections.

[0024] In an example in accordance with at least some embodiments, the probe line 101 comprises a notch frequency for depleting qubit excitations. In an example, the notch frequency is a frequency at which T1 of the qubits is decades smaller on a log -scale, than T1 on resonant frequencies of the qubits.

[0025] In an example in accordance with at least some embodiments, the notch frequency may be configured by a capacitor 103 arranged to the probe line 101 . The capacitor 103 may be arranged between an input terminal 108 and a readout connection of a qubit 114 that is closest to the input terminal. In an example, a position of the notch frequency, in frequency, may be adjusted based on a length of the probe line between the capacitor 103 and the bandpass filter 102. In an example, the notch frequency may be defined at a frequency that is below qubit frequencies. The qubit frequencies may be e.g. 4.3GHz and 4.5 GHz.

[0026] In an example, the qubits 114, 116, 118, 120, 214, 216, 218, 220, 314, 316, 318, resonators 106, 206, 308 and the probe line can be made of superconductor materials. However, this is not an essential requirement, and other kinds of qubit technologies could be used. A superconductor material means here a material that can be made superconductive by cooling it to a sufficiently low temperature. An example of such materials is aluminum, but also other superconductor materials like molybdenum, niobium, tin, tantalum, or lead can be used. For operation, a superconductive quantum processor circuit is cooled to a very low temperature, which can be some kelvins, or well under one kelvin, or in the order of some tens of millikelvins.

[0027] Fig. 4 illustrates a schematic example of a quantum computing system in accordance with at least some embodiments. The quantum computing system 400 comprises an apparatus and one or more control devices 402 that are operatively coupled 401 to one or more parts of the apparatus. The apparatus may comprise a circuit 100, 200, 300 described with Figs. 1 -3. In the example, the control device may be coupled to a probe line and one or more qubits 114, 116, 118, 120 and/or to one or more readout resonators of the apparatus and the control device is caused to feed a probe signal to the probe line for multiplexed readout of qubits at a readout band; bandpass filter the qubits 114, 116, 118, 120 at the readout band; read a readout signal from the probe line; and determine, one or more states of the qubits based on the readout signal.

[0028] In an example, the probe signal is fed to the probe line at an input terminal 108 of the probe line and the readout signal is read from the probe line at an output terminal 110 of the probe line. In an example, couplings between the control device and the apparatus may be electrical connections. It should be noted that in some embodiments a single terminal may serve for both input terminal and output terminal.

[0029] In an example in accordance with at least some embodiments, the control device 402 is operatively connected to the one or more qubits and caused to: generate a tuning signal for shifting one or more of the qubits 114, 116, 118, 120 to a notch frequency of the probe line for depleting excitations of said one or more of the qubits 114, 116, 118, 120, and feed the tuning signal to the one or more qubits 114, 116, 118, 120. In an example, the tuning signal may be configured to shift at least one of the qubits to a frequency notch, where T1 of the qubits is decades smaller on a log -scale, than T1 on resonant frequencies of the qubits. In an example, the one or more qubits are tunable, whereby each of the qubits may be tuned based on feeding a tuning signal to external control lines, or flux lines, of the qubit for tuning the qubit to the notch frequency.

[0030] In an example, the control device 402 comprises at least one processor 404. The at least one processor 404 may include, for example, one or more various processing devices such as a coprocessor, a microprocessor, a control unit 701 , a Digital Signal Processor (DSP), processing circuitry with or without an accompanying DSP, or various other 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.

[0031] In an example, the control device 402 comprises at least one memory 408. The memory 408 may be configured to store, for example, one or more of probe signal(s), tuning signal(s), computer program code, computer program instructions and computer programs. Execution of the computer program code, computer program instructions and computer programs may cause generating probe signal(s), generating tuning signal(s) and/or reading readout signal(s) for execution of one or more functionalities described herein.

[0032] Fig. 5 illustrates an example of performance of a probe line configured to perform bandpass filtering in accordance with at least some embodiments. The performance is illustrated by a diagram of scattering parameters S21 502 and S22 504 measured from the probe line, where a bandpass filter has been connected to at least one end of the probe line. From the diagram it may be derived that S21 is OdB or very close to OdB at 6 GHz, between 5.4 GHz and 6.4 GHz, therefore at a readout band 506 of the probe line. Accordingly, a readout signal may be read at the readout band at a high magnitude. From the diagram it may be further derived that the S22 is OdB outside 508 of the readout band of the probe line and at the readout band S22 is -25 dB or less. Therefore, reflections are attenuated at the readout band. From the diagram it may be further derived that at a qubit band 510, e.g. at qubit frequencies of 4.3GHz or 4.5 GHz, the S21 is 40 dB or close to -40 dB, which provides isolation to the readout band of the probe line.

[0033] Fig. 6 illustrates an example of performance of a probe line configured to perform bandpass filtering in accordance with at least some embodiments. In addition to the bandpass filtering the probe line is configured to deplete qubit excitations by a capacitor arranged between an input terminal and a readout connection of a qubit that is closest to the input terminal. The performance is illustrated by qubit energy relaxation time, T1 , measured from the probe line for each qubit. At the readout band 602 around 6Ghz, between 5.4GHz and 6.4 GHz, the qubits are shown by peaks, or modes. At 4GHz, the probe line has a notch frequency 604 having T1 s of the qubits are less than 300 ns. Therefore, tuning qubit(s) to the notch frequency provides depleting excitations of the qubit(s). At the qubit band 606, T1 s of the qubits are in a range of milliseconds, e.g. between 0.1 ms to 40 ms. At least some qubits may have T1 exceeding 10ms over a frequency band of ~10 MHz, which facilitates readout coupling and readout speed may be ~10MHz.

[0034] Fig. 7 illustrates an example of a method in accordance with at least some embodiments. The method may be performed by a quantum computing system described with Fig. 4. The method provides multiplexed readout of qubits. Phase 702 comprises feeding, by a control device, a probe signal to a probe line for multiplexed readout of qubits at readout band. Phase 706 comprises reading, by the control device, a readout signal from the probe line. Phase 708 comprises determining, by the control device, one or more states of the qubits based on the readout signal.

[0035] In an example in accordance with at least some embodiments, phase 702 comprises generating a tuning signal for shifting one or more of the qubits 114, 116, 118, 120 to a notch frequency of the probe line 101 for depleting excitations of said one or more of the qubits 114, 116, 118, 120; and feeding the tuning signal to the one or more of the qubits 114, 116, 118, 120. In an example, the one or more qubits are tunable, whereby each of the qubits may be tuned based on feeding a tuning signal to external control lines, or flux lines, for tuning the qubit to the notch frequency. In this way the qubits may be reset to their ground state without waiting for their decay.

[0036] Fig. 8 illustrates an example of sections of a probe line in accordance with at least some embodiments. The sections may be configured to form a bandpass filter for filtering signals communicated by the probe line. In this way, attenuation of a readout signal from the probe line may be alleviated over a readout band. The probe line may be a coplanar waveguide or a twin coplanar waveguide configuration. The probe line may comprise a series of sections 802, 804, where the number of sections defines the order of the filter, that form the bandpass filter at one end of the probe line. Fig. 8 shows the twin coplanar waveguide configuration, where each section has a coplanar waveguide comprising two parallel conductors. One of the parallel conductors 808 extends through the next section of the bandpass filter, where it couples to the next conductor. Accordingly, section 802 of the probe line comprises conductors 808, 812 and ground planes 806, 810 separated by gaps from the conductors 808, 812. A subsequent section 804, i.e. a consequent section, along a length of the probe line comprises conductors 808, 814 and the ground planes 806, 810 separated by gaps from the conductors 808, 814. The sections 802, 804 may have a stepped impedance profile, whereby impedance of section 802 is smaller than the impedance of the subsequent section 804. It should be noted that the probe line may comprise further sections that have a smaller impedance or a higher impedance than a previous section of the probe line along the length of the probe line.

[0037] 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.

[0038] 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, 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.

[0039] 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 understood that reference to ‘an’ item may refer to one or more of those items. [0040] 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 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.

[0041] 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. [0042] It will be understood that the above description 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 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.

LIST OF REFERENCE SIGNS

Probe line 101 , 201 , 301

Bandpass filter 102, 202, 204, 302

Capacitor 103

Readout resonators 106, 206, 306

Probe line terminals 108, 110, 208, 210, 308

Qubit 114, 116, 118, 120, 214, 216, 218,

220, 314, 316, 318, 320

Combined probe line input and output 308 terminal

Quantum computing system 400

Coupling(s) 401 Control device 402

Processor 404

521 502

522 504

Readout band 506

Frequencies outside of the readout 508 band

Qubit band 510

Readout band 602

Notch frequency 604

Qubit band 606

Phases of method in Fig. 7 702, 706, 708

Section 802, 804

Ground plane 806, 810

Conductor 808, 812, 814