Method for managing thermal transients within a quantum computing system

Abstract

Maintaining constant temperature during the operation of a quantum computing system by a method comprising: applying at least one thermal management signal to the quantum computing system; and changin

Description

The present disclosure relates to a method for managing thermal transients within a quantum computing system. BACKGROUND It is known in the art that performing quantum operations (or quantum gates) on quantum computing systems (such as ion-trap chips) can cause temperature change across the system which leads to the quantum system being disturbed. As such, it is desirable to implement techniques to maintain a constant temperature in quantum computing systems. Some known methods include applying single-frequency signals (or tones) to a quantum system while the system is idle in order to maintain temperature stability between “idle” and "experiment times”; and applying a "pre-pulse” to warm up the system before being used for control signals, to minimise changes in amplifier gain. However, these techniques are limited to time-averaged power delivery over timescales of hundreds of microseconds or longer, relying on there being no significant thermal fluctuation on shorter timescales. These techniques are also limited to controlling power delivery between idle and experiment times. Other known methods include connecting two different sources to input ports of a switch forming part of a quantum computing system such that a first source can be used when the system is active and a second source can be used when the system is idle, in order to keep the temperature of the switch constant. As such, it is desirable to implement improved techniques to maintain a constant temperature in quantum computing systems by controlling power delivery on timescales shorter than or comparable to the length of typical quantum operations. SUMMARY In a first aspect of the disclosure, there is provided a method for operating a quantum computing system, the method comprising: applying at least one thermal management signal to the quantum computing system; and changing at least one parameter of the at least one thermal management signal based on a change in at least one parameter of an applied control signal; wherein the control signal indicates a control operation to be performed on the quantum computing system; and wherein the at least one parameter of the at least one thermal management signal and the at least one parameter of the control signal are controlled such that at least one property of the quantum computing system is maintained. Optionally, wherein the at least one property is a temperature Optionally, wherein the at least one parameter of the at least one thermal management signal is an amplitude; and wherein the at least one parameter of the control signal is an amplitude. Optionally, further comprising: decreasing or increasing the amplitude of the at least one thermal management signal from a first amplitude to a second amplitude in response to an amplitude of the control signal increasing; and increasing the amplitude of the control signal from a minimum amplitude to a predetermined amplitude. Optionally, further comprising: decreasing or increasing the amplitude of the at least one thermal management signal from the second amplitude to the first amplitude in response to the amplitude of the control signal decreasing; and increasing the amplitude of the control signal from the predetermined amplitude to the minimum amplitude. Optionally, wherein the changing of the at least one parameter is performed within a predetermined time period. Optionally, wherein the changing the at least one parameter is performed simultaneously with the changing of the control signal. Optionally, wherein the control signal is applied as a series of pulses. Optionally, wherein the at least one parameter of the at least one thermal management signal and the at least one parameter of the control signal are controlled such that a total power dissipation for the quantum computing system is maintained Optionally, wherein the at least one thermal management signal is applied based on a set of predetermined thermalization timescales of the quantum computing system; wherein the set of predetermined thermalization timescales comprise a minimum time period and a maximum time period for maintaining a stable temperature in the quantum computing system. Optionally, wherein the at least one thermal management signal is applied continuously when the quantum computing system is turned on. Optionally, wherein the at least one thermal management signal is applied continuously for a time period longer than the maximum time period. Optionally, wherein the continuous application of the at least one thermal management signal comprises temporary switch off time periods having a time period shorter than the minimum time period by a predefined threshold; wherein the temporary switch off time periods are a period of time when the at least one thermal management signal is not applied to the quantum computing system. Optionally, wherein the predetermined time period is a time period shorter than the minimum time period. Optionally, wherein the amplitude of the at least one thermal management is changed according one of a plurality of preset crossfade modes; wherein the plurality of preset crossfade modes each comprise a set of values to define the at least one thermal management signal. Optionally, wherein the set of values includes at least one of a frequency and an amplitude. Optionally, wherein the at least one thermal management signal includes two thermal management signals. Optionally, wherein the quantum computing system comprises at least one quantum mechanical system; and wherein the at least one quantum mechanical system is at least one trapped-ion qubit. Optionally, wherein at least one parameter of the at least one thermal management signal is configured such that interaction between the at least one thermal management signal and the at least one quantum bit is minimized. Optionally, wherein configuring the at least one parameter comprises: determining a relative amplitude of the at least one thermal management signal by measuring an effect of the at least one thermal management signal on a frequency of the at least one trapped-ion qubit; and adjusting the at least one parameter of the at least one thermal management based on the determined relative amplitude. Optionally, wherein the at least one parameter comprises a frequency and an amplitude; wherein the frequency is detuned symmetrically from a frequency of the at least one trapped-ion qubit; and wherein the amplitude is calibrated to be equal at each position of the at least one trapped-ion qubit. Optionally, wherein the control operation is at least one of: state preparation, transport, loading, a quantum operation, a cooling operation, or a readout operation. BRIEF DESCRIPTION OF THE DRAWINGS The disclosure is described in further detail below by way of example and with reference to the accompanying drawings, in which: figure 1 is a flowchart illustrating a method for operating a quantum computing system; figure 2 is a signal flow diagram; figure 3 is a diagram illustrating timescales for operating a quantum computing system; figure 4 is a graph illustrating an example of operating a quantum computing system; and figure 5 is a graph illustrating a further example of operating a quantum computing system. DETAILED DESCRIPTION The following text will refer to a "quantum computing system” which refers to a device which utilises quantum physics in order to perform computations or simulations, or to store data. Quantum computing systems may utilise two-state quantum mechanical systems (qubits), three-state quantum mechanical systems, four-state systems, and quantum mechanical continuous variable systems. In some examples, the quantum mechanical systems may be controlled using "all-electronic control” wherein the quantum mechanical systems are controlled by applying voltages or currents to generate electric or magnetic fields. In other examples, the quantum mechanical systems may additionally be controlled using optical devices such as lasers. The quantum mechanical systems are controlled to perform control operations, or quantum gates, or when the system is simply idle. The quantum computing system further refers to a set of equipment, and the peripherals needed to control the equipment, as well as the quantum mechanical systems described above. That is, in addition to the quantum mechanical systems, the quantum computing system may also comprise trap chips or the like, mounting plates, wires or cables, cryogenic equipment, electronic devices or equipment configured to control the quantum mechanical systems, and the like. The quantum mechanical systems may, for example, be ions trapped by ion-traps;. The ion-traps may be formed (or mounted) on chips (so called "ion-trap chips”) In other examples, different quantum-mechanical systems may be used, such as quantum dots, nitrogen vacancy (NV) centres, photonic qubits, neutral atom systems and superconducting systems. The following text will refer to "maintain a constant temperature across components of the quantum computing system”, which refers to the management of thermal transients (transient behaviour that changes as temperature changes) across temperature-critical components. In some examples, it may not be necessary to maintain a constant temperature across the whole of the quantum computing system but rather across one or more (or several interconnected) components or parts. It should be understood that maintaining a constant temperature refers to keeping the temperature stable and thus preventing significant temperature change, and insignificant changes in temperature are anticipated. For example, maintaining constant temperature across the quantum computing system might be accomplished by maintaining a constant level of power dissipation throughout the running time of the quantum computing system. Figure 1 is a flowchart illustrating a method for operating a quantum computing system. The method comprises the following steps. In step SI 10, at least one thermal management signal is applied to the quantum computing system. The at least one thermal management signal may also be referred to as a "warm-up tone” and is used to maintain a stable temperature in the quantum computing system. That is, the at least one thermal management signal is used to prevent the introduction of thermal transients into the quantum computing system. For example, thermal transients may be introduced into the quantum computing system when a signal is applied to the system in order to perform a quantum operation. The at least one thermal management signal may include one or more thermal management signals. For example, two thermal management signals may be used. In another example, a plurality of thermal management signals may be used. In some examples, the at least one thermal management signal may be an oscillating current applied to an electrode of the quantum computing system (for example, the electrode may be included on the ion-trap chip) which generates an electromagnetic field, wherein the magnetic part of the electromagnetic field interacts with at least one quantum mechanical system of the quantum computing system when the control signal is applied. The addition of the at least one thermal management signal ensures that the same amount of power is dissipated whether or not the control signal is applied. A purpose of the at least one thermal management signal is to provide thermal management while limiting direct interaction with the quantum mechanical systems of the quantum computing system to a minimum. That is, ideally the at least one thermal management signal would not have any direct interaction with the quantum mechanical systems however, in practice some residual interaction may remain. In some examples, the at least one thermal management signal may be a beam of light such as a laser. In further examples, the at least one thermal management signal may have a frequency in the microwave range. In yet further examples, the at least one thermal management signal may be a direct current (DC), or applied voltage. In step S120, at least one parameter of the at least one thermal management signal is changed in response to a change in at least one parameter of an applied control signal. The control signal is a signal that indicates a control operation to be performed on the quantum computing system. The control operation may be, for example, a quantum gate, in which case the control signal may also be referred to as a "gate tone”. Alternatively or additionally, the control operation may be an operation such as cooling, readout, or transport. In some examples, more than one control signal may be used. For example, two or more (or a plurality) of control signals may be used. The at least one parameter of the at least one thermal management signal may be, for example, an amplitude. In another example, the at least one parameter of the at least one thermal management signal may be a frequency. For example, the at least one parameter may be changed in response to a control signal being applied to the quantum computing system, for example, at least one parameter of the control signal increasing from a zero value. In other examples, the at least one parameter of the at least one thermal management signal may be changed in response to a parameter of the control signal increasing or decreasing, or an average value of a parameter of the control signal changing over a predefined period of time. For example, the control signal may be applied as a series of pulses, wherein the maximum amplitude of the pulses decreases over time; thus, the at least one thermal management signal may be changed based on the average decrease in amplitude of the pulses of the control signal over time. For example, the amplitude of the at least one thermal management signal may be decreased when the application of the control signal causes an increase in temperature of the system. Thus, in another example, the amplitude of the at least one thermal management signal may be increased when the application of the control signal causes a decrease in temperature of the system. That is, the amplitude of the at least one thermal management signal is changed (increased or decreased) based on an effect the control signal has on the temperature of the system, such that the temperature of the system, or the temperature of specific temperature-critical components, is maintained. In more detail, in the case that increasing an amplitude of the control signal causes an increase in temperature in temperature-critical components of the quantum computing system, a default amplitude of the at least one thermal management signal may be calibrated such that when the control signal is applied, the amplitude of the at least one thermal management signal can be decreased in order to maintain the temperature of the temperature-critical components of the quantum computing system. Similarly, in the case that increasing an amplitude of the control signal would cause a decrease in temperature in temperature-critical components of the quantum computing system, the default amplitude of the at least one thermal management signal maybe calibrated such that when the control signal is applied, the amplitude of the at least one thermal management signal is increased in order to maintain the temperature of the temperature-critical components of the quantum computing system. That is, the at least one thermal management signal is controlled dynamically such that it is adapted to changes in the control signal; parameters of the at least one thermal management signal are changed to account for a thermal effect caused by a change in the control signal. In an example, the amplitude, or other parameter, of the at least one thermal management signal may be changed (for example, decreased or increased) from a first value to a second value such that the amplitude of the at least one thermal management signal is ramped down over a period of time. That is, the amplitude of the at least one thermal management signal may be decreased or increased by a predefined rate such that thermal change across the quantum computing system is minimal. The amplitude, or other parameter of the at least one thermal management signal may be changed (to the second value) at the same time as an amplitude of the control signal is increased. That is, for example, the amplitude of the at least one thermal management signal may be ramped down or up at the same time that the amplitude of the control signal is ramped up. Each time the control signal is changed, the at least one management signal may also be changed. For example, the amplitude of the control signal may be ramped down at the same time as the amplitude of the at least one thermal management signal may be ramped up. The rate at which the amplitude of the at least one thermal management signal is decreased may be the same as the rate at which the amplitude of the control signal is increased. Figure 2 is a flowchart representing a signal flow. The at least one thermal management signal is generated (or originates) at a source 201. The source may be a current or voltage source, an arbitrary waveform generator (AWG) or a direct digital synthesiser (DDS). The control signal may also be generated by the source 201 or, alternatively, may be generated by a separate source (not shown). The at least one thermal management signal may then be directed through (or pass through) at least one component 202 before being received by an input port 203 of the quantum computing system. The at least one component 202 may include an amplifier, a filter, a resonator, and the like. The input port 203 may be, for example, an electrode included in an ion-trap chip. The at least one thermal management signal may pass through the same path as the control signal, wherein the path may be known as the signal chain. Alternatively, the at least one thermal management signal may pass through a different signal chain to the control signal. For example, each thermal management signal may have a set of parameters which are set differently. The set of parameters may, for example, include amplitude and frequency, which may each be different to an amplitude and frequency of the control signal (or each control signal, in cases where there are a plurality of control signals). The amplitude and frequency of each signal may be controlled individually. For example, parameters of each thermal management signal may be set such that interaction with a state of each quantum mechanical system of the quantum computing system is minimised. The parameters of each thermal management signal may include frequency, amplitude, and polarisation. For example, the frequency of each thermal management signal may be set such that resonance with the quantum mechanical system of the quantum computing system is avoided. For example, in the case that the quantum mechanical system is a trapped-ion qubit, the frequency of each thermal management signal may be chosen such that there is no resonance with any motional mode of the ion. In some examples, the parameters of each thermal management signal may be set to adjust off-resonant shifts of transitions associated with the quantum mechanical systems of the quantum computing system. In some examples, relative amplitudes of each thermal management signal may be determined by directly measuring an effect of the thermal management signals on a frequency of the quantum mechanical system. For example, each thermal management signal may change the frequency by an amount based on parameters such as frequency and amplitude. For example, for a qubit (a two-state quantum mechanical system) implemented using two 4S1 / 2 ground states of a 40Ca+ ion, two signals which generate magnetic fields at the position of one or more ions may be applied with frequencies detuned symmetrically from the qubit frequency and amplitudes may be calibrated to be equal at the locations of the ions such that the total AC Zeeman shift on the qubit frequency is minimised. Any residual AC Zeeman shift is sensitive only to differential fluctuations in amplitude between the thermal management signals. Thus, electronic and / or motional states of the qubit are not significantly disturbed by the presence of the at least one thermal management signal. In an alternative example, an analogous shift can be accounted for when laser beams are being used, an AC Stark shift. In other examples, a qubit may be implemented using a pair of electronic states in a 137Ba+ ion. Each column in the tables 1 and 2 below shows the frequencies F_M and F_aux and relative voltage V_aux / V_M of two thermal management signals that may be applied to an ion trap in order to minimise their overall AC Zeeman shift on a 5 metastable qubit in the 5D5 / 2 manifold of a 137Ba+ ion. The left column refers to a qubit formed using the F=2, mF=-2 <-> F=3, mF=-2 states in an external magnetic field of magnitude 20.048 G. The right column refers to a qubit formed using the F=2, mF=0 <-> F=3, mF=0 states in an external magnetic field of magnitude 18.483 G. The "fractional adjustment" refers to the fractional reduction in AC Zeeman shift relative 10 to what the AC Zeeman shift would be with only the signal at frequency F_M. F=2, mF=-2«-^F=3, mp=-2 metastable 137Ba+ qubit Fm 32.6 MHz Faux 126.9 MHz Vaux / Vm 0.87 Fractional Adjustment 7.9e-6 Table 1 F=2, mp=(WF=3, m.==0 metastable 137Ba+ qubit Fm 24.6 MHz Faux 103.3 MHz Vaux / Vm 0.78 Fractional Adjustment 3.4e-6 Table 2 The total amplitude of the thermal management signals may be predefined (or set) by monitoring a temperature of a 4K stage of a cryogenic system of the quantum computing system when switching between two conditions in order to minimise temperature changes. For example, the two conditions may be a continual application of the thermal management signals and an application of a control signal (this may be a control signal of any kind, and may include more than one control signal). The total amplitude may then be adjusted until there is no measurable temperature difference under the two conditions. The result of the adjustment can be checked by monitoring a temperature of the 4K stage temperature when switching between the thermal management signals and the control signal. Thus, the at least one thermal management signal may be adjusted to manage effects on the quantum computing system other than thermal transients. For example, as described above, the at least one thermal management signal may also be adjusted to minimise AC Zeeman shift and the like. Figure 3 is a diagram illustrating an example of the method for operating a quantum computing system as discussed with regard to Figure 1. Operating time (t) represents the total time that the quantum computing system is switched on, including idle periods (for example, periods between experiments when the ions are still trapped and being cooled) and periods wherein control operations are being performed (periods when a control signal is being applied). The solid line represents a control signal (such as the control signal of Figure 1), wherein the control signal is received at time tl. At time t2, the control signal may be interrupted for a period of time, t2 to t3, before being received again at time t3. At time t4, the control signal may stop, the control operation having been performed. The line tmax represents a thermalisation timescale representing a maximum time period that the control signal may be applied to be taken into consideration when maintaining a stable temperature in the quantum computing system. The line tmin represents a thermalisation timescale representing a minimum time period to be taken into consideration when maintaining a stable temperature in the quantum computing system. For example, the at least one thermal management signal is applied based on a set of predefined thermalization timescales of the quantum computing system, wherein the set of predetermined thermalization timescales comprise a minimum time period and a maximum time period for maintaining a stable temperature in the quantum computing system. The dot-dashed line represents the at least one thermal management signal (such as the at least one thermal management signal discussed with regard to Figure 1). In the illustrated example, the at least one thermal management signal is applied for the total time that the quantum computing system is switched on, including idle periods and periods when the control signal is being applied. That is, the at least one thermal management signal is applied continuously when the quantum computing system is turned on. The continuous application of the at least one thermal management signal may include interruptions wherein the at least one thermal management signal stops being applied for a period of time. That is, the continuous application of the at least one thermal management signal comprises temporary switch off time periods having a time period shorter than the minimum time period by a predefined threshold, wherein the temporary switch off time periods are a period of time when the at least one thermal management signal is not applied to the quantum computing system. In order to maintain a stable temperature (or minimise thermal transients) across the quantum computing system, the at least one thermal management signal is applied such that the time it is applied is longer than tmax (tsstable»tmax) (for example, the at least one thermal management signal is applied continuously for a time period longer than the maximum time period) and such that any breaks or interruptions in the application of the at least one thermal management signal and / or control signal is shorter than tmin (tbreak«tmin). That is, the at least one thermal management signal is applied by keeping a total power dissipation of the quantum computing system stable (or maintained) such that the total power dissipation does not change significantly for a time longer than tmin at any time during the operating time of the quantum computing system. As such, it is ensured that the at least one thermal management signal is applied such that temperature change across the quantum computing system is minimised. For example, the at least one thermal management signal may be applied such that the period of time over which it is applied is longer than tmax by a predetermined amount of time (or indefinitely). Similarly, the at least one thermal management signal may be applied such that interruptions in the application of the at least one thermal management signal are ensured to be shorter than tmin by a predetermined amount of time. For example, at time t5, the at least one thermalisation signal may be interrupted for a period of time, t5 to t6, before being applied again at time t6. The time period t5 to t6 is shorter (preferably, much shorter) than the time tmin, such that no change in temperature is caused by the pause in the application of the at least one thermal management signal. In some examples (not illustrated), the at least one thermal management signal may be applied in pulses, wherein the length of the pulses is such that the at least one thermal management signal is applied for at least a period of time that is longer (preferably much longer) than tmax and such that the pause between pulses is shorter (preferably much shorter) than tmin. For example, the at least one thermal management signal may be applied as a plurality of pulses wherein the length of the pulse is longer than tmax (for example, tpulse»tmax) and wherein the period of time between pulses is shorter than tmin (for example, tpausecctmin). In another example, the at least one thermal management signal may be applied as a plurality of pulses wherein the length of a first pulse is longer than tmax and the length of subsequent pulses is shorter than tmax, and wherein the period of time between pulses is shorter than tmin. Figure 4 shows a graph representing a change in amplitude over time of the control signal and at least one thermal management signal. Following on from Figure 3, the control signal is represented by the solid line and the at least one thermal management signal is represented by the dot-dashed line. It can be seen that the at least one thermal management signal begins at a first amplitude (in this example, a maximum amplitude (Max)). At time tl, the amplitude of the at least one thermal management signal begins to decrease. The amplitude of the at least one thermal management signal is decreased to a minimum amplitude (Min) over a time period of tl to t2. As such, the decrease in amplitude is ramped, as can be seen in the dot-dashed line. In some examples, the amplitude of the at least one thermal management signal may be decreased to a minimum amplitude of zero. It should be understood that "a zero amplitude" or "amplitude of zero" may not refer merely to an amplitude of precisely zero and may also refer to an amplitude that causes an insignificant interaction with the at least one quantum mechanical system of the quantum computing system. That is, “a zero amplitude” or “amplitude of zero” may refer to an insignificant amplitude, wherein the amplitude causes a thermal change so small as to be considered insignificant to the quantum computing system or temperature-critical components of the quantum computing system. Alternatively, the amplitude of the at least one thermal management signal may be decreased in proportion to a change temperature change caused by the application of a given control signal. For example, if an applied control signal would cause only a small change in temperature in the quantum computing system, the amplitude of the at least one thermal management signal may decrease from a first amplitude to a second amplitude, wherein the second amplitude is not a near-zero or insignificant value. At time tl, when the amplitude of the at least one thermal management signal begins to decrease, the amplitude of the control signal begins to increase from the minimum amplitude [Min]. The amplitude of control signal increases to a second amplitude (in this example, the maximum amplitude (Max), however the maximum amplitude for the at least one thermal management signal and the control signal may not be the same in different examples) over a time period of tl to t2. The rate at which the amplitude of the control signal increases is the same as the rate at which the amplitude of the at least one thermal management signal decreases. At time t2 to t3, the control signal has maximum amplitude and control operations are performed. It should be understood that the amplitude of the control signal may vary in amplitude in the time period t2 to t3. For example, the amplitude may change a small amount for a short time such that no significant effect is had on the temperature of the quantum computing system (or specific temperature-critical components of the quantum computing system) and no corresponding change in thermal management signal is required. At time t3, the control operations end and the amplitude of the control signal begins to decrease while the amplitude of the at least one thermal management signal begins to increase. Over the period t3 to t4, the amplitude of the control signal decreases from the maximum amplitude to the minimum amplitude while the amplitude of the at least one thermal management signal increases from the minimum amplitude to the maximum amplitude. The rate at which the control signal decreases from the maximum amplitude to the minimum amplitude is the same as the rate at which the at least one thermal management signal increases from the minimum amplitude to the maximum amplitude. The example shown in Figure 4 is merely exemplary and it should be understood that the rate of increase / decrease of amplitude of the at least one thermal management signal and the control signal may be changed based on the control operations to be performed, the nature of the quantum computing system, and the like. It should be further understood that the rate of increase / decrease of amplitude of the at least one thermal management signal and the rate of increase / decreasing of amplitude of the control signal may be different. Additionally, the minimum amplitude and maximum amplitude of the control signal may be different from a total minimum amplitude and maximum amplitude of the at least one thermal management signal. The shape of the ramp is not limited to that shown in the graph of Figure 3, and it should be understood that the ramp can be shaped in multiple different ways according to an analytic expression calculated for how the signals should change. It should be understood that any shape of ramp can be used. In preferable examples, the ramping may be smooth (changing in a continuous and regular way). The different ramp shapes correspond to a plurality of different crossfade modes. The crossfade modes each represent a set of pre-set values (such as amplitude and frequency or the like) to define the control signal and to control the behaviour of the at least one thermal management signal relative to the control signal in order to maintain a constant temperature across the quantum computing system. For example, maintaining constant temperature across the quantum computing system might be accomplished by maintaining a constant level of power dissipation throughout the running time of the quantum computing system. Example crossfade modes include, for the control signal, smooth ramps (such as the sine-squared example discussed in detail with regard to Figure 5), square pulse, or a linear ramp (such as the example shown with regard to Figure 4) and the like. With regard to the at least one thermal management signal, the pulse shapes may be determined according to a predefined rule. For example, the pulse shapes may be defined such that the total sum squared amplitude (which would, for example, be weighted according a calculated correction factor for each signal) is constant throughout the operating time of the quantum computing system. It should be understood that although the graph of Figure 4 shows the signals (the control signal and the at least one thermal management signal) increasing and decreasing at the same rate, there may be differences in the rate of increase and decrease. For example, the control signal and the at least one thermal management signal may increase and / or decrease at different rates, as long as a constant temperature is maintained across the quantum computing system. In some examples, wherein the at least one thermal management signal includes two or more thermal management signals, the thermal management signals may each increase and / or decrease at different rates. It should further be understood that although the graph of Figure 4 shows the control signal and the at least one thermal management signal having the same maximum and minimum amplitude, in some examples the control signal may have a different maximum and / or minimum amplitude to the at least one thermal management signal. In some examples, wherein the at least one thermal management signal includes two or more thermal management signals, the thermal management signals may each have a different maximum and / or minimum amplitude. Figure 5 is a graph representing a change in amplitude over time of the control signal and at least one thermal management signal. Figure 5 represents an example utilising a "sine-squared ramp” with a "sum-squared crossfade", or, when correction factors for each signal are considered, a “weighted sum-squared crossfade”. In this example, there are two thermal management signals, 501 and 502, and a control signal 503. In more detail, in order for the quantum computing system to perform a control operation, in this example, a quantum operation (or "gate operation”), the control signal 503 maybe increased (or ramped) smoothly from a minimum amplitude (the minimum amplitude for the control signal 503) to an amplitude a3(t=tramp). In this example, the control signal 503 is ramped according to a sine-squared shape that is defined by equation 1: CO C^ ^ramp) Sin Tit ^ramp 12 [1] Thus, a rule must be defined also for controlling the amplitudes of the two thermal management signals 501 and 502. As discussed with regard to Figures 1 to 4, in order to maintain a constant temperature for the quantum computing system, the total power dissipation for all signals must be controlled. The power P dissipated for each tone is proportional to the amplitude of said tone, with a proportionality constant c which is different for each signal, according to equation 2: Pf(t) = c?af(t)2 (2) Thus, equation 3 must be satisfied: ¢0 + ^2(0 + = const = P,(0) + P2(0) (3) From equation 3, analytic expressions for how the amplitudes of the two thermal management signals 501 and 502 must change as the control signal 503 ramps up. These analytic expressions (equations 4 and 5] are as follows: ai^ a2(t) = ka^t) (5) where k is defined as the ratio of the initial amplitudes of the two thermal management signals. Figure 5 shows the amplitude of the control signal 503 increasing (ramping) from an amplitude of 0 to 0.4 with a sine-squared profile, according to equation 1, and the amplitude of the two thermal management signals 501,502 decreasing from 0.3 and 0.36 respectively. In this example, the quantum computing system operates in a mode wherein a squared sum of the amplitudes of the at least one thermal management signal and the control signal is maintained. The squared sum of the amplitudes is proportional to the total power of each of the signals involved (the control signal and the at least one thermal management signal), and can be adjusted (or corrected) based on differences in thermal response of the components involved in the different frequencies of the signals. In more detail, although the power of each signal input to the quantum computing system is proportional to the square of the amplitude of the signal, there exists an unknown proportionality constant. The proportionality constant is determined by measuring a temperature response of the quantum computing system to determine relative weighting of the amplitudes of signals to be input. For example, the quantum computing system may comprise a resonator component, wherein the at least one thermal management signal and the control signal pass through the resonator component. The resonator component may be frequency dependent, such that for a specific amplitude of an input signal, an output amplitude of an output signal is higher if the frequency of the input signal is comparable (or close to) a central frequency of the resonator component That is, in the case that the central frequency of the resonator component is a value fO, a first input signal with a frequency of fO may be input to the resonator component in order to measure the effect of the fO input signal on components downstream of (or beyond) the resonator. Based on a change in the temperature caused by the signal (for example, the temperature may be raised by a value, TO), a second input signal may be input to the resonator, the second input signal having a frequency fl, wherein fl is different to fO. A temperature response based on the second input signal can then be measured. For example, the second input signal may increase the temperature by a value Tl. In this case, it is thereby determined that to keep the temperature substantially constant when switching between signals with frequencies of fO and fl, the input amplitude of an input signal with a frequency of fl must be scaled by T0 / T1. Thus, the input amplitude can be controlled in order to measure the effect of the output amplitude on a temperature of temperature-critical components of the quantum computing system. Thus, a frequency dependent correction factor can be determined for each input frequency to account for the thermal response of the resonator component. It should be understood that in different examples, the control signal 503 may not be ramped smoothly. The control signal 503 may not start at a zero amplitude and may start at a non-zero amplitude. Similarly, the thermal management signals may not decrease to a zero amplitude and may decrease to a value wherein a temperature of the quantum computing system is maintained. Various improvements and modifications may be made to the above without departing from the scope of the disclosure.

Claims

1. A method for operating a quantum computing system, the method comprising:applying at least one thermal management signal to the quantum computing system; andchanging at least one parameter of the at least one thermal management signal based on a change in at least one parameter of an applied control signal;wherein the control signal indicates a control operation to be performed on the quantum computing system; andwherein the at least one parameter of the at least one thermal management signal and the at least one parameter of the control signal are controlled such that at least one property of the quantum computing system is maintained.

2. The method of claim 1, wherein the at least one property is a temperature.

3. The method of claim 1, wherein the at least one parameter of the at least onethermal management signal is an amplitude; andwherein the at least one parameter of the control signal is an amplitude.

4. The method of claim 3, further comprising:decreasing or increasing the amplitude of the at least one thermal management signal from a first amplitude to a second amplitude in response to an amplitude of the control signal increasing; andincreasing the amplitude of the control signal from a minimum amplitude to a predetermined amplitude.

5. The method of claim 4, further comprising:decreasing or increasing the amplitude of the at least one thermal management signal from the second amplitude to the first amplitude in response to the amplitude of the control signal decreasing; andincreasing the amplitude of the control signal from the predetermined amplitude to the minimum amplitude.

6. The method of any preceding claim, wherein the changing of the at least one parameter is performed within a predetermined time period.

7. The method of any preceding claim, wherein the changing the at least oneparameter is performed simultaneously with the changing of the control signal.

8. The method of any preceding claim, wherein the control signal is applied as a series of pulses.

9. The method of any preceding claim, wherein the at least one parameter of the at least one thermal management signal and the at least one parameter of the control signal are controlled such that a total power dissipation for the quantum computing system is maintained10. The method of any preceding claim, wherein the at least one thermal management signal is applied based on a set of predetermined thermalization timescales of the quantum computing system;wherein the set of predetermined thermalization timescales comprise a minimum time period and a maximum time period for maintaining a stable temperature in the quantum computing system.

11. The method of any preceding claim, wherein the at least one thermal management signal is applied continuously when the quantum computing system is turned on.

12. The method of claims 11, wherein the at least one thermal management signal is applied continuously for a time period longer than the maximum time period.

13. The method of claims 10 and 11, wherein the continuous application of the at least one thermal management signal comprises temporary switch off time periods having a time period shorter than the minimum time period by a predefined threshold;wherein the temporary switch off time periods are a period of time when the at least one thermal management signal is not applied to the quantum computing system.

14. The method of claims 10 to 12, wherein the predetermined time period is a time period shorter than the minimum time period.

15. The method of claim 1, wherein the amplitude of the at least one thermal management is changed according one of a plurality of preset crossfade modes;wherein the plurality of preset crossfade modes each comprise a set of values to define the at least one thermal management signal.

16. The method of claim 15, wherein the set of values includes at least one of a frequency and an amplitude.

17. The method of claim 1, wherein the at least one thermal management signal includes two thermal management signals.

18. The method of any preceding claim, wherein the quantum computing system comprises at least one quantum mechanical system; andwherein the at least one quantum mechanical system is at least one trappedion qubit.

19. The method of any preceding claim, wherein at least one parameter of the at least one thermal management signal is configured such that interaction between the at least one thermal management signal and the at least one quantum mechanical system is minimized.

20. The method of claim 18, wherein configuring the at least one parameter comprises:determining a relative amplitude of the at least one thermal management signal by measuring an thermal effect of the at least one thermal management signal 5 on a frequency of the at least one trapped-ion qubit; andadjusting the at least one parameter of the at least one thermal management based on the determined relative amplitude.

21. The method of claim 20, wherein the at least one parameter comprises a 10 frequency and an amplitude;wherein the frequency is detuned symmetrically from a frequency of the at least one trapped-ion qubit; andwherein the amplitude is calibrated to be equal at each position of the at least one trapped-ion qubit.1522. The method of claim 1, wherein the control operation is at least one of: state preparation, transport, loading, a quantum operation, a cooling operation, or a readout operation.

Images