Quantum state transmission and remote entanglement state establishment method of three-energy-level quantum bit

Abstract

The invention provides a quantum state transmission and remote entanglement state establishment method of a three-energy-level quantum bit, and the quantum state transmission method comprises the steps: 1, preparing a superconducting quantum bit into any three-energy-level quantum bit state alpha < gt > at a transmitting end; + beta egt; + gamma fgt; ; wherein alpha, beta and gamma are constants, gt; the state is the ground state of the superconducting quantum bit, egt; the first excitation state is the first excitation state of the superconducting quantum bit, fgt; the first excitation state is a second excitation state of the superconducting quantum bit; step 2, performing a complete exchange process by using transverse field modulation pulses, performing a complete exchange process by using longitudinal field modulation pulses, and generating a first time window flight photon-second time window flight photon combined quantum state; and step 3, at a receiving end, through a time inversion process, receiving the flight photons to the superconducting quantum bits of the receiving end by using the transverse field modulation pif0g1 pulse and the longitudinal field modulation pie0g1 pulse.

Description

Technical Field

[0001] This invention relates generally to the field of quantum networks based on superconducting quantum circuit systems, and particularly to a method for quantum state transmission and remote entanglement establishment of three-level qubits based on longitudinal-transverse field joint modulation technology. Background Technology

[0002] The statements in this section are merely to provide background information in relation to the present invention to aid in understanding the invention, and such background information does not necessarily constitute prior art.

[0003] Realizing quantum state transfer and long-range entanglement between superconducting quantum chips using flying microwave photons is crucial for establishing quantum networks with superconducting quantum chips as quantum processors, and also key to further expanding superconducting quantum chips through modularization. In previous work, researchers used cavity-assisted Raman processes (see Pechar 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) and superconducting gated qubit couplers (gmon) (see Zhong YP, et al. 2019 NATURE PHYSICS15) to adjust coupling and symmetrically shape photons, thus achieving long-range quantum state transfer of qubits and the establishment of long-range entanglement between two physical qubits. With the development of this field, various works have emerged to optimize quantum network performance, including interconnects between multi-bit chips (see Zhong YP, et al. 2021 NATURE 590, 571-575), long-distance interconnects (64m) (see Qiu J, et al. 2023 arXiv preprint arXiv: 2302.08756), bidirectional directional interconnects (see Almanakly A, et al. 2024 arXiv preprint arXiv: 2408.05164), and extremely high-fidelity interconnects (see Niu J, et al. 2023 Nature Electronics, 6(3): 235-241.). The main development trend is interconnect network structures with more chips, more bits, longer distances, higher fidelity, and higher efficiency.

[0004] In fact, besides improving the quantum channel capacity of a single channel in a quantum network and realizing the reuse of quantum channels to enhance the efficiency of quantum information transmission and entanglement distribution, this is also a key aspect of future quantum network research. In previous work, researchers used qubits for quantum state transmission and to establish long-range entangled states between two qubits, utilizing only the two-level subspace composed of the ground state and the first excited state of the superconducting qubit. However, by leveraging the inherent multi-level characteristics of commonly used superconducting qubits (e.g., transmons), more quantum information can be encoded using higher-dimensional state spaces, thereby enabling quantum computing physical media with encoding in three-level, four-level, or even higher-dimensional subspaces, such as three-level qubits (qutrits) and four-level ququarts. The aforementioned high-dimensional quantum systems can provide advantages in certain quantum algorithms (see Roy, et al. 2023 PHYS. REV. APPLIED 19, 064024), reducing the number of superconducting qubits and gate depth required when performing quantum algorithm tasks (see Liu P, et al. 2023 PHYS. REV. X 13, 021028). In recent years, researchers have realized a Walsh-Hadamard gate for a single three-level qubit on a superconducting quantum chip (see Yurtalan MA, et al. 2020 PHYS.REV.LETT. 125, 180504), a high-fidelity logic gate between two three-level qubits (see Goss N, et al. 2022 Nat Commun 13, 7481), random benchmarking of three-level qubits (see Morvan A, et al. 2021 PHYS.REV.LETT 126, 210504), and quantum information scrambling of a three-level qubit system (see Blok MS, et al. 2021 PHYS.REV.X 11, 021010), verifying the feasibility of quantum computing and other quantum information processing tasks based on three-level qubit systems. However, how to achieve remote three-level quantum bit interconnection between chips and achieve entanglement between remote three-level quantum bits remains an unsolved problem. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a method for quantum state transfer of a three-level qubit, comprising:

[0006] Step 1: At the transmitting end, prepare the superconducting quantum bit into an arbitrary three-level quantum bit state α|g>+β|e>+γ|f>; where α, β, and γ are constants, |g> is the ground state of the superconducting quantum bit, |e> is the first excited state of the superconducting quantum bit, and |f> is the second excited state of the superconducting quantum bit;

[0007] Step 2: Use transverse field modulation pulses to complete The exchange process, and the complete operation using longitudinal field modulation pulses. The exchange process generates a joint quantum state of a first-time-window photon and a second-time-window photon;

[0008] Step 3: At the receiving end, through a time reversal process, transverse field modulation π is used. f0g1 Pulse and longitudinal field modulation π e0g1 The pulse receives the flying photons onto the superconducting qubits at the receiving end.

[0009] In one embodiment, step 1 includes:

[0010] By using arbitrary rotation gates in the subspaces {|g>, |e>} and {|e>, |f>}, superconducting qubits can be prepared into arbitrary three-level qubit states.

[0011] In one embodiment, step 2 includes:

[0012] First, using transverse field modulation π f0g1 Pulse complete The exchange process forms a joint quantum state α|g0>+β|e0>+γ|g1> between the superconducting qubit at the transmitter and the photon flying in the first time window. Subsequently, π is modulated using the longitudinal field. e0g1 Pulse complete The exchange process generates a joint quantum state α|00>+β|01>+γ|10>, which is a combination of a first time window photon and a second time window photon.

[0013] In one embodiment, step 2 includes:

[0014] First, using longitudinal field modulation π e0g1 Pulse complete The exchange process forms a joint quantum state α|g0>+β|g1>+γ|f0> between the superconducting qubit at the transmitter and the photon flying in the first time window. Subsequently, transverse field modulation of π is used. f0g1 Pulse complete The exchange process generates a joint quantum state α|00>+β|10>+γ|01>, which is the first time window photon-second time window photon.

[0015] This invention also provides a method for establishing a long-range entangled state of a three-level qubit, comprising:

[0016] Step 1: At the transmitting end, prepare the superconducting quantum bit to the first excited state |e>;

[0017] Step 2: Partially modulated using longitudinal field pulses The exchange process utilizes π ef The pulse transforms the quantum state |e> to the quantum state |f>, utilizing π. ge Pulses induce a quantum state |g> to a quantum state |e>, and transverse field modulated pulses are used for partial... The exchange process yields a maximum entangled state of 3, consisting of the three-level qubits at the transmitter and the photons flying in the first and second time windows.

[0018] Step 3: At the receiving end, use longitudinal field modulation π e0g1 Pulse complete The exchange process involves receiving the photons from the first time window of the transmission resonant cavity at the receiving end onto the superconducting qubit at the receiving end, and then using transverse field modulation of π. f0g1 Pulse complete In the exchange process, the photons that enter the second time window of the receiving end transmission resonant cavity are received onto the receiving end superconducting qubit, so as to establish the maximum entanglement state of the two remote three-level qubits.

[0019] In one embodiment, step 1 includes: utilizing the π of the {|g>,|e>} subspace ge The pulse excites the superconducting qubit to the first excited state |e>.

[0020] In one embodiment, step 2 includes the following steps in sequence:

[0021] Using longitudinal field modulation Pulse execution section The exchange process forms a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window.

[0022] Using the π of the subspace {|e>,|f>} ef A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window.

[0023] Using π in the subspace {|g>,|e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window.

[0024] Using transverse field modulation Pulse execution section The exchange process yields the joint quantum state of the superconducting qubit at the transmitter, the photon flying in the first time window, and the photon flying in the second time window.

[0025] In one embodiment, step 3 includes the following steps in sequence:

[0026] First, using longitudinal field modulation π e0g1 Pulse complete In the exchange process, the photon transmitted to the receiving end transmission resonant cavity in the first time window is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, the flying photon in the second time window, and the receiving end superconducting qubit.

[0027] Then, using transverse field modulation π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit. To achieve the maximum entanglement state of two long-range three-level qubits The establishment of.

[0028] In one embodiment, step 2 includes the following steps in sequence:

[0029] Using the π of the subspace {|e>,|f>} ef The pulse excites the superconducting qubit to the |f> state;

[0030] Using transverse field modulation Pulse execution section The exchange process forms a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window.

[0031] Using π in the subspace {|g>,|e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state of the superconducting qubit at the transmitter and the flying photon in the first time window.

[0032] Using longitudinal field modulation Pulse execution section The exchange process yields the joint quantum state of the superconducting qubit at the transmitter, the photon flying in the first time window, and the photon flying in the second time window.

[0033] In one embodiment, step 3 includes the following steps in sequence:

[0034] Using longitudinal field modulation π e0g1 Pulse complete In the exchange process, the photon transmitted to the receiving end transmission resonant cavity in the first time window is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, the flying photon in the second time window, and the receiving end superconducting qubit.

[0035] Using π in the subspace {|g>,|e>} ge A pulse is applied to the superconducting qubit at the receiving end, resulting in a joint quantum state of the superconducting qubit at the transmitting end, the photon flying in the second time window, and the superconducting qubit at the receiving end.

[0036] Using transverse field modulation π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit.

[0037] Using π in the subspace {|g>,|e>} ge A pulse is applied to the superconducting qubits at the receiving end to obtain the final result. Maximum entanglement state of a three-level qubit.

[0038] This invention proposes a scheme based on longitudinal-transverse field joint modulation technology to realize the long-range quantum state transmission and the establishment of long-range maximally entangled states between three-level qubits, filling a gap in this field. This method leverages the higher-dimensional encoding space of three-level qubits to improve the quantum channel capacity in a single quantum channel and the entanglement degree of long-range entangled states. This is of great help in optimizing the information transmission efficiency of quantum networks and further expanding quantum computing systems based on three-level qubits. Based on the generated long-range three-level qubit entanglement, common applications such as quantum teleportation, dense coding, E91 quantum key distribution, and quantum precision measurement based on two-level qubits can be extended, thereby achieving higher precision and stronger noise robustness. Attached Figure Description

[0039] Figure 1A A schematic diagram of a quantum chip according to an embodiment of the present invention is shown.

[0040] Figure 1B A schematic diagram of a quantum chip according to another embodiment of the present invention is shown.

[0041] Figure 2A A physical diagram of a quantum chip according to an embodiment of the present invention is shown.

[0042] Figure 2B It shows the relationship with Figure 2A The corresponding lumped equivalent circuit diagram.

[0043] Figure 3A A schematic diagram of the quantum mechanical principle of longitudinal field modulation is shown.

[0044] Figure 3B A schematic diagram illustrating the quantum mechanical principle of transverse field modulation (cavity-assisted Raman process) is shown.

[0045] Figure 4A The Gaussian envelope pulse used for longitudinal field modulation is shown.

[0046] Figure 4B The sin square function envelope pulse used for longitudinal field modulation is shown.

[0047] Figure 4C The envelope pulse of the sech function used for longitudinal field modulation is shown.

[0048] Figure 5 A flowchart of a quantum state transfer method for a three-level qubit according to an embodiment of the present invention is shown.

[0049] Figure 6A The control pulse sequence of the transmitter and receiver for remote transmission of arbitrary quantum states of three-level qubits according to the first embodiment of the present invention is shown.

[0050] Figure 6B The control pulse sequence of the transmitter and receiver for remote transmission of arbitrary quantum states of three-level qubits according to a second embodiment of the present invention is shown.

[0051] Figure 7 A flowchart of a method for establishing a remote entangled state of a three-level qubit according to an embodiment of the present invention is shown.

[0052] Figure 8A The control pulse sequence for the transmitter and receiver for establishing a remote maximum entanglement state of a three-level qubit according to a first embodiment of the present invention is shown.

[0053] Figure 8B The control pulse sequence for the transmitter and receiver for establishing a remote maximum entanglement state of a three-level qubit according to a second embodiment of the present invention is shown. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments given in this invention are for illustrative purposes only and do not limit the scope of protection of this invention.

[0055] This invention combines longitudinal and transverse field modulation techniques to realize a quantum network node (interface) for symmetric shaping and transmission of single photons with an auxiliary transmission resonant cavity and high-efficiency reception of shaped single photons.

[0056] 1. Sample Design

[0057] This invention provides a sample design that can serve as both a transmitter and a receiver in a quantum network based on three-level qubits. To better utilize longitudinal field modulation techniques, the superconducting qubits of this invention are frequency-tunable, such as double Josephson junction transmon superconducting qubits. To achieve a large equivalent coupling between the superconducting qubits and the transmission resonator even under weak longitudinal-transverse field driving, the sample design employs a large coupling design between the transmission resonator and the superconducting qubits. Furthermore, to reduce the time-domain broadening of single photons, the sample design utilizes a large coupling design between the transmission resonator and the microwave transmission line used for single-photon transmission. However, this invention is not limited to these limitations; any quantum chip with capacitive or inductive coupling between the superconducting qubits and the transmission resonator can perform transverse and longitudinal field modulation.

[0058] Figure 1A A schematic diagram of a quantum chip according to an embodiment of the present invention is shown, which illustrates only one qubit. Figure 1A As shown, the quantum chip includes seven basic units: a superconducting quantum bit 101, a transmission resonant cavity 102, a microwave transmission line 103 for single-photon transmission, an XY control line 104 for superconducting quantum bit control, a Z control line 105 for superconducting quantum bit frequency biasing, a readout resonant cavity 106, and a microwave transmission line 107 for superconducting quantum bit discrete readout.

[0059] In this system, the superconducting quantum bit 101 is coupled to the transmission resonant cavity 102, with no limitation on the coupling method and a relatively large coupling coefficient, such as 30-50 MHz. The readout resonant cavity 106 is coupled to the transmission line 107, with no limitation on the coupling method and a coupling dissipation rate of 1-2 MHz, requiring an optimal readout signal-to-noise ratio (SNR) where the dispersion shift to dissipation rate ratio is 1 / 2. The superconducting quantum bit 101 has a weak capacitive coupling with the XY control line 104, with a coupling capacitance of, for example, 30 aF. The Josephson junction loop of the superconducting quantum bit 101 has a weak mutual inductance with the Z control line 105, with an inductance of, for example, 2 pH. The superconducting quantum bit 101 has a moderate coupling coefficient with the readout resonant cavity 106, with no limitation on the coupling method. The transmission resonant cavity 102 has a relatively large coupling coefficient with the microwave transmission line 103, with no limitation on the coupling method. The frequency difference between the superconducting quantum bit 101 and the readout resonant cavity 106 and the transmission resonant cavity 102 is about 1.5 GHz.

[0060] Considering the need to improve the transmission efficiency and fidelity of quantum communication between superconducting quantum chips, special design is required for the coupling between the superconducting quantum bit 101 and the transmission resonant cavity 102, as well as the coupling between the transmission resonant cavity 102 and the microwave transmission line 103, to increase the coupling coefficient and thus improve the emission and reception speed of microwave photons. Furthermore, increasing the coupling coefficient between the transmission resonant cavity 102 and the superconducting quantum bit 101 also improves the equivalent coupling adjustment range achieved using longitudinal field modulation technology. However, considering that the superconducting quantum bit will couple with the external environment through the transmission resonant cavity 102, thereby dissipating energy and affecting the energy decoherence time T1 of the superconducting quantum bit, which in turn reduces transmission efficiency and fidelity, a comprehensive trade-off must be considered when designing its coupling parameters. In this invention, the coupling coefficient between the superconducting quantum bit 101 and the transmission resonant cavity 102 is on the order of hundreds of MHz, for example, greater than 100 MHz. The coupling dissipation rate between the transmission resonant cavity 102 and the microwave transmission line 103 is on the order of 10 MHz, for example, greater than 10 MHz.

[0061] Figure 1B A schematic diagram of a quantum chip according to another embodiment of the present invention is shown, which shows only one qubit. Figure 1B As shown, the quantum chip includes five basic units: a superconducting quantum bit 101, an XY control line 104 for controlling the superconducting quantum bit, a Z control line 105 for frequency biasing the superconducting quantum bit, a resonant cavity 108 that serves both readout and transmission functions, and a microwave transmission line 109 that combines superconducting quantum bit dispersion readout and single-photon transmission functions. The superconducting quantum bit 101 has weak capacitive coupling with the XY control line 104, and the Josephson junction loop of the superconducting quantum bit 101 has weak mutual inductance with the Z control line 105. Figure 1AThe superconducting quantum bit 101 is coupled to the resonant cavity 108 in any manner. The resonant cavity 108 is coupled to the microwave transmission line 109 in any manner.

[0062] Combination Figure 1A and Figure 1B The XY control line 104 and Z control line 105 are connected to the microwave transmission line inside the dilution refrigerator at one point via bonding, PCB, and microwave connector. The microwave transmission line 107, used for superconducting quantum ratio characteristic spread readout, is connected to the microwave transmission line inside the dilution refrigerator at two points via bonding, PCB, and microwave connector. The microwave transmission line 103, used for single-photon transmission, and the microwave transmission line 109, which combines superconducting quantum ratio characteristic spread readout and single-photon transmission functions, are connected to the interconnect waveguide via bonding, PCB, and microwave connector, or directly via bonding. In this way, point-to-point quantum interconnection can be achieved by connecting two identically designed samples through the interconnect waveguide.

[0063] In the above embodiments, any type of superconducting quantum bit 101 can be used, such as flux quantum bit, phase quantum bit, capacitive shunt flux quantum bit, transmon, fluxonium, etc., as long as the frequency of the quantum bit can be adjusted by the magnetic flux added in the Josephson junction loop. The superconducting quantum bit 101 can be designed as a floating ground type or a grounded type. The transmission resonant cavity 102, the readout resonant cavity 106, and the resonant cavity 108 which combines readout and transmission functions can be coplanar waveguide resonant cavities of quarter wavelength type, half wavelength short-circuit type, or half wavelength open-circuit type, or they can be three-dimensional resonant cavities or other microwave resonators. The transmission resonant cavity 102, the readout resonant cavity 106, and the resonant cavity 108 which combines readout and transmission functions may or may not have a Purcell filter.

[0064] In one embodiment, a quantum chip may include multiple superconducting qubits, which may or may not be coupled, or may be coupled by a coupler.

[0065] 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 internal microwave circuit of the dilution refrigerator through the same output port, and split into two paths on the chip.

[0066] In the above embodiments, coupling can be capacitive coupling, inductive coupling, or a combination of both.

[0067] Figure 2A A physical diagram of a quantum chip according to an embodiment of the present invention is shown, which uses... Figure 1A The structure shown. Figure 2BIt shows the relationship with Figure 2A The corresponding lumped equivalent circuit diagram. The superconducting quantum bits utilize an Xmon-type grounded transmon superconducting quantum bit design. Figure 2A The quantum chip shown includes: a qubit capacitor plate 201; a transmission resonant cavity 202, which is a quarter-wavelength coplanar waveguide; a transmission line 203, which is coupled to the transmission resonant cavity via interdigital capacitance for single-photon transmission; an XY control line 204, which is capacitively coupled to the qubit; a Z control line 205, which is mutually inducted with the qubit Josephson junction loop; a qubit Josephson junction loop 206; a readout resonant cavity 207, which is a quarter-wavelength coplanar waveguide; and a microwave transmission line 208 for superconducting quantum ratio discrete readout. The transmission resonant cavity 202 can be equivalent to... Figure 2B The lumped LC circuit in the image, and the reading of the resonant cavity 207, can also be equivalent to... Figure 2B The lumped LC circuit diagram in the image.

[0068] Combination Figure 2A and Figure 2B The qubit capacitor plate 201 is coupled to the readout resonant cavity 207 via capacitor 216. The qubit capacitor plate 201 is coupled to the transmission resonant cavity 202 via capacitor 211. The readout resonant cavity 207 is coupled to the transmission line 208 via capacitors 218 and 219. The transmission resonant cavity 202 is coupled to the transmission line 203 via capacitor 209. The superconducting qubit capacitor plate 201 is coupled to the XY control line 204 via capacitor 212. The superconducting qubit capacitor plate 201 is coupled to the signal ground via capacitor 213. The superconducting qubit Josephson junction loop 206 is coupled to the Z control line 205 via inductor 214. The superconducting qubit Josephson junction 206 is a symmetrical junction, meaning it consists of two Josephson junctions with identical parameters forming a loop.

[0069] Although in the above Figure 1A-Figure 2B The embodiment shows a schematic diagram of a quantum chip capable of transverse and longitudinal field modulation, but the present invention is not limited thereto. Any quantum chip in which the superconducting quantum bits and the transmission resonant cavity are capacitively or inductively coupled can perform transverse and longitudinal field modulation.

[0070] 2. Regulation methods

[0071] This invention utilizes longitudinal-transverse joint modulation technology. Both longitudinal modulation and transverse modulation (cavity-assisted Raman process) can equivalently and dynamically control the coupling coefficient between superconducting quantum bits and transmission resonant cavity, thereby realizing controllable shaping and time-reversal reception of microwave photons.

[0072] In this context, the longitudinal field refers to the microwave drive applied through a transmission line that is mutually inductant with the Josephson junction loop of the superconducting qubit. This drive induces a periodic change in the frequency of the qubit, thereby inducing the σ operator in the Hamiltonian of the qubit. z Such a driving method does not change the population of the ground state or excited state of the qubit, but is reflected in the rotation along the z-axis on the Bloch sphere. Longitudinal field modulation (LFM) involves introducing periodically varying magnetic flux into the Josephson junction loop of the superconducting qubit, thereby inducing multiple sidebands in the superconducting qubit's frequency to couple with other physical degrees of freedom (energy levels of other qubits, resonant cavities, or waveguides, etc.). LFM can utilize longitudinal field pulses of different amplitudes to control the equivalent coupling coefficient, thus achieving the desired equivalent coupling coefficient size.

[0073] The principle of longitudinal field modulation is as follows: Since longitudinal field modulation utilizes only the interaction between the superconducting quantum bit and the transmission resonant cavity within a single exciter space, the superconducting quantum bit is truncated to a second energy level. The Hamiltonian operator of the system formed by the superconducting quantum bit and the transmission resonant cavity is:

[0074]

[0075] in ω is the instantaneous frequency of the superconducting quantum bit after longitudinal field modulation. q Let ω be the initial angular frequency of the qubit. r denoted as angular frequency of the transmission resonant cavity, g is the coupling coefficient between the superconducting quantum bit and the transmission resonant cavity, 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. For the generation operator of photons transmitted through the resonant cavity, For the annihilation operator of the transmission resonant cavity, σ + For the raise operator of the equivalent two-level system of a superconducting quantum bit, σ - For the reduction operator of the equivalent two-level system of a superconducting quantum bit, σ z Let be the Pauli z-operator for a quantum bit. h is Planck's constant, and c is the speed of light. Under the interaction representation, we obtain:

[0076]

[0077] Where Δ=ω q -ω r Therefore, when Δ = nμ (n is an integer), it is assumed that the nth-order sideband of the superconducting quantum bit induced by longitudinal field modulation resonates with the energy level of the resonant cavity, completely exchanging energy, while the other sidebands are in a state of large detuning with the resonant cavity. At this time, the equivalent coupling coefficient between the nth-order sideband of the superconducting quantum bit induced by longitudinal field modulation and the transmission resonant cavity is... J n It is a Bessel function of the first kind. Therefore, the equivalent coupling coefficient g can be dynamically controlled by dynamically adjusting the amplitude A(t) of the longitudinal field. eff,L The magnitude of A(t). In one embodiment, the amplitude of the longitudinal field A(t) can be dynamically adjusted to dynamically control the equivalent coupling coefficient g. eff,L The magnitude of (t) causes the time-domain envelope of the photons generated by the qubit to change from an approximately exponential decrease to a symmetric shape.

[0078] Since different longitudinal field amplitudes A(t) during actual control will cause different bit frequency drifts, this dynamic drift can be dynamically calibrated by dynamically adjusting the phase φ(t) of the longitudinal field.

[0079] The principle of transverse field modulation (cavity-assisted Raman process) is as follows: Since a superconducting quantum bit is actually a multi-level system, the general Hamiltonian operator for a superconducting quantum bit-transmission resonant cavity system is:

[0080]

[0081] Where, ω q ω is the initial angular frequency of the qubit, α is the anharmonicity of the superconducting qubit, and ω is the initial angular frequency of the qubit. r Let ω be the angular frequency of the transmission resonant cavity, and g be the coupling coefficient between the superconducting quantum bit and the transmission resonant cavity. For the generation operator of photons transmitted through the resonant cavity, An annihilation operator for superconducting qubits. is the excitation operator for superconducting qubits.

[0082] After incorporating the transverse field drive of the superconducting qubit, the Hamiltonian operator of the system is:

[0083]

[0084] Where Ω0(t) is the amplitude of the transverse field drive, ω d The angular frequency driven by the transverse field. This represents the phase of the transverse field drive. After a series of unitary transformations, when the transverse field drive frequency satisfies the condition... Then, the equivalent Hamiltonian operator can be obtained as:

[0085]

[0086] Where α represents the anharmonicity of the superconducting quantum bit. The autoker coefficient of the transmission resonant cavity, The cross-Kerr coefficient is the coefficient between the superconducting quantum bit and the transmission resonant cavity. This describes the second-order coupling between a superconducting quantum bit and a transmission resonant cavity induced by a cavity-assisted Raman process (transverse field modulation). The coupling coefficient g can be dynamically controlled by dynamically adjusting the amplitude Ω0(t) of the transverse field. eff，T The magnitude of (t). Because different transverse field amplitudes Ω0(t) during actual control will also cause different frequency drifts in the bit. This dynamic drift can be dynamically calibrated by dynamically adjusting the phase φ(t) of the longitudinal field.

[0087] Figure 3A A schematic diagram of the quantum mechanical principle of longitudinal field modulation is shown. Figure 3A The left side shows the three lowest states of a superconducting qubit in the superconducting state: the ground state |g>, the first excited state |e>, and the second excited state |f>. The horizontal lines in the figure represent the different states. Figure 3A The right side shows the zero-photon-number state |0> and the one-photon-number state |1> of the transmission resonant cavity. Figure 3A The process of shaping microwave photons emitted by the coupling of a superconducting quantum bit and a transmission resonant cavity under longitudinal field modulation is described: First, the superconducting quantum bit is prepared to a superposition state α|g>+β|e> of the first excited state |e> and the ground state |g>. Then, the superconducting quantum bit is coupled to the transmission resonant cavity through longitudinal field modulation of the nth-order sideband, inducing the emission of shaped microwave photons. The process (where |g1> represents the joint state of the qubit in the ground state transmission resonator with one photon, and |e0> represents the joint state of the qubit in the first excited state transmission resonator without photons; other joint states can be deduced similarly), and then the equivalent coupling strength g is controlled by the longitudinal field amplitude A(t). eff，L (t), this process satisfies the excitation number (t), After energy conservation and the completion of the full energy exchange between the superconducting quantum bit and the transmission resonant cavity, the state of the superconducting quantum bit, α|g>+β|e>, will be mapped to the state of the transmission resonant cavity, α|0>+β|1>. Microwave photons within the cavity radiate outwards along the transmission line from the cavity, eventually mapping to the quantum state α|0>+β|1> of the flying microwave photons. Simultaneously, this process also completes the time-domain envelope shaping of the radiated microwave photons. Theoretically, as long as the coupling coefficient g can be strictly controlled... eff，L (t) and dynamically eliminate side effects, which can realize microwave photon time-domain envelope shaping of arbitrary shape. However, in general, microwave photon time-domain envelope shaping is symmetrical, which is easy to control and easy to receive at the receiver.

[0088] Figure 3BA schematic diagram illustrating the quantum mechanical principle of transverse field modulation (cavity-assisted Raman process) is shown, describing the process by which a superconducting quantum bit emits shapeable microwave photons under transverse field modulation: First, the superconducting quantum bit is prepared to a superposition state α|g>+β|f> of the second excited state |f> and the ground state |g>. Then, a cavity-assisted Raman process is used to induce the superconducting quantum bit to interact with the transmission resonant cavity. The process (where |g1> represents the joint state of the qubit in the ground state transmission resonator with one photon, and |f0> represents the joint state of the qubit in the second excited state transmission resonator without photons; other joint states can be deduced similarly), and then the equivalent coupling strength g is controlled by the transverse field amplitude Ω0(t). eff，T After the complete energy exchange between the superconducting quantum bit and the transmission resonant cavity is completed (t), the state of the superconducting quantum bit α|g>+β|f> will be mapped to the state of the transmission resonant cavity α|0>+β|1>. The microwave photons inside the cavity radiate out along the transmission line from the transmission resonant cavity and will eventually be mapped to the quantum state α|0>+β|1> of the flying microwave photons. At the same time, this process can also complete the time-domain envelope shaping of the radiated microwave photons. Theoretically, as long as the coupling coefficient g can be strictly controlled, eff，T (t) and dynamically eliminate side effects, which can realize microwave photon time-domain envelope shaping of arbitrary shape. However, in general, microwave photon time-domain envelope shaping is symmetrical, which is easy to control and easy to receive at the receiver.

[0089] It can be noted that due to the different equivalent interaction orders resulting from longitudinal field modulation and transverse field modulation, the quantum state mappings of the superconducting qubit-transmission resonant cavity are different. Longitudinal field modulation achieves a mapping from α|g>+β|e> to α|0>+β|1>, while transverse field modulation achieves a mapping from α|g>+β|f> to α|0>+β|1>. Therefore, the method of this invention can achieve the transmission and long-range entanglement of three-level qubits (typically with quantum states of α|g>+β|e>+γ|f>) by combining longitudinal field modulation and transverse field modulation techniques.

[0090] In one embodiment, a first-order sideband of longitudinal field modulation (i.e., n=1) can be used. If the amplitude of the added longitudinal field modulation is small enough or the angular frequency of the longitudinal field modulation is high enough, then... Then the equivalent coupling coefficient can be obtained as Therefore, we can obtain g. eff，L Given that A(t) ∝ A(t), this proportional relationship makes it easy to achieve shaping and dynamic phase calibration of microwave photons. By utilizing the longitudinal field modulation principle to couple and modulate the superconducting quantum bit with the transmission resonant cavity, and using the first-order sideband, a linear driving amplitude-equivalent coupling coefficient relationship can be achieved under a small driving intensity, which is beneficial for shaping and dynamic phase calibration of microwave photons.

[0091] When using transverse field modulation (cavity-assisted Raman process), if the amplitude of the added transverse field is small enough, It is also directly proportional, which facilitates the shaping and dynamic phase calibration of microwave photons.

[0092] Both longitudinal and transverse field modulation cause frequency shifts in superconducting qubits. The amplitude and phase of the equivalent coupling can be adjusted using amplitude and phase modulation, thus eliminating dynamic qubit frequency shifts through dynamic phase adjustment, ultimately controlling the amplitude and phase of the emitted photons. In these schemes, photons with symmetric temporal envelope amplitude and constant phase are generally selected as the transmitted microwave photons because such photons have moderate time-domain broadening, and the transmitter and receiver can be controlled using time-reversed modulation, making them easy to implement experimentally.

[0093] Figure 4A The Gaussian envelope pulse used for longitudinal field modulation is shown. Figure 4B The sine square function envelope pulse for longitudinal field modulation is shown. Figure 4C The envelope pulse of the sech function used for longitudinal field modulation is shown. Figures 4A-4C The pulses used are all symmetrical about the central axis because the rising edge of the pulse is mainly used to shape the microwave photons, while the falling edge only serves to slowly shut off the coupling between the superconducting quantum bit and the transmission resonant cavity. However, for the receiver, in order to receive microwave photons with a symmetrical time-domain envelope, it is necessary to control the falling edge of the pulse to gradually reduce the coupling between the superconducting quantum bit and the transmission resonant cavity from large to small and then to zero. Therefore, if the control pulse used is centrally symmetrical, then theoretically the transmitter and receiver can use the same waveform to transmit and receive symmetrical microwave photons, reducing 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 symmetrical shaping of the microwave photon time-domain envelope.

[0094] In one embodiment, in a system where a superconducting quantum bit is coupled to a transmission resonant cavity, and then the transmission resonant cavity is coupled to a microwave transmission line, if a photon wave packet with a time-domain envelope in the form of a sech function is required... The required equivalent coupling coefficient can be obtained by analysis as follows:

[0095]

[0096] Among them κ eff ≤κ T , κ eff It is the frequency bandwidth of the emitted photons, κ T This is the frequency bandwidth of the transmission resonant cavity. The upper limit of the frequency domain broadening of microwave photons is the half-width at half maximum (FWHM) of the reflection spectrum of the transmission cavity, when κ... eff =κT At that time, we can obtain:

[0097]

[0098] It is in the form of the envelope of the sech function, due to the modulation of the pulse amplitude A(t)(Ω0(t)) and g eff,L(T) (t) is proportional, and a theoretical form of can be obtained by using the longitudinal field modulation pulse of the sech function envelope. The symmetric microwave photon time-domain envelope is used. Therefore, the sech function is also a commonly used form for controlling pulse wave packets. Gaussian envelopes and sin square function envelopes can also achieve similar effects, which will not be elaborated on in this paper.

[0099] 3. Transmission protocol (also known as transmission method)

[0100] This invention proposes a complete transmission protocol for three-level qubit state transmission and long-range maximally entangled state establishment. Its core idea is to utilize different state mapping methods, such as longitudinal field modulation and transverse field modulation, to map the populations of the |e> and |f> states onto microwave photon wave packets with different time windows, achieving a hybrid encoding method combining particle number-state encoding and time packet encoding. Among these, Figure 6A and Figure 6B This is a protocol for the remote transmission of arbitrary quantum states of two equivalent three-level qubits. Figure 8A and Figure 8B For two unequal three-level qubits, the maximum entangled state is... Establish an agreement. Figure 8A By using a microwave photonic encoding system with different time windows to define the |e> and |f> states of superconducting qubits, and Figure 8B Then, a microwave photonic encoded superconducting qubit in state |e> is used in the previous time window, and a microwave photonic encoded superconducting qubit in state |f> is used in each of the two time windows. Due to transmission loss in the interconnecting waveguide, Figure 8A The transmission protocol in [the context] utilizes only one photon-coded state |f>, while Figure 8B The transmission protocol in [the context] utilizes two photonic codes |f> states, therefore, Figure 8B The protocol in this context can theoretically achieve higher fidelity in entangled states.

[0101] Figure 5 A flowchart of a quantum state transfer method for a three-level qubit according to an embodiment of the present invention is shown, which includes the following steps:

[0102] Step 501: At the transmitting end, the superconducting quantum bit is prepared into an arbitrary three-level quantum bit state α|g>+β|e>+γ|f>; where α, β, and γ are constants, |g> is the ground state of the superconducting quantum bit, |e> is the first excited state of the superconducting quantum bit, and |f> is the second excited state of the superconducting quantum bit.

[0103] Step 502: Utilize transverse field modulation of π f0g1 Pulse complete The exchange process, and the use of longitudinal field modulation π e0g1 Pulse complete The exchange process generates a joint quantum state of a first-time-window flying photon and a second-time-window flying photon.

[0104] Wherein, the application of transverse field modulation π is not limited. f0g1 Pulse and longitudinal field modulation π e0g1 The order of the pulses is arbitrary.

[0105] Step 503: At the receiving end, through the time reversal process, transverse field modulation π is used. f0g1 Pulse and longitudinal field modulation π e0g1 The pulse receives the flying photon onto the superconducting qubit at the receiving end, realizing the entire process of transmitting the arbitrary three-level qubit state α|g>+β|e>+γ|f> from the transmitter to the receiver.

[0106] Figure 6A The diagram illustrates control pulse sequences for a transmitter and receiver performing remote transmission of arbitrary quantum states of a three-level qubit according to a first embodiment of the present invention. In this embodiment, firstly, an arbitrary rotation gate of the {|g>, |e>} subspace is used. (where φ is the azimuth angle of the rotation axis in the Bloch sphere, and θ is the angle of rotation of the state vector around the rotation axis) and arbitrary rotation gates in the subspaces {|e>, |f>}. (φ and θ have the same meaning as above) Superconducting qubits are prepared into arbitrary three-level qubit states α|g>+β|e>+γ|f>. Then, transverse field modulation (cavity-assisted Raman process) π f0g1 Pulse complete During the exchange process, a joint quantum state α|g0>+β|e0>+γ|g1> is generated between the superconducting qubit at the transmitter and the resonant cavity at the transmission. Subsequently, photons in the transmission resonant cavity dissipate into the interconnecting waveguide, forming a photon wave packet for the first time window. This results in the joint quantum state α|g0>+β|e0>+γ|g1> of the superconducting qubit at the transmitter and the photon flying in the first time window. Then, longitudinal field modulation of π... e0g1 Pulse complete The exchange process generates a joint quantum state α|g00>+β|g01>+γ|g10> of the superconducting qubit at the transmitter, the photon flying in the first time window, and the transmission resonant cavity, i.e. Similarly, photons in the transmission resonant cavity dissipate into the interconnect waveguide, forming a photon wave packet in the second time window. The overall quantum state then becomes a joint quantum state of the transmitting superconducting qubit, the first time window photon, and the second time window photon. Since the state of the transmitting superconducting qubit can be separated from the overall quantum state, the state that truly encodes quantum information is the joint quantum state α|00>+β|01>+γ|10> of the first and second time window photons. This is a hybrid encoded state combining particle number state encoding and time packet encoding. Essentially, it maps the superconducting qubit's state |g> to the state |00> where there are no photons in either time window, maps the superconducting qubit's state |e> to the single-photon state |01> in the second time window, and maps the superconducting qubit's state |f> to the single-photon state |10> in the first time window. Thus, the transmission process of the three-level qubit quantum state is realized. The receiving process is a time-reversal process of the transmitting process: First, a complete transverse field modulation (cavity-assisted Raman process) πf0g1 pulse is used for the receiving process. The exchange process involves receiving the photon from the first time window of the receiving end's transmission resonant cavity onto the receiving end's superconducting qubit, resulting in the joint quantum state α|00g>+β|01g>+γ|00f> of the receiving end's transmission resonant cavity, the second time window's flying photon, and the receiving end's superconducting qubit. Similarly, the transmission resonant cavity can be directly ignored. Then, longitudinal field modulation of π is used. e0g1 Pulse complete During the exchange process, the flying photon in the second time window of the transmission resonator at the receiving end is received onto the superconducting quantum bit at the receiving end, resulting in the joint quantum state α|0g>+β|0e>+γ|0f> of the transmission resonator and the superconducting quantum bit at the receiving end, i.e. Thus, the entire process of transmitting the state α|g>+β|e>+γ|f> of any three-level qubit from the transmitter to the receiver has been realized.

[0107] Figure 6B The diagram illustrates control pulse sequences for a transmitter and receiver performing remote transmission of arbitrary quantum states of a three-level qubit according to a second embodiment of the present invention. In this embodiment, firstly, an arbitrary rotation gate of the {|g>, |e>} subspace is used. (where φ is the azimuth angle of the rotation axis in the Bloch sphere, and θ is the angle of rotation of the state vector around the rotation axis) and arbitrary rotation gates in the subspaces {|e>, |f>}. (φ and θ have the same meaning as above) Superconducting qubits are prepared into arbitrary three-level qubit states α|g>+β|e>+γ|f>. Then, π is modulated using a longitudinal field. e0g1 Pulse complete The exchange process generates a joint quantum state α|g0>+β|g1>+γ|f0> between the transmitting superconducting qubit and the transmission resonant cavity. Subsequently, photons in the transmission resonant cavity dissipate into the interconnecting waveguide, forming a photon wave packet for the first time window. This results in the joint quantum state α|g0>+β|g1>+γ|f0> between the transmitting superconducting qubit and the photons flying in the first time window. This is then further modulated using transverse field modulation (cavity-assisted Raman process) π f0g1 Pulse complete The exchange process generates a joint quantum state α|g00>+β|g10>+γ|g01> of the transmitter superconducting qubit, the first time window flying photon, and the transmission resonant cavity, i.e. Similarly, photons in the transmission resonant cavity dissipate into the interconnected waveguide, forming a photon wave packet in the second time window. The overall quantum state then becomes a joint quantum state of the transmitting superconducting qubit, the first time window photon, and the second time window photon. Since the state of the transmitting superconducting qubit can be separated from the overall quantum state, the state that truly encodes quantum information is the joint quantum state α|00>+β|10>+γ|01> of the first and second time window photons. This is a hybrid encoded state combining particle number state encoding and time packet encoding. Essentially, it maps the superconducting qubit's state |g> to the state |00> where there are no photons in either time window, the superconducting qubit's state |e> to the single-photon state |10> in the first time window, and the superconducting qubit's state |f> to the single-photon state |01> in the second time window. Thus, the transmission process of the three-level qubit quantum state is realized. The receiving process is the time reversal of the transmission process: First, using longitudinal field modulation π... e0g1 Pulse complete In the exchange process, the photon entering the first time window of the receiving end's transmission resonant cavity is received onto the receiving end's superconducting qubit, resulting in the joint quantum state α|00g>+β|00e>+γ|01g> of the receiving end's transmission resonant cavity, the second time window's flying photon, and the receiving end's superconducting qubit. Similarly, the transmission resonant cavity can be directly ignored. Then, transverse field modulation (cavity-assisted Raman process) π f0g1 Pulse complete The exchange process involves receiving the flying photon from the second time window of the receiving end's transmission resonant cavity onto the superconducting quantum bit at the receiving end, resulting in the joint quantum state α|0g>+β|0e>+γ|0f> of the receiving end's transmission resonant cavity and the receiving end's superconducting quantum bit. Thus, the entire process of transmitting the state α|g>+β|e>+γ|f> of any three-level qubit from the transmitter to the receiver has been realized.

[0108] Figure 7 A flowchart illustrating a method for establishing a long-range entangled state of a three-level qubit according to an embodiment of the present invention is shown, comprising the following steps:

[0109] Step 701: At the transmitting end, prepare the superconducting quantum bit to the first excited state |e>.

[0110] Step 702: Partially using longitudinal field modulation pulses The exchange process utilizes π ef The pulse transforms the quantum state |e> to the quantum state |f>, utilizing π. ge Pulses induce a quantum state |g> to a quantum state |e>, and transverse field modulated pulses are used for partial... The exchange process yields a maximally entangled state with a Schmidt rank of 3, consisting of the three-level qubits at the transmitter and the photons flying in the first and second time windows.

[0111] Among them, the application of transverse field modulation pulse and π is not limited. ef Pulse, π ge The order of the pulses and the longitudinal field modulation pulses.

[0112] Step 703: At the receiving end, use longitudinal field modulation π e0g1 Pulse complete The exchange process involves receiving the photons from the first time window of the transmission resonant cavity at the receiving end onto the superconducting qubit at the receiving end, and then using transverse field modulation of π. f0g1 Pulse complete In the exchange process, the photons that enter the second time window of the receiving end transmission resonant cavity are received onto the receiving end superconducting qubit, so as to establish the maximum entanglement state of the two remote three-level qubits.

[0113] Figure 8A The diagram illustrates the control pulse sequences for the transmitter and receiver in establishing a long-range maximum entangled state of a three-level qubit according to a first embodiment of the present invention. In this embodiment, firstly, the π of the {|g>, |e>} subspace is utilized... ge The pulse excites the superconducting qubit to the |e> state, and then the longitudinal field is modulated. Pulse (here) It means The Rabi angle θ of the process, The process will form (quantum state) partial The exchange process allows us to obtain the joint quantum state of the transmitter superconducting qubit and the transmission resonant cavity. Subsequently, photons in the transmission resonant cavity dissipate into the interconnect waveguide, forming the photon wave packet of the first time window, i.e., forming the joint quantum state of the superconducting qubit at the transmitting end and the photon flying in the first time window. Then, using the π of the subspace {|e>, |f>} ef A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Reusing the π of the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Next, transverse field modulation (cavity-assisted Raman process) is utilized. Pulse execution section The exchange process forms a joint quantum state of the transmitter superconducting qubit, the first time window flying photon, and the transmitter transmission resonant cavity. Subsequently, the transmission resonant cavity dissipates the flying photons of the second time window into the interconnected waveguide, resulting in a joint quantum state of the superconducting qubit at the transmitter, the flying photons of the first and second time windows. At this point, the entire control waveform sequence for the transmitting end has been completed, and the entangled states of the three-level qubits at the transmitting end and the photons flying in the first and second time windows have been obtained. Receiving process: First, longitudinal field modulation of π... e0g1 Pulse complete In the exchange process, the photon transmitted to the receiving end transmission resonant cavity in the first time window is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, the flying photon in the second time window, and the receiving end superconducting qubit. Right now Therefore, the receiving end transmission resonant cavity can be ignored. Finally, transverse field modulation (cavity-assisted Raman process) π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit. Right now Thus, the maximum entanglement state of two long-range three-level qubits has been achieved. The entire process of establishing the protocol reveals that during the entire transmission process, no two time windows will simultaneously produce flying photons. This protocol requires at most one flying photon as a medium to establish the maximum entangled state of two remote three-level qubits, thus minimizing the impact of transmission losses from interconnected waveguides.

[0114] Figure 8B The control pulse sequence for the transmitter and receiver to establish a long-range maximum entangled state of a three-level qubit according to a second embodiment of the present invention is shown. In this embodiment, firstly, the π of the {|g>, |e>} subspace is utilized... ge The pulse excites the superconducting qubit to the |e> state, and then utilizes the π of the {|e>, |f>} subspace. ef A pulse excites the superconducting qubit to the |f> state. Then, transverse field modulation (cavity-assisted Raman process) is used. Pulse (here) It means The Rabi angle θ of the process, The process will form (quantum state) partial The exchange process forms a joint quantum state between the transmitter superconducting qubit and the transmission resonant cavity. Subsequently, the transmission resonant cavity dissipates photons into the interconnect waveguide, forming the photon wave packet of the first time window, i.e., forming the joint quantum state of the superconducting qubit at the transmitter and the flying photon in the first time window. Then, using the π of the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state of the superconducting qubit at the transmitter and the flying photon in the first time window. Then utilize longitudinal field modulation Pulse execution section The exchange process forms a joint quantum state consisting of the transmitter superconducting quantum bit, the first time window flying photon, and the transmitter transmission resonant cavity. Subsequently, after the transmission resonant cavity has dissipated, the joint quantum state of the superconducting qubit at the transmitter, the photon flying in the first time window, and the photon flying in the second time window is obtained. At this point, the entire control waveform sequence for the transmitting end has been completed, and the entangled states of the three-level qubits at the transmitting end and the photons flying in the first and second time windows have been obtained. Receiving process: First, longitudinal field modulation of π... e0g1 Pulse complete The exchange process involves receiving the photon from the first time window of the transmission resonant cavity at the receiving end onto the superconducting qubit at the receiving end, thus obtaining a joint quantum state of the superconducting qubit at the transmitting end, the transmission resonant cavity at the receiving end, the photon flying in the second time window, and the superconducting qubit at the receiving end. Right now Therefore, the receiving end transmission resonant cavity can be ignored. Then, using the π of the {|g>,|e>} subspace... ge A pulse is applied to the superconducting qubit at the receiving end, resulting in a joint quantum state of the superconducting qubit at the transmitting end, the photon flying in the second time window, and the superconducting qubit at the receiving end. Next, transverse field modulation (cavity-assisted Raman process) π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit. Right now Finally, using the π of the subspace {|g>,|e>} ge A pulse applied to the superconducting qubit at the receiving end can yield the final result. The maximum entangled state of a three-level qubit. It can be observed that... Figure 8A The difference in the process shown is that flying photons will appear simultaneously in the two time windows, and the simultaneous appearance of flying photons will correspond to the |f> state at the receiver. Relatively speaking, this is more affected by the transmission loss of the interconnect waveguide.

[0115] It is worth noting that, Figures 6A-6B as well as Figures 8A-8B The control pulse sequence shown is arranged from left to right according to the chronological order of the experimental operations. However, the time difference between the waveforms at the transmitting and receiving ends is actually determined by the distance between them and the speed of light in the transmission medium. In principle, the waveforms at the transmitting and receiving ends can overlap in timing; the transmitting process does not strictly follow the receiving process. Furthermore, there are no restrictions on the generation method, frequency, waveform envelope shape, or time width of all control pulses. It should be noted that this protocol does not consider any dynamic phase generated by evolution or the phase calibration issues between the transmitting and receiving ends. In practice, these issues can be resolved using a local single-bit phase gate.

[0116] In one embodiment, the photons at the transmitting and receiving ends are at the same frequency.

[0117] In one embodiment, there are no restrictions on the generation method, frequency, waveform envelope shape, and time width of all control pulses.

[0118] In one embodiment, if the quantum channel connecting two superconducting quantum chips is bidirectional, then the transmitter and receiver can be interchanged and can simultaneously transmit and receive each other.

[0119] In one embodiment, there is no limit to the number of superconducting quantum chips that achieve coherent interconnection using the transmission protocol described therein, and there is no limit to the number or type of superconducting qubits contained in the chip.

[0120] In one embodiment, the π of the transmitter and receiver f0g1 Pulse and π e0g1 The pulses are not necessarily in a one-to-one correspondence because the frequencies of the flying microwave photons generated by these two types of pulses are the same, so π is used. f0g1 The flying photons generated by the pulse can use π e0g1 Pulse can be used to receive signals, or vice versa.

[0121] In one embodiment, the entangled state established by the protocol for establishing remote maximum entanglement is: For a three-level qubit, there are nine mutually orthogonal maximally entangled states that can be interconverted through a local unitary transformation. These states can be interconverted simply by applying arbitrary rotation gates to the superconducting qubits at the transmitter and receiver. The final entangled state only needs to be a maximally entangled state of two three-level qubits; there are no restrictions. It should be explained that for the entangled states of a quantum system composed of two three-level qubits, there are only two equivalence classes for Stochastic Local Operation Classical Communication (SLOCC): one is the maximally entangled state, such as... The Schmitt order is 3; one type is partially entangled states, such as... With a Schmitt order of 2, the entangled state is actually a Bell state in a two-level subspace. This entangled state cannot reflect the special characteristics of the entanglement of two three-level qubits. Therefore, this invention establishes the maximally entangled state.

[0122] In one embodiment, photon symmetry shaping is performed at the transmitting end, the photon symmetry shaping comprising the following steps: coupling the nth-order sideband of the superconducting quantum bit induced by longitudinal field modulation based on the longitudinal field modulation angular frequency to the transmission resonant cavity; wherein the equivalent coupling coefficient between the nth-order sideband and the transmission resonant cavity is: Among them, J n It is a Bessel function of the first kind, where 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 quantum bit and the transmission resonant cavity, and μ is the angular frequency of the longitudinal field modulation; by adjusting the equivalent coupling coefficient through the amplitude of the longitudinal field modulation, the time-domain envelope shaping of the emitted microwave photons is completed.

[0123] This invention provides a sample design, control method, and transmission protocol for remote three-level qubit state transmission and entanglement state establishment using longitudinal-transverse field joint modulation technology. The longitudinal-transverse field joint modulation technology in this invention refers to using longitudinal field modulation to induce and control the equivalent coupling between the superconducting qubit and the transmission resonant cavity, thereby achieving the desired coupling between the superconducting qubit and the transmission resonant cavity. The exchange and photon shaping are achieved by using transverse field modulation to induce a cavity-assisted Raman process between the superconducting quantum bit and the transmission resonant cavity, thereby controlling the higher-order coupling between the superconducting quantum bit and the transmission resonant cavity. The exchange of photons and the realization of photon shaping.

[0124] Among them, longitudinal field modulation (LFM) refers to a quantum control technique that uses sinusoidal waves to periodically modulate the frequency of a superconducting quantum bit, thereby inducing different energy level sidebands. These sidebands are then used to couple the energy levels of other quantum systems, causing coherent energy exchange between the superconducting quantum bit and other quantum systems. The first-order sidebands of LFM can induce equivalent interacting Hamiltonian operators. (g eff，L This represents the equivalent coupling strength induced by the first-order sideband of the longitudinal field. For the annihilation operator of the transmission resonant cavity, For superconducting qubits, annihilation operator (hc denotes the Hermitian conjugate of the preceding term), define the excitation number. have This demonstrates that the excitation number is conserved during the interaction. Because the lower-order expansions of the interacting Hamiltonian operator are preserved, we have... Therefore, it is possible to induce a connection between the superconducting quantum bit and the transmission resonant cavity. exchange.

[0125] Furthermore, transverse field modulation techniques refer to the use of cavity-assisted Raman processes (see Pechar M, et al. 2014 PHYS.REV.X 4, 041010) to induce second-order coupling between qubits and the energy levels of other quantum systems. Here, second-order coupling refers to the coupling where the excitation number is not conserved and exactly two excitations of the qubit correspond to one excitation of the transmission resonant cavity. Cavity-assisted Raman processes induce equivalent interacting Hamiltonian operators. (g eff,T This represents the equivalent coupling strength induced by the transverse field. For the annihilation operator of the transmission resonant cavity, For superconducting qubits, annihilation operator (hc denotes the Hermitian conjugate of the preceding term), define the excitation number. have This indicates that the excitation number is not conserved during the interaction. Due to the preservation of the lower-order expansion of the interacting Hamiltonian operator, we have... Therefore, it is possible to induce a connection between the superconducting quantum bit and the transmission resonant cavity. exchange.

[0126] This invention employs longitudinal-transverse field modulation technology, combined with appropriate sample design and control methods, to dynamically adjust the equivalent coupling between the superconducting quantum bit and the transmission resonant cavity, thereby achieving time-domain envelope symmetry shaping and time-reversal reception of emitted photons. This invention proposes a complete transmission protocol for realizing long-distance transmission of three-level quantum bits and the establishment of long-distance maximally entangled states.

[0127] While the present invention has been described through preferred embodiments, it is not limited to the embodiments described herein, and various changes and modifications are made without departing from the scope of the invention.

Claims

1. A method for quantum state transfer of a three-level qubit, comprising: Step 1: At the transmitting end, prepare the superconducting quantum bit into an arbitrary three-level quantum bit state α|g>+β|e>+γ|f>; where α, β, and γ are constants, |g> is the ground state of the superconducting quantum bit, |e> is the first excited state of the superconducting quantum bit, and |f> is the second excited state of the superconducting quantum bit; Step 2: Use transverse field modulation pulses to complete The exchange process, and the complete operation using longitudinal field modulation pulses. The exchange process generates a joint quantum state of a first-time-window photon and a second-time-window photon; Step 3: At the receiving end, through a time reversal process, transverse field modulation π is used. f0g1 Pulse and longitudinal field modulation π e0g1 The pulse receives the flying photons onto the superconducting qubits at the receiving end.

2. The quantum state transfer method for a three-level qubit according to claim 1, wherein, Step 1 includes: By using arbitrary rotation gates in the subspaces {|g>, |e>} and {|e>, |f>}, superconducting qubits can be prepared into arbitrary three-level qubit states.

3. The quantum state transfer method for a three-level qubit according to claim 2, wherein, Step 2 includes: First, using transverse field modulation π f0g1 Pulse complete The exchange process forms a joint quantum state α|g0>+β|e0>+γ|g1> between the superconducting qubit at the transmitter and the photon flying in the first time window. Subsequently, π is modulated using the longitudinal field. e0g1 Pulse complete The exchange process generates a joint quantum state α|00)+β|01>+γ|10>, which is a combination of a first time window photon and a second time window photon.

4. The quantum state transfer method for a three-level qubit according to claim 2, wherein, Step 2 includes: First, using longitudinal field modulation π e0g1 Pulse complete The exchange process forms a joint quantum state α|g0>+β|g1>+γ|f0> between the superconducting qubit at the transmitter and the photon flying in the first time window. Subsequently, transverse field modulation of π is used. f0g1 Pulse complete The exchange process generates a joint quantum state α|00)+β|10>+γ|01>, which is the first time window photon-second time window photon.

5. A method for establishing a long-range entangled state of a three-level qubit, comprising: Step 1: At the transmitting end, prepare the superconducting quantum bit to the first excited state |e>; Step 2: Partially modulated using longitudinal field pulses The exchange process utilizes π ef The pulse transforms the quantum state |e> to the quantum state |f>, utilizing π. ge Pulses induce a quantum state |g> to a quantum state |e>, and transverse field modulated pulses are used for partial... The exchange process yields a maximum entangled state of 3, consisting of the three-level qubits at the transmitter and the photons flying in the first and second time windows. Step 3: At the receiving end, use longitudinal field modulation π e0g1 Pulse complete The exchange process involves receiving the photons from the first time window of the transmission resonant cavity at the receiving end onto the superconducting qubit at the receiving end, and then using transverse field modulation of π. f0g1 Pulse complete In the exchange process, the photons that enter the second time window of the receiving end transmission resonant cavity are received onto the receiving end superconducting qubit, so as to establish the maximum entanglement state of the two remote three-level qubits.

6. The method for establishing a long-range entangled state of a three-level qubit according to claim 5, wherein, Step 1 includes: utilizing the π of the subspace {|g>, |e>} ge The pulse excites the superconducting qubit to the first excited state |e>.

7. The method for establishing a long-range entangled state of a three-level qubit according to claim 6, wherein, Step 2 includes the following steps in sequence: Using longitudinal field modulation Pulse execution section The exchange process forms a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Using the π of the subspace {|e>, |f>} ef A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Using π in the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Using transverse field modulation Pulse execution section The exchange process yields the joint quantum state of the superconducting qubit at the transmitter, the photon flying in the first time window, and the photon flying in the second time window.

8. The method for establishing a long-range entangled state of a three-level qubit according to claim 7, wherein, Step 3 includes the following steps in sequence: First, using longitudinal field modulation π e0g1 Pulse complete In the exchange process, the photon transmitted to the receiving end transmission resonant cavity in the first time window is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, the flying photon in the second time window, and the receiving end superconducting qubit. Then, using transverse field modulation π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit. To achieve the maximum entanglement state of two long-range three-level qubits The establishment of.

9. The method for establishing a long-range entangled state of a three-level qubit according to claim 6, wherein, Step 2 includes the following steps in sequence: Using the π of the subspace {|e>, |f>} ef The pulse excites the superconducting qubit to the |f> state; Using transverse field modulation Pulse execution section The exchange process forms a joint quantum state between the superconducting qubit at the transmitter and the photon flying in the first time window. Using π in the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubit at the transmitter, forming a joint quantum state of the superconducting qubit at the transmitter and the first time window flying photon. Using longitudinal field modulation Pulse execution section The exchange process yields the joint quantum state of the superconducting qubit at the transmitter, the photon flying in the first time window, and the photon flying in the second time window.

10. The method for establishing a long-range entangled state of a three-level qubit according to claim 9, wherein, Step 3 includes the following steps in sequence: Using longitudinal field modulation π e0g1 Pulse complete In the exchange process, the photon transmitted to the receiving end transmission resonant cavity in the first time window is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, the flying photon in the second time window, and the receiving end superconducting qubit. Using π in the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubit at the receiving end, resulting in a joint quantum state of the superconducting qubit at the transmitting end, the photon flying in the second time window, and the superconducting qubit at the receiving end. Using transverse field modulation π f0g1 Pulse complete During the exchange process, the photon transmitted into the second time window of the receiving end transmission resonant cavity is received onto the receiving end superconducting qubit, resulting in a joint quantum state of the transmitting end superconducting qubit, the receiving end transmission resonant cavity, and the receiving end superconducting qubit. Using π in the subspace {|g>, |e>} ge A pulse is applied to the superconducting qubits at the receiving end to obtain the final result. Maximum entanglement state of a three-level qubit.

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