WO2025046206A1

WO2025046206A1 - Dynamic filtering

Info

Publication number: WO2025046206A1
Application number: PCT/GB2023/052212
Authority: WO
Inventors: Cameron SPENCE; Seyed Amir ALAVI
Original assignee: Riverlane Ltd
Priority date: 2023-08-25
Filing date: 2023-08-25
Publication date: 2025-03-06

Abstract

A method (100) of reading out a plurality of quantum systems (7, 9), the method (100) comprising: receiving (108) an output signal (25) comprising a plurality of frequency components (21), each corresponding to one of the plurality of quantum systems (7, 9); determining (104) operational filter parameters based on the plurality of frequency components (21); configuring (106) a set of filters (33) to filter the output signal (25) based on the determined operational filter parameters; and using the set of filters (33) to divide (110) the output signal (25) into a plurality of separate components corresponding to each of the quantum systems (7, 9).

Description

DYNAMIC FILTERING

The present disclosure relates to a method of reading out states of a plurality of quantum systems and to a system for reading out states of a plurality of quantum systems. In particular, but not exclusively, the present disclosure relates to methods and systems for qubit readout and characterisation.

In a quantum computer, the basic operating block is a qubit. One way to read out the state of the qubit is to couple a resonator to the qubit. The state of the qubit shifts the resonant frequency of the resonator. This shift can be detected by monitoring the phase and amplitude of a reference signal used to probe the resonator.

Qubits are generally operated in a low temperatures (often in the mK range), with the circuitry for performing readout at room temperature. This is because the readout circuity does not work in low temperatures, and space in the low temperature environment is limited. The link between the low temperature environment and the room temperature environment is constricted and often represents a limitation in the design of a quantum computer. In order to optimise the use of available space, several resonators may be coupled to a single feedline. The output signal on the feedline is mixed with a local oscillator and then passed to a polyphase filter bank to separate out the signals from the different resonators. A readout operation is performed using IQ demodulation.

A polyphase filter bank is a set of filters that splits an incoming signal into a plurality of fixed bands of equal bandwidth. In order to read out each qubit, there can only be one resonator probe per band. In some cases, it may be necessary to sweep the reference signal around the resonant frequency of the resonator to perform the readout operation. The entire sweep must be within the same filter band.

The use of polyphase filters provides a further restriction on circuit design. Different read out systems are provided for different purposes, and use of a particular readout system is limited. It would be desirable to have an easy to implement readout system, where the same design of system can be implemented across a wide range of different applications. According to a first aspect of the invention, there is provided a computer-implemented method of reading out a plurality of quantum systems, the method comprising: receiving an output signal comprising a plurality of frequency components, each corresponding to one of the plurality of quantum systems; determining operational filter parameters based on the plurality of frequency components; configuring a set of filters to filter the output signal based on the determined operational filter parameters; and using the set of filters to divide the output signal into a plurality of separate components corresponding to each of the quantum systems.

Determining operational filter parameters based on the plurality of frequency components means that the method of the first aspect can be used to readout signals from multiple quantum systems (e.g. resonators coupled with qubits) that operate at different frequencies. Existing systems operate using fixed filter bands and sampling frequencies, which limits the types of application that can be performed on the quantum systems and makes it difficult to reconfigure which quantum systems are being readout. In contrast, the use of dynamic operational filter parameters in the method of first aspect means that filter bands can be dynamically updated depending upon the quantum system(s) being measured and the type of operations being performed on the quantum systems. The method of the first aspect is therefore more versatile than known readout methods for quantum systems.

The operational filter parameters define bands (or channels) of the set of filters. In other words, the operational filter parameters indicate how the set of filters should be configured.

The method of the first aspect may be performed by a quantum control system (that is, a control system configured to control the plurality of quantum systems) comprising a classical processor. The classical processor may be configured to perform the method steps of the first aspect.

The set of filters, configured based on the operational filter parameters, may divide the output signal into a plurality of channels, wherein each channel comprises, at most, one frequency component corresponding to one of the plurality of quantum systems. The operational filter parameters may (implicitly or explicitly) define the total bandwidth of the output signal that is passed through the set of filters and the bandwidth of each channel. The operational filter parameters may (implicitly or explicitly) define the boundaries between the channels.

The set of filters may split the output signal into a plurality of channels, each channel extending over a range of frequencies between a lower boundary and an upper boundary.

The operational filter parameters may comprise a number of channels that the output signal is split into and/or a maximum cut-off frequency of the set of filters.

The maximum cut-off frequency of the set of filters may be determined based on a sampling rate of an analogue-to-digital converter arranged to provide the output signal to the set of filters. The operational filter parameters may comprise the sampling rate of an analogue-to-digital converter and configuring the set of filters may comprise setting the sampling frequency of the analogue-to-digital converter.

The number of channels may be set at the minimum value at which there is at most a single one of the plurality of separate components corresponding to each of the quantum systems in each channel with lower and upper boundaries above 0 Hz. Setting the number of channels to this minimum value reduces memory requirements, which is particularly important when the set of filters is implemented using an FPGA (or similar) because FPGAs (and similar devices) generally have restricted memory capabilities.

Alternatively, the number of channels may be set higher than the minimum value at which there is at most a single one of the plurality of separate component corresponding to each of the quantum systems in each channel with lower and upper boundaries above 0 Hz.

The set of filters may be a digital polyphase filter bank arranged to allow lower and upper boundaries of each filter in the set of filters to be modified by a controller (e.g. a controller of the quantum control system). Digital polyphase filter banks can by dynamically reconfigured in real-time (e.g. once deployed). The digital polyphase filter bank is preferably implemented using an FPGA.

The method may comprise: transmitting a reference signal to the plurality of quantum systems, the reference signal comprising a plurality of probe signal components at different frequencies, each corresponding to one of the plurality of quantum systems. The frequency components of the output signal may correspond to the probe signal components in the reference signal (following interaction with the corresponding quantum system).

The operational filter parameters may be determined based on known information about the probe signal components of the reference signal.

The reference signal may be provided on a single feedline.

The method may further comprise: sweeping the frequency of the reference signal, such that each probe signal component is swept across a range of frequencies, preferably centred at the resonant frequencies of the plurality of quantum systems.

The boundaries between channels formed by the set of filters may be spaced from the resonant frequencies of the plurality of quantum systems by at least half the range of the sweep. Spacing the boundaries from the resonant frequencies by at least half the range of the sweep ensures that the entire frequency range of the sweep is within a single channel when the sweep is centred on the resonant frequency.

The output signal may be received on a single feedline.

At least the set of filters may be provided on an FPGA. In some embodiments, all components of the quantum control system may be provided on an FPGA. In other embodiments, at least some of the components may be provided on other device types, e.g. an ASIC.

The output signal may comprise reflections of negative frequency components. The method may comprise separating the reflections from the components corresponding to each of the quantum systems.

The quantum systems may comprise qubits coupled to resonators for readout of states of the qubits. The method may comprise providing each separate component to a controller to perform a readout operation.

The readout method may be used at a single frequency to measure the states of quantum systems such as qubits. In addition or alternatively, the readout method may be used to characterise a quantum system, such as a qubit, by measuring over a range of frequencies (i.e. sweeping).

According to a second aspect of the invention, there is provided a system (e.g. a quantum control system) comprising: an analogue to digital converter arranged to receive an output signal comprising information on states of a plurality of quantum systems and convert the output signal from an analogue signal to a digital signal; a set of filters arranged to divide the converted output signal into a plurality of separate components corresponding to each of the quantum systems; and a (classical) processor arranged to determine operational filter parameters based on the resonant frequencies of the plurality of quantum systems; and configure the set of filters to filter the output signal based on the determined operational filter parameters.

The system of the second aspect provides the same advantages as the method of the first aspect.

The set of filters may be configured to split the output signal into a plurality of channels, each channel extending over a range of frequencies between a lower boundary and an upper boundary.

The operational filter parameters may comprise a number of channels that the output signal is split into and/or a maximum cut-off frequency of the set of filters and/or a sampling frequency of the analogue to digital converter.

The the set of filters may be a digital polyphase filter bank arranged to allow the filter frequencies to be modified by the processor.

The analogue to digital converter and the set of filters may be provided on an FPGA. According to a third aspect of the invention, there is provided a computer readable medium comprising instructions which, when executed by a processor, cause the processor to perform the steps of the first aspect. The computer readable medium may be a non-transitory computer readable medium.

According to a fourth aspect of the invention, there is provided a quantum control system comprising a (classical) processor configured to perform the method of the first aspect.

All or some of the steps of any of the disclosed methods could be provided as instructions on a (non-transitory) computer readable medium. These instructions may cause classical and/or quantum processors to perform the method steps as appropriate.

The output signal may also be referred to as a readout signal.

It will be appreciated that features discussed in relation to any embodiment or aspect may be applied, mutatis mutandis, to any other embodiment or aspect.

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 schematically illustrates a control system for a plurality of qubits;

Figure 2 is a flow chart of a method of a quantum readout operation;

Figure 3 shows an example output signal, showing filter bands defined according to a first example; and

Figure 4 shows an example output signal, showing filter bands defined according to a second example.

Figure 1 schematically illustrates a control system 1 having a first portion implemented in a temperature-controlled environment 3, such as a cryostat, dilution refrigerator or the like, and a second portion implemented at room temperature, used to control and readout the first portion.

In the temperature-controlled environment 3, a chip 5 is provided having n qubits 7i._n, which are operated by the control system 1. Each qubit 7i._n is coupled to a resonator 9i-_n. The state of each qubit 7 influences the state of the corresponding resonator 9, which can be detected by a corresponding probe signal 1 li-_n to measure the qubit state.

The resonator 9i._n is a structure that allows a signal (for example electrical or electromagnetic) to be transmitted through it. Each resonator 9i._n has an individual transmission characteristic showing the amount of transmission as a function of frequency, with a peak at the natural resonant frequency f_res,i (the resonant frequency without any external influence). By coupling an external system, such as a qubit 7i._n to the resonator 9i._n the state of the external system alters the transmission characteristic. This can be measured by a change in the transmission in the probe signal 11 i._n. Correlation of the qubit state to the change in transmission at a fixed frequency allows for measurement of the qubit state. It will be appreciated that this type of measurement can be employed with many types of qubits (e.g. charge, spin, electrical, magnetic) and can also be employed with reflective resonators instead of the transmissive.

In the example shown, the qubits 7i__n are connected in series, and the probe signals 1 l i-_n are provided at different frequencies in a reference signal 15 provided to the chip 3. To allow the set of resonators 9i._n to be read out individually, and at the same time, each resonator 9i has a different natural resonant frequency f_res,i and so each resonator 9i._n is responsive only to the corresponding probe signal portion 1 li-_n of the reference signal 15..

In order to measure the state of the qubit 7i, the probe signal Hi for each resonator 9i._n is fixed at a measurement frequency fi-_n corresponding to a slope in the resonator response (preferably a high gradient slope). In this way, a small modification in the resonator state will result in a large shift of the probe signal Hi, and the state of the qubit can be measured.

In order to determine the resonator responses, and thus the measurement frequency, the resonators 9i._n are calibrated. To calibrate the resonators 9i-_n, a frequency sweep measurement of the resonator is performed on a regular basis, with known (or no) input from the qubit 7i._n. During this operation, the probe signal l l i-n is swept across a frequency range Af centred on the natural resonant frequency f_res,i and the response of the resonation the probe signal is measured. In other words, for a given resonator 9i, the frequency is swept between f_res,i - Af/2 to f_res,i + Af/2. To generate the probe signals 11 i-_n, for a state measurement or calibration operation, a Digital -to-Analogue Converter 13 (DAC) is used to generate a reference signal 15. The reference signal 15 has n different frequency components at different frequencies, forming the probe signals 11 i-_n.

For a state measurement, the frequency components correspond to the measurement frequencies fi-_n of the different resonators 9i._n. For a calibration operation, the frequency component is set to f_res,i - Af/2 and then varied over time to f_res,i + Af/2. It will be appreciated that the sweep may follow a different pattern to this to measure the desired response curve.

The reference signal 15 is provided to the series chain of qubits 7i._n, and an output signal 25 is extracted following interaction of the reference signal 15 with the qubits 7i-_n. The individual output signal 21i__n from each resonator 9i._n forms a frequency component of the overall output signal 25.

Readout of the phase and amplitude shift of the probe signal is achieved by heterodyne measurement, which upconverts the signal generated by the DAC 13 and downconverts the output signal 25. To do this, the output signal 25 is mixed with a signal from a local oscillator 31 after the DAC 13 and prior to the ADC 29. The local oscillator 31 is referenced to the same clock as the DAC 13. Mixing occurs outside the cold environment 3.

After mixing with the local oscillator 31, the downconverted output signal 25 is provided to an Analogue-to-Digital converter 29 (ADC) and then to a digital polyphase filter bank 33 to separate out the signals from the different qubit 7 i-_n/re senator 9i._n pairs.

The digital polyphase filter bank 33 comprises a set of filters, spread over the range -f_s/2 to +f_s/2, where f_s is the sampling frequency of the ADC 29. The filters split the range into a plurality of equally spaced bands (also referred to as channels).

Each band may be thought of as a band-pass filter, which allows passage of signals having frequency between a lower frequency boundary and an upper frequency boundary. The set of filters are arranged such that the upper frequency boundary of one band forms the lower frequency boundary of the next filter.

Where the sampling rate of the ADC is f_s and the signal is divided in N channels/bands, the filter boundaries, fb,_x are defined by:

Where x = 0, 1, 2...N.

As can be seen from equation (1), the minimum cut-off frequency of the set of filters (i.e. the lowest frequency allowed to pass) is -f_s/2 whilst the maximum cut-off frequency (i.e. the highest frequency allowed to pass) is +f_s/2. Apart from the minimum cut-off and maximum cut-off, each boundary for a filter can be considered the high pass for the channel below the boundary, and the low pass for the channel above the boundary.

The ADC 29 and digital polyphase filter bank 33 are software controlled so that both f_s and N are selectable parameters to allow the upper and lower boundaries of the channels to be controlled, as will be discussed below.

The channels separated by the filter bank 33 are individually provided to a digital signal processor (DSP) 35 for comparison to the output from the DAC 13 and hence I/Q demodulation and readout. This may provide measurement of the qubit states or characterisation of the resonators 9i._n.

The DSP includes a local control unit 37i-_n for each individual qubit 7i-_n and a multi qubit control unit 39 for control of the ensemble. In addition to providing readout, the local control units 37i__n and multi qubit control unit 39 provide inputs for operation and control of the qubits 7i._n and resonators 9i._n. The outputs from the local control units 37i-_n are provided to a software defined channel combiner 41, which combines the outputs into a single signal, which is provided to the DAC 13. This includes the components necessary for generating the reference signal 15.

A memory 51 may also be provided. The memory 51 may include a programme storage portion 53 and data storage portion 55. The program storage portion may store computer program code which, when executed on the DSP or other suitable processor, causes the operation of the qubits 7i._nand control system 1. The data storage portion 55 may contain data on the qubits 7i-_n, resonators 9i-_n, resonator transmission characteristic and the like.

Figure 2 illustrates a flow chart of a method 100 of performing a readout operation (state measurement or resonator characterisation) using the control system 1 discussed above.

In a first step 102, the reference signal 15 is generated by the DSP 35 and DAC 13. The reference signal 15 comprises frequency components for probing each resonator 9i._n.

The natural resonant frequency f_res,i of each resonator 9i._n is fixed by the structure of the resonator 9i._n. However, different operations (different qubit operations or calibration operations) may address a different subset of qubits 7i._n on the chip 5, and where the probe signal is swept across a range, different sweeps may be used for different subsets of the qubits 7i__n and in different situations. Therefore, the components of the reference signal 15 may vary from operation to operation.

At a second step 104 of the method 100, the operational filter parameters (f_s and N) of the ADC 29 and filter bank 33 are determined based on the frequency components of the reference signal 15. This information may be based directly on the reference signal 15 and/or may be based on known information regarding the reference signal 15 and/or the qubit 7i-_n / resonator 9i._n pairs to be addressed. Step 104 may optionally be performed prior to step 102. f_s is selected so that the resonant frequencies fall within the first Nyquist zone of the ADC 29, after up and down conversion. f_s and N are also chosen such that the each of the different frequency components of the received signal is in a dedicated channel, with no other frequency component. As discussed above, where a sweep is performed in a calibration operation, the full range of the sweep is within the channel.

As can be seen from equation 1, channels with negative frequency are defined by the filters. This is an inherent property of the polyphase filter. The channels having any frequency component < 0 Hz (i.e. channels in which any part of the frequency range covered by the channel is negative) are ignored as these do not form real components of the signal. Therefore, for M qubits, the minimum number of channels N_min = 2M Example 1

Consider, by way of a first example, a qubit operation where: fres.l, fre_S,2, fres,3, fres.4 = { 100 MHz, 200 MHz, 400 MHz, 410 MHz}

For this example, assume there is no sweep, or Af «< f_resi,2,3,4.

In this example, the lowest possible value of N required to address all qubit 7 i-_n/re senator 9i._n pairs is chosen, and then f_s is selected such that each resonator is sufficiently spaced from the boundaries to fit in any sweep without the sweep overlapping into an adjacent channel.

As discussed above, channels with both negative and positive frequency are generated, but channels covering any frequency < 0 Hz are ignored. Therefore, for a system with four qubits, the minimum possible value of N is 8 (to define four channels with positive frequency).

In the first example, with N = 8, f_s is set to 1080 MHz. This produces filters with boundaries = {0 MHz, 135 MHz, 270 MHz, 405 MHz, 540 MHz} . Where Af < 10MHz, this allows all four qubits to be addressed individually.

Figure 3 illustrates the output signal 25 with the channels 431-4 as defined in example 1.

Example 2

In a second example, consider again a qubit operation where: fres.l, fres.2. fres.3. fres.4 = { 100 MHz, 200 MHz, 400 MHz, 410 MHz}

For this example, again assume there is no sweep, or Af «< f_resi,2,3,4

In this example, the requirement to use N_min is not followed. Instead, f_s is set at 1000 MHz and N is set at 11. The filters having any frequency component < 0 Hz are again ignored as these are not real components. This produces filters with boundaries = {45 MHz, 136 MHz, 227 MHz, 318 MHz, 409 MHz, 500 MHz} .

Figure 4 illustrates the output signal 25 with the channels 43I-₅ as defined in example 1. As can be seen in both Figures 3, and 4, the signal from each resonator is in a dedicated channel. In the Figure 3, each channel has a corresponding signal, whilst in Figure 4 there is an empty channel.

In a next step 106 of the method 100, the ADC 29 and filter 33 are configured based on the determined parameters.

After the qubit operation has been performed, the output signal 25 is received at step 108. The signal is then processed at step 110 to divide the signal into the separate channels 43. The readout operation is then performed at a final step 112. The readout operation 112 may be part of qubit state measurement or resonator characterisation.

Any suitable search method could be used to find the value of f_s and N. For example, linear search algorithms and/or minimisation algorithms may be used to identify the values of f_s and N to be used.

The lower limit of possible values for f_s is set by the requirement of the frequencies being measured to fall within the first Nyquist zone whilst the lower limit of N (Nmin) is set by the number of qubits to be measured.

The upper limit of f_s is set by the limitations of the ADC 29.

The upper limit of N is typically set by available memory and/or the minimum size of channel allowed by Af. As N increases, further memory is required and so keeping N as low as possible (as in example 1 above) reduces memory requirements.

In at least some embodiments, it is preferable to set N = N_min to reduce memory usage. However, in some cases, this may not be possible. For example, the upper limit of f_s may be such that N = N_min cannot separate each component of the signal into a dedicated channel and so N has to be increased. Furthermore, in other situations for example, where memory is less constricted it may not be necessary to keep N = N_min.

It will be appreciated that the order of the method steps shown in Figure 2 is given by way of example only. In particular, the steps of determining the operational filter parameters 104 and configuring the filters 106 may occur at any suitable time before the step of dividing the output signal 110. For example, the operational filter parameters may be determined prior to the reference signal being generated or the output signal being received.

In one example embodiment, the qubits 7i-_n are superconducting qubits. Typically, resonators for readout of superconducting qubits have resonant frequencies in the range of 4 GHz to 12 GHz, with spacing of between 10 MHz and 100 MHz between resonant frequencies. In these examples, Af is between 100 KHz and 5 MHz. These frequencies are by way of example only, and superconducting qubits may have higher or lower resonant frequencies, with higher or lower spacing and larger or smaller sweep.

Whilst a superconducting qubit is given by way of example, the control system 1 discussed above can be used for multiplexed readout of any type of qubit or resonator at any frequency range may be used.

In one example, the DAC 13, ADC 29, filter bank 33, DSP 35 and combiner 41 are implemented on an FPGA chip 45. However, any suitable type of control circuit may be used.

The reference signal 15 and output signal 25 are coupled into the low temperature environment 3 by respective feedlines 47, 49. By multiplexing the signal 15 that is provided into the low temperature environment 3 and the signal that is extracted from the low temperature environment 3, the limited space can be used with greater efficiency. The variation of the operational filter parameters f_s and N used to divide the output signal 25 into channels also allows for dynamic variation of the filtering, which accommodates the variability in frequencies that may be needed for different operations and applications.

Typically, between three and five qubits may be coupled on a single feedline 47, 49. However, this is by way of example. In some examples, more than five qubits may be coupled on a single feedline. Where a large number of qubits are provided, multiple control systems 1 as described above may be provided, each coupled to a different subset of the qubits. A digital polyphase filter bank is an example of a software controllable linear filter bank (i.e. the filter bank divides the incoming signal into equal size channels). Other types of filter bank may also be used. For example, a digital filter bank with non-equal channels may be used. In this case, the operational filter parameters may include upper and lower boundaries of each individual filter, in addition to N and f_s. This will allow for greater control over filters. It will, however, be appreciated, that this will significantly increase memory requirements.

In the above examples, both N and f_s are varied. It will be appreciated that one of N and f_s may be fixed, and only one of the parameters varied.

In the above, the local oscillator 31 is provided externally of the FPGA 45. However, it will be appreciated that the local oscillator 31 may be provided on the FPGA 45, and the heterodyning may even be done on the DSP 35.

In the above examples, it is assumed that the sampling frequency of the DAC 13 is set to be the same as the sampling frequency of the ADC 29. This need not be the case, and in some cases, the sampling frequencies may be different. In this case, negative frequencies may be generated by the mixing of the DAC signal and ADC signal during the readout operation. Reflections of these frequencies can then fall within the same channels as signals to be measured. However, correct selection of the operating parameters of the filters can allow these to be filtered out, as the frequencies of these reflections will be known.

In the above examples, the qubits 7i-_n are arranged in series on the chip 3, along a single feedline. It will be appreciated that this is by way of example only and the qubits may be in parallel or independently connected. In these examples, a multiplexer may be provided to split the reference signal 15 into separate channels for each qubit 7i._n, and a demultiplexer may be used to recombine the signals 21 i__n from each qubit 71-n into the output signal 25.

In the examples discussed above, local control units are provided for qubit control. It will be appreciated that this is by way of example only. A single control unit may be provided or groups of qubits may be controlled by a single control unit. Any suitable controller for control and readout from the chip 3 may be used. The control system 1 discussed above has been described in relation to readout of qubits 7i-n and resonators 9i._n. It will, however, be appreciated that the control system has applicability to the readout of any type of quantum system (such as quantum memory, or other quantum processing units) or other types of system requiring multiplexed readout from the low temperature environment.

Claims

1. A method of reading out a plurality of quantum systems, the method comprising: receiving an output signal comprising a plurality of frequency components, each corresponding to one of the plurality of quantum systems; determining operational filter parameters based on the plurality of frequency components; configuring a set of filters to filter the output signal based on the determined operational filter parameters; and using the set of filters to divide the output signal into a plurality of separate components corresponding to each of the quantum systems.

2. The method of claim 1, wherein the set of filters splits the output signal into a plurality of channels, each channel extending over a range of frequencies between a lower boundary and an upper boundary.

3. The method of claim 1 or claim 2, wherein the operational filter parameters comprise a number of channels that the output signal is split into and/or a maximum cut-off frequency of the set of filters.

4. The method of claim 3, wherein the maximum cut-off frequency of the set of filters is determined based on a sampling rate of an analogue-to-digital converter arranged to provide the output signal to the set of filters, wherein the operational filter parameters comprise the sampling rate of an analogue-to-digital converter and configuring the set of filters comprises setting the sampling frequency of the analogue- to-digital converter.

5. The method of claim 3 or claim 4, wherein the number of channels such that there is at most a single one of the plurality of separate components corresponding to each of the quantum systems in each channel with lower and upper boundaries above 0Hz.

6. The method of claim 5, wherein the number of channels is set at the minimum value at which there is at most a single one of the plurality of separate components corresponding to each of the quantum systems in each channel with lower and upper boundaries above 0Hz.

7. The method of any preceding claim, wherein the set of filters is a digital polyphase filter bank arranged to allow the lower and upper boundaries of each filter in the set of filters to be modified by a controller.

8. The method of any preceding claim, comprising: transmitting a reference signal to the plurality of quantum systems, the reference signal comprising a plurality of probe signal components at different frequencies, each corresponding to one of the plurality of quantum systems, wherein the frequency components of the output signal correspond to the probe signal components in the reference signal.

9. The method of claim 8, wherein the operational filter parameters are determined based on known information about the probe signal components of the reference signal.

10. The method of claim 8 or claim 9, wherein the reference signal is provided on a single feedline.

11. The method of any of claims claim 8 to 10, comprising: sweeping the frequency of the reference signal, such that each probe signal component is swept across a range of frequencies preferably centred at the resonant frequencies of the plurality of quantum systems.

12. The method of claim 11, when dependent on claim 2 or any claim dependent thereon, wherein the boundaries between channels formed by the set of filters are spaced from the resonant frequencies of the plurality of quantum systems by at least half the range of the sweep.

13. The method of any preceding claim, wherein the output signal is received on a single feedline.

14. The method of any preceding claim, wherein at least the set of filters is provided on an FPGA.

15. The method of any preceding claim, wherein the output signal comprises reflections of negative frequency components, wherein the method comprises separating the reflections from the components corresponding to each of the quantum systems.

16. The method of any preceding claim, wherein the quantum systems comprise qubits coupled to resonators for readout of states of the qubits.

17. The method of any preceding claim, comprising: providing each separate component to a controller to perform a readout operation.

18. A system comprising: an analogue to digital converter arranged to receive an output signal comprising information on states of a plurality of quantum systems and convert the output signal from an analogue signal to a digital signal; a set of filters arranged to divide the converted output signal into a plurality of separate components corresponding to each of the quantum systems; and a processor arranged to determine operational filter parameters based on the resonant frequencies of the plurality of quantum systems; and configure the set of filters to filter the output signal based on the determined operational filter parameters.

19. The system of claim 18, wherein the set of filters is configured to split the output signal into a plurality of channels, each channel extending over a range of frequencies between a lower boundary and an upper boundary.

20. The system of claim 18 or claim 19, wherein the operational filter parameters comprise a number of channels that the output signal is split into and/or a maximum cut-off frequency of the set of filters and/or a sampling frequency of the analogue to digital converter.

21. The system of claim 20, wherein the set of filters is a digital polyphase filter bank arranged to allow the filter frequencies to be modified by the processor.

22. The system of any of claims 18 to 21, wherein the analogue to digital converter and the set of filters are provided on an FPGA.

23. A computer readable medium comprising instructions which, when executed by a processor, cause the processor to perform the steps of any one of claims 1 to 17.