Discrete-frequency modulation gates for conditional logic in captured-ion quantum computers

Abstract

A system includes a controller configured to reconstruct a continuous waveform into a discrete analog version. The system includes a numerical optimizer configured to determine the frequency of a pulse sequence. The numerical optimizer uses radial motion mode frequencies and desired gate times. The numerical optimizer generates the pulse sequence by disabling phase space trajectories, unwrapping spins and motion, and limiting the Rabi frequencies of motion sideband transitions. The system also includes a display configured to illustrate the discrete-frequency modulated pulse sequence based on the determined frequencies.

Description

[0001] Statement on Federally Funded Research

[0002] This disclosure was made with government support under Federal Grant No. Phy-181891 granted by the National Science Foundation. The federal government has specific rights to this disclosure.

[0003] Cross-citation of related applications

[0004] This application claims the benefit of U.S. Provisional Application No. 62 / 994,998, filed March 26, 2020, entitled "Discrete Frequency Modulated Gates For Conditional Logic In Trapped Ion Quantum Computers" (Attorney General's No.: DU7032PROV), which is incorporated herein by reference. If there is any linguistic contradiction or inconsistency between this application and one or more of the incorporated applications that could affect the interpretation of the claims herein, then the claims herein shall be interpreted as consistent with the language used herein. Technical Field

[0005] This disclosure relates to discrete frequency modulation gates in quantum computers. More specifically, this disclosure relates to generating discrete frequency modulation pulse sequences given a measured radial motion mode frequency and a desired gate time. Background Technology

[0006] Due to their long coherence time, high-fidelity initialization, detection, and qubit gate operations, captured atomic ions are the primary qubit platform for realizing quantum computers. The Molmer-Sorensen (MS) gate is a two-qubit gate that has demonstrated fidelity exceeding 99.9% in two-ion systems using axial mode.

[0007] In dual-ion or quad-ion chains, individual optical addressing of ions and modulation pulse techniques are crucial for MS gates. Multichannel acousto-optic modulation has been used for individual addressing of atomic qubits. Additionally, acousto-optic / electro-optic modulation and beam steering using microelectromechanical systems (MEMS) tilt mirrors have also been employed for individual addressing of atomic qubits.

[0008] Negligible crosstalk has been demonstrated in MEMS-based individually addressable qubit systems. Furthermore, a gate scheme insensitive to optical phase drift between addressing beams has been developed. However, phase drift can still occur, leading to spin and motion entanglement in motion patterns. Phase drift can also cause deviations in the gate's rotation angle.

[0009] Other methods used include amplitude modulation (AM) gates, frequency modulation (FM) gates, and multi-tone MS gates. Furthermore, high fidelity has been demonstrated in these AM, FM, and MS gates. Using ion chains of five or more ions, fidelity has been proven to typically range from approximately 97% to 98.5%. Therefore, these modulation pulses attempt to improve the gate's robustness to any occurring frequency drift.

[0010] For any type of high-fidelity quantum logic gate operation in a large qubit array, poor optical coherence must be considered. Poor optical coherence between individual address bundles can affect gate fidelity. Another factor affecting gate fidelity is crosstalk from the address bundle to adjacent qubits. Both factors can influence gate fidelity, and the method described above must handle poor phase coherence as well as crosstalk between the address bundle and adjacent qubits.

[0011] Regarding crosstalk, the system has demonstrated negligible crosstalk between the addressing bundle and adjacent qubits. For example, MEMS addressing systems and gate schemes insensitive to optical phase drift between addressing bundles have been developed. Various modulation pulse techniques can unwrap any internal qubit state from all collective motion modes. Because the internal qubit state is unwrapped from all collective motion modes, robustness is improved despite any frequency drift. Such drift can occur with the motion mode frequency.

[0012] Therefore, methods for individual optical addressing of ions in chains of two or more ions using MS gates have been developed. These methods include MEMS addressing systems. Furthermore, methods using PM, AM, and FM gates have been used to attempt to untangle internal qubit states from all collective motion modes, where frequency drift can lead to undesired entanglement. Such methods have been used for ion chains of five or more ions.

[0013] However, it is necessary to demonstrate high-fidelity two-qubit gates in both two-ion and four-ion chains. A system should be developed that effectively addresses the frequency drift of motion patterns that leads to entanglement and amplitude errors.

[0014] In large-scale captured atom-ion quantum computers, high-fidelity two-qubit gates need to be extended to all qubits through individual control. In systems using radial-mode two-ion and four-ion chains, the characterization and realization of high-fidelity two-qubit gates are required. The gate fidelity in two-ion and four-ion chains needs to be derived. Suitable qubit gate sequences need to be measured. Methods need to be developed to further improve the fidelity of gate pairs for values ​​compatible with fault-tolerant quantum computing.

[0015] Therefore, it is necessary to generate pulse sequences that are unaffected by unwanted spin motion and entanglement caused by motion mode frequency drift. Furthermore, it is necessary to more accurately correct amplitude errors caused by phase deviations or amplitude errors. Therefore, there should be a method to generate pulse sequences that simultaneously addresses drift in the spin and unwanted entanglement frequencies of the motion mode that cause radial motion modes, as well as deviations in the gate rotation angles that cause amplitude errors. Summary of the Invention

[0016] Embodiments of this disclosure employ a process for generating a discrete frequency-modulated pulse sequence of symmetrical segments given a radial frequency of a measurement mode and a desired gate time.

[0017] For high-fidelity quantum logic gate operations, optical phase coherence loss between individual addressing bundles and crosstalk from the addressing bundle to adjacent qubits can affect gate fidelity. Gate schemes that are insensitive to optical phase drift between addressing bundles have been developed to overcome fluctuations in the optical bundle paths between different bundles.

[0018] Modulated pulse techniques are used to unwrap internal qubit gates from collective motion modes and also improve robustness to frequency drift. Discrete frequency modulated pulse sequences are generated by shutting down the phase space trajectories of all radial motion modes and unwrapping the spins and motions of the radial motion modes. Amplitude errors due to deviations in the gate rotation angles are corrected by intentional offset detuning, rather than tuning the laser intensity.

[0019] An illustrative embodiment of this disclosure is a system comprising a controller configured to reconstruct a discrete analog version of a continuous waveform. The system further includes a numerical optimizer configured to determine the frequency of a pulse sequence in the discrete analog version, wherein the numerical optimizer uses radial motion mode frequencies and desired gate times. The numerical optimizer generates the pulse sequence via a phase space trajectory with the radial motion modes disabled, unwrapping spins and motion, and limiting the Rabi frequencies of the motion sideband transitions. The system also includes a display configured to illustrate the discrete frequency modulated pulse sequence based on the determined frequencies. The discrete frequency modulated pulse sequence is designed as a sequence of equal time intervals, each of which has a constant frequency.

[0020] In some embodiments, the desired gate time is less than or equal to 200 microseconds.

[0021] In some embodiments, the numerical optimizer is configured to correct for drift in radial motion patterns that cause spin motion entanglement and deviation from geometric phase.

[0022] In some embodiments, the numerical optimizer is configured to correct any phase deviations that cause amplitude errors.

[0023] In some embodiments, the field-programmable gate array is configured to trigger frequency updates of the direct digital synthesizer (DDS) channels in real time.

[0024] An embodiment of this disclosure is a system comprising a controller configured to obtain a predetermined gate time and measured mode frequencies. The system further includes a numerical optimizer configured to receive the predetermined gate time and measured mode frequencies to determine the frequency of a pulse sequence. The numerical optimizer eliminates phase space trajectories containing motion mode frequency drifts that cause spin motion entanglement and geometric phase deviations, and wherein the numerical optimizer limits the Rabi frequencies of motion sideband transitions. The system also includes a display device configured to illustrate the pulse sequence based on the predetermined gate time, the measured mode frequencies, and the frequencies determined by eliminating the spin motion entanglement and deviations from the geometric phase.

[0025] In some embodiments, the numerical optimizer calculates the frequency of the pulse sequence so that the pulse sequence has equal time intervals.

[0026] In some embodiments, the numerical optimizer disables the phase space trajectory for all radial motion modes.

[0027] In some embodiments, the numerical optimizer unwraps the spin and motion of at least four motion modes.

[0028] In some embodiments, the numerical optimizer eliminates all amplitude errors so that the pulse sequence can be generated at equal time intervals.

[0029] Another embodiment of this disclosure is a method comprising reconstructing a continuous waveform into a discrete analog version via a controller. The method further comprises determining the frequency of a pulse sequence of the discrete analog version using a numerical optimizer, wherein the numerical optimizer uses radial motion mode frequencies and desired gate times. The numerical optimizer generates the pulse sequence by disabling the phase space trajectory of the radial motion mode, wherein the numerical optimizer unwraps spins and motion and limits the Rabi frequencies of the motion sideband transitions. The method further comprises displaying a discrete frequency modulated pulse sequence based on the determined frequencies via a display, wherein the discrete frequency modulated pulse sequence is designed as a sequence of equal time intervals, each of which has a constant frequency.

[0030] In some embodiments, the total gate error of a plurality of cascaded Morse-Sorensen gates is estimated.

[0031] In some embodiments, the final state fidelity of the continuum gate is estimated, wherein the estimation takes into account residual spin motion entanglement.

[0032] In some embodiments, the final state fidelity of a continuous gate with deviations in the Rabi frequency of moving sideband transitions is estimated.

[0033] In some embodiments, one or more sets of microelectromechanical system (MEMS) mirrors are configured to deliver a bundle modified by a direct digital synthesizer (DDS). Attached Figure Description

[0034] Figure 1 A block diagram depicting a direct digital synthesizer according to an illustrative embodiment of the present disclosure.

[0035] Figure 2 A display depicting a discrete frequency modulated pulse sequence according to an illustrative embodiment of the present disclosure.

[0036] Figure 3A The phase space trajectory of the motion mode of the illustrative embodiment of this disclosure is described.

[0037] Figure 3B Another phase space trajectory of the motion pattern of the illustrative embodiment of this disclosure is shown.

[0038] Figure 3C The phase space trajectory of the motion pattern of the illustrative embodiment of this disclosure is also depicted.

[0039] Figure 3D Another phase space trajectory depicting the motion pattern of an illustrative embodiment of this disclosure.

[0040] Figure 4 The diagram illustrates the estimated total gate error for 1, 5, 13, and 21 cascaded gates with different detuning offsets in the illustrative embodiments of this disclosure.

[0041] Figure 5 A graph illustrating the final state error of 21 consecutive gates in an illustrative embodiment of this disclosure is shown.

[0042] Figure 6A This describes the gate fidelity in the dual-ion chain in the illustrative embodiments of this disclosure.

[0043] Figure 6B This demonstrates the gate fidelity in a four-ion chain in an embodiment of the present disclosure.

[0044] Figure 7A A schematic representation depicting a Raman beam optical setup in an embodiment of this disclosure.

[0045] Figure 7B Another schematic representation of the Raman beam optical setup in the embodiments of this disclosure is provided.

[0046] Figure 7C Examples of embodiments shown in this disclosure171 Yb + A schematic diagram of the energy levels of an ion.

[0047] Figure 8 The flowchart describes a process according to an embodiment of the present disclosure. Detailed Implementation

[0048] The following disclosure can be performed on an arbitrary waveform generator (AWG) or a direct digital synthesizer (DDS). The diagram (Figure) 1 described below is not intended to limit this disclosure to a particular device (such as an arbitrary waveform generator or a DDS).

[0049] Figure 1 A block diagram of DDS 100 is shown. DDS 100 includes a system clock 110, a tuning word 120, and a phase accumulator 130. Additionally, DDS 100 includes a phase register 140. DDS 100 also includes a phase-to-amplitude converter 150 and a digital-to-analog (D / A) converter 160. Further, DDS 100 includes a controller 170 and a numerical optimizer 180. Controller 170 can reconstruct a continuous waveform into its discrete analog version compatible with DDS 100. In other embodiments, other components of DDS 100 can also reconstruct a continuous waveform into its discrete analog version compatible with DDS 100. Additionally, as will be shown in later figures (e.g.) Figure 2 As described in [the document], the numerical optimizer 180 performs a series of steps to enable the display of the frequency pulse modulation sequence. The numerical optimizer 180 can shut down the phase space trajectories of all involved radial motion modes. The numerical optimizer 180 can also unwrap unwanted spins and motions of the radial motion modes. Frequency drift of the radial motion modes can cause unwanted spins and motions. Detuning errors caused by frequency drift of the motion modes result in phase deviations in the rotation angle of the frequency modulation (FM) gate. Phase deviations of the FM gate are considered amplitude errors. The numerical optimizer can compensate for amplitude errors more accurately by using intentional detuning offsets instead of tuning the laser intensity.

[0050] refer to Figure 2 This describes a frequency pulse modulation sequence (pulse sequence) 200, in which a continuous waveform is reconstructed into a discrete analog version. Furthermore, the pulse sequence 200 is designed as a sequence of equal time intervals. Each time interval may have a constant frequency. The numerical optimizer 180 can perform a series of steps to eliminate amplitude errors at the FM gate using intentional detuning offsets, so that the pulse sequence 200 can be generated as the output of the DDS 100.

[0051] exist Figure 2In this embodiment, the numerical optimizer 180 determines the frequency of the pulse sequence 200. The numerical optimizer utilizes the measured radial motion mode frequency and the desired gate time. In this embodiment, the desired gate time is shown as 200 microseconds. In other embodiments, the desired gate time may be different. Furthermore, the gate time refers to a preset period that the numerical optimizer 180 can preset to determine the frequency of the pulse sequence 200. The desired gate time can be any time less than or equal to 200 microseconds. The numerical optimizer 180 can shut down the phase space trajectories of all radial motion modes. Additionally, the numerical optimizer 180 can unwrap unwanted spins and motions of the radial motion modes.

[0052] about Figure 2 The detuning error is caused by a drift in the motion mode frequency. This drift also leads to unwanted spin entanglement. The detuning error caused by the drift in the motion mode frequency can also result in a deviation in the geometric phase of the Morse-Sorenson (MS) evolution. As mentioned above, the accumulated phase deviation can refer to a deviation in the rotation angle of the FM gate. Therefore, the deviation in the rotation angle of the FM gate can be considered an amplitude error. One way to correct the amplitude error is by tuning the laser intensity. To obtain the pulse sequence 200, the numerical optimizer 180 must eliminate the amplitude error. In other embodiments, the amplitude error is corrected by tuning the laser intensity. However, in those embodiments, if the detuning error changes faster on the time scale than the time between calibration and the experimental circuit, then the intensity calibration will no longer be accurate, and the tuning of the laser intensity will be insufficient.

[0053] exist Figure 2 In contrast to the tuning laser intensity, intentional detuning offset can be applied to more accurately compensate for small amplitude errors. Residual spin entanglement and deviations in the rotation angle of the FM gate can be used in conjunction with intentional detuning offset. Intentional detuning offset can utilize negligible residual spin entanglement to counteract any detuning error in the FM gate. Intentional detuning offset is more accurate than tuning laser intensity. In an embodiment, calibration can be performed by scanning the detuning offset with twenty-one cascaded gates, where cascade refers to gates tightly connected in a chain, series, or continuous sequence. Calibration can be applied to state |00>. Therefore, detuning at states |00> and |11> with equal probability will indicate the perfect rotation angle of the MS gate. In an embodiment, and as an example, intentional detuning offset is applied to up to twenty-one consecutive MS gates, where amplitude errors are corrected. In other embodiments, intentional detuning offset can be applied to more or fewer than twenty-one consecutive MS gates. Instead of tuning laser intensity, intentional detuning offset eliminates amplitude errors caused by deviations in the rotation angle of the gates.

[0054] exist Figure 2In this configuration, the numerical optimizer 180 can correct for detuning errors caused by drift in the motion mode frequency, which results in unwanted spin motion entanglement and deviations in the geometric phase of the radial motion mode. Instead of tuning the laser intensity, an intentional detuning offset can be used, which can more accurately compensate for small-amplitude errors caused by the drift in the motion mode frequency.

[0055] all in all, Figure 2 This demonstrates how the numerical optimizer 180 can generate a pulse sequence 200 based on a determined gate time and a measured radial motion mode frequency. The numerical optimizer can shut down the phase space trajectory of the radial motion mode and unwrap the spin and motion of the radial motion mode due to frequency drift. The numerical optimizer 180 can also eliminate geometric phase deviations in the MS evolution. Phase deviations can be considered as deviations in the rotation angle of the FM gate, or amplitude errors. Instead of tuning the laser intensity, intentional detuning offsets can be used to more accurately compensate for amplitude errors.

[0056] Figures 3A to 3D Describe the phase space trajectories of the four radial motion modes 310, 320, 330, and 340. For example... Figure 2 As described above, the spin and motion of the radial motion mode require entanglement to produce the aforementioned... Figure 2 The pulse sequence 200 described herein. A numerical optimizer 180 generates the pulse sequence 200, which shuts down the phase space trajectories of radial motion modes 310, 320, 330, and 340. Additionally, the numerical optimizer 180 unwraps the spins and motions of the radial motion modes 310, 320, 330, and 340. Amplitude errors are compensated by intentional detuning offsets. The numerical optimizer 180 uses intentional detuning offsets to precisely compensate for phase drift or shift in the motion mode frequencies, which causes unwanted spins and motions, as well as deviations in geometric phase. Intentional detuning offsets compensate for phase drift in the motion mode frequencies. As a result, the numerical optimizer 180 can shut down the phase space trajectories of radial motion modes 310, 320, 330, and 340, and also unwraps the unwanted spins and motions of the radial motion modes 310, 320, 330, and 340. Therefore, the pulse sequence 200 can be generated as the output of the DDS 100.

[0057] exist Figures 3A to 3DIn this process, drift in the motion mode frequency will cause unwanted spin motion entanglement in radial motion modes 310, 320, 330, and 340. Drift in the motion mode frequency of radial motion modes 310, 320, 330, and 340 also causes deviations in the geometric phase of the MS evolution. Furthermore, the residual entanglement error of radial motion modes 310, 320, 330, and 340 can be neglected in the ±1kHz detuning error of the FM gate. The phase deviation, or geometric phase deviation, is represented by the deviation of the FM gate's rotation angle. The deviation of the FM gate's rotation angle can be determined as an amplitude error. The amplitude error of the FM gate can be precisely corrected by using intentional detuning offsets to compensate for the amplitude error. By tuning the laser intensity, if the detuning error changes faster on the time scale than the time between calibration and experimental circuitry, then intensity calibration will no longer be accurate. Therefore, intentional detuning offsets are preferred over tuning the laser intensity.

[0058] exist Figures 3A to 3D Intentional detuning offset can correct amplitude errors in FM gates. Intentional detuning offset can be applied to consecutive gates. Furthermore, detuning offset can be scanned using up to twenty-one cascaded gates. As a result, the corresponding calibration can significantly reduce and / or eliminate amplitude errors caused by deviations in rotation angles due to drift in the motion mode frequency. In addition, unwanted spin motion entanglement in radial motion modes 310, 320, 330, and 340 can also be corrected. As a result, a pulse sequence 200 with equal time intervals at a constant frequency can be generated.

[0059] Figure 4 System diagram 400 illustrates the application of intentional detuning offsets on one MS gate, five MS gates, thirteen MS gates, and twenty-one MS gates. In other embodiments, intentional detuning offsets may be applied to more or fewer than twenty-one MS gates. Furthermore, system diagram 400 illustrates applications... Figure 1 DDS 100 in the middle to generate Figure 2 The illustration shows the intentional detuning offset of pulse sequence 200. It illustrates the estimated total gate error for one, five, thirteen, and twenty-one cascaded gates with different detuning offsets. The estimation of final-state fidelity after one, five, thirteen, and twenty-one consecutive MS gates is used as a function of the detuning offset. The estimation of final-state fidelity applies both to residual spin motion entanglement in radial motion modes and to deviations in the rotation angle of FM gates. Intentional detuning offsets can be introduced to prevent detuning errors in FM gates by utilizing negligible spin motion entanglement. A ±100Hz detuning offset can compensate for approximately ±0.8% deviation in the Rabi frequency of moving sideband transitions. Intentional detuning offsets can be used instead of tuning laser intensity, where intentional detuning offsets are a more accurate method for obtaining final-state fidelity and correcting any amplitude errors in FM gates.

[0060] refer to Figure 5 System diagram 500 illustrates the estimated final state error for twenty-one consecutive MS gates, with a deviation of ±0.8% of the Rabi frequency of the moving sideband transition. In other embodiments, the estimated final state error for more or fewer than twenty-one consecutive MS gates can be estimated. System diagram 500 shows... Figure 1 The final state error of the twenty-one MS gates within the DDS 100 shown in the figure is used to generate Figure 2 The pulse sequence is 200. Amplitude errors due to imperfect laser intensity can be compensated for by intentional detuning offset, rather than tuning the laser intensity. A ±100Hz detuning offset can compensate for approximately ±0.8% deviation in the Rabi frequency of the moving sideband transition.

[0061] exist Figure 5 In this process, calibration is performed to compensate for small drifts in mode frequency and laser intensity. Furthermore, unlike tuning the laser intensity, intentional detuning offsets can be used to more precisely compensate for small drifts in laser intensity. Calibration is accomplished by scanning the detuning offsets applied to the twenty-one consecutive / serialized gates of |00>. Moreover, |00> and |11> have equal probabilities of detuning to indicate the perfect rotation angle of the MS gate. Therefore, unlike coarse calibration or tuning the laser intensity, this calibration technique improves gate fidelity.

[0062] Two-qubit MS gates can be verified in both two-ion and four-ion chains. As will be shown below, state fidelity can be extracted, and population and isotope contrast can be measured. Furthermore, distortions due to population leakage and decreased isotope contrast are explained.

[0063] Figure 6A A two-qubit MS gate in a dual-ion chain is shown. Figure 600 illustrates the distortion caused by population leakage and reduced isotope contrast. Figure 6A In the diagram, the rhombus indicates group leakage into the |01> and |10> spaces. The square indicates loss of isotopic contrast. Additionally, the circle indicates distortion of the final state. Initially, the target qubit is initialized to the |00> state. A series of one, five, thirteen, and twenty-one MS gates are applied to create the maximally entangled state. State fidelity can be extracted by measuring population and isotopic contrast. Random and coherent errors can be accumulated linearly and quadratically using cascaded MS gates. Additionally, state preparation and measurement (SPAM) errors remain constant. However, using a linear fitting / method, gate or state fidelity can be extracted without SPAM errors. Therefore, the two-qubit gate fidelity for the two-ion chain is 99.49%. Thus, the data matches the linear fitting / method, and therefore any systematic errors are negligible for the two-qubit gate.

[0064] refer to Figure 6B Figure 610 illustrates the distortion caused by group leakage and reduced isotopic contrast in the four-ion chain. (As shown in...) Figure 6A In the diagram, the rhombuses indicate group leakage into the |01> and |10> spaces. Additionally, squares indicate loss of isotopic contrast, while circles indicate distortion of the final state. As in the bichain, in the four-ion chain, the target qubit is initialized to the state |00>. Sequences of one, five, thirteen, and twenty-one MS gates are applied to create the maximally entangled state. In order to extract state fidelity (e.g.) Figure 6B (Indicated by the circle in the diagram), it is necessary to measure population and in-situ contrast. Even though random and coherent errors can accumulate linearly and quadratically within the gate, population and in-situ contrast must still be measured. Furthermore, SPAM error can remain constant. However, using methods such as... Figure 6A The linear fit in the model allows for gate fidelity extraction without SPAM error. For the four-ion chain, the two-qubit gate fidelity is 99.30%. Since the data for the four-ion chain matches the linear fit, any coherent systematic errors are negligible, as are those for the two-ion chain. Furthermore, gate fidelity can therefore be extracted without SPAM error. Because the data matches the linear fit, any systematic errors in the two-qubit gate are also negligible.

[0065] about Figures 6A to 6B The simulation error values ​​for laser phase shifting, motion phase shifting, Raman beam intensity fluctuations, and non-resonant coupling of four-ion and two-ion chains are the same. Furthermore, the simulation error values ​​for motion heating, spontaneous emission, and defects in the FM solution are also the same.

[0066] A high-fidelity two-qubit gate in microelectromechanical systems (MEMS) can be demonstrated using an optimized automated calibration pipeline for ion trapping systems. The qubits can... 171 Yb + Among ions 2 S 1 / 2 The hyperfine level in the hyperfine level of the manifold is encoded as |0>≡|F=0; m F =0> and |1>≡|F=1; m F =0>, where the qubit frequency is split into 12.642821 GHz, such as Figure 7C As shown in the illustration. In other embodiments, similar methods can be used with other atomic species and isotopes.

[0067] exist Figure 7AThe diagram illustrates a MEMS-based qubit addressing system 700. A first parallel beam (beam) 705 is incident on a focusing lens 710. The first parallel beam 705 is a pair of closely focused individual addressing beams that can be independently manipulated across a qubit chain using a MEMS device. The beam 705 passes through the focusing lens 710 and is incident on a first lens 715. The beam 705 then passes through the first lens 715 and is incident on a first MEMS mirror 720 within the MEMS device. The first MEMS mirror 720 is part of the MEMS device, which also includes a second MEMS mirror 730. After being reflected from the first MEMS mirror 720, the beam 705 is incident on a concave mirror 725. The beam 705 is reflected from the concave mirror 725 and then reflected onto the second MEMS mirror 730 within the MEMS device. The beam 705 then travels from the second MEMS mirror 730 to a second lens 735. The beam 705 is reflected from the second lens 735 onto the Fourier lens 740. The beam 705 travels through the Fourier plane onto the projection and beam combination optics 745. The beam 705 can then be incident on the dichroic mirror 750.

[0068] exist Figure 7A In this configuration, fiber array 760 can provide another beam 775 to another lens or detection optics 755. Beam 775 can also be incident as beam 705 on dichroic mirror 750. Beams 705 and 775 are incident from dichroic mirror 750 onto high-NA imaging lens 765. Beams 705 and 775 pass through high-NA imaging lens 765 to qubit 770. Therefore, the combination of fiber array 760 with MEMS mirrors 720 and 730 results in clean Gaussian beams and low-intensity crosstalk on adjacent qubits 770.

[0069] exist Figure 7B The diagram also illustrates the Raman beam optics setup. The well surface 780 is shown. The well axis is rotated 45 degrees relative to the two tilt axes of the MEMS mirrors 720 and 730 to maximize the addressable qubits using orthogonal tilt mirrors. The projection and beam combining optics 745 can be represented by a black box.

[0070] Figure 7C illustrate 171 Yb + Schematic diagram of ion energy levels 785. Red and blue lines indicate two-photon Raman transitions operated on by qubits.

[0071] In summary, the optical setup generates a clean pair of Gaussian beams and low-intensity crosstalk on adjacent qubits 770. Intensity crosstalk can lead to gate crosstalk, or the ratio of the Rabi frequencies between the target qubit and its neighboring qubits.

[0072] Figure 8The process 800, which generates a pulse modulation sequence, is described. A numerical optimizer 180 can realize the pulse sequence 200 using the measured radial mode frequency and a desired gate time of up to 200 microseconds. The desired gate time can be less than or equal to 200 microseconds. The numerical optimizer 180 can unwrap the pulses caused by drift in the motion mode frequency. Figures 3A to 3D The diagram shows the unwanted spin and motion of the radial motion mode. Additionally, the numerical optimizer 180 also disables the phase space trajectory of the radial motion mode caused by drift in the motion mode frequency. Accumulated phase deviations or deviations in the gate rotation angle can be considered amplitude errors. However, intentional detuning offsets can compensate for amplitude errors.

[0073] exist Figure 8 In step 810, the controller 170 within the DDS 100 can reconstruct the continuous waveform into its discrete analog version. In other embodiments, other components of the DDS 100 can reconstruct the continuous waveform into its discrete analog version.

[0074] exist Figure 8 In step 820, the numerical optimizer 180 is configured to determine the frequency of the pulse sequence 200 using the radial motion mode frequency and a desired gate time. The desired gate time may be less than or equal to 200 microseconds.

[0075] exist Figure 8 In step 830, the numerical optimizer 180 generates a pulse sequence 200 by closing the phase space trajectory and unwinding unwanted spins and motions of the radial motion mode. Shifts in the motion mode frequency cause entanglement of unwanted spin motions and phase deviations in the motion mode. The numerical optimizer 180 can unwind the unwanted spins and motions of the motion mode. Additionally, the accumulated phase deviation is represented by the deviation of the FM gate's rotation angle. The deviation of the FM gate's rotation angle can be determined as an amplitude error. Intentional detuning offsets can be used to precisely compensate for the amplitude error or the deviation of the FM gate's rotation angle.

[0076] exist Figure 8 In step 840, the numerical optimizer generates pulse sequence 200 by limiting the Rabi frequency of the moving sideband transitions. The numerical optimizer 180 limits the Rabi frequency of the moving sideband transitions to less than 7 kHz. Furthermore, in the embodiment, the required sideband Rabi frequency is 5.55 kHz for the FM gate in a two-ion chain and 5.47 kHz for the FM gate in a four-ion chain, respectively.

[0077] refer to Figure 8At step 850, a discrete frequency modulated pulse sequence / pulse sequence 200 is displayed. Pulse sequence 200 is designed as a sequence of equal time intervals, each of which has a constant frequency. Undesired spins and entanglements, as well as phase deviations, have been eliminated. The pulse sequence may have a total gate time of less than or equal to 200 microseconds and also consists of twenty symmetrical segments.

[0078] In summary, the numerical optimizer 180 generates the pulse sequence 200 by unwinding the unwanted spins and motions of the radial motion mode caused by the drift in the motion mode frequency. Furthermore, the accumulated phase deviation of the FM gate's rotation angle caused by the drift in the motion mode frequency can be precisely compensated by using intentional detuning offset. Intentional detuning offset can precisely compensate for small-amplitude errors caused by deviations in the FM gate's rotation angle. In an embodiment, a ±100Hz detuning offset can compensate for approximately ±0.8% deviation in the Rabi frequency of the moving sideband transition.

[0079] It should be understood that this disclosure teaches only some examples of embodiments according to this disclosure, and many variations of this disclosure can be readily designed by those skilled in the art upon reading it, and the scope of this disclosure will be determined by the appended claims.

Claims

1. A system comprising: A controller configured to reconstruct a continuous waveform into a discrete analog version; A numerical optimizer configured to determine the frequency of the pulse sequence in the discrete simulation version, wherein the numerical optimizer uses the radial motion mode frequency and the desired gate time, wherein the numerical optimizer generates the pulse sequence by disabling the phase space trajectory of the radial motion mode and unwrapping the spin and motion, and limiting the Rabi frequency of the motion sideband transitions. and A display configured to describe a discrete frequency modulated pulse sequence based on the frequency determined by the numerical optimizer, wherein the discrete frequency modulated pulse sequence is designed as a sequence of equal time intervals, each of which has a constant frequency.

2. The system of claim 1, wherein the desired gate time is less than or equal to 200 microseconds.

3. The system of claim 1, wherein the numerical optimizer limits the Rabi frequency to less than 7 kHz.

4. The system of claim 1, wherein the numerical optimizer is configured to correct the drift of the radial motion pattern that causes spin motion entanglement and deviation from geometric phase.

5. The system of claim 1, wherein the numerical optimizer is configured to correct any phase deviations that cause amplitude errors.

6. The system of claim 1, wherein the field-programmable gate array is configured to trigger frequency updates of the direct digital synthesizer channels in real time.

7. A system comprising: A controller configured to obtain a predetermined gate time and a measured pattern frequency; A numerical optimizer configured to receive the predetermined gate time and the measured mode frequency to determine the frequency of the pulse sequence, wherein the numerical optimizer eliminates the phase space trajectory of the motion mode frequency drift that includes deviations in spin motion entanglement and geometric phase, and wherein the numerical optimizer limits the Rabi frequency of the motion sideband transition. and A display device configured to illustrate the pulse sequence based on the predetermined gate time, the measured mode frequency, and the frequency determined by eliminating the spin motion entanglement and deviation from the geometric phase.

8. The system of claim 7, wherein the deviation of the geometric phase is used for a Mormer-Sorenson two-qubit gate.

9. The system of claim 7, wherein the numerical optimizer calculates the frequency of the pulse sequence such that the pulse sequence has equal time intervals.

10. The system of claim 7, wherein the numerical optimizer disables the phase space trajectory for all radial motion modes.

11. The system of claim 7, wherein the numerical optimizer eliminates all amplitude errors so that the pulse sequence can be generated at equal time intervals.

12. The system of claim 7, wherein the numerical optimizer unwraps the spins and motions of at least four motion modes.

13. The system of claim 8, wherein the numerical optimizer determines the deviation of the rotation angle of the two-qubit gate.

14. A method comprising: The controller reconstructs a discrete analog version of the continuous waveform. The frequency of the discrete simulation version of the pulse sequence is determined by a numerical optimizer, wherein the numerical optimizer uses the radial motion mode frequency and the desired gate time, wherein the numerical optimizer generates the pulse sequence by turning off the phase space trajectory of the radial motion mode, and wherein the numerical optimizer unwraps the spin and motion and limits the Rabi frequency of the motion sideband transition. and The discrete frequency modulated pulse sequence is described by a display based on the frequency determined by the numerical optimizer, wherein the discrete frequency modulated pulse sequence is designed as a sequence of equal time intervals, each of which has a constant frequency.

15. The method of claim 14, further comprising: Estimate the total gate error of multiple tandem Mormer-Sorensen gates.

16. The method of claim 14, wherein the frequency modulation pulse sequence is generated by turning off the phase space trajectories of one or more radial motion modes.

17. The method of claim 14, further comprising: Estimate the final state fidelity of the continuum gate, wherein the estimation takes into account the entanglement of residual spin motion.

18. The method of claim 14, further comprising: Estimate the final state fidelity of the continuous gate with the deviation of the Rabi frequency for the moving sideband transition.

19. The method of claim 14, further comprising: Configure one or more sets of microelectromechanical system mirrors to deliver bundles modified by a direct digital synthesizer.

20. The method of claim 14, further comprising: Intentional detuning offsets are applied to compensate for amplitude errors caused by laser intensity.

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