Rapid intensity stabilization of multi-controller beams

Abstract

This disclosure describes techniques for rapidly stabilizing multiple controller beams using a continuous integral filter. For example, a method for stabilizing the intensity of a laser beam (e.g., an ion controller beam) in a trapped ion system is described, wherein the method includes: applying a linear array of laser beams to corresponding ions in a linear array of ions in a trap; performing parallel measurements on the ions in response to the applied laser beams, the parallel measurements including multiple individual measurements for each said ion to identify intensity fluctuations of the corresponding laser beam at each ion; and adjusting the intensity of one or more laser beams in response to fluctuations identified from the parallel measurements. A corresponding system for stabilizing the intensity of a laser beam in a trapped ion system is also described.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. non-provisional application No. 16 / 995,642, filed August 17, 2020, entitled "Fast Intensity Stabilization of Multiple Controller Beams with Continuous Integrating Filter," and U.S. provisional application No. 62 / 888,668, filed August 19, 2019, the contents of which are incorporated herein by reference in their entirety. Technical Field

[0003] The aspects of this disclosure generally relate to the stabilization of laser beam intensity, and more specifically, to the rapid stabilization of a multi-controller beam through continuous integration. Background Technology

[0004] In trapped-ion quantum computers, or quantum information processing (QIP) systems, a linear array of laser beams is focused downwards onto a linear array of ions. Each laser beam is tightly focused on a corresponding ion to provide some form of control over that ion. The diameter of the laser beam at the ion location is approximately 1 micrometer (μm) to 1.5 μm, while the spacing between the ions can be approximately 5 μm.

[0005] For a quantum computer or QIP system to function properly, it is crucial that the light intensity of each laser beam on each ion remains constant. Many factors can cause variations in laser beam intensity; for example, the laser beam or ions may shift, reducing the intensity at the ion's location, or the power of the laser beam itself may change. In some cases, changes in the trap holding the ions can cause them to move to different spots with varying laser beam intensities. Variations in the laser beam or ions on the order of tens or hundreds of nanometers can severely impact system performance. Pressure gradients across the laser beam can produce destructive interference at the focal point (e.g., at the narrowest point of the laser beam, ideally where the ion is located), resulting in a decrease in laser beam intensity. Therefore, monitoring and stabilizing the laser beam intensity over time is essential.

[0006] One solution is to use a photodiode to monitor the power of the laser beam and then provide measurement feedback to adjust the amplitude of the radio frequency (RF) signal applied to the acousto-optic modulator (AOM), controlling the laser beam to stabilize its power. The intensity of the laser beam can refer to the amount of power per unit area; therefore, the terms "intensity" and "power" related to the laser beam are used interchangeably in this disclosure. However, the technique of monitoring laser power with a photodiode cannot correct for intensity variations caused by fluctuations in laser beam pointing, ion position, or gas pressure. Moreover, it only stabilizes the laser power at the location of the photodiode and does not account for fluctuations in the laser beam path caused by corresponding ions behind and near the photodiode.

[0007] Therefore, a technique that allows for more accurate measurements closer to the ions is desired. One way to do this is to actually measure the intensity or power of the laser beam using the ions themselves and use these measurements to control the laser beam intensity. The laser beam intensity can be calibrated periodically by scanning within a certain range while simultaneously observing the ion response. The scan results need to be fitted before selecting the optimal intensity point from the scan. The laser beam intensity is set to the value of the optimal point until the next calibration run. This process is typically slow, with calibration taking 30 seconds to a minute, so it cannot be run more frequently than approximately every 10 minutes. There is a significant amount of noise that fluctuates on a timescale much faster than this 10-minute interval, and the type of calibration process described above cannot correct for any of it.

[0008] New technologies are needed that enable faster stabilization or control of the intensity or power of a laser beam applied to ions, while still allowing measurements at or near the ions where the laser beam is controlled. Summary of the Invention

[0009] The following is a simplified summary of one or more aspects to provide a basic understanding of these aspects. This summary is not a comprehensive overview of all anticipated aspects, nor is it intended to identify key or necessary elements of all aspects, nor to depict the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed descriptions given later.

[0010] In one aspect of this disclosure, a method for stabilizing the intensity of a laser beam in a trapped ion system is described, the method comprising: applying a linear array of laser beams to corresponding ions in a linear array of ions in a trap; performing parallel measurements on the ions in response to the applied laser beams, the parallel measurements including multiple individual measurements for each of the ions to identify intensity fluctuations of the corresponding laser beam at each ion; and adjusting the intensity of one or more laser beams in response to fluctuations identified from the parallel measurements.

[0011] In another aspect of this disclosure, a system for stabilizing the intensity of a laser beam in a trapped ion system is described, the system comprising: a laser source configured to apply a linear array of laser beams to corresponding ions in a linear array of ions in a trap; an imaging system configured to perform parallel measurements on the ions in response to the applied laser beams, the parallel measurements including multiple individual measurements for each ion to identify intensity fluctuations of the corresponding laser beam at each ion; and an optical controller configured to adjust the intensity of one or more laser beams in response to fluctuations identified from the parallel measurements.

[0012] To achieve the foregoing and related objectives, the one or more aspects include the features fully described below and specifically pointed out in the claims. The following description and drawings illustrate certain illustrative features of the one or more aspects in detail. However, these features represent only a few of the various ways in which the principles of the aspects can be employed, and this description is intended to include all such aspects and their equivalents. Attached Figure Description

[0013] This document will describe the disclosed aspects in conjunction with the accompanying drawings, for the purpose of illustration and not limitation, wherein the same reference numerals denote the same elements.

[0014] Figure 1 A view showing trapped atomic ions in a linear crystal according to various aspects of this disclosure.

[0015] Figure 2A This is an illustration showing an example of Raman beam geometry according to various aspects of this disclosure.

[0016] Figure 2B This is an illustration showing an example of a fluctuation in the position of a laser beam or ion that results in a fluctuation in intensity at the ion, according to various aspects of this disclosure.

[0017] Figure 3 This is an illustration showing an example of a multi-channel acousto-optic modulator (AOM) for multi-qubit control according to various aspects of this disclosure.

[0018] Figure 4 This is a diagram illustrating the ion brightness in response to the pulse area according to various aspects of this disclosure.

[0019] Figure 5A This is a block diagram illustrating an example of a quantum information processing (QIP) system according to various aspects of this disclosure.

[0020] Figure 5B This is a block diagram illustrating an example of an optical controller according to various aspects of this disclosure.

[0021] Figure 6 This is a flowchart illustrating examples of methods according to various aspects of this disclosure. Detailed Implementation

[0022] The detailed description that follows, illustrated with reference to the accompanying drawings, is intended as a description of various configurations and not as representing the only configuration in which the concepts described herein can be practiced. This detailed description includes specific details intended to provide a thorough understanding of the various concepts. However, it will be apparent to those skilled in the art that these concepts can be practiced without these specific details. In some cases, well-known components are shown in block diagram form to avoid confusion with these concepts.

[0023] One object of this disclosure is to perform rapid experiments to measure the response of individual ions to their respective laser beams at the end of an experimental cycle (e.g., every few milliseconds) in order to stabilize the laser beam intensity as frequently as possible over time. By performing these rapid calibration or stabilization techniques, fluctuations on timescales faster than the 10-minute intervals currently used in periodic calibrations can be compensated for. In some cases, measurements can be performed after each of several experimental cycles. The results of these measurements can be used to increase or decrease the intensity of each laser beam, if desired and appropriate, by driving the RF amplitude of a channel in an AOM (e.g., a multi-channel AOM). Because the system is configured to detect the response of each ion individually, and because there is a single AOM channel driving each laser beam on each ion, the intensity of all laser beams can be measured and calibrated or stabilized in parallel (e.g., simultaneously, at the same time). Therefore, this disclosure enables numerous measurements to be performed and the results of these measurements to control the intensity of numerous laser beams in parallel. Furthermore, to avoid shot noise caused by the measurements, this disclosure describes techniques for filtering out such noise, one example of which involves using an integral filter to remove shot noise.

[0024] In trapped-ion quantum computers, trapped-ion systems, or QIP systems, the ability to individually address each ion may be required to control its phase, frequency, and / or amplitude, and / or polarization, depending on the specific quantum gate or experiment being implemented using ions. For example, some trapped-ion systems have 32 individually controlled ions, but this number can be dynamically adjusted to fewer or more, in some cases up to 100 or more ions. This same ability to individually address each ion can also be used to perform independent measurements in each ion, such as the rapid calibration or stable experiments of laser beam intensity proposed in this paper. In systems supporting individual ion control, a single global laser beam can be applied or supplied to ion chains (e.g., ion chains in an ion trap or linear arrangements of ions, see example...). Figure 1In a qubit ion cluster, all ions are controlled by a single global laser beam, which is applied or supplied to those ions to perform or implement quantum gates, experiments, or measurements. These backpropagating beams, called Raman beams or simply Raman beams, are typically laser beams with a very high center frequency (e.g., 850 THz). However, these laser beams have a well-defined frequency difference that produces a beatnote (e.g., 12.6 GHz), which is used as the qubit frequency. An RF signal is used to control the frequency or phase of the beatnote produced by the laser beam, which is then used to drive qubits (e.g., atomic or ionic qubits) in the ion cluster. As used in this disclosure, the terms “atomic ion,” “atom,” and “ion” are used interchangeably to describe particles that will be confined or actually confined in a trap to form a crystal, linear, or similar arrangement or configuration. This type of control has been achieved in the past by using a single global laser beam as a means of adjusting the frequency or phase of the beatnote, but this approach has some limitations, and therefore systems using individual laser beams to control ions are preferred.

[0025] Therefore, Raman transitions can be used to control the state of trapped ions, where beats between two Raman laser beams can be used to coherently drive the internal qubit states. When controlling individual trapped ions in a quantum computer or QIP system, an array of addressable laser beams is generated, one beam for each individual trapped ion. By using a multichannel AOM, each addressable laser beam in the array can be controlled, giving it the ability, for example, to individually correct any systematic errors collected by the trapped ions or to perform measurements on the ions. It should be understood that while the multichannel AOM is referred to herein as being for individual trapped ion control, this disclosure is not intended to be so restrictive, and the multichannel AOM can be implemented using multiple single-channel AOMs or multiple smaller multichannel AOMs. Multiple arbitrary waveform generators (AWGs) or direct digital synthesizers (DDSs) can be used with the multichannel AOM, where each AWG / DDS independently controls a channel of the AOM for the corresponding addressable laser beam.

[0026] Regarding the above methods Figure 1 Illustration 100 shows multiple atomic ions 106a-106d trapped in a linear or one-dimensional arrangement, such as linear crystal 110, using a linear RF trap, such as a linear RF Paul trap (linear crystal 100 may be located in a vacuum chamber not shown). For example, linear crystal 110 may also be referred to as an ion chain. Figure 1 In the example shown, the trap may include traps for confining multiple atomic ytterbium ions (e.g., 171 Yb +The electrodes (containing ytterbium atoms) are used to confine these ytterbium atoms within a linear crystal 110 and are laser-frozen to near rest. It should be understood that the techniques described herein are applicable to a wide range of atomic ions besides ytterbium ions; therefore, this disclosure is not necessarily limited to the use of ytterbium ions. The number of trapped atomic ions can be configurable, and more or fewer atomic ions can be trapped. In one example, the number of ions that can be trapped is N, where N > 1 and where N is a number as large as 100 or even larger; in some embodiments, N = 32, as described above. The atoms are tuned to... 171 Yb + Resonant laser (light) radiation is applied, and the fluorescence of the atomic ions is imaged onto a camera. In this example, the atomic ions are separated from each other by approximately 5 micrometers (μm), which can be observed through fluorescence. The separation of the atomic ions depends on the balance between external confinement forces and Coulomb repulsion. While atomic ions 10⁶a–10⁶d can be confined for computational or experimental purposes, they can also be used, as described herein, to measure the intensity of their respective laser beams.

[0027] Figure 2A Illustration 200a illustrates an example of Raman beam geometry. In illustration 200a, individual laser beams 210 (e.g., one for each atomic ion) and a global laser beam 220 are pointed to a linear crystal or chain, such as linear crystal 110, which has a linear array of atomic ions or qubits. The measurement techniques described herein can be used to control the intensity of laser beams 210 such that the intensity of each of the individual laser beams 210 is stable, at least from the perspective of the corresponding ion. Laser beams propagating or traveling in the same direction may be referred to as co-propagating laser beams, and laser beams propagating or traveling in different or opposite directions may be referred to as non-co-propagating or anti-propagating laser beams, respectively. Laser beam 210 (co-propagating) is a laser beam focused or individually addressed for the corresponding atomic ion, while the global laser beam 220 (as shown, anti-propagating relative to laser beam 210) can be a global beam, which is typically focused to a broad elliptical spot covering all ions. As used herein, the terms “laser beam,” “beam,” “beam,” “laser,” “light field,” and “field” are used interchangeably. Furthermore, as used in this article, the terms “atom,” “atomic ion,” and “ion” can be used interchangeably.

[0028] Figure 2BIllustration 200b shows an example illustrating how fluctuations in the position of a laser beam or ion cause intensity fluctuations at the ion. In this example, a laser beam 210 (e.g., a individually addressed laser beam) is focused at the location (solid line) of ion 106. The diameter 230 of the focused portion of the laser beam 210 is approximately 1 μm to 1.5 μm. The intensity distribution 240 on the right side of illustration 200b shows ion 106 aligned with the highest point in the intensity distribution 240.

[0029] The change in the position of ion 106 or the change in the position of laser beam 210 (dashed line) will change the alignment position of ion 106 with intensity distribution 240, thereby causing a decrease in the intensity of laser beam 210 seen by ion 106.

[0030] The techniques described herein are used to correct these types of fluctuations by changing the intensity of the laser beam 210, wherein the intensity can be increased or decreased so that the ion 106 sees a stable or constant laser beam intensity over time.

[0031] Figure 3 Figure 300 illustrates a portion of a trapped-ion quantum computer or QIP system that can be used to perform measurements to rapidly stabilize multiple controller laser beams, employing continuous integration for multiple measurements. While as... Figure 3As shown in Figure 300, four ions 106a-106d are depicted as being confined in a linear crystal 110, but the linear crystal 110 may have fewer or more ions, and it may measure all or any subset of the ions to stabilize their respective laser beam intensities. Figure 300 also shows a multi-channel AOM 330, waveform generators 350a-350d, an imaging system 360, a stabilization measurement controller 370, and a multi-channel AOM controller 380. In one example, the AOM 330 may be a multi-channel Bragg cell with transducers 312a-312d arranged in parallel (e.g., piezoelectric transducers) that locally apply acoustic waves to the AOM 330 to adjust one or more characteristics (e.g., intensity) of the respective individual addressed laser beams 210a-210d applied to the transducers. These laser beams 210a-210d may also be referred to as controller laser beams or simply controller beams because they control aspects of operating and measuring the ions 106a-106d. Furthermore, laser beams 210a-210d can be referred to as a linear array of laser beams because their linear arrangement is used to match the linear arrangement of ions 106a-106d in the linear crystal 110. AOM 330 may include a separate channel (e.g., a separate transducer) for each ion 106a-106d and their corresponding laser beam 210a-210d. In this example, four channels are shown with transducers 312a-312d, which can be controlled by corresponding waveform generators 350a-350d. Waveform generators 350a-350d can be arbitrary waveform generators (AWGs) and / or direct digital synthesizers (DDS), or some other type of signal generation device.

[0032] During operation, in some embodiments, a global laser beam 220 may be provided from a first direction to ions 106a-106d. Laser beams 210a-210d may be provided to irradiate some or all of ions 106a-106d individually or separately from a second direction. For example, during quantum operation, the irradiated ions depend on the quantum gate implemented in the current phase of a sequence as part of a quantum operation or algorithm. During calibration or stabilization, the irradiated ions depend on the intensity of those laser beams being measured for calibration or stabilization. In the example shown in Figure 300, laser beam 210a may irradiate or focus on ion 106a, laser beam 210b may irradiate or focus on ion 106b, laser beam 210c may irradiate or focus on ion 106c, and laser beam 210d may illuminate or focus on ion 106d. In some examples, some ions in the linear crystal 110 may not be irradiated by any laser beam, and laser beam intensity stabilization measurements may be performed in parallel using only those irradiated ions. In other embodiments, it may be advantageous to irradiate all ions in the linear crystal 110 to perform laser beam intensity stabilization measurements in parallel for all of these ions.

[0033] It should be understood that, although Figure 2A Figure 200a and Figure 3 The diagram 300 uses a global laser beam 220 in one direction and a set of separate addressing laser beams 210 in another direction, but alternatively two sets of separate addressing laser beams can be used, one in one direction and the other in another direction (e.g., at different angles or on opposite sides of the trap).

[0034] Still referencing Figure 3 In some embodiments, certain characteristics of each of the laser beams 210a-210d can be individually modulated by the AOM 330. For example, the waveform generator 350a can generate and / or control the generation of an RF signal that causes a transducer 312a in one of the channels of the AOM 330 to generate an acoustic wave to control the characteristics (e.g., frequency, amplitude, and / or phase) of the laser beam 210a incident on the transducer 312a. By controlling the frequency of the laser beam 210a, the difference between this frequency and the frequency of the global laser beam 220 can be used to generate a beat, which in turn controls the state of the ion 106a. The waveform generator 350a can dynamically change the RF signal to alter the characteristics of the laser beam 312a over time. For example, the amplitude of the RF signal can be used to control the intensity and / or power of the laser beam 210a applied to the ion 106a, and the waveform generator 350a may be able to dynamically adjust or change the amplitude of the RF signal to change the intensity based on the type of calculation or experiment being performed. This feature can also be used to stabilize the intensity of the laser beam 210a.

[0035] The same method described above can be performed with respect to waveform generators 350b-350d, transducers 312b-312d, and laser beams 210b-210d. In other words, the intensity of each of the laser beams 210b-210d can be individually and dynamically controlled by controlling the amplitude of the RF signal applied to the respective channel (e.g., the corresponding transducer) in the AOM 330.

[0036] exist Figure 3 Figure 300 also shows an imaging system 360 configured to image and analyze the effects of the interaction between the linear array of laser beams 210a-210d and the corresponding linear array of their ions 106a-106d. Imaging system 360 can be used as part of a rapid and stable measurement of the laser beams 210a-210d. For example, imaging system 360 can be used to detect the brightness (or lack thereof) of each of the ions 106a-106d, and, for example, assign a value "0" to ions in a dark state and a value "1" to ions in a bright state.

[0037] Figure 3Figure 300 also shows a stabilization measurement controller 370, which can be configured to control rapid experiments for measuring the response of individual ions to the corresponding laser beam at the end of an experimental cycle (e.g., every few milliseconds) to stabilize the laser beam intensity as frequently as possible over time. The stabilization measurement controller 370 can be configured to control one or more of the following: the scheduling of measurements (e.g., when to perform measurements and for how long), the measurements to be performed (e.g., which ions to perform which measurements and how many measurements to perform, and how to prepare the ions for the measurements), and the processing of measurements (e.g., determining whether the intensity of the laser beam needs to be adjusted). The stabilization measurement controller 370 can also be configured to generate instructions to a multi-channel AOM controller 380 to control, when necessary, the adjustment of RF signals generated by waveform generators 350a-350d, which are in turn applied to channels in the AOM 330 to modify the intensity of the laser beams 210a-210d. In one example, the stabilization measurement controller 370 may include an integrating filter 375 configured to integrate the measurement results over time (e.g., continuous integration) to obtain a more accurate representation of the laser beam intensity fluctuations at ions 106a–106d. The integrating filter 375 can be effectively used to set a threshold such that when too many measurements of a particular ion indicate that a lower-than-expected laser beam intensity is being measured, the stabilization measurement controller 370 instructs the multi-channel AOM controller 380 to increase the intensity of the corresponding laser beam by adjusting the amplitude of the RF signal of the corresponding waveform generator. Similarly, when too many measurements of a particular ion indicate that a higher-than-expected laser beam intensity is being measured, the stabilization measurement controller 370 instructs the multi-channel AOM controller 380 to decrease the intensity of the corresponding laser beam by adjusting the amplitude of the RF signal applied to the corresponding channel in the AOM 330.

[0038] In some implementations, some or all of the functions of the stable measurement controller 370 and / or the integral filter 375 may be implemented as part of the multi-channel AOM controller 380, the imaging system 360, or some of the imaging system 360 and some of the multi-channel AOM controller 380.

[0039] Figure 3The trapped-ion quantum computer or QIP system shown in Figure 300 is flexible enough to perform not only quantum computing and experiments, but also experiments or measurements to rapidly stabilize multiple controller laser beams (e.g., laser beams 210a-210d) through continuous integration. That is, the system can perform rapid experiments to measure the response of the ion linear array 106a-106d to the laser beam linear array 210a-210b at the end of one or more consecutive experimental cycles, where the measurement results are used to increase or decrease the laser beam intensity by adjusting the amplitude of the RF signal driving the AOM 330. Because the system can detect the response of each ion separately, and because there are separate channels in the AOM 330 to drive the corresponding laser beam for each ion, all laser beam intensities can be measured and / or adjusted in parallel.

[0040] For each measurement to be performed (e.g., for each ion), a proposed method can be performed as follows. First, each ion in the chain to be measured is prepared in the quantum state |0>. Next, the corresponding laser beam for each ion to be measured is turned on for a fixed time t at a frequency set to drive Rabi oscillations between the |0> and |1> quantum states. The time t for each laser beam is set such that, if the laser beam power or intensity is correct, the corresponding ion is driven to an equal superposition of the |0> and |1> quantum states. The state of each ion is then measured as either "0" or "1", where "1" represents the bright state of the ion and "0" represents the dark state of the ion. Further details regarding this method will be described in more detail below.

[0041] Rabi oscillations, or Rabi periods, are the periodic behavior of a two-level quantum system in the presence of an oscillating field. For example, when irradiated by a laser beam, atoms or ions can periodically absorb photons from the beam and move to one energy level, then emit photons and return to the other. This behavior is reflected in what is called Rabi oscillations, which indicate that a two-level quantum system in a first quantum state (e.g., quantum state |0>) will eventually be in a second quantum state (e.g., quantum state |1>). The duration of the Rabi period and its reciprocal are called the Rabi frequency of the laser beam.

[0042] Figure 4Figure 400 illustrates an example of Rabi oscillation, showing the ion brightness (vertical axis) in response to the pulse area (horizontal axis), which is proportional to the laser beam intensity and time t. Figure 400 shows a scan for the intensity of a laser beam (e.g., one of laser beams 210a-210d). The pulse area, i.e., the horizontal axis of Figure 400, is a parameter proportional to the intensity (I) and the fixed amount of time t for which the laser beam is applied. For example, the ion brightness detectable by the imaging system 360, i.e., the vertical axis of Figure 400, corresponds to an oscillation or sinusoidal behavior of sin(k·I·t), where k is a scaling factor, and I and t are as described above.

[0043] As described above, the proposed method for each measurement involves preparing the ion in an initial quantum state (e.g., quantum state |0>) and setting a time quantity t for applying the laser beam to drive Rabi oscillations between the |0> and |1> quantum states. If the intensity is chosen appropriately and the corresponding ion is driven to an equal superposition of the |0> and |1> quantum states, the operating point (indicated by the black dot) will be at 50% ion brightness level (or 0.5 in the vertical scale), at which intensity as many bright states (“1”) as dark states (“0”) are measured for that ion. When measurements begin to show more bright states (e.g., the imaging system 360 detects “1” for that ion) than dark states (e.g., the imaging system 360 detects “0” for that ion), the operating point (black dot) moves up the curve (white dot) to a higher ion brightness. In this case, calibration or stabilization operation may require reducing the amplitude of the RF signal used to control the channels in the AOM 330 to modify the intensity of the laser beam. When measurements begin to show more dark states (e.g., the imaging system 360 detects "0" for the ion) than bright states (e.g., the imaging system 360 detects "1" for the ion), the operating point (black dot) shifts down the curve (white dot) to a lower ion brightness. In this case, calibration or stabilization may require increasing the amplitude of the RF signal used to control the channels in the AOM 330 to modify the laser beam intensity.

[0044] In the example shown in Figure 400, the duration of each laser beam's on-time is set such that the laser beam intensity is correct and the ion will be measured in the bright state (e.g., |1> quantum state) for 50% of the time, as indicated by the black dot located in the middle of the ion brightness range (e.g., 0.0–1.0). In this particular case, time t is set to drive a 9π / 2 pulse (e.g., pulse area of ​​k·I·t), although any odd multiple of π / 2 will also work. Time t can be set to drive pulses that do not need to be odd multiples of π / 2; however, using odd multiples of π / 2 maximizes sensitivity to intensity fluctuations. If the intensity increases or decreases, the pulse area also decreases, and the black dot moves up or down along a sine curve, indicating Rabi oscillations, i.e., away from the case where the ion is measured in the bright state for 50% of the time. For small intensity fluctuations (e.g., small changes with respect to the black dot), this response is approximately linear. Another aspect of the flexibility offered by the proposed method is that pulses at higher odd multiples of π / 2 are more sensitive to intensity fluctuations than those at lower odd multiples of π / 2. This allows for the selection of the optimal pulse when adjusting the laser beam intensity.

[0045] Since each measurement of a particular ion returns either "0" or "1", these measurements can exhibit significant shot noise. Therefore, it is helpful to pass these measurements through an integrating filter (or multiple integrating filters) to integrate multiple individual measurements and better identify intensity fluctuations. One way to reduce shot noise through continuous integration is as follows.

[0046] As mentioned above Figure 3 As depicted in Figure 300, the intensity of the laser beams (e.g., laser beams 210a-210d) can be controlled by controlling the amplitude of an RF signal, which modulates each laser beam via a corresponding channel / transducer in the AOM 330. A combination of a multi-channel AOM controller 380 or a stable measurement controller 370 and a multi-channel AOM controller 380 can be used to provide instructions for controlling the amplitude of the RF signals generated by the waveform generators 350a-350d.

[0047] In one implementation, the amplitude of each RF signal can be physically determined by a 16-bit number (or some M-bit number). This digital number can be referred to as the physical number or physical bits provided to the waveform generators 350a-350d to produce the appropriate amplitude of the RF signal and thus the appropriate laser beam intensity. In one example, the multi-channel AOM controller 380 can provide each of the waveform generators 350a-350d with its corresponding physical number (e.g., 16-bit number), that is, the number of bits representing the amplitude of the RF signal produced by each of the waveform generators 350a-350d. The number of bits representing the amplitudes of different RF signals can be provided to the multi-channel AOM controller 380 by the stable measurement controller 370. However, internally within the stable measurement controller 370, which can be implemented via a field-programmable gate array (FPGA) or application-specific integrated circuit (ASIC), the amplitude of each RF signal, and therefore the amplitude of each ion i, can instead be based on a 32-bit (or some 2M-bit) A i To determine. Generally speaking, A i It doesn't have to be limited to 2M digits; it can be any (M+N) digits, where M and N are integers. A i The 16 least significant bits (LSBs) do not affect the amplitude of the corresponding RF signal because they are truncated at the output (i.e., A). i The 16 MSBs are physical bits, A i The 16 LSBs are non-physical bits. The stable measurement controller 370 determines the second bit B for each ion i. i It is the gain of the measured feedback loop and is 16 bits or less. The second bit B i The result of the integral filtering performed by the integral filter 375 is represented in a certain way, wherein multiple measurements are performed to determine whether the amplitude of the corresponding RF signal needs to be increased or decreased. In one example, A i It is the amplitude of ion i in 32-bit form, which can be based on a base amplitude A0 and a scaling factor K of feedback gain less than 1 (e.g., integral gain less than 1). In the example described herein, when the second digit B... i When the number of bits is 16, the scaling factor can be equal to 1 / 16. The integration operation provides the second bit B. i In this form, S(t) is determined by a series of "1"s and "0"s; for example, if the measurement at time t is "1", then S(t) = 1, and if the measurement at time t is "0", then S(t) = -1. The scaling factor is an adjustable parameter of this stable system, which can be obtained through B. i The value is adjusted. Since the integrands are "1" and "0", the integral is simply the sum of the integrands. Overall, when the number of "1"s exceeds the number of "0"s by 16 or more samples during integration, the adjustment magnitude A is adjusted in one direction.i To make the intensity decrease along the curve and return to such a state. Figure 4 The black dot is shown in the Rabi oscillation diagram. When the number of "0"s exceeds the number of "1"s by 16 or more samples during integration, the amplitude A is adjusted in the opposite direction. i This causes the intensity to rise along the curve and return to the previous state. Figure 4 The black dot is shown in the diagram of the Rabi oscillation.

[0048] In other words, after each measurement of ion i, if the measurement result is "0" (e.g., a dark state measurement), then the digit A of ion i is... i The value will be replaced with A i +B i The value of , and if the measurement result is "1" (e.g., a bright state measurement), then the digit A of ion i. i The value will be replaced with A i -B i The value of is used to adjust the amplitude of the RF signal used to control the intensity of the laser beam for each ion i. Due to B i Added to A i 16 LSBs, therefore B i A single measurement in A does not affect A i The first 16 MSBs, meaning this has no effect on the physical amplitude, because it only affects A. i The non-physical position. If the ion is in an equal superposition of "0" and "1", then statistically there will be the same number of "0" measurements and "1" measurements, and the physical amplitude will remain almost constant (for sufficiently small B). i That is, when the number of "0" measurements and "1" measurements are equal, the measurement integral processed by, for example, the integrating filter 375 is zero or close to zero. However, if the ion superposition is not balanced (e.g., the number of "0" measurements and "1" measurements are not equal), the integrating filter 375 will eventually push A in one direction. i The physical position is used to stabilize the power or intensity of the corresponding laser beam. In this case, when there are significantly more "1"s than "0"s or significantly more "0"s than "1", B i The value may be large enough to make A i Replace the value with A i +B i Or A i -B i When the value is A, this pair i The physical bits are affected, and therefore the physical amplitude of the corresponding RF signal is affected.

[0049] As described above, this process can be performed in parallel for all laser beams. Furthermore, because these measurements can be performed in parallel, these measurements and their feedback stabilization mechanism can take less than 1 millisecond (<1 ms), thus allowing them to be interleaved between experimental cycles and run every few milliseconds. This provides a relatively fast feedback loop that can eliminate slow drift and timescale fluctuations faster than achievable today. Moreover, while the feedback stabilization mechanism described herein has been described in conjunction with an integral filter, it should be understood that the feedback stabilization mechanism is not limited to this and is more generally applicable to more complex filter functions, with the integral filter being a specific implementation.

[0050] Figure 5A This is a block diagram illustrating an example of a QIP system 500 according to various aspects of this disclosure. The QIP system 500 may also be referred to as a quantum computing system, computer device, trapped ion system, trapped ion quantum computer, etc. In one aspect, the QIP system 500 can be configured to perform quantum computing and quantum experiments. Furthermore, the QIP system 500 can be configured to perform rapid experiments to measure the response of individual ions to their respective laser beams at the end of an experimental period (e.g., every few milliseconds) in order to stabilize the laser beam intensity associated with each individual ion as frequently as possible over time. This stabilization procedure can be performed in parallel for multiple laser beams and their associated ions.

[0051] QIP system 500 may include source 560 that supplies an atomic species (e.g., flux of neutral atoms) to chamber 550 having ion trap 570, which, once ionized (e.g., photoionized) by photocontroller 520, is trapped in ion trap 570 (see example). Figure 5B The ion trap 570 can be used to confine ions in a linear array, as described above in conjunction with... Figure 1 and Figure 3 The linear crystal 110 is depicted in Figures 100 and 300. The light source 530 in the light controller 520 may include one or more laser sources (e.g., a source of a beam or laser stream) that can be used for the ionization of atomic species, the control of atomic ions, the fluorescence of atomic ions, which can be monitored and tracked by an image processing algorithm operating in the imaging system 540 of the light controller 520, and / or perform the light control functions related to laser beam intensity stability described in this disclosure. The light source 530 may be configured to control and generate a linear array of laser beams, such as those described above. Figure 3 The laser beams 210a-201d are depicted in Figure 300. In one aspect, the light source 530 can be implemented separately from the optical controller 520.

[0052] Imaging system 540 may include a high-resolution imager (e.g., a CCD camera) for monitoring atomic ions while they are being provided to ion trap 570 or after they have been provided to ion trap 570. In one aspect, imaging system 540 may be implemented separately from light controller 520; however, using image processing algorithms to detect, identify, and label atomic ions using fluorescence may require coordination with light controller 520. Imaging system 540 may be a combination of the above. Figure 3 The figure 300 illustrates an example of an imaging system 360. Therefore, the imaging system 540 can be configured to image and analyze the effects of the interaction between a linear array of laser beams generated by the light source 530 and their corresponding linear arrays of ions trapped in the ion trap 570.

[0053] The QIP system 500 may also include an algorithm component 510, which can operate together with other parts of the QIP system 500 (not shown) to perform quantum algorithms or quantum operations, including single-qubit operations and / or multi-qubit operations (e.g., two-qubit operations) and stacks or combinatorial sequences of extended quantum computing. In this way, the algorithm component 510 can provide instructions to various components of the QIP system 500 (e.g., to the optical controller 520) to implement quantum algorithms or quantum operations.

[0054] Figure 5B At least a portion of the light controller 520 is shown. In this example, the light controller 520 may include a light source 530 and an imaging system 540. As shown by the dashed lines, one or both of the light source 530 and the imaging system 540 may optionally be implemented separately from the light controller 520 but in communication with it.

[0055] Imaging system 540 may include CCD 541 (or a similar imager or camera) and image processing algorithm component 542 to process the information captured by CCD 541. Imaging system 540 can be used to detect the results of the measurements described herein for rapid calibration or rapid stabilization of laser beam intensity. Light source 530 may include AWG (or DDS) 532a-532d and lasers 534a-534d, which can be used to control ions in ion trap 570. AWG 532a-532d can be a combination of the above. Figure 3 The waveform generators 350a-350d are illustrated in Figure 300, while lasers 534a-534d can be used to generate a linear array of laser beams 210a-210d, also shown in Figure 300. The light source 530 may also include a global modulator 535 and a global laser 536 for emitting and controlling a global Raman laser beam 220.

[0056] The optical controller 520 may include a multi-channel AOM controller 537 configured to control the operation of the multi-channel AOM 538, which may correspond to the multi-channel AOM controller 380 and the multi-channel AOM 330 described above, respectively. The multi-channel AOM 538 may be implemented using a single AOM device with multiple channels, multiple AOM devices with a single channel, or multiple AOM devices with multiple and / or a single channel.

[0057] The optical controller 520 may also include a stable measurement controller 539 corresponding to the stable measurement controller 370 described above. The stable measurement controller 539 may include an integrating filter (not shown). An integrating filter or integrator is a device or component whose output signal is integrated over time with its input signal. That is, the integrating filter accumulates the input quantity over a defined time period to produce a representative output. The integrating filter can be used to filter out the effects of shot noise generated by multiple measurements performed as part of the laser beam intensity stabilization described herein. The integrating filter may be an example of the integrating filter 375 described above.

[0058] It should be understood that one or more components or sub-components of the optical controller 520 may be implemented separately from the optical controller 520. Furthermore, one or more components or sub-components of the optical controller 520 may be implemented as part of one or more integrated circuits (e.g., FPGA, ASIC, central processing unit, microprocessor). In one example, the multi-channel AOM controller 537 and the stable measurement controller 539 may be implemented as a single component on the same integrated circuit or as separate components in different integrated circuits. When in the same integrated circuit, the multi-channel AOM controller 537 and the stable measurement controller 539 may use an internal 32-bit AOM controller. i A i The 16 MSBs are physical bits, A i The 16 LSBs are non-physical bits, and A i The 16 LSBs may be truncated in the output.

[0059] refer to Figure 6 A method 600 for stabilizing the intensity of a laser beam in a trapped ion system. In one aspect, the function of method 600 may be performed by one or more components of the trapped ion system or QIP system, such as QIP system 500 and its components (e.g., optical controller 520 and its components or sub-components).

[0060] In 610, method 600 includes applying a linear array of laser beams (e.g., laser beams 210a-210d) to corresponding ions in a linear array of ions (e.g., ions 106a-106d) in a trap (e.g., ion trap 570).

[0061] At 620, method 600 includes performing parallel measurements on the ions (e.g., via imaging system 360) in response to an applied laser beam, wherein the parallel measurements include multiple individual measurements for each ion to identify intensity fluctuations of the corresponding laser beam at each ion. For example, the measurements can be performed immediately after (e.g., immediately following) the application of the laser beam.

[0062] In 630, method 600 includes adjusting the intensity of one or more laser beams (e.g., via a stabilizing measurement controller 370, a multi-channel AOM controller 380, and / or waveform generators 350a-350d) in response to fluctuations identified from parallel measurements.

[0063] Method 600 typically corresponds to applying a pulsed laser beam, measuring the ion state in parallel, and updating the laser beam power based on the measurements. Such a sequence can be repeated multiple times.

[0064] In one aspect of method 600, each of the multiple individual measurements of a particular ion is a measurement of the ion's response to the corresponding laser beam.

[0065] In one aspect of method 600, performing parallel measurements includes integrating and filtering multiple individual measurements of each ion (e.g., via integrating filter 375) to identify intensity fluctuations in the corresponding laser beam.

[0066] In one aspect of method 600, adjusting the intensity of one or more laser beams includes controlling each laser beam using an RF signal applied to a respective channel in a multi-channel AOM (e.g., multi-channel AOM 330). Controlling each laser beam using the RF signal includes adjusting the amplitude of the RF signal in response to identifying intensity fluctuations in the respective laser beam.

[0067] In another aspect of method 600, for each of a plurality of individual measurements of a particular ion, method 600 includes preparing the ion to a quantum state |0>, wherein a corresponding laser beam is applied to the ion at a frequency for a fixed time period t, which, if the intensity of the laser beam is correct, produces an equal superposition of the |0> and |1> quantum states, the frequency driving Rabi oscillations of the ion between the |0> and |1> quantum states (see, for example...). Figure 4 The response of the ion to the application of the corresponding laser beam is measured (e.g., via imaging system 360) as either "1" or "0", where "1" represents the bright state of the ion and "0" represents the dark state of the ion. A fixed time period t can be set to drive laser beam pulses that are odd multiples of π / 2, where higher odd multiples of π / 2 are more sensitive to intensity fluctuations than lower odd multiples of π / 2. Alternatively, a fixed time period t can be set to drive 9π / 2 laser beam pulses.

[0068] In another aspect of method 600, each laser beam has a diameter of approximately 1 μm to 1.5 μm at the position of the corresponding ion, and the ions in the linear ion array are separated from each other by a distance of approximately 5 μm.

[0069] In another aspect, method 600 is executed at the end of an experimental cycle of the trapped ion system (e.g., QIP system 500) and can be executed between consecutive experimental cycles of the trapped ion system. Overall, method 600 can be executed in less than 1 millisecond, which is much faster than existing methods that do not execute in parallel.

[0070] In one aspect of method 600, controlling each laser beam using an RF signal includes adjusting a first bit A corresponding to the amplitude of the RF signal based on a second bit B of the gain corresponding to a feedback loop of multiple individually measured values, in response to identifying intensity fluctuations in the respective laser beam. The most significant bit (MSB) of the first bit A is a bit representing the physical value of the amplitude of the respective RF signal.

[0071] In another aspect of method 600, each measurement may first involve preparing each ion in the chain to be measured to a quantum state |0>. Next, a corresponding laser beam for each ion to be measured is turned on at a frequency for a fixed time length t, which is set to drive Rabi oscillations between the |0> and |1> quantum states. The time t for each laser beam to be turned on is set such that, if the laser beam power or intensity is correct, the corresponding ion is driven to an equal superposition of the |0> and |1> quantum states. The state of each ion is then measured as either “0” or “1”, where “1” represents a bright state of the ion and “0” represents a dark state of the ion.

[0072] Generally speaking, the above text combined Figure 1-6 The described technique can be implemented using a system for stabilizing the intensity of a laser beam in a trapped ion system. This system may include: a laser source configured to apply a linear array of laser beams to corresponding ions in a linear array of ions in the trap; an imaging system configured to perform parallel measurements of the ions while the laser beams are applied, the parallel measurements including multiple individual measurements for each ion to identify intensity fluctuations of the corresponding laser beam at each ion; and an optical controller configured to adjust the intensity of one or more laser beams in response to fluctuations identified from the parallel measurements.

[0073] In combination Figure 1-6In another aspect of the described system, each of a plurality of individual measurements of a specific ion is a measurement of the ion's response to a corresponding laser beam. For each of the plurality of individual measurements of a specific ion, the optical controller is configured to prepare the ion to a quantum state |0>, wherein a corresponding laser beam is applied to the ion at a frequency for a fixed time period t, which, if the intensity of the laser beam is correct, produces an equal superposition of the |0> and |1> quantum states, the frequency driving the ion to Rabi oscillations between the |0> and |1> quantum states, and the imaging system is configured to measure the ion's response to the application of the corresponding laser beam as "1" or "0", where "1" represents the bright state of the ion and "0" represents the dark state of the ion. The fixed time period t can be set to drive laser beam pulses that are odd multiples of π / 2, where higher odd multiples of π / 2 are more sensitive to intensity fluctuations than lower odd multiples of π / 2. The fixed time period t can be set to drive laser beam pulses of 9π / 2.

[0074] In combination Figure 1-6 In another aspect of the described system, the optical controller is further configured to perform integral filtering of multiple individual measurements for each ion to identify intensity fluctuations in the corresponding laser beam. The optical controller, configured to adjust the intensity of one or more laser beams, is also configured to control each laser beam using an RF signal applied to a corresponding channel in the multi-channel AOM. The optical controller configured to control each laser beam using the RF signal is further configured to adjust the amplitude of the RF signal in response to the identification of intensity fluctuations in the corresponding laser beam. The optical controller configured to control each laser beam using the RF signal is also configured to adjust a first bit A corresponding to the amplitude of the RF signal, in response to the identification of intensity fluctuations in the corresponding laser beam, to a second bit B corresponding to the gain of the feedback loop of the multiple individual measurements. The MSB of the first bit A is a bit representing the physical value of the amplitude of the corresponding RF signal.

[0075] In combination Figure 1-6 In another aspect of the system described, each laser beam has a diameter of approximately 1 μm to 1.5 μm at the position of the corresponding ion, and the ions in the linear ion array are spaced approximately 5 μm apart from each other.

[0076] In combination Figure 1-6 In another aspect of the described system, the imaging system is configured to perform parallel measurements at the end of an experimental cycle on the trapped ion system. The imaging system is also configured to perform parallel measurements between experimental cycles on the trapped ion system. Furthermore, the imaging system is configured to perform parallel measurements in less than 1 millisecond.

[0077] The above description of this disclosure is provided to enable those skilled in the art to perform or use it. Various modifications to this disclosure will be apparent to those skilled in the art, and the common principles defined herein may be applied to other variations without departing from the spirit or scope of this disclosure. Furthermore, although elements of the described aspects may be described or claimed in the singular, the plural form may be considered unless explicitly stated to be limited to the singular. Moreover, unless otherwise stated, all or part of any aspect may be used in conjunction with all or part of any other aspect. Therefore, this disclosure is not limited to the examples and designs described herein, but is consistent with the widest scope of the principles and novel features disclosed herein.

Claims

1. A method for stabilizing the intensity of a laser beam in a trapped ion system, the method comprising: A laser beam is applied to the corresponding ions in the linear array of ions in the trap; In response to the application of the laser beam, parallel measurements are performed on each of the ions, the parallel measurements comprising multiple individual measurements of each of the corresponding ions in the linear array, such that each of the multiple measurements for each ion indicates either the bright state or the dark state of the ion. Based on multiple individual measurements of the corresponding ions, the intensity fluctuation of the corresponding laser beam at each ion is identified; and In response to fluctuations identified from the parallel measurements, the intensity of one or more of the laser beams is adjusted.

2. The method of claim 1, wherein each of the plurality of individual measurements for each ion is a measurement of the ion's response to the corresponding laser beam.

3. The method of claim 1, wherein performing the parallel measurements includes integrating the plurality of individual measurements for each of the ions to identify intensity fluctuations in the corresponding laser beam.

4. The method of claim 1, wherein for each of the plurality of individual measurements for each ion, the method comprises: The ion is prepared to quantum state |0>, wherein a corresponding laser beam is applied to the ion at a frequency for a fixed time period t. If the intensity of the laser beam is correct, the fixed time period produces an equal superposition of the quantum states |0> and |1>. The frequency drives the ion to oscillate between the quantum states |0> and |1>. and The response of the ion to the application of the corresponding laser beam is measured as "1" or "0", where "1" represents the bright state of the ion and "0" represents the dark state of the ion.

5. The method of claim 4, wherein the fixed time period t is set to drive a laser beam pulse that is an odd multiple of π / 2, wherein a higher odd multiple of π / 2 is more sensitive to intensity fluctuations than a lower odd multiple of π / 2.

6. The method according to claim 4, wherein the fixed time period t is set to drive a 9π / 2 laser beam pulse.

7. The method of claim 1, wherein adjusting the intensity of one or more of the laser beams comprises controlling each of the laser beams using a radio frequency (RF) signal applied to a respective channel in a multi-channel acousto-optic modulator (AOM).

8. The method of claim 7, wherein controlling each of the laser beams using an RF signal comprises adjusting the amplitude of the RF signal in response to identifying intensity fluctuations in the respective laser beam.

9. The method of claim 7, wherein controlling each of the laser beams using an RF signal comprises, in response to identifying an intensity fluctuation of the respective laser beam, adjusting a first digit A corresponding to the amplitude of the RF signal based on a second digit B of the gain of the feedback loop corresponding to the plurality of individually measured values.

10. The method of claim 9, wherein the most significant bit (MSB) of the first bit A is a bit representing the physical value of the amplitude of the corresponding RF signal.

11. The method according to claim 1, wherein: Each laser beam has a diameter of 1 μm to 1.5 μm at the location of the corresponding ion, and The ions in the linear ion array are separated from each other by a distance of 5 μm.

12. The method of claim 1, wherein the method is performed at the end of an experimental cycle on the trapped ion system.

13. The method of claim 1, wherein the method is performed between experimental cycles on the trapped ion system.

14. The method of claim 1, wherein the method is executed in less than 1 millisecond.

15. A system for stabilizing the intensity of a laser beam in a trapped ion system, the system comprising: A laser source configured to apply a linear array of laser beams to corresponding ions in a linear array of ions in a trap; An imaging system configured to perform parallel measurements for each of the ions in response to the application of the laser beam, the parallel measurements comprising multiple individual measurements for each of the corresponding ions in the linear array, such that each of the multiple measurements for each ion indicates a bright state or a dark state of the ion, and the imaging system is further configured to identify intensity fluctuations of the corresponding laser beam at each ion based on the multiple individual measurements of the corresponding ion; and An optical controller is configured to adjust the intensity of one or more of the laser beams in response to fluctuations identified from the parallel measurements.

16. The system of claim 15, wherein each of the plurality of individual measurements for each ion is a measurement of the ion’s response to the corresponding laser beam.

17. The system of claim 15, wherein the optical controller is further configured to perform integral filtering of the plurality of individual measurements for each of the ions to identify intensity fluctuations of the corresponding laser beam.

18. The system of claim 15, wherein for each of the plurality of individual measurements for each ion: The optical controller is configured to prepare the ion into a quantum state |0>, wherein a corresponding laser beam is applied to the ion at a frequency for a fixed time period t, and if the intensity of the laser beam is correct, the fixed time period t produces an equal superposition of the |0> and |1> quantum states, and the frequency drives the ion to Rabi oscillate between the |0> and |1> quantum states. The imaging system is configured to measure the response of the ion to the application of a corresponding laser beam as "1" or "0", where "1" represents the bright state of the ion and "0" represents the dark state of the ion.

19. The system of claim 18, wherein the fixed time period t is set to drive a laser beam pulse that is an odd multiple of π / 2, wherein a higher odd multiple of π / 2 is more sensitive to intensity fluctuations than a lower odd multiple of π / 2.

20. The system of claim 18, wherein the fixed time period t is set to drive a 9π / 2 laser beam pulse.

21. The system of claim 15, wherein the optical controller configured to adjust the intensity of one or more of the laser beams is further configured to control each of the laser beams using radio frequency (RF) signals applied to the respective channels of the multichannel acousto-optic modulator (AOM).

22. The system of claim 21, wherein the optical controller configured to control each of the laser beams using an RF signal is further configured to adjust the amplitude of the RF signal in response to identifying intensity fluctuations in the respective laser beam.

23. The system of claim 21, wherein the optical controller configured to control each of the laser beams using an RF signal is further configured to adjust a first bit A corresponding to the amplitude of the RF signal in response to identifying an intensity fluctuation of the respective laser beam, corresponding to a second bit B of the gain of the plurality of individually measured feedback loops.

24. The system of claim 23, wherein the most significant bit (MSB) of the first bit A is a bit representing the physical value of the amplitude of the corresponding RF signal.

25. The system according to claim 15, wherein: Each laser beam has a diameter of 1 μm to 1.5 μm at the location of the corresponding ion, and The ions in the linear ion array are separated from each other by a distance of 5 μm.

26. The system of claim 15, wherein the imaging system is configured to perform the parallel measurement at the end of an experimental cycle on the trapped ion system.

27. The system of claim 15, wherein the imaging system is configured to perform the parallel measurements between experimental cycles on the trapped ion system.

28. The system of claim 15, wherein the imaging system is configured to perform the parallel measurement in less than 1 millisecond.

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