Quantum chip and longitudinal field modulation method for quantum chip interconnection

Abstract

The invention provides a quantum chip and a longitudinal field modulation method for quantum chip interconnection. The method comprises the following steps: exciting superconducting quantum bits in the quantum chip to a first state through a transverse field; the n-order sideband of the superconducting quantum bit induced by longitudinal field modulation based on the angular frequency of longitudinal field modulation is coupled with the transmission resonant cavity; wherein the equivalent coupling coefficient of the n-order sideband and the transmission resonant cavity is # imgabs0 #, Jn is a first Bessel function, n is an integer, A (t) is the amplitude of longitudinal field modulation, phi (t) is the phase of longitudinal field modulation, g is the coupling coefficient of the superconducting quantum bit and the transmission resonant cavity, and mu is the angular frequency of longitudinal field modulation; and the equivalent coupling coefficient is regulated and controlled through the amplitude of the longitudinal field modulation, so that the time domain envelope shaping of the radiated microwave photons is completed.

Description

Technical Field

[0001] The present invention generally relates to the field of quantum networks based on superconducting quantum circuit systems, and particularly to a quantum chip and a longitudinal field modulation method for interconnecting quantum chips. Background Art

[0002] The statements in this section are only to provide background information related to the present invention to help understand the present invention, and these background information do not necessarily constitute the prior art.

[0003] By using the switchable, high-dynamic-range, and fast-response dynamic tunable coupling between qubits and resonators, resonators and waveguides, and qubits and waveguides, microwave photon symmetric shaping can be achieved. Using waveguides to connect two (or more) superconducting quantum chips through the same interface and protocol can achieve remote interconnection therebetween. Using this quantum channel, superconducting quantum chips can achieve coherent interconnection and remote entanglement, so that the number of superconducting qubits can be further expanded, and distributed quantum computing becomes possible.

[0004] Existing such schemes include the following designs: The first one uses microwave-driven qubits and a resonator to assist the Raman process to adjust the coupling between the qubit and the resonator, achieving symmetric shaping of microwave photons. On this basis, a transmission protocol is designed to achieve long-distance transmission of quantum states with various encoding methods and the establishment of long-distance entangled states (see Pechal M, et al. 2014 PHYS.REV.X 4,041010; Kurpiers P, et al. 2018 NATURE 558,264–267; Kurpiers P, et al. 2019 PHYS.REV.APPLIED 12,044067). This process can be turned off, has a high dynamic range, can respond quickly, and has relatively small side effects during dynamic adjustment. However, it requires the use of high-energy levels of qubits for the long-distance transmission of quantum states and the establishment of long-distance entangled states. Since the coupling between the high-energy levels of qubits and the environment is stronger than that of the low-energy levels, their decoherence times are often relatively low. Therefore, during the process of quantum state transmission and the establishment of long-distance entangled states, the loss of transmission efficiency caused by the decoherence process of the high-energy levels of qubits is relatively large. The second design uses a superconducting gate-controlled qubit (Gmon) coupler (see Chen Y, et al. 2014 PHYS.REV.LETTERS 113,220502) to directly adjust the coupling between the qubit and the waveguide, achieving symmetric shaping of microwave photons. On this basis, a transmission protocol is designed, and the long-distance transmission of quantum states and the establishment of long-distance entangled states are also achieved (see Zhong Y P, et al. NATURE PHYSICS 15,741-744; Zhong YP, et al. 2021 NATURE 590,571-575). This method does not involve a resonator, reducing the dissipation channels and increasing the speed of the transmission process. In theory, higher transmission efficiency can be obtained. However, because there is no resonator involved, its encoding method is relatively single. Moreover, using a Gmon, an inductive device, to dynamically adjust the coupling between the qubit and the waveguide by adjusting the equivalent mutual inductance between them has relatively large side effects and is not easy to accurately calibrate, resulting in a decrease in transmission efficiency. The third design uses a capacitively tunable coupler (see Y. Fei, et.al. 2018 PHYS.REV.APPLIED 10,054062) to adjust the coupling between the data qubit and the auxiliary transmission qubit, and dynamically adjusts the coupling between the data qubit and the auxiliary transmission qubit through parametric coupling, thereby achieving symmetric shaping of microwave photons (see Yang J, etal. 2023 PHYS.REV.APPLIED 20,054018). There is a strong nonlinear relationship between the parametric drive of this method and the coupling coefficient between the data qubit - auxiliary transmission qubit, making the processes of microwave photon shaping and dynamically calibrating side effects difficult.Moreover, the coupler bits introduce new dissipation channels, resulting in a decrease in transmission efficiency. Summary of the Invention

[0005] Based on the above problems of the prior art, the present invention proposes a longitudinal field modulation method for quantum chip interconnection, including:

[0006] Exciting superconducting qubits in the quantum chip to the first state through a transverse field;

[0007] Based on the angular frequency of the longitudinal field modulation, coupling the nth-order sideband of the superconducting qubit induced by the longitudinal field modulation with the transmission resonator; wherein the equivalent coupling coefficient between the nth-order sideband and the transmission resonator is:

[0008]

[0009] where J n is the first kind of Bessel function, n is an integer, A(t) is the amplitude of the longitudinal field modulation, φ(t) is the phase of the longitudinal field modulation, g is the coupling coefficient between the superconducting qubit and the transmission resonator, and μ is the angular frequency of the longitudinal field modulation;

[0010] Regulating the equivalent coupling coefficient through the amplitude of the longitudinal field modulation, thereby completing the time-domain envelope shaping of the radiated microwave photons.

[0011] In one embodiment, the first state is the quantum state α|g> + β|e>, where α and β are constants, |g> is the ground state of the superconducting qubit, and |e> is the first excited state of the superconducting qubit.

[0012] In one embodiment, using any rotation gate between the ground state and the first excited state of the superconducting qubit to prepare the superconducting qubit into the quantum state α|g> + β|e>, where, within the subspace formed by the ground state and the first excited state, it rotates by an angle θ around the axis with azimuth angle φ on the Bloch sphere.

[0013] In one embodiment, when n = 1, setting the amplitude of the longitudinal field modulation or the angular frequency of the longitudinal field modulation such that approaches 0, obtaining the equivalent coupling coefficient as:

[0014]

[0015] In one embodiment, dynamically adjusting the amplitude of the longitudinal field modulation to dynamically control the magnitude of the equivalent coupling coefficient, so that the time-domain envelope of the photons generated by the qubit changes from an approximately exponential decay to a symmetric shape.

[0016] In one embodiment, the longitudinal field modulation function is a Gaussian envelope pulse, a sine-squared function envelope pulse, or a sech function envelope pulse.

[0017] In one embodiment, the longitudinal field modulation function is a sech function envelope pulse. When κ eff = κ T the equivalent coupling coefficient is:

[0018]

[0019] where κ eff is the frequency bandwidth of the emitted photons, and κ T is the frequency bandwidth of the transmission resonator.

[0020] In one embodiment, the method further includes dynamically calibrating the frequency shift of the qubit caused by the amplitudes of different longitudinal field modulations by dynamically adjusting the phase of the longitudinal field modulation or the bias of the superconducting qubit.

[0021] In one embodiment, the step of dynamically calibrating the frequency shift of the qubit caused by the amplitudes of different longitudinal field modulations by dynamically adjusting the phase of the longitudinal field modulation further includes:

[0022] Calibrating the amplitude of the longitudinal field modulation and the frequency shift;

[0023] Applying a time-dependent phase modulation to the longitudinal field modulation such that to compensate for the frequency shift;

[0024] where is the derivative of the phase of the longitudinal field modulation, and Δ(t) is the frequency shift.

[0025] The present invention also provides a quantum chip, including:

[0026] Mutually coupled superconducting qubits and a transmission resonator, with a coupling coefficient on the order of hundreds of MHz;

[0027] wherein the nth-order sideband of the superconducting qubit is coupled to the transmission resonator using the above longitudinal field modulation method for quantum chip interconnection, and the equivalent coupling coefficient is regulated by the amplitude of the longitudinal field modulation, thereby completing the time-domain envelope shaping of the radiated microwave photons.

[0028] The present invention utilizes longitudinal field modulation technology to dynamically adjust the equivalent coupling coefficient between qubits and resonators, improving the transmission efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1A Shows a schematic diagram of a quantum chip according to an embodiment of the present invention.

[0030] Figure 1B Shows a schematic diagram of a quantum chip according to another embodiment of the present invention.

[0031] Figure 2A Shows a physical diagram of a quantum chip according to an embodiment of the present invention.

[0032] Figure 2B Shows the Figure 2A corresponding lumped equivalent circuit diagram.

[0033] Figure 3 Shows the energy level structures of superconducting qubits and transmission resonators and a schematic diagram of the energy level transitions occurring during the control process.

[0034] Figure 4 Shows a flowchart of a longitudinal field modulation method for a quantum chip according to an embodiment of the present invention.

[0035] Figure 5A Shows a Gaussian envelope pulse for longitudinal field modulation.

[0036] Figure 5B Shows a sin-squared function envelope pulse for longitudinal field modulation.

[0037] Figure 5C Shows a sech function envelope pulse for longitudinal field modulation. Detailed implementation manners

[0038] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be noted that the embodiments given in the present invention are only for illustration and do not limit the protection scope of the present invention.

[0039] In the field of superconducting quantum chip interconnection, that is, in a quantum network, if the time-domain waveform of microwave photons is not controlled, the generated photon time-domain envelope will be approximately exponentially decaying, resulting in a very low transmission efficiency, only 54% (one-dimensional waveguide propagation). However, if the equivalent coupling coefficient between the qubit and the resonator is adjusted to shape the time-domain envelope of the microwave photons, quantum state transmission with 100% efficiency can be achieved, where the control methods at the transmitting end and the receiving end are time-reversal processes of each other. The present invention provides a longitudinal field modulation technology that can equivalently and dynamically control the equivalent coupling coefficient between superconducting qubits and transmission resonators, thereby realizing controllable shaping of microwave photons.

[0040] Figure 1A Shows a schematic diagram of a quantum chip according to an embodiment of the present invention, which only shows one qubit. As Figure 1AAs shown, the quantum chip includes 7 basic units, namely superconducting qubits 101, transmission resonators 102, microwave transmission lines 103 for single-photon transmission, XY control lines 104 for superconducting qubit control, Z control lines 105 for superconducting qubit frequency biasing, readout resonators 106, and microwave transmission lines 107 for superconducting qubit dispersive readout.

[0041] Among them, there is mutual coupling between the superconducting qubit 101 and the transmission resonator 102, and the coupling method is not limited. The coupling coefficient is relatively large, and the coupling coefficient can be, for example, 30 - 50 MHz. There is mutual coupling between the readout resonator 106 and the transmission line 107, and the coupling method is not limited. The coupling dissipation rate is 1 - 2 MHz, and it is necessary to satisfy the optimal readout signal-to-noise ratio relationship where the ratio of the dispersion shift to the dissipation rate is 1 / 2. There is a weak capacitive coupling between the superconducting qubit 101 and the XY control line 104, and the coupling capacitance can be, for example, 30 aF. There is a weak mutual inductance between the Josephson junction loop of the superconducting qubit 101 and the Z control line 105, and the inductance can be, for example, 2 pH. The superconducting qubit 101 and the readout resonator 106 have a moderate coupling coefficient, and the coupling method is not limited. The coupling coefficient between the transmission resonator 102 and the microwave transmission line 103 is relatively large, and the coupling method is not limited. The frequency difference between the superconducting qubit 101 and the readout resonator 106 and the transmission resonator 102 is about 1.5 GHz.

[0042] Considering the need to improve the transmission efficiency and transmission fidelity of quantum communication between superconducting quantum chips, it is necessary to specially design the coupling between the superconducting qubit 101 and the transmission resonator 102 and the coupling between the transmission resonator 102 and the microwave transmission line 103 to increase the coupling coefficient in order to increase the emission and reception speed of microwave photons. Moreover, another advantage of increasing the coupling coefficient between the transmission resonator 102 and the superconducting qubit 101 is to increase the equivalent coupling adjustment range achieved by using the longitudinal field modulation technique. However, considering that the superconducting qubit will couple with the external environment through the transmission resonator 102, thereby dissipating energy and affecting the energy decoherence time T1 of the superconducting qubit, which in turn will reduce the transmission efficiency and transmission fidelity, so it is necessary to comprehensively consider and balance when designing its coupling parameters. In the present invention, the coupling coefficient between the superconducting qubit 101 and the transmission resonator 102 adopted is on the order of hundreds of MHz, for example, greater than 100 MHz. The coupling dissipation rate between the transmission resonator 102 and the microwave transmission line 103 is on the order of 10 MHz, for example, greater than 10 MHz.

[0043] Figure 1B The schematic diagram of a quantum chip according to another embodiment of the present invention is shown, which only shows one qubit. As Figure 1BAs shown, the quantum chip includes 5 basic units, a superconducting qubit 101, an XY control line 104 for superconducting qubit control, a Z control line 105 for superconducting qubit frequency biasing, a resonator 108 with both reading and transmission functions, and a microwave transmission line 109 with both superconducting qubit dispersive reading and single-photon transmission functions. Among them, the superconducting qubit 101 has a weak capacitive coupling with the XY control line 104, and the Josephson junction loop of the superconducting qubit 101 has a weak mutual inductance with the Z control line 105, which is Figure 1A the same as that in

[0044] Combined with Figure 1A and Figure 1B , the microwave transmission line 103 for single-photon transmission, the XY control line 104, the Z control line 105, and the microwave transmission line 109 with both superconducting qubit dispersive reading and single-photon transmission functions are all connected to the microwave transmission line inside the dilution refrigerator at one point through bonding, PCB, or microwave connectors. The microwave transmission line 107 for superconducting qubit dispersive reading is connected to the microwave transmission line inside the dilution refrigerator at two points through bonding, PCB, or microwave connectors. The microwave transmission line 107 for superconducting qubit dispersive reading can also have only one connection with the microwave transmission line inside the dilution refrigerator, and the quantum state of the superconducting qubit 101 can be dispersively read through the reading resonator 106 using reflective reading.

[0045] In the above embodiments, any type of superconducting qubit 101 can be used as long as the frequency of the qubit can be adjusted by the magnetic flux added to the Josephson junction loop. The superconducting qubit 101 can use a floating-ground or grounded design. The transmission resonator 102, the reading resonator 106, and the resonator 108 with both reading and transmission functions can be quarter-wavelength type, half-wavelength short-circuit type, half-wavelength open-circuit type coplanar waveguide resonators, or three-dimensional resonators or other microwave resonators. The transmission resonator 102, the reading resonator 106, and the resonator 108 with both reading and transmission functions can have Purcell filters outside.

[0046] In one embodiment, the quantum chip can include multiple superconducting qubits, and the superconducting qubits can be coupled or uncoupled, or can be coupled through a coupler.

[0047] In one embodiment, the XY control line and the Z control line can also be combined into one line, which can be connected to the microwave line inside the dilution refrigerator from the same output port and split into two paths on the chip.

[0048] In the above embodiments, the coupling can be capacitive coupling, inductive coupling, or both.

[0049] Figure 2A Fig. shows a physical diagram of a quantum chip according to an embodiment of the present invention, which uses Figure 1A the structure shown. Figure 2B Fig. shows the Figure 2A corresponding lumped equivalent circuit diagram. Among them, the superconducting qubit uses the design of the Xmon-type grounded transmon superconducting qubit. Figure 2A The quantum chip shown includes: qubit capacitor plates 201; a transmission resonator 202, which is a quarter-wavelength coplanar waveguide; a transmission line 203, which is coupled to the transmission resonator by interdigital capacitors for single-photon transmission; an XY control line 204, which is capacitively coupled to the qubit capacitor; a Z control line 205, which has a mutual inductance with the Josephson junction loop of the qubit; the Josephson junction loop 206 of the qubit; a read resonator 207, which is a quarter-wavelength coplanar waveguide; and a microwave transmission line 208 for dispersive readout of superconducting qubits. The transmission resonator 202 can be equivalent to Figure 2B the lumped LC circuit in Figure 2B and the read resonator 207 can also be equivalent to

[0050] Figure 2A Figure 2B and

[0051]

[0052] Although the schematic diagram of a quantum chip capable of longitudinal field modulation is shown in the above embodiments, the present invention is not limited thereto. Any quantum chip in which the superconducting qubit and the transmission resonator are capacitively or inductively coupled can perform longitudinal field modulation.

[0052] The principle of longitudinal field modulation of the present invention is described below. Here, the longitudinal field refers to: applying a microwave drive through a transmission line having a mutual inductance with the Josephson junction loop of the superconducting qubit. Such a drive will induce a periodic change in the frequency of the qubit, thereby inducing a σ term in the qubit Hamiltonian operator. Such a drive will not change the populations of the ground state and excited state of the qubit, which is manifested as a rotation along the z-axis on the Bloch sphere. The longitudinal field modulation technique is to add a periodically changing magnetic flux to the Josephson junction loop of the superconducting qubit, so that the frequency of the superconducting qubit changes periodically to induce multi-order sidebands to couple with other physical degrees of freedom (energy levels of other qubits or energy levels of a resonator or energy levels of a waveguide, etc.). The longitudinal field modulation technique can use longitudinal field pulses with different amplitudes to control the equivalent coupling coefficient, so as to achieve the required magnitude of the equivalent coupling coefficient. z The Hamiltonian operator of a system formed by a superconducting qubit (truncated to a two-level system) and a transmission resonator is

[0053]

[0054]

[0055]

[0055] where is the instantaneous frequency of the superconducting qubit after adding longitudinal field modulation, ω q is the initial angular frequency of the qubit, ω r is the angular frequency of the transmission resonator, g is the coupling coefficient between the superconducting qubit and the transmission resonator, A(t) is the amplitude of the longitudinal field modulation, μ is the angular frequency of the longitudinal field modulation, and φ(t) is the phase of the longitudinal field modulation. is the creation operator of photons in the transmission resonator, a is the annihilation operator of photons in the transmission resonator, σ + is the raising operator of the superconducting qubit equivalent two-level system, σ - is the lowering operator of the superconducting qubit equivalent two-level system. h is the Planck constant, and c is the speed of light. In the interaction representation, we get:

[0056]

[0057] where, Δ = ω q - ω r , so when Δ = nμ (n is an integer), it is considered that the nth-order sideband of the superconducting qubit induced by longitudinal field modulation resonates with the energy level of the transmission resonator and can completely exchange energy, while other sidebands are in a large detuning state with the resonator. At this time, the equivalent coupling coefficient between the nth-order sideband of the superconducting qubit induced by longitudinal field modulation and the transmission resonator is where j n is the first kind of Bessel function. Therefore, the equivalent coupling coefficient g can be dynamically controlled by dynamically adjusting the amplitude A(t) of the longitudinal field. effThe magnitude of (t). In one embodiment, the amplitude A(t) of the longitudinal field can be dynamically adjusted to dynamically control the equivalent coupling coefficient g eff (t) such that the temporal envelope of the photons generated by the qubit changes from an approximately exponential decay to a symmetric shape.

[0058] Since different longitudinal field amplitudes A(t) during actual regulation will cause different frequency offsets of the qubit, the dynamic frequency offset can be dynamically calibrated by adjusting the phase φ(t) of the longitudinal field. Different longitudinal field modulation amplitudes A(t) when using the longitudinal field modulation technique will induce different degrees of frequency offset Δ(t) of the superconducting qubit. Since the frequency offset Δ(t) corresponds to the amplitude A(t) of the longitudinal field modulation, this frequency offset Δ(t) can be calibrated experimentally, and then a time-dependent phase modulation φ(t) is added to the longitudinal field modulation, satisfying to compensate for the frequency offset of the qubit. This frequency calibration is very crucial as it can ensure that the photon frequency does not change during the emission of microwave photons. Those skilled in the art should understand that the above frequency calibration method is only an example, and other frequency calibration methods can also be used in actual applications, including but not limited to adding a dynamically changing flux bias to the superconducting qubit to eliminate in real time the frequency offset of the superconducting qubit caused by the change in the longitudinal field amplitude.

[0059] Figure 3 Shows the energy level structure of the superconducting qubit and the transmission resonator and the schematic diagram of the energy level transitions occurring during the regulation process, which describes the process of the temporal envelope of the microwave photons radiated by the regulation and shaping of the coupling between the superconducting qubit and the transmission resonator under the longitudinal field modulation. Figure 3 The left side shows the lowest three states of the superconducting qubit in the superconducting state, namely the ground state |g>, the first excited state |e>, and the second excited state |f>. The different states are represented by horizontal lines in the figure. By applying a transverse field, the qubit can be excited to any state. Among them, the transverse field refers to: the microwave drive applied through the transmission line capacitively coupled to the superconducting qubit, and such a drive will induce the σ x and σ y terms in the qubit Hamiltonian operator, and such a drive will change the population of the ground state and the excited state of the qubit, manifested as rotating a certain angle along a certain rotation axis in the xy plane on the Bloch sphere. Figure 3 The right side shows the zero-photon number state |0> and the one-photon number state |1> of the transmission resonator.

[0060] Quantum chip interconnection means that the qubits on one quantum chip can transmit quantum states and establish entanglement with the qubits on another quantum chip. Since there is no physical interaction, it is necessary to use the transmission of microwave photons to establish an entangled state.

[0061] Figure 4 The flowchart of a longitudinal field modulation method for quantum chip interconnection according to an embodiment of the present invention is shown, in combination with Figure 3 and Figure 4 , the method includes:

[0062] Step 101: Excite a superconducting qubit to the state α|g> + β|e> through a transverse field.

[0063] Where α and β are constants, and by controlling the values of the constants α and β, the superconducting qubit can be excited to any state within the subspace composed of the ground state and the excited state.

[0064] In one embodiment, any rotation gate between the ground state and the excited state (within the subspace formed by the ground state and the first excited state, rotating by an angle θ around the axis with azimuth angle φ on the Bloch sphere) is used to prepare the superconducting qubit into the quantum state α|g> + β|e>.

[0065] In one embodiment, the superconducting qubit can be excited to the first excited state |e> through a transverse field.

[0066] Step 102: Couple the nth-order sideband of the superconducting qubit induced by longitudinal field modulation with the transmission resonator based on the angular frequency μ of the longitudinal field modulation.

[0067] Where Δ = ω q -ω r = nμ (n is an integer), so that the nth-order sideband of the superconducting qubit induced by longitudinal field modulation resonates with the energy levels of the transmission resonator, and the energy can be completely exchanged.

[0068] Where the equivalent coupling coefficient between the superconducting qubit and the transmission resonator is

[0069] Step 103: Regulate the equivalent coupling coefficient g eff (t) through the amplitude A(t) of the longitudinal field modulation, thereby completing the shaping of the time-domain envelope of the radiated microwave photons.

[0070] Where this process satisfies the conservation of the excitation number After completing a half-exchange of energy, the state α|g> + β|e> of the superconducting qubit will be mapped to the state α|0> + β|1> of the transmission resonator. As the microwave photons radiate out from the transmission resonator along the transmission line, they will ultimately be mapped to the quantum state α|0> + β|1> of the flying microwave photons. At the same time, this process also completes the shaping of the time-domain envelope of the radiated microwave photons. Theoretically, as long as the equivalent coupling coefficient g eff(t) and dynamically eliminate side effects (frequency shift of superconducting qubits), arbitrary-shaped microwave photon time-domain envelope shaping can be achieved. Preferably, the microwave photon time-domain envelope is shaped into a symmetric type, which is easier to control and receive at the receiving end.

[0071] Although in the above embodiments, the longitudinal field modulation technique is used to dynamically adjust the coupling between two energy levels, |g1> (which represents the joint quantum state of the qubit in the ground state |g> and the resonator in the one-photon state |1>) and |e0> (which represents the joint quantum state of the qubit in the first excited state |e> and the resonator in the zero-photon state |0>), to shape the time-domain envelope of the microwave photons radiated by the transmission line. However, the present invention is not limited thereto. Those skilled in the art should understand that other energy level couplings can also be used, as long as it is within the subspace of excitation number conservation. For example, |e0> and |g1> coupling, |f0> and |e1> coupling, etc. can be used, and they can all complete the coupling adjustment of single excitation number exchange, and then shape the time-domain envelope of the microwave photons radiated by the transmission line.

[0072] In one embodiment, in fact, to achieve high-efficiency photon transmission in an efficient quantum network node, it is not necessary to complete the symmetric shaping of the photon time-domain envelope. Such a method is only a special case. It is only necessary to dynamically adjust the coupling between the qubits at the transmitting end and the receiving end and their transmission resonators to meet the dark state condition of the cascaded quantum system (all the photon energy emitted by the transmitting end is received by the receiving end). Therefore, the time-domain envelope of the microwave photons emitted by the transmitting end can be either symmetric or exponentially rising, etc. In one embodiment, techniques such as machine learning and quantum optimization control can be used to generate the longitudinal field modulation waveforms at the transmitting end and the receiving end.

[0073] Figure 5A Shows a Gaussian envelope pulse for longitudinal field modulation, Figure 5B Shows a sin-squared function envelope pulse for longitudinal field modulation, Figure 5C Shows a sech function envelope pulse for longitudinal field modulation. Figures 5A - 5C The pulses used in are all axisymmetric about the center axis because mainly the rising edge of the pulse is used to shape the microwave photons, and the falling edge only serves to slowly turn off the coupling between the superconducting qubit and the transmission resonator. However, for the receiving end, in order to receive the microwave photons with a symmetric time-domain envelope, it is necessary to control the falling edge of the pulse to gradually reduce the coupling between the superconducting qubit and the transmission resonator from large to small and then to zero. Therefore, if the control pulse used is centrosymmetric, then in theory, the same waveform can be used at the transmitting end and the receiving end to emit and receive symmetric microwave photons, reducing the experimental parameters. Those skilled in the art should understand that other shapes of longitudinal field modulation waveforms can also be used. Preferably, the shape of the longitudinal field modulation pulse waveform used can achieve the symmetric shaping of the microwave photon time-domain envelope.

[0074] In one embodiment, a first-order sideband (i.e., n = 1) of longitudinal field modulation can be used. If the amplitude of the applied longitudinal field modulation is small enough or the angular frequency of the longitudinal field modulation is high enough such that an equivalent coupling coefficient of can be obtained. Thus, g eff (t) ∝ A(t). Using such a proportional relationship, the shaping and dynamic phase calibration of microwave photons can be conveniently achieved. By using the longitudinal field modulation principle to modulate the coupling between a superconducting qubit and a transmission resonator, a linear drive amplitude-equivalent coupling coefficient relationship at a small drive strength can be achieved using the first-order sideband, which is beneficial for the shaping and dynamic phase calibration of microwave photons.

[0075] In one embodiment, in a system where a superconducting qubit is coupled to a transmission resonator and the transmission resonator is further coupled to a microwave transmission line, if a photon wave packet with a sech function-form time-domain envelope is required the required equivalent coupling coefficient can be analytically obtained as:

[0076]

[0077] where κ eff ≤ κ T , κ eff is the frequency bandwidth of the emitted photons, and κ T is the frequency bandwidth of the transmission resonator. The upper limit of the frequency bandwidth of the microwave photons is the frequency bandwidth of the transmission resonator. When κ eff = κ T , the following can be obtained:

[0078]

[0079] which is in the form of a sech function envelope. When the amplitude of the control pulse A(t) is proportional to g eff (t), that is, when using the first sideband and the amplitude of the pulse is small enough, a symmetric microwave photon time-domain envelope of the form can be obtained using a longitudinal field modulation pulse with a sech function envelope. Therefore, the sech function is also a commonly used form of the control pulse wave packet.

[0080] The present invention uses longitudinal field modulation technology to adjust the coupling between a superconducting qubit and a transmission resonator, thereby performing microwave photon shaping and quantum communication between chips. The longitudinal field modulation technology used in the present invention has the following advantages:

[0081] (1) In the prior art, a longitudinal field with a fixed amplitude (A is time-independent) is used to achieve an equivalent coupling coefficient that does not change with time. The present invention realizes the time-dependent regulation of the equivalent coupling coefficient (the amplitude A(t) of the longitudinal field modulation is time-dependent) to achieve the controllable shaping of the microwave photon time-domain envelope. Usually, the symmetric type is used because the symmetric microwave photon time-domain envelope is beneficial for the regulation of the transmitting end and the receiving end.

[0082] (2) When using the longitudinal field modulation technique, different longitudinal field modulation amplitudes A(t) will induce different degrees of frequency shift Δ(t) of the superconducting qubit. This frequency shift can be calibrated experimentally. Then, by adding a time-dependent phase modulation φ(t) to the longitudinal field modulation, it satisfies This frequency calibration can ensure that the photon frequency does not change during the process of transmitting microwave photons.

[0083] (3) If the first-order sideband induced by the longitudinal field modulation is coupled with the transmission resonator, the Taylor expansion of the first-order Bessel function J n (x) near 0 can be observed to be linear J n (x) ≈ x / 2. Thus, When (which is actually well satisfied because the longitudinal field modulation amplitude can be very small and the angular frequency of the longitudinal field modulation is very large), g(t) ∝ A(t) can be obtained, which is very beneficial for regulating the microwave photon time-domain envelope and frequency calibration, greatly reducing the difficulty.

[0084] (4) The angular frequency of the longitudinal field modulation used in the present invention is much larger than that in the prior art, making the frequencies of other sidebands far apart, and it is not easy to couple with other qubits or parasitic degrees of freedom (two-level impurities) in the superconducting quantum chip, thus affecting the quantum communication effect between chips.

[0085] Although the present invention has been described through preferred embodiments, the present invention is not limited to the embodiments described herein. Various changes and variations are also included without departing from the scope of the present invention.

Claims

1. A longitudinal field modulation method for quantum chip interconnection, comprising: Exciting superconducting qubits in a quantum chip to a first state through a transverse field; Coupling the nth-order sideband of the superconducting qubit induced by longitudinal field modulation with a transmission resonator based on the angular frequency of the longitudinal field modulation; wherein the equivalent coupling coefficient between the nth-order sideband and the transmission resonator is: where J n is the Bessel function of the first kind, n is an integer, A(t) is the amplitude of the longitudinal field modulation, φ(t) is the phase of the longitudinal field modulation, g is the coupling coefficient between the superconducting qubit and the transmission resonator, and μ is the angular frequency of the longitudinal field modulation; Regulating the equivalent coupling coefficient through the amplitude of the longitudinal field modulation, thereby completing the time-domain envelope shaping of the radiated microwave photons.

2. The longitudinal field modulation method for quantum chip interconnection according to claim 1, wherein The first state is a quantum state α|g> + β|e>, where α and β are constants, |g> is the ground state of the superconducting qubit, and |e> is the first excited state of the superconducting qubit.

3. The longitudinal field modulation method for quantum chip interconnection according to claim 2, wherein Any rotation gate between the ground state and the first excited state of the superconducting qubit Prepare the superconducting qubit into the quantum state α|g> + β|e>, where within the subspace formed by the ground state and the first excited state, it rotates by an angle θ around the axis with azimuth angle φ on the Bloch sphere.

4. The longitudinal field modulation method for quantum chip interconnection according to claim 1, wherein In the case of n = 1, set the amplitude of the longitudinal field modulation or the angular frequency of the longitudinal field modulation such that approaches 0, and the obtained equivalent coupling coefficient is:

5. The longitudinal field modulation method for quantum chip interconnection according to claim 1, wherein Dynamically adjusting the amplitude of the longitudinal field modulation to dynamically control the magnitude of the equivalent coupling coefficient, such that the time-domain envelope of the photons generated by the superconducting qubit changes from an approximately exponential decay to a symmetric shape.

6. The longitudinal field modulation method for quantum chip interconnection according to claim 5, wherein, The longitudinal field modulation function is a Gaussian envelope pulse, a sin-squared function envelope pulse, or a sech function envelope pulse.

7. The longitudinal field modulation method for quantum chip interconnection according to claim 5, wherein, The longitudinal field modulation function is a sech function envelope pulse. When κ eff = κ T , the equivalent coupling coefficient is as follows: where κ eff is the frequency bandwidth of the emitted photons, and κ T is the frequency bandwidth of the transmission resonator.

8. The longitudinal field modulation method for quantum chip interconnection according to any one of claims 1-7, wherein The method further comprises: dynamically calibrating the frequency offset of the qubit caused by different amplitudes of the longitudinal field modulation by dynamically adjusting the phase of the longitudinal field modulation or the bias of the superconducting qubit.

9. The longitudinal field modulation method for quantum chip interconnection according to claim 8, wherein, The step of dynamically calibrating the frequency offset of the qubit caused by different amplitudes of the longitudinal field modulation by dynamically adjusting the phase of the longitudinal field modulation further comprises: Calibrating the amplitude of the longitudinal field modulation and the frequency offset; Apply a time-dependent phase modulation to the toroidal field modulation such that compensate for the frequency shift; where, is the derivative of the phase of the toroidal field modulation, and Δ(t) is the frequency offset.

10. A quantum chip, comprising: A superconducting qubit and a transmission resonator that are mutually coupled, and their coupling coefficient is on the order of hundreds of MHz; Wherein, the nth-order sideband of the superconducting qubit is coupled with the transmission resonator by using the longitudinal field modulation method for quantum chip interconnection according to any one of claims 1-9, and the equivalent coupling coefficient is regulated through the amplitude of the longitudinal field modulation, thereby completing the time-domain envelope shaping of the radiated microwave photons.

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