A control system

Abstract

A control system 100 for manipulating a first charged particle, e.g. an ion 104, comprises a controller 106 for providing a control signal 108, said control signal comprising one or more adjustment fr

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 first charged particle, the control system comprising a controller configured to provide a control signal, wherein the control signal comprises one or more adjustment frequency components for applying a first adjustment force to the first charged particle. Optionally, the control signal is for manipulating the classical or quantum state of the first charged particle. Optionally, the control signal generates electric and / or magnetic fields affecting the first charged particle, and / or the one or more adjustment frequency components generates electric fields affecting the first charged 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 the control signal, 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 frequency components. 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 frequency component 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 frequency component 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 first charged particle experiences a first offset force. Optionally, the first offset force is generated through intermodulation of the control signal, and / or ponderomotive effects of the charged particle which arises from the control signal, and / or non-linear components within the signal chain of the control signal. Optionally, the control signal comprises the one or more adjustment frequency components for applying the first adjustment force to the first charged particle to substantially cancel or otherwise reduce the first offset force. Optionally, the one or more adjustment frequency components use intermodulation and / or ponderomotive effects with themselves and / or other frequency components of the control signal. Optionally, the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having an amplitude that is approximately equal to the amplitude of the first offset force, and / or a frequency that is approximately equal to the frequency of the first offset force. Optionally, the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having a phase that is approximately out of phase with respect to the first offset force. Optionally, the control system comprises a detection system configured to detect at least one characteristic of the first offset force experienced by the first 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 first offset force. Optionally, the at least one property of the first offset force comprises an amplitude of the first offset force, and / or a frequency of the first offset force, and the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having an amplitude that is approximately equal to the amplitude of the first offset force, as detected by the detection system, and / or a frequency that is approximately equal to the frequency of the first offset force, as detected by the detection system. Optionally, the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having a phase that is approximately out of phase with respect to the first offset force. Optionally, the first charged particle is a first ion. Optionally, the control system is for a trapped ion system comprising an ion trap, wherein the first charged particle is a first ion. Optionally, the control signal is for manipulating the classical or quantum state of the first ion. Optionally, the control signal is for performing a first quantum gate operation on the first ion within the ion trap Optionally, the control signal generates electric and / or magnetic fields affecting the first ion, and / or the adjustment frequency components generate electric fields affecting the first ion. 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 the control signal, 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 frequency components. 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 frequency component 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 frequency component 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 control signal is for generating a control field to perform the first quantum gate operation on the first ion within the ion trap. Optionally, the control field is a control electric field or a control magnetic field. Optionally, the ion trap comprises a control electrode, the control system comprising a signal generator configured to generate a control voltage and / or currents at the control electrode to generate the control field. Optionally, the control electrode comprises a DC electrode, an RF electrode or a microwave electrode. Optionally, the first ion experiences a first offset force when confined within the ion trap. Optionally, the first offset force is generated through intermodulation of the control signal, and / or ponderomotive effects of the first ion which arises from the control signal, and / or non-linear components within the signal chain of the control signal. Optionally, the control signal comprises the one or more adjustment frequency components for applying the first adjustment force to the first ion to substantially cancel or otherwise reduce the first offset force. Optionally, the one or more adjustment frequency components use intermodulation and / or ponderomotive effects with themselves and / or other frequency components of the control signal. Optionally, the controller is configured to provide an amplitude, a frequency and / or a phase of each of the one or more adjustment frequency components suitable for substantially cancelling or otherwise reducing the first offset force. Optionally, the controller is configured to provide the amplitude, the frequency and / or the phase of each of the one or more adjustment frequency components suitable for substantially cancelling or otherwise reducing the first offset force through non-linear interaction with the adjustment frequency components and / or other frequency components of the control signal. Optionally, the trapped ion system comprises a qubit manipulation system configured to encode a first qubit in the first ion. Optionally, the trapped ion system is part of a quantum computer. Optionally, the controller is configured to provide the first control signal for performing a second quantum gate operation on a second ion within the ion trap, wherein the control signal comprises the one or more adjustment frequency components for applying a second adjustment force to the second ion. Optionally, the control signal is for generating a control field to perform the first quantum gate operation on the first ion and perform the second quantum gate operation on the second ion within the ion trap. Optionally, the control field is a control electric field or a control magnetic field. Optionally, the ion trap comprises a control electrode, the control system comprising a signal generator configured to generate a control voltage and / or currents at the control electrode to generate a control field. Optionally, the control electrode comprises a DC electrode, an RF electrode, or a microwave electrode. Optionally, the first ion experiences a first offset force when confined within the ion trap and the second ion experiences a second offset force when confined within the ion trap. Optionally, the first and / or second offset force is generated through intermodulation of the control signal, and / or ponderomotive effects of the first ion and / or second ion which arises from the control signal, and / or non-linear components within the signal chain of the control signal. Optionally, the control signals comprises the one or more adjustment frequency components for applying the first adjustment force to the first ion to substantially cancel or otherwise reduce the first offset force and / or for applying the second adjustment force to the second ion to substantially cancel or otherwise reduce the second offset force. Optionally, the controller is configured to provide an amplitude, a frequency and / or a phase of each of the one or more adjustment frequency components suitable for substantially cancelling or otherwise reducing the first offset force and / or the second offset force. Optionally, the trapped ion system comprises a qubit manipulation system configured to encode a first qubit in the first ion and to encode a second qubit in the second ion. Optionally, the first and / or second quantum gate operations are multiple qubit gates. Optionally, the trapped ion system is part of a quantum computer. Optionally, the multiple qubit gate is a Mplmer-Sprensen gate. Optionally, the control signal comprises a first sideband component and a second sideband component for driving the multiple qubit gate. Optionally, the one or more adjustment frequency components are configured to substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. Optionally, the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component, the first and second adjustment frequency components being symmetrically at approximately three times the sideband detuning frequency. Optionally, the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component, and the first and second adjustment frequency components each comprise an amplitude, a frequency and / or a phase arranged to substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. Optionally, the control signal comprises a first carrier component for generating dynamic decoupling. Optionally, the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component and the first and second adjustment frequency components being symmetrically at approximately two or three times the sideband detuning frequency. Optionally, the first and second adjustment frequency components each have an amplitude substantially equal to an amplitude of the first carrier component Optionally, the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component, and the first and second adjustment frequency components each comprise an amplitude, a frequency and / or a phase arranged to substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. Optionally, the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component, and the first and second adjustment frequency components being symmetrically at approximately half the sideband detuning frequency. According to a second aspect of the disclosure there is provided a trapped ion system comprising the control system of the first aspect. According to a third aspect of the disclosure there is provided a quantum computer comprising trapped ion system of the second aspect. According to a fourth aspect of the disclosure there is provided a method of manipulating a first charged particle using the control system of the first aspect. It will be appreciated that the method of the fourth aspect may include providing and / or using features set out in the first and / or second aspects, and can incorporate other features described herein. BRIEF DESCRIPTION OF THE DRAWINGS The disclosure is described in further detail be low 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 a trapped ion system 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 trapped ion system, in accordance with a third embodiment of the present disclosure; Figure 2 is a frequency domain graph showing an example control signal in accordance with a specific embodiment of the present disclosure, and as may be applied in the system of Figure 1(a) or 1(b); Figure 3 is a schematic of a specific implementation of the trapped ion system comprising a specific implementation of the control system and a specific implementation of the ion trap, in accordance with a fourth embodiment of the present disclosure; Figure 4 is a schematic of a quantum computer comprising the control system and the trapped ion system, in accordance with a fifth embodiment of the present disclosure; Figure 5(a) is a schematic of a specific embodiment of the control system and a specific embodiment of the trapped ion system, in accordance with a sixth embodiment of the present disclosure, Figure 5(b) is a schematic of a specific embodiment of the control system and a specific embodiment of the trapped ion system, in accordance with a embodiment of the present disclosure; Figure 6 is a frequency domain graph 600 showing an example control signal in accordance with a specific embodiment of the present disclosure as may be applied in the system shown in Figure 5(a) or Figure 5(b); and Figure 7 is a schematic of an ion trap system showing an example of a signal chain resulting in intermodulation; Figure 8 is a frequency domain graph showing a signal exhibiting intermodulation; Figure 9 is a frequency domain graph showing an example embodiment of the control signal; Figure 10 is a frequency domain graph showing a further example embodiment of the control signal; Figure 11 is a frequency domain graph showing a further example embodiment of the control signal; and Figure 12 shows example waveforms of the offset force and the adjustment force as may be experienced by the charged particle in embodiments of the present disclosure. DETAILED DESCRIPTION Controlling the forces experienced by charged particles is an important problem in ion-trapping. When we apply control signals, 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 problems: • 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 apply adjustment frequency components to cancel additional frequency components due to non-linearities by using the non-linear interaction of the adjustment frequency components with each other and the control signals. ■ This has several advantages. These advantages derive from being able to choose adjustment frequency components to be similar in frequency to the control signals being applied: ■ This simplifies hardware requirements as the required signal frequency range is reduced. ■ The adjustment frequency components may be applied via the same signal chain and electrodes as the control signal. This means any drifts in signal amplitude and / or phase will be common to the control signal and the adjustment frequency components. Such common drifts do not degrade the cancellation of the undesired frequencies in the offset force. Therefore, such an approach allows for better stability of the cancellation. ■ When choosing to apply adjustment frequency components and the control signal at similar frequencies and via the same signal chain, discrepancies in the spatial variation of the fields produced by the control signal and adjustment frequency components are reduced. This improves the quality of the cancellation of the offset force that is achieved by the adjustment frequency components over extended spatial regions. 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 103 in accordance with a first embodiment of the present disclosure. The control system 100 comprises a controller 106 configured to provide a control signal 108. The control signal 108 comprises one or more adjustment frequency components for applying an adjustment force 112 to the charged particle 103. The charged particle 103 may experience an offset force 113. The offset force 113 may be time varying. The offset force 113 may be a result of the control signal 108, or may be from another source. The controller 106 may be configured to provide the control signal 108 comprising the one or more adjustment frequency components for applying the adjustment force 112 to the charged particle 103 that substantially cancels, or otherwise reduces, the offset force 113. In summary, there is applied an additional force, in the form of the adjustment force 112, to cancel out the undesired offset force 113. In a specific embodiment, the controller 106 may be configured to provide an amplitude, frequency and / or phase of each of the one or more adjustment frequency to generate an adjustment force 112 that is suitable for substantially cancelling the offset force 113. The substantial cancellation may be through non-linear interaction with adjustment frequency components and / or other frequency components of the control signal 108. Figure 1(b) is a schematic of a specific embodiment of the control system 100 for a trapped ion system 101 in accordance with a second embodiment of the present disclosure. The trapped ion system 101 comprises an ion trap 102 for trapping an ion 104. In the present example, the charged particle 103 is the ion 104. The ion 104 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 103 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. It will be appreciated that in further embodiments, the trapped ion system 101 may comprise one or more ion traps, with each of the ion traps being configured to trap one or more ions. It will be appreciated that the trapped ion system 101 may comprise the control system 100. The control system 100 comprises a controller 106. During operation of the trapped ion system 101, the controller 106 provides a control signal 108 for performing a quantum gate operation on the ion 104 within the ion trap 102. The control signal 108 may, for example, be used to generate a control field to perform a quantum gate operation on the ion 104 within the ion trap 102. The quantum gate operate may, for example, be a single-qubit gate operation, or a multiple qubit gate operation such as a two-qubit gate operation. The control field may be, for example, a control electric field or a control magnetic field. The control signal 108 comprises one or more adjustment frequency components for applying an adjustment force 112 to the ion 104. In the present example, and to simplify the accompanying description, there is provided a single control signal 108. However, further embodiments of the disclosure may use a plurality of control signals. When confined within the ion trap 102, the ion 104 may experience an offset force 113. The offset force 113 may be time varying. The offset force 113 may be a result of the control signal 108, or may be from another source. The controller 106 may be configured to provide the control signal 108 comprising the one or more adjustment frequency components for applying the adjustment force 112 to the ion 104 that substantially cancels, or otherwise reduces, the offset force 113. In summary, there is applied an additional force, in the form of the adjustment force 112, to cancel out the undesired offset force 113. In a specific embodiment, the controller 106 may be configured to provide an amplitude, frequency and / or phase of each of the one or more adjustment frequency to generate an adjustment force 112 that is suitable for substantially cancelling the offset force 113. The substantial cancellation may be through non-linear interaction with adjustment frequency components and / or other frequency components of the control signal 108. Figure 1(c) is a schematic of a specific embodiment of the control system 100 and a specific embodiment of the trapped ion system 101, in accordance with a third embodiment of the present disclosure. In the present embodiment, the ion trap 102 comprises a plurality of control electrodes 114a, 114b and the control system 100 comprises a signal generator 116 configured to generate the control voltages Via, Vlb at the control electrodes 114a, 114b to generate the control electric field. Each of the control electrodes 114a, 114b may comprise one or more of a DC electrode, an RF electrode or a microwave electrode. The signal generator 116 generates the control voltages Via, Vlb based on the control signal 108. As the control signal 108 includes the one or more adjustment frequency components, the resultant control electric field applied to the ion 104 applies the adjustment force 112. The trapped ion system 101 may further comprise a qubit manipulation system 118 configured to encode a qubit in the ion 104. It will be appreciated that in further embodiments comprising a plurality of trapped ions, the qubit manipulation system 118 may be configured to encode a qubit in each of the trapped ions. Figure 2 is a frequency domain graph 200 showing an example control signal 108 in accordance with a specific embodiment of the present disclosure, and as may be applied in the system 101 of Figure 1(a) or 1(b). The control signal 108 comprises a plurality of frequency components with one or more of the frequency components being adjustment frequency components (for example, as labelled by numeral 202) for providing the adjustment force. The remaining frequency components may be used for aspects of control of the trapped ion system 101, for example for manipulating the quantum information encoded within the ion 104, or may simply relate noise within the system 101. Figure 3 is a schematic of a specific implementation of the trapped ion system 101 comprising a specific implementation of the control system 100 and a specific implementation of the ion trap 102, in accordance with a fourth embodiment of the present disclosure. The trapped ion system 101 may comprise dedicated electrodes for control signals 108 that are used to manipulate the quantum information of the ions 104. 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 101 of the present embodiment comprises a vacuum chamber 302, a barium ion source 304, the qubit manipulation system 118, a detection system 307, and a magnetic field source 308a, 308b. The trapped ion system 101 may further comprise electrodes 312, with the electrodes 312 corresponding to the electrodes 114a, 114b as previously described. The qubit manipulation system 118 may comprise a pair of antennas. The detection system 307 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 ion 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. RF electrodes typically used for confinement within the field, with other electrodes being for manipulating quantum information. 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 118 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, and for the generation of the adjustment force 112. It will be appreciated that further embodiments may include providing the control signal 108 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 a quantum computer 400 comprising the control system 100 and the trapped ion system 101, in accordance with a fifth embodiment of the present disclosure. It will be appreciated that in further embodiments, the control system 100 and / or the trapped ion system 101 may be implemented by any of the specific embodiments described herein and in accordance with the understanding of the skilled person. Figure 5(a) is a schematic of a specific embodiment of the control system 100 and a specific embodiment of the trapped ion system 101, in accordance with a sixth embodiment of the present disclosure. In the present embodiment, the control signal 108 is for performing a quantum gate operation on the ion 104 and an ion 500 within the ion trap 102. The one or more adjustment frequency components of the control signal 108 are for applying an adjustment force 502 to the ion 500. The ion 500 may experience an offset force 504. The one or more adjustment frequency components of the control signal 108 may result in the adjustment force 113 substantially cancelling the offset force 112 and / or the adjustment force 502 substantially cancelling the offset force 504. In the present embodiment, the control signal 108 is for generating a control electric field within the ion trap 102 to perform a quantum gate operation on the ions 104, 500. Figure 5(b) is a schematic of a specific embodiment of the control system 100 and a specific embodiment of the trapped ion system 101, in accordance with a seventh embodiment of the present disclosure. The signal generator 116 generates the control voltages Via, Vlb based on the control signal 108. As the control signal 108 includes the one or more adjustment frequency components, the resultant control electric field applied to the ions 104, 500 also applies the adjustment forces 112, 502. Figure 6 is a frequency domain graph 600 showing an example control signal 108 in accordance with a specific embodiment of the present disclosure as may be applied in the system 101 shown in Figure 5(a) or Figure 5(b). The control signal 108 comprises a plurality of frequency components with one or more of the frequency components being adjustment frequency components for providing the adjustment forces 112, 502. The remaining frequency components may be used for aspects of control of the trapped ion system 101, for example manipulating the quantum information encoded within the ion 104, or may simply relate noise within the system 101. By way of example, in Figure 6, the frequency component 602a may be used to generate the adjustment force 112 and the frequency component 602b may be used to generate the adjustment force 502. In a further embodiment, the same adjustment frequency components may be used to generate two or more adjustment forces 112, 502. For example, the adjustment frequency component 602a may generate both adjustment forces 112, 502. In a further example, both adjustment frequency components 602a, 602b may both be used for the generation of both adjustment forces 112, 502. Returning to Figure 5(b), the trapped ion system 101 may further comprise the qubit manipulation system 118 configured to encode a qubit in the ion 104 and a qubit in the ion 500. During operation of the trapped ion system 101, the controller 106 provides the control signal 108 for performing a quantum gate operation on the ion 104 within the ion trap 102. The quantum gate operation may be a multiple qubit gate, and specifically a two-qubit gate in the present example. The multiple qubit gate may be a Mplmer-Sprensen (MS) gate. 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. Figure 7 is a schematic of an ion trap system 700 showing an example of a signal chain resulting in intermodulation. The ion trap system 700 comprises a signal source 702 for providing a control signal 704 to an ion trap 706 for trapping ions in a potential well, for example using the ponderomotive force. The signal 706 is passed through a component 708 with non-linear characteristics, thereby resulting in intermodulation of the signal 706. 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. It will be appreciated that in specific embodiments, the adjustment frequency components may use non-linearities to substantially cancel the offset force 113. 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 7). In summary, embodiments of the present disclosure may use an adjustment frequency components in combination with using non-linearity to make the adjustment frequency components perform the desired cancellation. Figure 8 is a frequency domain graph 800 showing a signal exhibiting intermodulation at Af which is the difference between frequency components 802, 804. As a result of the intermodulation and / or ponderomotive effects, the ion trap system 700 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 7, 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 introduce adjustment frequency components into the control signal 108 itself. When applied to a system such as the ion trap system 700 where the control signal 108 drives 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. Embodiments of the present disclosure may provide a detuning of the spinindependent force from the mode frequency. In a standard (optionally dynamically decoupled) MS two-qubit gate there are no remaining degrees of freedom that would allow the shaping of the spectrum of the microwave-induced pseudopotential. Embodiments of the present disclosure may include one or two additional microwave tones into a two-qubit gate as provided by the control signal 108 which allows reducing or cancelling a chosen frequency of the microwave pseudo-potential. The microwave tones (the adjustment frequency components of the control signal 108) may have equal and opposite detuning from the nominal qubit frequency of the two qubit gate. Returning to Figure 5(b), the control signal 108 may comprise a first sideband component and a second sideband component, both of the first and second sideband components being for driving the multiple qubit gate. As discussed previously, 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. The mechanism that drives multi-qubit gates is called the "statedependent force", which in the present embodiment is generated by the first and second sideband components. The first and second sideband components are tones that generate the state dependent force, and maybe referred to as “sideband drives”. In a specific embodiment, the one or more adjustment frequency components of the control signal 108 may be configured to substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. In a specific embodiment, the one or more adjustment frequency components of the control signal 108 may be configured to substantially cancel 2nd order intermodulation resulting from the first and second sideband components. It will be appreciated that sideband has its conventional meaning, in that it refers to bands of frequencies that are higher or lower than a central frequency (such as a carrier frequency), as will be clear to the skilled person. In a specific embodiment, the adjustment frequency components of the control signal 108 may comprise a first adjustment frequency component and a second adjustment frequency component with the first and second adjustment frequency components being symmetrically at approximately three times a sideband detuning frequency. Figure 9 is a frequency domain graph 900 showing an example embodiment of the control signal 108 having sideband components 902, 904 that are detuned by Af from a carrier frequency; and adjustment frequency components 906, 908 that are detuned by 3Af from the carrier frequency (such that they are at approximately three times the sideband detuning frequency). The use of additional frequency components in the control signals can result in (partial or complete) cancellation of undesired nonlinear spectral-effects that are introduced via control fields driving quantum logic operations. This cancellation may be achieved through appropriate choice of the amplitude, frequency and phase of the additional control signals relative to the control fields at issue. The additional control fields generate new spectral content which is at a different frequency to the cancelled spectral content. In a specific embodiment, the first and second adjustment frequency components each comprise an amplitude, a frequency and / or a phase arranged to at substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. In a specific embodiment, the trapped ion system 101 may be configured to function as a 4-tone gate. The "4-tones” is descriptive of the control signal 108 comprising the four components: the first and second sideband components, and the first and second adjustment frequency components. Cancellation of the 2nd order sidebandsideband intermodulation via microwave pseudo-potential in a MS-style two-qubit gate on ions (the 4 tones gate) may, for example, be achieved by one of the following: • Use two adjustment frequency components that have frequency, amplitude, and difference-phase splitting set to cancel the sideband-sideband intermodulation of the MS gate. The frequency difference between the additional signals may match the original frequency. However, their absolute frequency may be chosen to differ significantly. • Use two adjustment frequency components that are at symmetrically around three times the original sideband detuning. The above options may provide cancellation of the 2nd order sideband-sideband intermodulation via signal chain non-linearities. In a specific embodiment, the control signal 108 may comprise a first carrier component for generating dynamic decoupling. Dynamic decoupling is a quantum control technique that will be known the skilled person. In the present embodiment, by providing the first carrier component, the trapped ion system 101 may be configured to function as a dynamically decoupled (DD) two-qubit gate, for example a dynamically decoupled Mplmer-Sprensen (DDMS) two-qubit gate. A DD two-qubit gate is created by applying the three signal frequencies of the control signal 108 at once. Specifically, two of the tones (the sideband drives being the first and second sideband components) generate the “state-dependent force". The remaining tone (called the carrier drive and provided by the first carrier component) generates the "dynamic decoupling", improving gate performance. “State-independent forces” are particularly impactful on gate performance during dynamically decoupled two qubit gates (worse than during regular two-qubit gates which do not have the “carrier drive”). Embodiments of the present disclosure may add two additional tones (the first and second adjustment frequency components) into the gate to reduce the “state-independent force", improving gate performance. In a specific embodiment, the adjustment frequency components of the control signal 108 may comprise the first adjustment frequency component and the second adjustment frequency component with the first and second adjustment frequency components being symmetrically detuned from the central carrier frequency by 3 times the (symmetric) detuning of the control signal from the carrier frequency. In a specific embodiment, the first and second adjustment frequency components each comprise an amplitude, a frequency and / or a phase arranged to at substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components. In a specific embodiment, the first and second adjustment frequency components may each have an amplitude substantially equal to an amplitude of the first carrier component. When performing a DDMS gate, applying two additional tones (being the first and second adjustment frequency components) at the carrier amplitude, where the first and second adjustment frequency components are at twice the sideband-tone detuning, and for a suitable choice of phase, can result in coherent cancellation of the pseudo-potential intermodulation term that oscillates at the sideband detuning. Figure 10 is a frequency domain graph 1000 showing an example embodiment of the control signal 108 having sideband components 1002,1004 that are detuned by △ from a carrier frequency 1006; and adjustment frequency components 1008,1010 that are detuned by 2A from the carrier frequency 1006 (such that they are at approximately two times the sideband detuning frequency). The adjustment frequency components 1008, 1010 and the carrier frequency 1006 amplitudes are approximately equal. In a specific embodiment, the adjustment frequency components of the control signal 108 may comprise the first adjustment frequency component and the second adjustment frequency component with the first and second adjustment frequency components being symmetrically at approximately half a sideband detuning frequency. When performing a DDMS gate, apply two additional tones (being the first and second adjustment frequency components at an amplitude of sqrt(2VsbVc). There will also be some empirical tuning of the amplitudes. These tones have equal and opposite detuning from the qubit frequency by half the sideband-tone detuning. For suitable choice of phase, this can result in coherent cancellation of the pseudopotential intermodulation term that oscillates at the sideband detuning. "sqrt" denotes a square root function, VSb is an amplitude of one of the first and second sideband components and Vc is an amplitude of the first carrier component. Figure 11 is a frequency domain graph 1100 showing an example embodiment of the control signal 108 having sideband components 1102,1104 that are detuned by A from a carrier frequency 1106; and adjustment frequency components 1108,1110 that are detuned by A / 2 from the carrier frequency 1106 (such that they are at approximately half times the sideband detuning frequency). In summary, the above mentioned embodiments (relating to “5-tone” schemes) may be summarised as follows: 1. When performing a DDMS gate, apply two additional tones at the carrier amplitude which are at twice the sideband-tone detuning. For suitable choice of phase, this results in coherent cancellation of the pseudo-potential intermodulation term that oscillates at the sideband detuning. 2. When performing a DDMS gate, apply two additional tones at amplitude of sqrt(2VsbVc). These tones have equal and opposite detuning from the qubit frequency by half the sideband-tone detuning. For suitable choice of phase, this results in coherent cancellation of the pseudo-potential intermodulation term that oscillates at the sideband detuning. In a specific embodiment, the trapped ion system 101 may be configured to function as a 5-tone gate. The "5-tones" is descriptive of the control signal 108 comprising the five components: the first carrier component, the first and second sideband components, and the first and second adjustment frequency components. Cancellation of the 2nd order sideband-decoupling tone intermodulation via the microwave pseudo-potential in a DDMS-style two-qubit gate on ions (the 5 tone gate) may, for example, be achieved by one of the following: • Use two additional control signals that have frequency, amplitude, and difference-phase splitting set to cancel the sideband-decoupling tone intermodulation of the MS gate. The frequency difference between the additional signals matches the original frequency. However, their absolute frequency may be chosen to differ significantly. • Use two additional control signals that are at symmetrically around twice times the original sideband detuning. The above options may provide cancellation of the 2nd order sideband-decoupling tone intermodulation via signal chain non-linearities. Specifically, and in the present example, the additional two frequency components (the first and second adjustment frequency components) result in the five frequency components of the control signal 108 experiencing intermodulation that may produce a net zero force on the ion 104, or ions. With reference to Figure 8, embodiments of the present disclosure may provide the controller 106 configured to provide the control signal 108 to apply one or more adjustment frequency components at the frequency Af to directly cancel the offset force 113 arising through intermodulation of the control signal 108. Figure 12 shows example waveforms of the offset force 113 and the adjustment force 112 as may be experienced by the charged particle 103 in embodiments of the present disclosure. A timing graph 1200 shows the offset force 113 as it varies with time and a timing graph 1202 shows the adjustment force 112. In specific embodiments of the present disclosure, the one or more adjustment frequency components of the control signal 108 are 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 frequency components of the control signal 108 may provide the adjustment force 112 having a substantially equal amplitude and / or frequency to that of the offset force 113. In summary, embodiments of the present disclosure may apply electrical signals (through the control signal 108) to the ion trap 102 in order to drive qubit logic gates. These electrical signals produce undesired (effective) forces on the ion 102 through intermodulation effect when performing quantum logic gates. These forces are coherent with the electrical signals that are applied to the ion trap 102. We cancel the resulting forces experienced by the ion 102 by applying additional electrical signals (the one or more adjustment frequency components) through the same signal chain. These signals are coherent with the electrical signals used to drive the logic gate. The additional signals intermodulation with each other and the original signal driving the logic gate. This intermodulation results in cancellation of undesired frequency components in the (effective) force experienced by the ion 102. In specific embodiments of the present disclosure, may substantially cancel undesired intermodulation spectral content by applying additional high-frequency tones - these adjustment high-frequency tones then intermodulate with themselves and / or the control signal to coherently cancel the undesired intermodulation products. Additional advantages offered by this technique including the following: • Using the same signal chain as the logic signal results in improved stability of the cancellation. As dominant drifts will be common to both the quantum logic signal and additional tones. • As the signal produced by the quantum logic drive and the additional tones are applied via the same electrode and at comparable frequencies this technique is expected to result in adequate cancellation throughout the spatial extent of interest for a quantum charge-coupled device (QCCD) architecture. 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 first charged particle, the control system comprising a controller configured to:provide a control signal; wherein:the control signal comprises one or more adjustment frequency components for applying a first adjustment force to the first charged particle.

2. The control system of claim 1, wherein:the control signal generates electric and / or magnetic fields affecting the first charged particle; and / orthe one or more adjustment frequency components generates electric fields affecting the first charged particle.

3. The control system of claim 2, 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 the control signal; 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 frequency components.

4. The control system of any of claims 1 to 3, wherein the first charged particle experiences a first offset force.

5. The control system of claim 4, wherein the first offset force is generated through:intermodulation of the control signal; and / orponderomotive effects of the charged particle which arises from the control signal; and / ornon-linear components within the signal chain of the control signal.

6. The control system of claim 5, wherein the control signal comprises the one or more adjustment frequency components for applying the first adjustment force to the first charged particle to substantially cancel or otherwise reduce the first offset force.

7. The control system of claim 6, wherein the one or more adjustment frequency components use intermodulation and / or ponderomotive effects with themselves and / or other frequency components of the control signal.

8. The control system of claim 6 or 7, wherein the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having:an amplitude that is approximately equal to the amplitude of the first offset force; and / ora frequency that is approximately equal to the frequency of the first offset force.

9. The control system of claim 8, wherein the controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having a phase that is approximately out of phase with respect to the first offset force.

10. The control system of claim 6 or 7 comprising:a detection system configured to detect at least one characteristic of the first offset force experienced by the first charged particle; whereinthe controller is configured to provide the one or more adjustment signals based on the detected at least one characteristic of the first offset force.

11. The control system of claim 10, whereinthe at least one property of the first offset force comprises: an amplitude of the first offset force; and / or a frequency of the first offset force; andthe controller is configured to provide one or more adjustment frequency components for applying the first adjustment force having:an amplitude that is approximately equal to the amplitude of the first offset force, as detected by the detection system; and / ora frequency that is approximately equal to the frequency of the first offset force, as detected by the detection system.

12. The control system of any preceding claim wherein the first charged particle is a first ion.

13. The control system of claim 1 for a trapped ion system comprising an ion trap, wherein the first charged particle is a first ion.

14. The control system of claim 13, wherein, the control signal is for performing a first quantum gate operation on the first ion within the ion trap15. The control system of claim 13 or 14, wherein the controller is configured to: provide the first control signal for performing a second quantum gate operation on a second ion within the ion trap; wherein:the control signal comprises the one or more adjustment frequency components for applying a second adjustment force to the second ion.

16. The control system of claim 15, wherein the trapped ion system comprises a qubit manipulation system configured to encode a first qubit in the first ion and to encode a second qubit in the second ion.

17. The control system of claim 16, wherein the first and / or second quantum gate operations are multiple qubit gates.

18. The control system of claim 17, wherein the control signal comprises a first sideband component and a second sideband component for driving the multiple qubit gate.

19. The control system of claim 18, wherein the one or more adjustment frequency components are configured to substantially cancel at least a portion of the intermodulation resulting from the first and second sideband components.

20. The control system of claim 18 or 19, wherein the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component, the first and second adjustment frequency components being symmetrically at approximately three times the sideband detuning frequency.

21. The control system of claim 18 or 19, wherein the control signal comprises a first carrier component for generating dynamic decoupling.

22. The control system of claim 21, wherein:the one or more adjustment frequency components comprises a first adjustment frequency component and a second adjustment frequency component andthe first and second adjustment frequency components being symmetrically at approximately two or three times the sideband detuning frequency, or symmetrically at approximately half the sideband detuning frequency.

23. A trapped ion system comprising the control system of any preceding claim.

24. A quantum computer comprising trapped ion system of claim 23.

25. A method of manipulating a first charged particle using the control system of any of claims 1 to 22.34

Images