Implementation Method of SWAP Gate in Cold Atom Quantum Bit Platform

Abstract

A method for implementing a fast Rydberg blockade SWAP quantum gate based on continuous modulation of a laser. This method uses an analytical waveform generated by Fourier series calculation to continuously modulate the laser, driving the highly coherent Rydberg state transition of atomic qubits to achieve precise atomic state control that meets the operation requirements of the SWAP quantum gate. The present invention effectively reduces errors by suppressing high-frequency noise, while avoiding defects related to mechanical motion and preventing heating effects generated during operation, significantly improving the connectivity and fidelity of neutral atomic qubits in large-scale systems and achieving fast and high-fidelity SWAP quantum gate operations. Moreover, it is applicable to low Rydberg blockade intensities, can effectively resist adverse effects such as laser fluctuations, and is compatible with the buffer atom framework, thereby enhancing the strength of quantum entanglement connections.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing, and specifically to a method for implementing a SWAP gate in a cold atom qubit platform based on Rydberg blockade and continuous laser modulation driving. Background Art

[0002] In the progress of advancing large-scale neutral atom quantum computing, a core problem lies in how to effectively implement entangled quantum logic gates with high connectivity and fast high fidelity due to the limited range of Rydberg dipole-dipole interaction, which has become an urgent challenge at present. In the prior art, although the method of mechanically transporting qubits in a one-dimensional optical lattice (Demonstration of Quantum Brachistochrones between Distant States of an Atom, authors Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco, and Andrea Alberti) can improve the connectivity between qubits to a certain extent, this method has significant defects, such as slow operation speed and easy occurrence of quantum state leakage, thus affecting the efficiency and accuracy of quantum computing.

[0003] On the other hand, by optimizing the designed Rydberg CZ gate pulse (quoted from Architecture for fast implementation of qLDPC codes with optimized Rydberg gates, authors C. Poole, T. M. Graham, M. A. Perlin, M. Otten, and M. Saffman), the dependence on the two-atom interaction strength can be minimized, while ensuring high fidelity and speed of quantum operations. This progress undoubtedly opens up a new path for the implementation of quantum logic gates. However, it is worth noting that the current Rydberg gate design still lacks in terms of functional coverage, especially the key component of the SWAP gate is not included, which is crucial for constructing complex quantum circuits. Summary of the Invention

[0004] To overcome the deficiencies of the above prior art, the present invention provides a method for designing a high-speed and high-fidelity Rydberg SWAP gate, which not only has the characteristics of high speed and high fidelity, but also is compatible with the buffer atom framework, achieving high connectivity in the atomic stationary state.

[0005] The present invention aims to improve the qubit connectivity of a large-scale neutral atom quantum computing platform. By using Rydberg blockade and continuous modulation driving, a SWAP gate similar to that on a superconducting computing platform is realized, with entanglement characteristics of high speed, high connectivity, and high fidelity. This method is compatible with the auxiliary and buffer qubit architectures, keeps the qubits stationary, and provides an efficient and robust solution to enhance the scalability and performance of quantum computing.

[0006] The technical solution of the present invention is as follows:

[0007] A method for implementing a SWAP gate in a cold atom qubit platform, characterized in that the method comprises the following steps:

[0008] Step 1.1 Select two non-degenerate and magnetically insensitive ground states as qubit states |0> and |1>;

[0009] Step 1.2 Use two coherent laser beams to drive the ground state - Rydberg state transition, and set the Rabi frequencies of the two laser beams to ensure that the light intensity is uniformly distributed on the control qubit atoms and the target qubit atoms;

[0010] Step 1.3 Consider the Rydberg blockade effect, and generate a Rabi frequency waveform that satisfies the SWAP gate condition through continuous modulation driving of the laser.

[0011] Further, the specific content of step 1.2 includes:

[0012] Step 2.1 Select two coherent laser beams, where the frequency of the first laser beam is ω0, the frequency of the second laser beam is ω1, the frequency ω0 of the first laser beam matches the transition frequency from the qubit state |0> to the Rydberg state |r>, and the frequency ω1 of the second laser beam matches the transition frequency from the qubit state |1> to the Rydberg state |r>;

[0013] Step 2.2 Ensure that the action regions of the two light beams are much larger than the regions where all the control qubit atoms and the target qubit atoms are located, and ensure uniform light intensity distribution so that the Rabi frequency is uniformly distributed on the qubit atoms;

[0014] Step 2.3 Use the first laser beam to excite the atom from the qubit state |0> to the Rydberg state |r>, and use the second laser beam to excite the atom from the qubit state |1> to the Rydberg state |r>.

[0015] Further, the specific content of step 1.3 includes:

[0016] Step 3.1 Describe the Rydberg blockade interaction through the quantum mechanical model of Rydberg atom dipole interaction, and predict and adjust the dynamic behaviors of the singlet and triplet states;

[0017] Step 3.2 Generate a Rabi frequency waveform that meets the SWAP gate conditions, ensuring that the initial and ending intensities of the Rabi frequency waveform are zero, and its first derivative with respect to time is also zero;

[0018] Step 3.3 Implement the corresponding Rabi frequency waveform through amplitude, frequency, or hybrid modulation, and filter out high-frequency components;

[0019] Step 3.4 Regulate the phase accumulation of the atomic wave function to achieve efficient population transfer and generate various SWAP phase gates.

[0020] Furthermore, the specific content of Step 3.2 includes:

[0021] Step 3.2.1 Represent all optical field Rabi frequencies through Fourier series coefficients [a0, a1,..., a N ;

[0022]

[0023] Step 3.2.2 Use direct numerical search or optimization algorithms to determine the coefficients to generate a waveform that meets the SWAP gate conditions.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] 1. The Rydberg-blockade-based SWAP gate implemented using a synthesized continuous modulation drive promotes the connection and entanglement of large-scale neutral atom qubits.

[0026] 2. Automatically trigger the two-atom dark state mechanism, and improve the fidelity of the SWAP gate by filtering high-frequency noise.

[0027] 3. It does not require mechanical transport of atoms, is compatible with quantum logic gates for buffered atom control and buffered atom architectures, and has the potential to suppress crosstalk and enhance entanglement connectivity. That is, by applying the SWAP gate between buffered atoms and atom qubits, buffered atoms or buffered atom relays can effectively implement the SWAP gate between qubits, and because buffered atoms and qubits are different elements, crosstalk can be effectively avoided.

[0028] 4. When two laser beams propagate parallel and in the same direction, the net atomic and photon momentum average exchange is zero. Therefore, the Rydberg-blockade-based SWAP gate does not cause heating effects. On the other hand, it provides a tool to cool qubits heated for any reason during quantum logic gate operations. Brief Description of the Drawings

[0029] Figure 1 is a schematic diagram of the atomic transition link structure under single-photon drive and light-atom interaction.

[0030] Figure 2It is a complete schematic diagram of singlet and triplet states.

[0031] Figure 3 It is a schematic diagram of the atomic qubit transition dynamics under the modulation driving scheme.

[0032] Figure 4 It is a schematic diagram of the Rydberg blockade effect and the two-photon transition scheme.

[0033] Figure 5 It is a diagram showing the input-output relationship of two SWAP gate states. Detailed implementation manner

[0034] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention should not be limited thereby.

[0035] In the cold atom qubit platform, for qubit atom 1-1, two non-degenerate and magnetic field-insensitive ground states or metastable states are selected as the qubit states |0> and |1>. Single qubit operation 1-2 can be achieved through microwave or Raman transitions. Two mutually coherent laser beams are used to drive the transition from the ground state to the Rydberg state respectively and The laser frequencies are ω0 and ω1 respectively. Ensure that the action regions of the two laser beams are much larger than the regions where all the controlled qubit atoms and the target qubit atom are located, and ensure that the light intensity is evenly distributed, so that the Rabi frequency is evenly distributed on the atomic qubits. Consider the Rydberg blockade effect of three Rydberg states, and use the quantum mechanical model of the Rydberg atom dipole interaction to describe the Rydberg blockade interaction 1-3, and the blockade intensity is B. Consider the singlet state and triplet state |00> and |11> in the superposition state under the two-atom basis have different dynamic responses 1-4. The corresponding complete dynamics involve the wave functions of the singlet state 2-1 and the triplet state 2-2, which are C singlet =[C 1- , C 0r , C 1r and C triplet =[C0, C 1+ , C2, C r0 , C r1 , C rr , C qq' respectively. Use the synthesized continuous modulation driving lasers 1 and 2 to regulate the phase accumulation of the atomic qubit wave function required for the SWAP phase gate, realize coherent population transfer, and enable the qubit to undergo coherent transitions 3-1 and 3-2 to realize the SWAP gate. The specific modulation scheme is as follows: Ensure that the initial and ending intensities of the Rabi frequency waveform and its first-order time derivative are both zero, and use the Fourier series coefficients [a0, a1,..., a N to represent the waveform of the Rabi frequency Appropriate Fourier coefficients are found through numerical search or optimization algorithms to generate a Rabi frequency waveform that meets the conditions of the SWAP gate. The waveforms of the two laser beams can have the same ratio. Subsequently, according to the required Rabi frequency waveform, the amplitude or phase modulation of the laser or a hybrid modulation combining both is used, and high-frequency components are filtered to achieve the final output waveform. This scheme is applicable not only to single-photon transitions but also to the scheme 4-1 of two-photon ground state-Rydberg transitions. Finally, the input-output relationship of the SWAP gate as shown in Figure 5 is achieved.

[0036] To construct a stable qubit, two non-degenerate and magnetic field-insensitive ground states or metastable states are selected to represent the qubit states |0> and |1>. This helps reduce the interference of the external environment on the qubit state and improve the accuracy of quantum computing.

[0037] Single-qubit operations 1-2 are usually achieved through microwave or Raman transitions, and both methods can effectively manipulate the state of the qubit.

[0038] Two mutually coherent laser beams are used to drive the transition from the ground state to the Rydberg state, thereby realizing the interaction between qubits. The frequencies of these two laser beams are ω0 and ω1 respectively, and the light intensity is uniformly distributed on the control qubit atom and the target qubit atom.

[0039] The Rydberg state is a highly excited state with a large electric dipole moment, which can generate strong interactions. This interaction is called the Rydberg blockade effect. In the Rydberg blockade effect of three Rydberg states, a quantum mechanical model of the Rydberg atom dipole interaction is used to describe the Rydberg blockade interaction 1-3, and the blockade strength B describes the intensity of this interaction.

[0040] In the two-atom basis, the singlet and triplet 00> and |11> in the superposition state have different dynamic responses 1-4. The wave functions of the singlet 2-1 and triplet 2-2 corresponding to the complete dynamics are C singlet =[C 1- ,C 0r ,C 1r and C triplet =[C0,C 1+ ,C2,C r0 ,C r1 ,C rr ,C qq' ; The synthetic continuous modulation driving lasers 1 and 2 are used to regulate the phase accumulation of the atomic qubit wave function required by the SWAP phase gate, realize coherent population transfer, so that the qubit experiences coherent transitions 3-1 and 3-2, and finally the SWAP gate is achieved.

[0041] The specific modulation scheme is as follows:

[0042] Ensure that the initial and ending intensities of the Rabi frequency waveform and its first-order time derivative are both zero. Use the Fourier series coefficients [a0, a1,..., a N to represent the waveform of the Rabi frequency Find the appropriate Fourier coefficients through numerical search or optimization algorithms to generate a Rabi frequency waveform that satisfies the conditions of the SWAP gate. The waveforms of the two lasers can be in the same proportion. Subsequently, according to the required Rabi frequency waveform, use amplitude modulation, phase modulation, or a combination of both (hybrid modulation) of the lasers, and filter out the high-frequency components to achieve the final output waveform. This scheme is applicable not only to single-photon transitions but also to the scheme 4-1 of two-photon ground state-Rydberg transitions. Finally, achieve the input-output relationship of the SWAP gate as Figure 5 shown

[0043] Figure 5 Shows the implementation of two SWAP gate schemes 5-1 and 5-2, taking a large-scale array of cold rubidium-87 atoms as an example Figure 1 Displays the atomic transition link structure under single-photon driving and light-atom interaction. As shown in the figure, for qubit atom 1-1, two magnetic field-insensitive ground states F = 1, m = 0 and F = 2, m = 0 are selected as the qubits |0> and |1> Figure 4 Shows the Rydberg blockade effect and the two-photon transition scheme. As shown in the figure, two pairs of 480 nm and 780 nm lasers achieve two-photon transitions 4-1 to the 89S Rydberg state. The frequencies of the two pairs of lasers are ω e1 、ω r1 and ω e2 、ω r2 , with corresponding detunings of Δ e1 、Δ r1 and Δ e2 、Δ r2 . The Rabi frequencies of the two pairs of lasers are Ω e1 、Ω r1 and Ω e2 、Ω r2 . Ensure that the light field is uniformly distributed over the target qubit atoms to improve the fidelity and make the equivalent Rabi frequencies consistent. Use a beam splitter to make the two pairs of lasers completely overlap and irradiate the target qubit atoms in the same direction, manage the momentum exchange between the lasers and the atoms, and suppress the heating effect caused by Rydberg transitions Figure 2Describes the wave functions of the complete singlet and triplet states participating in the transition process under Rydberg blockade. The Rydberg blockade interaction is described by a quantum mechanical model of Rydberg atom dipole interaction 1-3, predicting and regulating the dynamics of the singlet state 2-1 and the triplet state 2-2. The ground state to Rydberg transitions of these two pairs of lasers are selected to the 89S energy level, and the corresponding Rydberg dipole-dipole interaction strength is about 100-200 MHz.

[0044] Using the Fourier series coefficients [a0, a1,..., a N to represent the waveforms of all optical field Rabi frequencies Ω e1 , Ω r1 and Ω e2 , Ω r2 . The selected reference time τ = 0.25 μs. Ensure that f(0) = f(t end ) = 0 and f'(0) = f'(t end ) = 0 within the time from the start of the waveform t = 0 to the end of the SWAP gate operation t = t end . Find the appropriate Fourier coefficients of each optical field through a direct numerical search method to obtain the Rabi frequency waveforms that satisfy the SWAP gate conditions. Implement the corresponding Rabi frequency waveforms through a method of combined modulation of the intensity and phase of light, and filter out the high-frequency components. Figure 3 Shows the coherent transition dynamics of the atomic qubit under the modulation driving scheme within the time of t end . For the path design of the SWAP gate 5-1, the |01> state starts to experience two paths. The first path is |01> → |0r> → |00> → |r0> → |10>, and the second path is |01> → |r1> → |11> → |1r> → |10>. At the same time, the layout of the qubits remains unchanged during the coherent transition. For the path design of the SWAP gate 5-2, starting from the |00> state, it experiences two paths. The first path is

[0045] 00> → |0r> → |01> → |r1> → |11>, and the second path is |00> → |r0> → |10> → |1r> → |11>. The proportions of the |01> and 10> states remain unchanged during the cycle. Finally, through precise waveform design and regulation, the two SWAP gate schemes shown in Figure 5 are achieved.

[0046] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for implementing a SWAP gate in a cold atom quantum bit platform, characterized in that, The method includes the following steps: Step 1.1 Select two non-simple and magnetically insensitive ground states as qubit states |0> and |1>; Step 1.2 Use two coherent laser beams to drive the ground state-Rydberg state transition, and set the Rabi frequencies of the two laser beams to ensure that the light intensity is evenly distributed over the control qubit atoms and the target qubit atoms; Step 1.3 Consider the Rydberg blockade effect, and generate a Rabi frequency waveform that satisfies the SWAP gate condition through continuous laser modulation driving; The specific content of Step 1.3 includes: Step 3.1 Describe the Rydberg blockade interaction through the quantum mechanical model of Rydberg atom dipole interaction, and predict and adjust the dynamic behavior of the singlet and triplet states; Step 3.2 Generate a Rabi frequency waveform that meets the SWAP gate condition, ensuring that the initial and ending intensities of the Rabi frequency waveform are zero, and its first derivative with respect to time is also zero; Step 3.3 Implement the corresponding Rabi frequency waveform through amplitude, frequency or mixed modulation, and filter out the high-frequency components; Step 3.4 Regulate the phase accumulation of the atomic wave function to achieve efficient population transfer and generate multiple SWAP phase gates.

2. The method for implementing a SWAP gate in the cold atom qubit platform according to claim 1, wherein The specific content of Step 1.2 includes: Step 2.1 Select two coherent laser beams. Among them, the frequency of the first laser beam is ω0, and the frequency of the second laser beam is ω1. The frequency ω0 of the first laser beam matches the transition frequency from the qubit state |0> to the Rydberg state |r>, and the frequency ω1 of the second laser beam matches the transition frequency from the qubit state |1> to the Rydberg state |r>; Step 2.2 Ensure that the action regions of the two light beams are much larger than the regions where all the control qubit atoms and the target qubit atoms are located, and ensure that the light intensity is evenly distributed so that the Rabi frequency is evenly distributed over the atomic qubits; Step 2.3 Use the first laser beam to excite the atom from the qubit state |0> to the Rydberg state |r>, and use the second laser beam to excite the atom from the qubit state |1> to the Rydberg state |r>.

3. The implementation method of the SWAP gate in the cold atomic quantum bit platform according to claim 1, characterized in that The specific content of Step 3.2 includes: Step 3.2.1 represents all optical field Rabi frequencies through Fourier series coefficients [a0, a1,..., a N Step 3.2.2 Use direct numerical search or optimization algorithm to determine the coefficients to generate a waveform that meets the SWAP gate condition.

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