Method for managing thermal transients within a quantum computing system

Abstract

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 5 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 0 maintained.

Description

[0001]METHOD^FOR^MANAGING^THERMAL^TRANSIENTS^WITHIN^A^QUANTUM^ COMPUTING^SYSTEMThe present disclosure relates to a method for managing thermal transients withina quantum computing system. BACKGROUND It is known in the art that performing quantum operations (or quantum gates) onquantum computing systems (such as ion-trap chips) can cause temperature changeacross 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 aquantum 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 thesystem before being used for control signals, to minimise changes in amplifier gain.However, these techniques are limited to time-averaged power delivery overtimescales of hundreds of microseconds or longer, relying on there being nosignificant thermal fluctuation on shorter timescales. These techniques are alsolimited to controlling power delivery between idle and experiment times.Other known methods include connecting two different sources to input ports of aswitch forming part of a quantum computing system such that a first source can beused 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 constanttemperature in quantum computing systems by controlling power delivery ontimescales shorter than or comparable to the length of typical quantum operations. SUMMARYIn a first aspect of the disclosure, there is provided a method for operating aquantum computing system, the method comprising: applying at least one thermalmanagement signal to the quantum computing system; and changing at least oneparameter of the at least one thermal management signal based on a change in atleast one parameter of an applied control signal; wherein the control signal indicatesa 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 leastone 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 leastone thermal management signal from a first amplitude to a second amplitude inresponse to an amplitude of the control signal increasing; and increasing theamplitude of the control signal from a minimum amplitude to a predeterminedamplitude.Optionally, further comprising: decreasing or increasing the amplitude of the at leastone thermal management signal from the second amplitude to the first amplitude inresponse to the amplitude of the control signal decreasing; and increasing theamplitude 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 timeperiod shorter than the minimum time period by a predefined threshold; whereinthe 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 ischanged according one of a plurality of preset crossfade modes; wherein theplurality 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 onequantum mechanical system; and wherein the at least one quantum mechanicalsystem is at least one trapped-ion qubit.Optionally, wherein at least one parameter of the at least one thermal managementsignal is configured such that interaction between the at least one thermalmanagement signal and the at least one quantum bit is minimized.Optionally, wherein configuring the at least one parameter comprises: determininga 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 leastone trapped-ion qubit; and adjusting the at least one parameter of the at least onethermal 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 theat least one trapped-ion qubit; and wherein the amplitude is calibrated to be equalat 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^DESCRIPTIONThe following text will refer to a “quantum computing system” which refers to adevice 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-electroniccontrol” wherein the quantum mechanical systems are controlled by applyingvoltages or currents to generate electric or magnetic fields. In other examples, the quantum mechanical systems may additionally be controlled using optical devicessuch as lasers. The quantum mechanical systems are controlled to perform controloperations, 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”) Inother examples, different quantum-mechanical systems may be used, such asquantum dots, nitrogen vacancy (NV) centres, photonic qubits, neutral atomsystems and superconducting systems.The following text will refer to “maintain a constant temperature acrosscomponents of the quantum computing system”, which refers to the management ofthermal transients (transient behaviour that changes as temperature changes)across temperature-critical components. In some examples, it may not be necessaryto maintain a constant temperature across the whole of the quantum computing system but rather across one or more (or several interconnected) components orparts. It should be understood that maintaining a constant temperature refers tokeeping the temperature stable and thus preventing significant temperature change,and insignificant changes in temperature are anticipated. For example, maintainingconstant 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 computingsystem. The method comprises the following steps. In step S110, 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 thermalmanagement 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 leastone quantum mechanical system of the quantum computing system when thecontrol signal is applied. The addition of the at least one thermal management signalensures that the same amount of power is dissipated whether or not the controlsignal is applied. A purpose of the at least one thermal management signal is toprovide thermal management while limiting direct interaction with the quantummechanical systems of the quantum computing system to a minimum. That is, ideallythe 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 oflight such as a laser. In further examples, the at least one thermal management signalmay 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 signalis 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 may be 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 thermalmanagement signal may be changed (for example, decreased or increased) from afirst value to a second value such that the amplitude of the at least one thermalmanagement signal is ramped down over a period of time. That is, the amplitude ofthe at least one thermal management signal may be decreased or increased by apredefined rate such that thermal change across the quantum computing system is minimal.The amplitude, or other parameter of the at least one thermal management signalmay be changed (to the second value) at the same time as an amplitude of the controlsignal is increased. That is, for example, the amplitude of the at least one thermalmanagement signal may be ramped down or up at the same time that the amplitudeof 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 source201. The source may be a current or voltage source, an arbitrary waveformgenerator (AWG) or a direct digital synthesiser (DDS). The control signal may alsobe generated by the source 201 or, alternatively, may be generated by a separatesource (not shown).The at least one thermal management signal may then be directed through (or passthrough) at least one component 202 before being received by an input port 203 ofthe quantum computing system. The at least one component 202 may include anamplifier, 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 managementsignal may pass through the same path as the control signal, wherein the path maybe known as the signal chain. Alternatively, the at least one thermal managementsignal may pass through a different signal chain to the control signal.For example, each thermal management signal may have a set of parameters whichare set differently. The set of parameters may, for example, include amplitude andfrequency, which may each be different to an amplitude and frequency of the controlsignal (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 setto 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 frequencyby 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 / 2ground states of a 40Ca+ ion, two signals which generate magnetic fields at theposition of one or more ions may be applied with frequencies detunedsymmetrically 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 thepresence 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 a137Ba+ ion. Each column in the tables 1 and 2 below shows the frequencies F_M andF_aux and relative voltage V_aux / V_M of two thermal management signals that maybe applied to an ion trap in order to minimise their overall AC Zeeman shift on a 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 to what the AC Zeeman shift would be with only the signal at frequency F_M. F=2, mF=-2↔F=3, mF=-2 metastable 137Ba+qubit FM32.6 MHz FAUX 126.9 MHz VAUX / VM 0.87 Fractional 7.9e-6 Adjustment Table 1 Table 2The 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 quantumcomputing system when switching between two conditions in order to minimisetemperature changes. For example, the two conditions may be a continualapplication 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 controlsignal). The total amplitude may then be adjusted until there is no measurabletemperature difference under the two conditions. The result of the adjustment canbe 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 effectson 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 quantumcomputing system as discussed with regard to Figure 1. Operating time (t) represents the total time that the quantum computing system isswitched on, including idle periods (for example, periods between experimentswhen the ions are still trapped and being cooled) and periods wherein controloperations 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 t1. 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 timeperiod that the control signal may be applied to be taken into consideration when maintaining a stable temperature in the quantum computing system. The line tminrepresents a thermalisation timescale representing a minimum time period to betaken 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 timeperiod and a maximum time period for maintaining a stable temperature in thequantum 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 forthe total time that the quantum computing system is switched on, including idleperiods and periods when the control signal is being applied. That is, the at least onethermal management signal is applied continuously when the quantum computingsystem is turned on. The continuous application of the at least one thermalmanagement signal may include interruptions wherein the at least one thermalmanagement signal stops being applied for a period of time. That is, the continuousapplication 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) acrossthe quantum computing system, the at least one thermal management signal isapplied such that the time it is applied is longer than tmax (tsstable>>tmax) (forexample, the at least one thermal management signal is applied continuously for atime period longer than the maximum time period) and such that any breaks orinterruptions in the application of the at least one thermal management signaland / or control signal is shorter than tmin (tbreak<<tmin). That is, the at least onethermal 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 thatthe period of time over which it is applied is longer than tmax by a predeterminedamount of time (or indefinitely). Similarly, the at least one thermal managementsignal may be applied such that interruptions in the application of the at least onethermal 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 fora period of time, t5 to t6, before being applied again at time t6. The time period t5 tot6 is shorter (preferably, much shorter) than the time tmin, such that no change intemperature 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 maybe applied in pulses, wherein the length of the pulses is such that the at least onethermal 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 isshorter (preferably much shorter) than tmin. For example, the at least one thermalmanagement signal may be applied as a plurality of pulses wherein the length of thepulse is longer than tmax (for example, tpulse>>tmax) and wherein the period oftime between pulses is shorter than tmin (for example, tpause<<tmin). In anotherexample, 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 controlsignal 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 firstamplitude (in this example, a maximum amplitude (Max)). At time t1, the amplitudeof the at least one thermal management signal begins to decrease. The amplitude ofthe at least one thermal management signal is decreased to a minimum amplitude(Min) over a time period of t1 to t2. As such, the decrease in amplitude is ramped, ascan be seen in the dot-dashed line.In some examples, the amplitude of the at least one thermal management signal maybe decreased to a minimum amplitude of zero. It should be understood that “a zeroamplitude” 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 withthe at least one quantum mechanical system of the quantum computing system. Thatis, “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 t1, when the amplitude of the at least one thermal management signal begins to decrease, the amplitude of the control signal begins to increase from theminimum amplitude (Min). The amplitude of control signal increases to a secondamplitude (in this example, the maximum amplitude (Max), however the maximumamplitude for the at least one thermal management signal and the control signal maynot be the same in different examples) over a time period of t1 to t2. The rate atwhich 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 operationsare performed. It should be understood that the amplitude of the control signal mayvary 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 inthermal management signal is required.At time t3, the control operations end and the amplitude of the control signal beginsto decrease while the amplitude of the at least one thermal management signalbegins 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 understoodthat 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 thelike. It should be further understood that the rate of increase / decrease of amplitudeof 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 thermalmanagement signal. The shape of the ramp is not limited to that shown in the graphof 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. Inpreferable examples, the ramping may be smooth (changing in a continuous andregular 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 andfrequency or the like) to define the control signal and to control the behaviour of theat least one thermal management signal relative to the control signal in order tomaintain 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 thesine-squared example discussed in detail with regard to Figure 5), square pulse, ora linear ramp (such as the example shown with regard to Figure 4) and the like. Withregard 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 bedefined such that the total sum squared amplitude (which would, for example, beweighted according a calculated correction factor for each signal) is constantthroughout the operating time of the quantum computing system.It should be understood that although the graph of Figure 4 shows the signals (thecontrol signal and the at least one thermal management signal) increasing anddecreasing 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 ormore thermal management signals, the thermal management signals may eachincrease and / or decrease at different rates.It should further be understood that although the graph of Figure 4 shows thecontrol 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 signaland at least one thermal management signal. Figure 5 represents an exampleutilising a “sine-squared ramp” with a “sum-squared crossfade”, or, when correctionfactors for each signal are considered, a “weighted sum-squared crossfade”. In thisexample, there are two thermal management signals, 501 and 502, and a controlsignal 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 may be increased (or ramped) smoothly from a minimum amplitude (the minimum amplitude for the control signal 503) to an amplitude a3(t=tramp). In thisexample, the control signal 503 is ramped according to a sine-squared shape that isdefined by equation 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, thetotal power dissipation for all signals must be controlled. The power P dissipated foreach tone is proportional to the amplitude of said tone, with a proportionality constant cwhich is different for each signal, according to equation 2: Thus, equation 3 must be satisfied: ^^(^) + ^^(^) + ^^(^) = ^^^^^ = ^^(0) + ^^(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: (4) ^^(^) = ^^^(^) (5)where k is defined as the ratio of the initial amplitudes of the two thermalmanagement signals.Figure 5 shows the amplitude of the control signal 503 increasing (ramping) froman 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 f0, a first input signal with a frequency of f0 may be input to the resonator component in order to measure theeffect of the f0 input signal on components downstream of (or beyond) theresonator. Based on a change in the temperature caused by the signal (for example, the temperature may be raised by a value, T0), a second input signal may be input to the resonator, the second input signal having a frequency f1, wherein f1 is different to f0. 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 T1. In this case, it is thereby determined that to keep the temperature substantially constant when switching between signals with frequencies of f0 and f1, the input amplitude of an input signal with a frequency of f1 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 andmay start at a non-zero amplitude. Similarly, the thermal management signals maynot 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. CLAIMS1. A method for operating a quantum computing system, the methodcomprising: applying at least one thermal management signal to the quantum computing system; and changing at least one parameter of the at least one thermal managementsignal 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 thatat 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 thermalmanagement signal from a first amplitude to a second amplitude in response to anamplitude of the control signal increasing; and increasing the amplitude of the control signal from a minimum amplitude toa 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 oneparameter 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 asa series of pulses.

9. The method of any preceding claim, wherein the at least one parameter ofthe 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 thermalmanagement 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 thermalmanagement signal is applied continuously when the quantum computing system is turned on.

12. The method of claims 11, wherein the at least one thermal managementsignal 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 theat 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 atime period shorter than the minimum time period.

15. The method of claim 1, wherein the amplitude of the at least one thermalmanagement 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 afrequency and an amplitude.

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

18. The method of any preceding claim, wherein the quantum computing systemcomprises at least one quantum mechanical system; and wherein the at least one quantum mechanical system is at least one trapped-ion qubit.

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

20. The method of claim 18, wherein configuring the at least one parametercomprises: determining a relative amplitude of the at least one thermal managementsignal by measuring an thermal effect of the at least one thermal management signalon 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 afrequency 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.

22. The method of claim 1, wherein the control operation is at least one of: statepreparation, transport, loading, a quantum operation, a cooling operation, or areadout operation.

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