CN113487034A - Reading device for superconducting qubits - Google Patents

Reading device for superconducting qubits Download PDF

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CN113487034A
CN113487034A CN202110847640.6A CN202110847640A CN113487034A CN 113487034 A CN113487034 A CN 113487034A CN 202110847640 A CN202110847640 A CN 202110847640A CN 113487034 A CN113487034 A CN 113487034A
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刘丰铭
陈明城
王粲
陆朝阳
潘建伟
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University of Science and Technology of China USTC
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Abstract

The invention provides a reading device of superconducting qubits, comprising: a qubit, a read cavity, and a josephson junction, wherein the qubit and the read cavity are coupled through the josephson junction. The invention realizes the longitudinal coupling (ZZ coupling) of the bit and the reading cavity, reduces the driving error of the transverse coupling (XX coupling) to the quantum bit during reading in the prior art, and improves the reading fidelity by improving the reading power in application.

Description

Reading device for superconducting qubits
Technical Field
The invention relates to the field of quantum computing, in particular to a reading device of a superconducting quantum bit.
Background
Dispersion measurement of superconducting qubits refers to coupling the qubit to be measured to a linear resonator, so that the state of the bit changes the frequency of the resonator. In this way we can indirectly measure the state of a bit by measuring the frequency of the cavity.
The key to the dispersion measurement is to couple the qubit to the read cavity. It is common in the art to capacitively couple a superconducting qubit to a resonant cavity. The effect of this coupling structure is the lateral coupling in quantum mechanics, or XX coupling. Its Hamiltonian can be written as follows:
Figure BDA0003177834790000011
wherein ω isrFor reading the frequency, omega, of the cavityqIs the transition frequency of the bit and g is the coupling strength of the bit to the read cavity. Detuning delta-omega between bit and read cavityq-ωrWhen the intensity of the coupler is large enough (g < delta), the Hamiltonian can be used as the reference frame transformation
Figure BDA0003177834790000012
The representation of which on the energy eigenstates of the bit-read cavity system is obtained:
Figure BDA0003177834790000013
as can be seen from the above hamiltonian, at the fundamental vector of the energy eigenstates of the system, the coupling form of the bit and the read cavity becomes longitudinal coupling (ZZ coupling), and the state of the bit changes the frequency of the read cavity, which is also called AC Stark effect.
In implementing the concept of the present invention, the inventors found that at least the following problems exist in the related art: the bit-read cavity coupling mode adopted by the method is substantially transverse coupling, and longitudinal coupling is shown under the energy eigen-state basis vector of the whole bit-read cavity only under the condition of large detuning approximation. Therefore, when the reading signal is strong and the number of photons in the reading cavity is large, the bit is driven by the reading cavity to cause the measurement error. Therefore, the strength of the read signal in the prior art is limited. The read signal strength limitation translates directly into read fidelity limitations, taking into account the presence of noise in the read signal.
Disclosure of Invention
In view of the above, the present invention provides a reading apparatus for superconducting qubits, which is intended to solve at least one of the above technical problems.
In order to achieve the above object, the present invention provides a reading apparatus of superconducting qubits, the reading apparatus comprising: a qubit, a read cavity, and a josephson junction, wherein the qubit and the read cavity are coupled through the josephson junction.
Wherein a qubit of the reading device couples with the read cavity in the presence of ZZ of the Josephson junction at respective independent energy eigen-state basis vectors.
Wherein, the reading cavity is a distributed transmission line type resonant cavity.
Wherein the number of the Josephson junctions connecting the qubits and the transmission line type resonant cavity is one; the connection point position of the Josephson junction and the transmission line type resonant cavity and the characteristic impedance of the transmission line are determined according to parameters such as required coupling strength.
Wherein the number of Josephson junctions connecting the qubits and the transmission line type resonant cavity is two or more.
Wherein the coupling of the qubit to the read chamber further comprises simultaneous coupling via the josephson junction and a capacitance.
Wherein the qubit is a Transmon qubit or a Plasonium qubit.
The read cavity is coupled to a read line, and the read cavity and the read line are coupled in a capacitive coupling or an inductive coupling manner.
Wherein separate flux control lines are included to control the flux in the loop in which the josephson junction for coupling is located.
Wherein a target value of magnetic flux control in a circuit in which the josephson junction for coupling is located is an integer number of magnetic flux quanta.
Based on the above technical solution, the reading apparatus and the reading method for the superconducting qubit of the present invention have at least one of the following advantages over the prior art:
the invention realizes the longitudinal coupling (ZZ coupling) of the bit and the reading cavity, reduces the driving error of the transverse coupling (XX coupling) to the quantum bit during reading in the prior art, and improves the reading fidelity by improving the reading power in application.
Drawings
Fig. 1 is a schematic diagram of a coupling structure of a qubit and a read cavity according to an embodiment of the present invention;
FIG. 2 is a phase distribution diagram of a transmission line according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a structure of a reading cavity and a qubit coupled by a dual josephson junction according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a read chamber and qubits simultaneously coupled by a Josephson junction and capacitance provided by an embodiment of the present invention;
fig. 5 is a design diagram of a reading apparatus according to an embodiment of the present invention.
Detailed Description
The invention realizes the real longitudinal coupling (ZZ coupling) of a bit-reading cavity system, namely the Hamiltonian formed by the energy eigenstate coding of the bit and the reading cavity which are independent respectively shows ZZ coupling. The reading device adopting the coupling structure can greatly improve the strength of the reading signal so as to increase the signal-to-noise ratio of the reading signal and improve the reading fidelity.
The invention mainly changes the coupling structure of the bit and the reading cavity system. Different from the traditional mode that the bit and the reading cavity are coupled through capacitance, the invention adopts the Josephson junction to couple the bit and the reading cavity, namely, the quantum bit is coupled with the reading cavity through the Josephson junction.
In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.
The reading cavity in the invention can adopt a transmission line type resonant cavity structure. The transmission line type resonant cavity is a reading cavity which is most widely used and is easier to manufacture at present, and therefore the embodiment mainly aims at the transmission line type reading cavity.
FIG. 1 exemplarily showsThe invention relates to a coupling structure of a quantum bit and a reading cavity; the qubit is connected to a point on the transmission line resonator via a josephson junction. The lines indicated by oblique lines in FIG. 1 form a loop in which the applied magnetic flux is present
Figure BDA0003177834790000031
And passing through.
The Hamiltonian of this system is derived below to illustrate the particular coupling of the qubits to the read cavity in this system.
The read cavity and qubits are first quantized as separate systems. The state on the transmission line can be represented by the phase of each point on the transmission line. Due to the conservation of charge, the phase on the transmission line satisfies a sinusoidal function distribution. Taking a quarter-wave transmission line resonator as an example, the phase distribution is phi ═ phirsin (π x/2 l). Wherein x is the distance between the point and the short-circuited end of the resonant cavity, and l is the total length of the resonant cavity, phirIs the maximum value of the phase on the cavity. Thus, the state of the cavity can be passed through the phase φrThe conjugate variable (denoted by Cooper operator n)r) To describe. Phase operator, Cooper pair operator and annihilation operator for generating resonant cavity
Figure BDA0003177834790000041
The relationship of (c) can be written as follows:
Figure BDA0003177834790000042
Figure BDA0003177834790000043
where a is a parameter related to the properties of the resonant cavity, and its value is related to the length of the cavity, the characteristic impedance of the transmission line, etc.
The states of qubits are discussed here by way of example for the most common Transmon qubits currently used in superconducting quantum computing. It can use the phase as wellOperator (note as
Figure BDA0003177834790000044
) Cooper operator (noted as
Figure BDA0003177834790000045
) Annihilation operator with generation of qubits
Figure BDA0003177834790000046
To indicate. The relationship between the phase operator, the cooper pair operator and the annihilation operator is as follows:
Figure BDA0003177834790000047
Figure BDA0003177834790000048
wherein EJ、ECJosephson energy and charge energy, respectively, of the Transmon qubit.
As shown in fig. 2, the phase of any point on the transmission line can be obtained by calculation according to the distribution of the sine function of the phase of each point on the transmission line. Taking a quarter-wavelength transmission line as an example, if the distance between the connection point of the transmission line and the coupling Josephson junction and the short-circuited end of the transmission line is x, the phase thereof is
Figure BDA0003177834790000049
For convenience of description, the distribution weight sin (π x/2l) of the phase is simply replaced with a coefficient k as shown in the above equation.
The system couples the Hamiltonian of the Josephson junction, i.e. the coupling term of the bit and the read cavity is
Figure BDA0003177834790000051
Wherein EJCJosephson energy, phi, for coupling josephson junctionsextThe applied magnetic flux passing through the loop (shown by oblique lines in figure 1) where the josephson junction and the bit josephson junction are coupled in the system. When the external magnetic flux is an integer number of magnetic flux quanta, the coupling term is
Figure BDA0003177834790000052
Taylor expansion of the trigonometric function in the above equation to a second order term, i.e.
Figure BDA0003177834790000053
sinψ～ψ
The coupling term can be written in the form of an annihilation operator with the bit and read cavity generating, respectively
Figure BDA0003177834790000054
The above equation has omitted coupling-independent terms such as constant terms. The first term of the above equation represents longitudinal coupling, the second term represents lateral coupling, and the third term represents two-photon lateral coupling. Therefore, the coupling structure in the invention can realize longitudinal coupling and transverse coupling as realized by the capacitive coupling structure in the prior art. The coupling strength of each form is related to parameters such as the energy of the coupling Josephson junction, the connection position of the coupling Josephson junction and the transmission line type resonant cavity, and the characteristic impedance of the transmission line. Therefore, the above parameters can be determined according to the requirements of coupling strength and the like.
To further illustrate the feasibility of the present invention, a specific design parameter is used as an example.
Assuming that the transmission line cavity is a quarter-wavelength transmission line cavity
Figure BDA0003177834790000055
Wherein Z is0To transmitCharacteristic impedance of the transmission line, e is electron charge amount, and h is Planck constant. Taking coupled Josephson energy EJCBit charge energy E of 200MHzCJosephson energy E at 0.24GHzJ15GHz, transmission line resonant cavity frequency 6.4GHz, characteristic impedance 50 omega, coupling Josephson junction and resonant cavity connection are in the one end that opens a way of resonant cavity. According to the above parameters, the bit transition frequency is about 5.1GHz, k is 1, and a is 0.176. At this point, a bit with ZZ coupling intensity of 0.78MHz, XX coupling intensity of 12.5MHz, and two-photon XX coupling intensity of 0.20MHz to the read cavity can be obtained. I.e. the bit in the ground or first excited state has a 0.78MHz change to the frequency of the read cavity. If the pure lateral coupling mode in the prior art is adopted, under the condition that the frequency of the bit and the frequency of the reading cavity are not changed, the lateral coupling strength of about 52MHz is required, and is 3 times larger than the 12.5MHz lateral coupling in the invention. Therefore, the invention can greatly improve the power of the reading signal. Furthermore, the two-photon XX coupling and other higher order terms omitted in the taylor expansion have negligible effect due to the minimal coupling strength.
The above discussion has been made with an applied magnetic flux in the circuit equal to an integer number of flux quanta. When the external magnetic flux is not equal to an integral number of magnetic flux quanta, the calculation is carried out by referring to the method, XZ coupling terms and the like appear in the coupling Hamiltonian, and the XX coupling and ZZ coupling are reduced in equal proportion. In fact, newly appeared coupling terms such as XZ and the like can be ignored due to the frequency mismatch effect. But a reduced ZZ coupling strength affects the reading. Therefore, in practical applications, it is necessary to control the applied magnetic flux as much as possible around an integer number of magnetic flux quanta (usually 0 in practice). Separate flux control lines may be employed to adjust the magnitude of the flux if necessary.
The above discussion is of a read device that couples a read cavity to a qubit using a josephson junction. Multiple josephson junctions may also be used to couple the read cavity to the qubit. A scheme of dual josephson junction coupling that can further cancel the XX coupling term using the symmetry of the two josephson junctions to further improve read fidelity is listed below.
As shown in fig. 3, two josephson junctions and the transmission line type resonators are connected at positions point-symmetrical to the phase 0, and the phases of the resonators at the coupling are phi and-phi, respectively. The phase operator of the remaining bits is
Figure BDA0003177834790000061
In this system, there are two loops through which the applied magnetic flux is shown at phiext1And phiext2And (4) showing. When the two external magnetic fluxes are integral magnetic flux quanta, the system has a coupling Hamiltonian
Figure BDA0003177834790000062
Reference to the calculation method when discussing single josephson junction coupling reveals that the XX coupling term is absent from the coupling hamiltonian, but the ZZ coupling term is still present. Therefore, this structure can further solve the driving error when the residual XX coupling pair bit is read, which helps to further improve the reading fidelity.
The coupling of the reading cavity and the qubit can be realized only by a Josephson junction, and coupling forms such as capacitive coupling and the like can be added on the basis. Figure 4 shows schematically a read-out arrangement comprising both josephson junction coupling and capacitive coupling. Wherein coupling of the josephson junction may produce the aforementioned XX coupling and ZZ coupling, while capacitive coupling may produce the XX coupling as described in the background. By adjusting parameters such as the size of the coupling josephson junction and the coupling capacitance and their location with the read chamber junction, the strength of the XX coupling can be at least partially cancelled.
The reading device mainly comprises a quantum bit, a reading cavity and a coupling Josephson junction. The qubit may be a Transmon qubit which is most commonly used at present, or may be another form of qubit such as a Plasonium qubit (patent publication No. CN 111723936 a). The reading cavity can be a distributed transmission line type resonant cavity or an LC resonator under a lumped parameter model. If a distributed transmission line type resonant cavity is adopted, the cavity can be divided into a quarter-wavelength cavity, a half-wavelength cavity, a quarter-wavelength cavity and the like according to the length of the cavity. The quarter-wave cavity occupies less space, and has better integration and optimal practicability.
The embodiment of the invention mainly aims at the situation that the reading cavity is a transmission line type resonant cavity, but the content can be easily expanded to other situations that the reading cavity is an LC resonator under a lumped model and the like. For example, an LC resonator in the lumped model can also represent its state by a phase operator and a cooper pair operator, and calculate its coupling to a qubit. The detailed process is not described herein.
As shown in fig. 5, a partial layout of the reading apparatus is shown in a solid line box. In the figure, the white part is a superconductor, and the black part is a substrate without the superconductor. The qubits are coupled to the resonator via a josephson junction, the coupling being shown enlarged in the dashed box. The resonator is formed by a quarter-wave length transmission line, one end of which is short-circuited and the other end of which is open-circuited, and couples the josephson junction with the read cavity at its open-circuited end. The resonator is coupled to a read line. The resonant cavity and the read line may be coupled in a capacitive manner or in an inductive manner, and the coupling illustrated in the figure is capacitive coupling. The read signal is input from one end of the read line and output from the other end. The state of the qubit can be determined by measuring the output read signal.
The reading device and the reading method provided by the present disclosure are all under the framework of dispersion measurement, and can be combined with any other dispersion measurement means. For example, a read signal may be input from one end and output from the other end; it is also possible to input and output from the same end. A filter structure can be introduced on the reading line to reduce the loss of the reading cavity signal and the relaxation phenomenon of the quantum bit caused by the Purcell effect.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A superconducting qubit reading device, the reading device comprising: a qubit, a read cavity, and a josephson junction, wherein the qubit and the read cavity are coupled through the josephson junction.
2. A reading apparatus according to claim 1, wherein qubits of the reading apparatus couple ZZ of the josephson junction with the reading chamber at respective independent basis vectors of energy eigenstates.
3. A reading apparatus according to claim 1 or 2, wherein the reading chamber is a distributed transmission line type resonant chamber.
4. The reading apparatus according to claim 3, wherein the number of the Josephson junctions connecting the qubit and the transmission line type resonant cavity is one; the connection point position of the Josephson junction and the transmission line type resonant cavity and the characteristic impedance of the transmission line are determined according to parameters such as required coupling strength.
5. The apparatus according to claim 3, wherein the number of Josephson junctions connecting the qubit and the transmission line type resonant cavity is two or more.
6. A reading apparatus according to claim 1 or 2, wherein the coupling of the qubit to the reading chamber further comprises simultaneous coupling via the josephson junction and a capacitance.
7. A reading device as claimed in claim 1 or 2, characterized in that the qubit is a Transmon qubit or a Plasonium qubit.
8. A reading apparatus according to claim 1 or 2, wherein the read cavity is coupled to a read line, and the read cavity is coupled to the read line in a capacitive or inductive manner.
9. A reading apparatus according to claim 1 or 2, comprising separate flux control lines to control the flux in the loop in which the josephson junction for coupling is located.
10. A reading apparatus according to claim 1 or 2, wherein the target value for flux control in the loop in which the josephson junction is coupled is an integer number of flux quanta.
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WO2023226598A1 (en) * 2022-05-27 2023-11-30 本源量子计算科技（合肥）股份有限公司 Reading circuit, reading method and quantum computer
CN115115054A (en) * 2022-06-28 2022-09-27 合肥本源量子计算科技有限责任公司 Circuit structure, quantum chip and quantum computer
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