A control system

Abstract

A control system 100 for manipulating a charged particle, e.g. an ion 104, the control system comprising a controller 106 configured to provide one or more adjustment signals 110 for applying an adjus

Description

The present disclosure relates to a control system for manipulating a charged particle. BACKGROUND Charged particles may experience undesired forces. An ion is an example of a charged particle. An ion trap is a device used to spatially confine in an ion. Trapped ion systems may be used to encode a qubit, where a qubit is a fundamental unit of information used in quantum computing. During quantum operations, trapped ions may experience undesired forces caused by electric fields that can adversely impact the operation of the trapped ion system. SUMMARY It is desirable to provide a system that mitigates or overcomes issues relating to undesired forces on charged particles such as ions during operation. According to a first aspect of the disclosure there is provided a control system for manipulating a charged particle, the control system comprising a controller configured to provide one or more adjustment signals for applying an adjustment force to the charged particle, the adjustment force being time varying. Optionally, the controller is configured to provide one or more control signals. Optionally, each of the one or more control signals is for manipulating the classical or quantum state of the charged particle. Optionally, each of the one or more control signals generates electric and / or magnetic fields affecting the charged particle, and / or each of the one or more adjustment signals generates electric fields affecting the charge particle. Optionally, the control system comprises a plurality of electrodes, the control system comprising a signal generator configured to generate control voltages and / or currents at a first electrode of the plurality of electrodes to generate the control electric field and / or magnetic field, for each of the one or more control signals, and / or generate adjustment voltages at a second electrode of the plurality of electrodes to generate the adjustment electric field, for each of the one or more adjustment signals. Optionally, the plurality of electrodes comprises at least one of a DC electrode, an RF electrode, and a microwave electrode. Optionally, control voltages are generated at a first DC electrode, or a first RF electrode, or a first microwave electrode, and / or adjustment voltages are generated at a second DC electrode, or a second RF electrode, or a second microwave electrode. Optionally, control voltages and adjustment voltages are both generated at one or more of a first DC electrode, a first RF electrode, or a first microwave electrode. Optionally, the controller is configured to provide a first adjustment signal for generating a first adjustment electric field by generating a first adjustment voltage at a first electrode and / or a second adjustment voltage at a second electrode, and provide a second adjustment signal for generating a second adjustment electric field by generating a third adjustment voltage at a third electrode and / or a fourth adjustment voltage at a fourth electrode. Optionally, the charged particle experiences an offset force, the offset force being time varying. Optionally, the time varying offset force is generated through intermodulation of the one or more control signals, and / or ponderomotive effects of the charged particle which arises from the one or more control signals, and / or non-linear components within the signal chain of the one or more control signals. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force to the charged particle to substantially cancel or otherwise reduce the offset force. Optionally, the controller is configured to provide one or more adjustment signals for applying that adjustment force having an amplitude that is approximately equal to the amplitude of the offset force, and / or a frequency that is approximately equal to the frequency of the offset force. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force. Optionally, the control system comprises a detection system configured to detect at least one characteristic of the offset force experienced by the charged particle, wherein the controller is configured to provide the one or more adjustment signals based on the detected at least one characteristic of the offset force. Optionally, the at least one property of the offset force comprises an amplitude of the offset force, and / or a frequency of the offset force, and the controller is configured to provide one or more adjustment signals for applying the adjustment force having an amplitude that is approximately equal to the amplitude of the offset force, as detected by the detection system, and / or a frequency that is approximately equal to the frequency of the offset force, as detected by the detection system. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force. Optionally, the charged particle is an ion. Optionally, the charged particle is an ion. Optionally, the controller is configured to provide one or more control signals. Optionally, each of the one or more control signals is for manipulating the classical or quantum state of the ion. Optionally, each of the one or more control signals for performing a quantum gate operation on the ion within the ion trap Optionally, each of the one or more control signals generates electric and / or magnetic fields affecting the charged particle, and / or each of the one or more adjustment signals generates electric fields affecting the charged particle. Optionally, each of the one or more control signals is for generating a control field to perform the quantum gate operation on the ion within the ion trap, and / or each of the one or more adjustment signals is for generating an adjustment electric field to apply the adjustment force to the ion, each of the one or more adjustment electric fields being time varying such that the adjustment force is time varying. Optionally, the control field is a control electric field or a control magnetic field. Optionally, the ion trap comprises a plurality of electrodes, the control system comprising a signal generator configured to generate control voltages and / or currents at a first electrode of the plurality of electrodes to generate the control field, for each of the one or more control signals, and / or generate adjustment voltages at a second electrode of the plurality of electrodes to generate the adjustment electric field, for each of the one or more adjustment signals. Optionally, the plurality of electrodes comprises at least one of a DC electrode, an RF electrode, and a microwave electrode. Optionally, control voltages are generated at a first DC electrode, or a first RF electrode, or a first microwave electrode, and / or adjustment voltages are generated at a second DC electrode, or a second RF electrode, or a second microwave electrode. Optionally, the controller is configured to provide a first adjustment signal for generating a first adjustment electric field by generating a first adjustment voltage at a first electrode and / or a second adjustment voltage at a second electrode, and provide a second adjustment signal for generating a second adjustment electric field by generating a third adjustment voltage at a third electrode and / or a fourth adjustment voltage at a fourth electrode. Optionally, the ion experiences an offset force when confined within the ion trap, the offset force being time varying. Optionally, the time varying offset force is generated through intermodulation of the one or more control signals, and / or ponderomotive effects of the ion which arises from the one or more control signals, and / or non-linear components within the signal chain of the one or more control signals. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force to the ion to substantially cancel or otherwise reduce the offset force. Optionally, the controller is configured to provide one or more adjustment signals for applying that adjustment force having an amplitude that is approximately equal to the amplitude of the offset force, and / or a frequency that is approximately equal to the frequency of the offset force. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force. Optionally, the control system comprises a detection system configured to detect at least one characteristic of the offset force experienced by the ion, wherein the controller is configured to provide the one or more adjustment signals based on the detected at least one characteristic of the offset force. Optionally, the at least one property of the offset force comprises an amplitude of the offset force, and / or a frequency of the offset force, and the controller is configured to provide one or more adjustment signals for applying the adjustment force having an amplitude that is approximately equal to the amplitude of the offset force, as detected by the detection system, and / or a frequency that is approximately equal to the frequency of the offset force, as detected by the detection system. Optionally, the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force. Optionally, the offset force is a result of intermodulation. Optionally, the ion trap is part of a quantum computer. According to a second aspect of the disclosure there is provided an apparatus comprising the control system of the first aspect and the ion trap. Optionally, the apparatus comprises a quantum computer comprising the ion trap and the control system. According to a third aspect of the disclosure there is provided a method of manipulating a charged particle using a control system, the method comprising providing one or more adjustment signals for applying an adjustment force to the charged particle, the adjustment force being time varying. It will be appreciated that the method of the third aspect may include providing and / or using features set out in the first and / or second aspects, and can incorporate other features as described herein. BRIEF DESCRIPTION OF THE DRAWINGS The disclosure is described in further detail below by way of example only and with reference to the accompanying drawings, in which: Figure 1(a) is a schematic of a control system for manipulating a charged particle, in accordance with a first embodiment of the present disclosure, Figure 1(b) is a schematic of a control system for an ion trap for trapping an ion in accordance with a second embodiment of the present disclosure, Figure 1(c) is a schematic of a specific embodiment of the control system and a specific embodiment of the ion trap, in accordance with a third embodiment of the present disclosure; Figure 2 shows example waveforms of the offset force and the adjustment force as may be experienced by the ion in a specific implementation of the ion trap of Figure 1(c); Figure 3 is a schematic of a trapped ion system comprising specific implementations of the control system and the ion trap, in accordance with a fourth embodiment of the present disclosure; Figure 4 is a schematic of an apparatus comprising a quantum computer in accordance with a fifth embodiment of the present disclosure; Figure 5(a) is a schematic of an ion trap system showing an example of a signal chain resulting in intermodulation, Figure 5(b) is a frequency domain graph showing a signal exhibiting intermodulation, Figure 5(c) is a frequency domain graph showing a signal exhibiting intermodulation; and Figure 6 is a frequency domain graph showing a signal exhibiting intermodulation. DETAILED DESCRIPTION Controlling the forces experienced by charged particles is an important problem in ion-trapping. When control signals are applied, non-linear processes generate undesired forces on the ion. In the case of quantum computing these undesired forces can generate errors in quantum logic operations, or otherwise degrade computer performance. The present disclosure addresses the following points and solves the aforementioned problem: • Non-linearities cause signal intermodulation which adds additional frequency components to the offset forces generated by control signals. • There are several sources of such non-linearities, key examples include: o non-linear components in the control signal chain. Examples include the signal generator, or a signal amplifier o The ponderomotive force experienced by the ion • We can add an electric field to directly cancel the additional offset forces generated by non-linearities. • It is possible to use many different electrodes to cancel the resulting force at the location of all charged particles. The adjustment signals / frequencies can be applied to prevent the offset force from being generated in the first place, for example as demonstrated by a net zero force on a charged particle. Figure 1(a) is a schematic of a control system 100 for manipulating a charged particle 101 in accordance with a first embodiment of the present disclosure. The control system 100 comprises a controller 106 configured to provide one or more adjustment signals 110 for applying an adjustment force 112 to the charged particle 101. The adjustment force 112 is time varying. The charged particle 101 may experience a time varying offset force 113. The controller 106 may be configured to provide one or more control signals 108. The one or more control signals 108 may, for example, be for manipulating the classical or quantum state of the charged particle 101. Figure 1(b) is a schematic of a specific embodiment of the control system 100 for an ion trap 102 for trapping an ion 104 in accordance with a second embodiment of the present disclosure. In the present example, the charged particle 101 is the ion 104. The control system 100 comprises a controller 106 that may be configured to provide one or more control signals 108. Each of the one or more control signals 108 may be for performing quantum gate operations on the ion 104 within the ion trap 102. The ion may, for example, be a barium ion. In the present example, and in subsequent examples, embodiments of the present disclosure are described in relation the charged particle 101 being an ion 104. It will be appreciated that further embodiments of the present disclosure may be applied generally to charged particles, and not only to ions that are trapped within ion trap systems, in accordance with the understanding of the skilled person. Additionally, embodiments described herein primarily are described in relation to single ions. It will be appreciated that further embodiments of the control system 100 may be used with two or more charged particles, which may be ions, and in accordance with the understanding of the skilled person. A quantum gate operation may alternatively be referred to as a quantum gate or a quantum logic gate, as will be clear to the skilled person. In a specific embodiment, using two or more control signals 108, each of the control signals 108 may apply a different quantum gate operation on the ion 104. In a further specific embodiment, using two or more control signals 108, each of the control signals 108 may apply the same quantum gate operation on the ion 104. The controller 106 is further configured to provide one or more adjustment signals 110 for applying an adjustment force 112 to the ion 104. The adjustment force 112 is time varying. In the present example, and to simplify the accompanying description, there is provided a single control signal 108 and a single adjustment signal 110. However, further embodiments of the disclosure may use a plurality of control signals and / or a plurality of adjustment signals, in accordance with the understanding of the skilled person. In a specific embodiment, each of the control signals 108 may be used to generate a control field to perform the quantum gate operation on the ion 104, and / or each of the adjustment signals 110 may be used to generate an adjustment electric field to apply the adjustment force 112 to the ion 104. Each of the adjustment electric fields may be time varying such that adjustment force 112 is time varying. The control field may be, for example, a control electric field or a control magnetic field. When confined within the ion trap 102, the ion 104 may experience a time varying offset force 113. The offset force may be a result of the control signals 108, or may be from another source. The controller 106 may be configured to provide the one or more adjustment signals 110 for applying an adjustment force 112 to the ion 104 that substantially cancels, or otherwise reduces, the offset force 113. The offset force 113 may be generated by oscillating electric fields within the ion trap 102. In the present embodiment, during operation, the control signal 108 is used to generate the control field, and the adjustment signal 110 is used to generate the adjustment electric field. It will be appreciated that in specific embodiments, the adjustment force 112 may be used simply to apply a force to the ion 104, without cancellation of any other force such as the offset force 113. For example, in a specific embodiment, the adjustment signal 110 may have a frequency f_l with its amplitude modulated with frequency f_2 such that the ion 104 experiences an effective force at frequency f_2. In a specific example having no amplitude modulation, the force on the ion 104 would be a static force and the physical mechanism in this case would be the ponderomotive effect. The frequency f_l may be much higher than the ion trapping frequency f_trap - in this case, the effective force of the electric field at f_l may be proportional to the time-averaged amplitude square of the amplitude of the adjustment signal 110 at f_l. Figure 1(c) is a schematic of a specific embodiment of the control system 100 and a specific embodiment of the ion trap 102, in accordance with a third embodiment of the present disclosure. The ion trap 102 comprises a plurality of electrodes 114a, 114b, 114c, 114d, and the control system 100 comprises a signal generator 116. The signal generator 116 may be configured to generate control voltages V la, Vlb at a one or both of the electrodes 114a, 114b to generate the control field. The control voltages Via, Vlb and therefore the control field is dependent on the controls signal 108 as received by the signal generator 116. The signal generator 116 may drive a low voltage a high current load. It will be appreciated that in a further embodiment including multiple control signals 108, each of the control signals may be used by the signal generator 116 to generate different control voltages at different electrodes. In such an example, the resultant confining electric fields all contribute to the performing of the quantum gate operation, or quantum gate operations, on the ion. The signal generator 116 may be further configured to generate adjustment voltages Vic, Vid at a one or both of the electrodes 114c, 114d to generate the adjustment electric field. The adjustment voltages Vic, Vid and therefore the adjustment electric field is dependent on the adjustment signal 110 as received by the signal generator 116. An oscillating adjustment force 112 at a frequency f may be generated by applying a voltage at the frequency f to an electrode. It will be appreciated that in a further embodiment including multiple adjustment signals 110, each of the adjustment signals maybe used by the signal generator 116 to generate different adjustment voltages at different electrodes. In such an example, the resultant adjustment electric fields all contribute to the adjustment force on the ion. Each of the adjustment electric fields is time varying such that the adjustment force is time varying. The control system 100 further comprises a detection system 118. During operation, the detection system 118 detects at least one characteristic of the offset force 113 experienced by the ion 104. The controller 106 provides the one or more adjustment signals 110 based on the detected characteristic. It will be appreciated that the characteristic may be determined by direct measurement of the offset force 113, or may otherwise be determined, for example, by measuring a property of the system, such as an offset electric field, and determining, or otherwise inferring, a characteristic of the offset force based on the offset electric field. In a further embodiment, the offset force 113 may be estimated or determined by simulation or experimental results. In specific embodiments, the detection system 118 may detect the at least one characteristic of the offset force 113 by measuring the excitation of ion-motion and / or measuring the displacement (or other motion) of the ion. Figure 2 shows example waveforms of the offset force 113 and the adjustment force 112 as may be experienced by the ion 104 in a specific implementation of the ion trap 102 of Figure 1(c). It will be appreciated that the waveforms are shown for illustrative purposes and for an idealised system. In a practical implementation of such a system there is likely to be noise and imperfections that result in variations in the waveforms. A timing graph 200 shows the offset force 113 as it varies with time and a timing graph 202 shows the adjustment force 112. In the present example, the adjustment signal 110 is used to provide the adjustment force 112 having an amplitude al and a frequency fl equal to the amplitude a2 and frequency f2 of the offset force 113, respectively. It will be appreciated that in further embodiments, the one or more adjustment signals 110 may provide the adjustment force 112 having a substantially equal amplitude and / or frequency to that of the offset force 113. In the present embodiment, the adjustment signal 110 is used to provide the adjustment force 112 being out of phase with respect to the offset force 113, as shown by the 180° phase shift A0 between the waveforms. In further embodiments, the one or more adjustment signals 110 may provide a different phase shift between waveforms. In a specific embodiment, the property detected by the detection system 118 may be the amplitude and or frequency of the offset force 113, with the controller 106 providing the necessary adjustment signal 110 or signals to cancel the amplitude and / or frequency of the offset force 113 using the adjustment force 112 based on the detected property. In summary, in a specific embodiment of the present disclosure, the detection system 118 may be used to measure the oscillation of the ion 102, and specifically in relation to its amplitude and frequency. The controller 106 may then use this amplitude and frequency information to apply an oscillating adjustment force 112 at the same frequency that reduces the undesired oscillation of the ion 102 substantially to zero. In the present example, the adjustment force 112 and offset force 113 are coherent waves with respect to each other, in that they have the same frequency and a constant phase difference. As the waveforms 112,113 have the same amplitude and are 180° out of phase with respect to each other, in the present example, the offset force 113 will effectively be substantially cancelled by the adjustment force 112, meaning that the ion 104 will no longer experience the undesired offset force 113 during operation. In summary, embodiments of the present disclosure may be used to coherently cancel undesired forces (the offset force 113) experienced by the ion 102 by coherently cancelling undesired electric fields. Cancellation is achieved by applying an additional force (the adjustment force 112) that is out of phase with respect to the undesired force, with the additional force being applied through oscillating electric fields. The one or more adjustment signals 110 may be used to generate the required electric fields to cancel the undesired electric fields at specific frequencies. Returning to Figure 1(c), the plurality of electrodes 114a, 114b, 114c, 114d may comprise at least one of a DC electrode, an RF electrode and a microwave electrode. In specific embodiments of the present disclosure, the coherent oscillating electric fields for cancellation of the offset force may be applied at a DC electrode, a microwave electrode and / or an RF electrode. In consideration of an embodiment where the adjustment signals 110 are applied to a DC electrode, the resultant electric fields can cause a force on the trapped ion 104 (or ions) due to their charge. The adjustment force 112 can then be used to coherently cancel the undesired electric fields. By combining fields produced by different DC electrodes, forces experienced in different locations may be turned. Figure 3 is a schematic of a trapped ion system 300 comprising specific implementations of the control system 100 and the ion trap 102, in accordance with a fourth embodiment of the present disclosure. Trapped ion systems for quantum computing purposes, in general, comprise an ion trap in a vacuum chamber, a voltage source coupled to the ion trap, a source of neutral atoms, a source of a static magnetic field, a plurality of lasers and a fluorescence detector. The plurality of lasers may serve several purposes, for example including the excitation and photoionization of the neutral atoms into ions and trapping the ions in the ion trap. The trapped ion system 300 of the present embodiment comprises a vacuum chamber 302, a barium ion source 304, a qubit manipulation system 306, and a magnetic field source 308a, 308b. The trapped ion system 300 may further comprise electrodes 312, with the electrodes 312 corresponding to the electrodes 114a, 114b, 114c, 114d as previously described. The qubit manipulation system 306 may comprise a pair of antennas. The detection system 118 may, for example, comprise a fluorescence detector. The signal generator 116 may comprise a voltage source. The ion trap 102 is configured to trap a barium ion in the present embodiment, with the 104 being situated within the vacuum chamber 302. The ion trap 102 comprises the electrodes 312 which couple the ion trap 104 to the voltage source of the signal generator 116. The electrodes in the present embodiment comprise RF electrodes and DC electrodes. It will be appreciated that in further embodiments, alternative electrodes and electrode configurations may be used, in accordance with the understanding of the skilled person. The ion trap 102 is coupled with the barium source 304 which is configured to provide the ion 104 to the ion trap 102. The barium ion source 304 comprises a neutral atom source to provide the neutral barium atom and an ionisation device configured to ionise the barium atom and hence provide the barium ion. The neutral atom source and ionisation device are not shown in the Figure. The neutral atom source could be, for example, a resistively heated atomic oven or an ablation target. The ionisation device could be, for example, a network of lasers of various operational wavelengths. The qubit manipulation system 306 is configured to encode a qubit in the states of the ion 104. The magnetic field source 308a, 308b may be positioned within the vacuum chamber 302 or outside the vacuum chamber 302 and is configured to apply a magnetic field to the ion trap 102. In the present example, the control signal 108 is provided to one or more digital to analog converters (DAC], which is used to generate voltages at one or more DC electrodes for performing the quantum gate operation on the ion 104. In the present example, the adjustment signal 110 is provided to one or more digital to analog converters (DAC], which is used to generate voltages at one or more DC electrodes for adjustment of the ion 104. It will be appreciated that further embodiments may include providing the signals 108,110 to other components of Figure 3, to provide the required functionality, in accordance with the understanding of the skilled person. Figure 4 is a schematic of an apparatus 400 comprising a quantum computer 402 in accordance with a fifth embodiment of the present disclosure. The quantum computer 402 comprises the control system 100 and the ion trap 102. The control system 100 and / or the ion trap 102 may be implemented as described in relation to any of the embodiments described herein. In quantum computing, a quantum gate (which may be referred to as a "gate" or a "quantum gate operation”] is a circuit operation that is performed on one or more qubits. In the context of the present disclosure, a quantum gate is analogous to logic gates used in electronic circuits. The operation of qubit gates is dependent on a mechanism that controls (also referred to as "drives"] the gate operations by switching qubits between states. In trapped ion systems, single-qubit gates and multi-qubit gates (such as two-qubit gates) are driven by different mechanisms. In embodiments described herein, the control signal 108 is used to drive the gate operations by, for example, performing a quantum gate operation on one or more ions within an ion trap. The mechanism that drives multi-qubit gates is called the "state-dependent force”, which may also be referred to as a "spin-dependent force”, and may be generated using magnetic fields and / or electrical signals. “State-dependent” refers to the ion being able to occupy one of several quantum states, with the next state being dependent on the current state. The generation of state-dependent forces may result in the unwanted generation of “state-independent forces”, which may be generated by electric fields. "Stateindependent" means that the force applied to the ion as a result of the stateindependent force is unaffected by the present quantum state. Intermodulation is a non-linear process that leads to the generation of state independent forces. Intermodulation will be well-known by the person skilled in the art and generally describes a process under which modulation of signals containing multiple frequencies occurs due to non-linearities in a system. In a specific embodiment, the control signal 108 may be high frequency and have multiple tones that results in the generation of lower frequency (effective) forces through non-linear processes and intermodulation. These undesirable (effective) forces that are generated by the control signal 108 may be coherent with the control signal 108. Embodiments of the present disclosure may substantially cancel the low-frequency intermodulation products by applying an adjustment signal at a frequency matching the intermodulation product (using suitable amplitude and phase). For example, in specific embodiments, the offset force 113 may be a result of intermodulation, and the adjustment force 112 may, for example, be used to substantially cancel the offset force 113 thereby substantially cancelling the undesired effects of intermodulation. Figure 5(a) is a schematic of an ion trap system 500 showing an example of a signal chain resulting in intermodulation. The ion trap system 500 comprises a signal source 502 for providing a control signal 504 to an ion trap 506 for trapping ions in a potential well, for example using the ponderomotive force. The signal 506 is passed through a component 508 with non-linear characteristics, thereby resulting in intermodulation of the signal 506. It will be appreciated that intermodulation caused by a component is only one of the sources of intermodulation that we seek to address. There is another important mechanism: The high frequency control signal may generate a pondermotive force. The effect causing the pondermotive force is intrinsically non-linear. In our case the pondermotive force generated by the control signal is NOT used for trapping and is not intended to confine the ion. However, the fact that it generates a pondermotive force and that this is a non-linear process leads to intermodulation. Figure 5(b) is a frequency domain graph 510 showing a signal exhibiting intermodulation at Af. It will be appreciated that in specific embodiments, the adjustment signal 110 may use non-linearities to substantially cancel the offset force 113 (for example, see Figure 5(b)). The non-linearities may be the same non-linearities that result in the generation of the offset force 113 itself, for example relating to intermodulation of the one or more control signals 108, the ponderomotive effect, and / or non-linear components within the signal chain (for example as shown in Figure 5(a)). In summary, embodiments of the present disclosure may use an adjustment signal 110 in combination with using non-linearity to make the adjustment signal 110 perform the desired cancellation. Figure 5(c) is a frequency domain graph 512 showing a signal exhibiting intermodulation at Af. It will be appreciated that in specific embodiments, the adjustment signal 110 may use non-linearities and the control signal 108 to substantially cancel the offset force 113 (for example see Figure 5(c)). The non-linearities may be the same nonlinearities that result in the generation of the offset force 113 itself, for example relating to intermodulation of the one or more control signals 108, the ponderomotive effect, and / or non-linear components within the signal chain (for example as shown in Figure 5(a)). Figure 6 is a frequency domain graph 600 showing a signal exhibiting intermodulation at Af which is the difference between frequency components 602, 604. As a result of the intermodulation and / or ponderomotive effects, the ion trap system 500 may exhibit spin-independent (effective) forces near the mode frequencies when there is applied a dynamically decoupled two-qubit gate. These dynamics do not commute with the two-qubit gate and may result in gate errors. These “state-independent forces” cause gate errors. The magnitude of the error depends on magnitude of the force (the stronger the force, the larger the error) and the frequency of the force (the closer the force frequency is to the motional frequency the worse). Ideally, we want "state-independent forces” to be weak and far-detuned from motion. Known practices to resolve the intermodulation problem as described in relation to Figure 5(a), introduce additional tones during operation of the two-qubit gates to make the effect of the quantum mechanical interaction driving quantum logic more resilient to environmental errors. This resilience is achieved using a field coupling directly to the qubit state. A limitation of existing techniques is that they do not address the presence of undesired effects impacting qubit operation. Further, they fail to account that the control signals may themselves introduce undesired effects. Embodiments of the present disclosure may introduce an adjustment signal to cancel the low-frequency intermodulation products by applying the adjustment signal at a frequency matching the intermodulation product (using suitable amplitude and phase). When applied to a system such as the ion trap system 500 being configured as a two-qubit gate and exhibiting intermodulation, embodiments of the present disclosure can address the presence of undesired effects impacting qubit operation, and can also account for the result of the undesired forces generated by the control signal 108 itself. In summary, in an ion trap system, an ion may experience an undesired oscillating force. Embodiments of the present disclosure provides a control system 100 that functions to apply a second force at the same frequency but opposite phase. As a result, the ion 104 experiences zero net force, thereby improving operations. Such improvements can provide improved quantum systems including, but not limited to, quantum logic gates and / or quantum computers. Embodiments of the present disclosure have been described primarily in relation to a single ion. However, it will be appreciated that further embodiments may be applicable to multiple ions, in accordance with the understanding of the skilled person. Various improvements and modifications may be made to the above without departing from the scope of the disclosure.

Claims

1. A control system for manipulating a charged particle, the control system comprising a controller configured to:provide one or more adjustment signals for applying an adjustment force to the charged particle, the adjustment force being time varying.

2. The control system of claim 1, wherein the controller is configured to provide one or more control signals.

3. The control system of claim 2, wherein each of the one or more control signals is for manipulating the classical or quantum state of the charged particle.

4. The control system of claim 2 or 3, wherein:each of the one or more control signals generates electric and / or magnetic fields affecting the charged particle; and / oreach of the one or more adjustment signals generates electric fields affecting the charge particle.

5. The control system of claim 4, comprising a plurality of electrodes, the control system comprising a signal generator configured to:generate control voltages and / or currents at a first electrode of the plurality of electrodes to generate the control electric field and / or magnetic field, for each of the one or more control signals; and / orgenerate adjustment voltages at a second electrode of the plurality of electrodes to generate the adjustment electric field, for each of the one or more adjustment signals.

6. The control system of claim 5, wherein the plurality of electrodes comprises at least one of:a DC electrode;an RF electrode; anda microwave electrode.

7. The control system of claim 6, wherein:control voltages are generated at a first DC electrode, or a first RF electrode, or a first microwave electrode; and / oradjustment voltages are generated at a second DC electrode, or a second RF electrode, or a second microwave electrode.

8. The control system of claim 6 or 7, wherein the controller is configured to:provide a first adjustment signal for generating a first adjustment electric field by generating a first adjustment voltage at a first electrode and / or a second adjustment voltage at a second electrode; andprovide a second adjustment signal for generating a second adjustment electric field by generating a third adjustment voltage ata third electrode and / or a fourth adjustment voltage ata fourth electrode.

9. The control system of any of claims 2 to 8, wherein the charged particle experiences an offset force, the offset force being time varying.

10. The control system of claim 9, wherein the time varying offset force is generated through:intermodulation of the one or more control signals and / orponderomotive effects of the charged particle which arises from the one or more control signals; and / ornon-linear components within the signal chain of the one or more control signals.

11. The control system of claim 10, wherein the controller is configured to provide one or more adjustment signals for applying the adjustment force to the charged particle to substantially cancel or otherwise reduce the offset force.

12. The control system of claim 10 or 11, wherein the controller is configured to provide one or more adjustment signals for applying that adjustment force having:an amplitude that is approximately equal to the amplitude of the offset force; and / ora frequency that is approximately equal to the frequency of the offset force.

13. The control system of claim 12, wherein the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force.

14. The control system of claim 10 or 11 comprising:a detection system configured to detect at least one characteristic of the offset force experienced by the charged particle; whereinthe controller is configured to provide the one or more adjustment signals based on the detected at least one characteristic of the offset force.

15. The control system of claim 14, whereinthe at least one property of the offset force comprises: an amplitude of the offset force; and / or a frequency of the offset force; andthe controller is configured to provide one or more adjustment signals for applying the adjustment force having:an amplitude that is approximately equal to the amplitude of the offset force, as detected by the detection system; and / ora frequency that is approximately equal to the frequency of the offset force, as detected by the detection system.

16. The control system of claim 15, wherein the controller is configured to provide one or more adjustment signals for applying the adjustment force having a phase that is approximately out of phase with respect to the offset force.

17. The control system of any preceding claim wherein the charged particle is an ion.

18. The control system of claim 1 for an ion trap, wherein the charged particle is an ion.

19. The control system of claiml8, wherein the ion experiences an offset force when confined within the ion trap, the offset force being time varying.

20. The control system of claim 30, wherein the time varying offset force is generated through:intermodulation of the one or more control signals and / orponderomotive effects of the ion which arises from the one or more control signals; and / ornon-linear components within the signal chain of the one or more control signals.

21. The control system of claim 19 or 20, wherein the controller is configured to provide one or more adjustment signals for applying the adjustment force to the ion to substantially cancel or otherwise reduce the offset force.

22. The control system of any of claims 19 to 21, wherein the offset force is a result of intermodulation.

23. The control system of any of claims 18 to 22, wherein the ion trap is part of a quantum computer.

24. An apparatus comprising:the control system of any of claims 18 to 23; andthe ion trap.

25. A method of manipulating a charged particle using a control system, the method comprising:providing one or more adjustment signals for applying an adjustment force to the charged particle, the adjustment force being time varying.

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