Quantum error correction

Abstract

Measurement outcome data from quantum devices in a quantum computing system describing analogue readout measurements is compressed by, after performing quantum state discrimination on read-out measure

Description

Field of the Invention The present invention relates to quantum computing. Background Unlike a classical computer, which operates in a single state at any given moment, a quantum computer can exist in a superposition of quantum states simultaneously. However, advantages that flow from this “quantum parallelism” come at the cost of increased noise arising from entanglement with the environment. This complicates the processing of the information coded by the quantum states. Noise within quantum systems, manifesting as computational errors, can originate from several sources including: the preparation of the initial state; the computation process itself; and, at the point of quantum state readout / measurement to determine the results of a quantum computation. Consequently, the interpretation of the output results of a quantum computer can be challenging. Measurement in quantum computing systems involves coupling a qubit, qudit or qutrit with a “readout” measurement apparatus. One example is a readout resonator in a superconducting qubit system. The quantum state being measured influences the state of the readout measurement apparatus, which is then read out. This readout is then processed to yield quantum state measurement outcome signals. The readout signals do not directly reveal the quantum state that has been measured. Rather, they represent certain physical properties that the readout measurement apparatus is configured to measure, such as frequency shifts in a resonator of a superconducting qubit system. These physical properties correlate with the quantum state in question. A process of “discrimination” is used to map the readout measurement signals back to the collapsed quantum state of the measured qubit, qudit or qutrit. In other words, the “discrimination” interprets each signal from the readout measurement apparatus, determining whether it represents the result of measuring a quantum state |0) or a quantum state |1>, in the case of a qubit. This step is more generally known as “quantum state discrimination” and is an important component in unveiling the results of a quantum computation. Quantum state discrimination may include determining a probability of any particular readout measurement value occurring as a result of performing the readout measurement operation, and using these probability values to discriminate the measured quantum state. For example, a readout measurement value, mh may be assigned a probability of pL = 0.75 as having resulted from performing the readout measurement operation on a |0) qubit state. Quantum state discrimination may then classify the readout as a having measured a |0) qubit state, thereby mapping the readout measurement to a particular qubit state. By contrast, for example, another readout measurement value, mj, may be assigned a probability of pj = 0.45 as having resulted from performing the readout measurement operation on a |0) qubit state. Quantum state discrimination may then classify the readout measurement as a having measured a |1) qubit state, thereby mapping the readout measurement to a different qubit state. These analogue readout measurement values are often referred to in the art as describing “soft measurement information”. The mapping of a readout measurement value, mj, to a particular qubit state in quantum state discrimination is sometimes referred to in the art as applying a “hardening map”, or as converting “soft” measurement information into “hard” binary measurement outcomes (see ref. [2], [8], [9],

[10] ,

[11] and

[12] , below). The “hard” binary measurement outcome values of “0” or“1” representing the final result of quantum state discrimination link a qubit readout measurement value (analogue: from a continuum) to a deduced qubit quantum state (binary: 0 or 1, representing |0) or 11), respectively). It has been shown that exploiting soft measurement information before it is converted into hard, binary information can improve decoding performance (see ref. [8], below). However, the quantity of analogue readout measurement data describing soft measurement information produced by a qubit readout device during a given quantum computation can be very large, and managing the flow of this data between elements of a quantum computing system can be problematic. The present invention has been devised in light of the above considerations. Summary of the Invention The term “quantum information” may include reference to information of the state of a quantum system. The storage and transmission of quantum information can be accomplished using quantum mechanical systems. The quantum-mechanical properties of physical systems can be exploited to achieve the storage and transmission of quantum information. A quantum computing system (also referred to herein as a quantum computer) is a computing system that exploits quantum mechanical phenomena using quantum devices. The quantum devices may be any quantum devices capable of storing quantum information (i.e. any physical devices suitable for encoding information using quantum computational states). The quantum devices may be qubits. Alternatively, the quantum devices may be other devices capable of storing quantum information, such as qudits orqutrits. While the description herein will primarily refer to qubits, any reference herein to qubits should be understood to also encompass other types of quantum devices unless explicitly stated otherwise. The physical quantum state of a quantum device may be assigned a symbolic value (e.g., “1” or “0”) for use in representing quantum information that can be processed and manipulated according to the physical constraints (physics) of quantum mechanics. A quantum device may be referred to as a quantum state carrier. Quantum error correction (QEC) is used in quantum computing to reduce the effects of noise on stored quantum information, or the effects of faulty quantum state preparation, faulty quantum gates, or faulty qubit readout measurements. Error correction protocols for quantum computers, such as surface codes, repeatedly perform qubit readout measurements in order to measure parity operators to detect and correct qubit errors. A given qubit measurement readout process produces an analogue readout measurement value in the form of a measured physical quantity appropriate to the physical embodiment of the qubit (quantum device) being used to hold the quantum information. For example, a qubit readout operation suitable for a qubit embodied in electron spin states may involve performing a charge measurement operation resulting an analogue readout measurement value describing a charge measurement result, as discussed in reference [3], below. In another example a qubit readout operation suitable for a qubit embodied in trapped ion states may involve performing a photon count measurement operation resulting an analogue readout measurement value describing a photon count measurement result, as discussed in reference

[15] , below. In a further example, a qubit readout operation suitable for a qubit embodied in a superconducting qubit may involve performing a voltage measurement operation resulting an analogue readout measurement value describing a voltage measurement result. As a detailed example, useful for understanding the broader context of the invention, the following discussion focusses on a qubit readout process performed upon a Transmon qubit (a superconducting qubit comprising a Josephson Junction). It is to be understood that the invention is not limited to use in association with Transmon qubits, and the choice of a Transmon qubit as the subject of the following discussion is purely for ease of description. For the avoidance of doubt, the invention is applicable equally to any quantum device capable of storing quantum information, whether that be a Transmon, or other superconducting qubit, or a spin-state qubit, a neutral atom qubit, an ion qubit, a photonic qubit or any other qubit, qudit or qutrit. A Transmon qubit may be measured dispersively by a qubit readout device comprising a “readout resonator” coupled to the qubit. A quantum measurement can be described as an entanglement of the qubit degree of freedom with a “pointer variable” of a measurement probe, followed by classical measurement of the state of the probe. In a Transmon, the qubit (the quantum system) is entangled with an observable of a superconducting readout resonator (acting as a probe) allowing one to gain information about the qubit state by interrogating the readout resonator rather than directly interacting with the qubit. In particular, the resonance frequency (resonance energy) of the readout resonator is configured to be far away from the energy difference between the energy eigenstates of the qubit. However, a carefully selected coupling between the qubit and the readout resonator induces a shift in the resonance frequency of the readout resonator which depends upon the quantum state of the qubit. This shift can be seen as a shift in the frequency position (e.g., a few MHz) of a resonance dip in a reflection spectrum of the readout resonator according to whether the qubit to which it is coupled is in the ground state or the excited state. In turn, if a probe pulse signal (e.g., radio-frequency electromagnetic wave pulse) is directed into the readout resonator, a corresponding shift will be seen in the phase of the reflected part of the probe pulse signal relative to the phase of the incident pulse signal. By observing this phase shift in the reflected probe pulse signal, one may observe the quantum state of the Transmon qubit. This observation is a quantum measurement, as depicted schematically in Figure 1. In other words, given a Transmon qubit in the superposition state described by the following wavefunction: |ip> = a|0) + jff|l) the Transmon qubit readout measurement will result in the collapse of the wavefunction to one of the two energy eigenstates, |0) or 11>, such that the collapsed state of the qubit will be in either its ground state, 10), with energy Eo, or in its excited state, 11>, with energy E1. According to the “Born Rule”, the collapse of the wavefunction into the ground state arises with a probability given by \a\2, and the collapse of the wavefunction into the excited state arises with a probability given by |^|2. However, an important distinction must now be made between, on the one hand, the probabilities associated with wavefunction collapse caused by the act of measurement of the superposition state |^) and, on the other hand, the probability that the qubit readout measurement will generate a particular physical readout measurement value associated with the very same act of measurement. The former probabilities are determined by the random quantum-mechanical process of wavefunction collapse, whereas the latter probabilities are determined by the random classical process of an imperfect, noisy qubit readout measurement. In more detail, the classical process of qubit readout measurement may be done, in the example of the Transmon qubit, by injecting into the readout resonator a microwave probe pulse having a frequency close to the readout resonator’s resonant frequency. This probe pulse is partially reflected by the readout resonator and a phase shift is imposed on the reflected pulse which varies according to the quantum state of the qubit. Thus, the properties of the reflected probe pulse differ depending upon the quantum state of the qubit. The phase shift is manifest in changes to the “in-phase” ( / ) and “quadrature phase” (Q) voltage components of the reflected probe pulse, which are each measurable as a voltage. For example, a readout process may commence with a short microwave probe pulse having a frequency mr0 directed to the readout resonator. After interacting with the readout resonator, the reflected part of the microwave probe pulse signal, s(t), has the form: s(t) = Ar0 cos ^ROt + 0fiO) Here, AR0 and 0RO are, respectively, the qubit-state-dependent amplitude and phase to be measured. One can equivalently use a complex analytic representation of the signal: s(t) = Re^oe^0^ e«o)} = Re{AROei6R° x e^ot) Here, a static “phasor” is separated out from the time dependence exp(kofiOt) as: A „p^R0 To perform a Transmon qubit readout measurement, one may measure the “in-phase” component ( / ) and a “quadrature” component (Q) of the complex number represented by the phasor: AROe16RO = AROcos0RO + MfiOsin0fiO = I + IQ to determine the amplitude AR0 and the phase 0RO as: aro = V / 2 + Q2 0RO = arctan (Q / / ) Note that what matters is the change in AR0 and 0RO between the qubit being in state |0) and state 11), rather than the specific values of AR0 and 0RO. For example, it can be shown (see ref. [7]) that for a Transmon qubit in an energy eigenstate |i), i = 0 or 1, the energy eigenvalue, Eit of this quantum eigenstate is related to the parameters of the readout phasor as follows: tan0fiO = Q / I = k2QL d2Et q d*2 Here, k is the coupling constant between the qubit and the readout resonator, Lq is the qubit selfinductance, O is the flux through the qubit loop and <Pdc is the flux bias through a qubit loop. Thus, by observing the phase 0RO in the reflected probe pulse, one may differentiate between the quantum states, |i), of the Transmon qubit. An example of the typical variation in qubit readout measurement values is shown schematically in the graph 1 of Figure 2. Here, the distribution of many readout measurement values is shown, each value being an individual data point corresponding to the tip of the phasor AROe18RO associated with the readout measurement in question, collectively for very many repeated measurement events (known in the art as “shots”) in which a Transmon qubit was prepared and measured many times in each of the following states an equally large number of times: W = |0) or ^) = |1) The great multitude of shots are represented as a pair of scatter plots, 2 associated with l^) = |0) and 4 associated with l^) = 11), shown in plan view, with I and Q axes lying in the plane of the page and a “frequency-of-occurrence” axis extending vertically from the page. The result is to display a pair of data clouds each of which is greyscale shaded to a degree indicative of a density of data points (dark shading indicating greater density). A lower graph 5 shows two “readout histograms”, 6 and 8, each associated with a respective one of the two data cloud clouds, 2 and 4, and each being normalised by the total number of data points in its corresponding data cloud, such that the vertical axis of each readout histogram represents the probability of occurrence of a particular value of I being produced by the act of readout measurement of a given quantum state: |0) for histogram 6; |1) for histogram 8. Each readout histogram is typically Gaussian in shape and bimodal so as to comprise two Gaussian shapes: a primary Gaussian-shaped part (6 or 8) and a subsidiary Gaussian-shaped part (10 or 12, respectively). Each subsidiary Gaussian part arises due to random errors in qubit state preparation or random transitions of a qubit from one state to another after state preparation. A side graph 7 shows one readout histogram 14 associated with each one of the two data cloud clouds, 2 and 4, due to the respective centroids (marked by an “X”) sharing a common value of Q. The side graph 7 is also normalised by the total number of data points a corresponding data cloud, such that the vertical axis of the readout histogram represents the probability of occurrence of a particular value of Q being produced by the act of readout measurement of a given quantum state. A first data cloud 2 corresponds to the cloud of readout measurement data points broadly associated with the wavefunction collapse: l^) -> |0). A second data cloud 4 corresponds to the cloud of readout measurement data points broadly associated with the wavefunction collapse: l^) -> |1). Each one of the data clouds is centred upon a respective centroid (marked by an “X”) corresponding to the notional position one would expect to find, on the one hand, a perfectly noise-free readout measurement phasor: 4fl0eie™ = with amplitude and phase 0^ , associated with a perfectly-noise-free readout measurement of the |0) eigenstate (ground state) of the Transmon, and on the other hand, a perfectly noise-free readout measurement phasor: AROeie*° = A^e^o with amplitude 44 and phase 44 associated with a perfectly-noise-free readout measurement of the |1) eigenstate (excited state) of the Transmon. Of course, qubit readout measurement is not a noise-free process and the circular shaded area surrounding each respective centroid represents a random variation in the values of amplitude, A^ and 44 and phase, 0^ and 44 °fa multitude of phasors over many repeated qubit readout measurement events. Each readout measurement phasor possesses an in-phase, I, component and a quadrature component, Q, and the value of each of these components is analogue in nature and correspond to a “soft” measurement value. In the example shown, the centroids of each of the first and second data clouds share a common quadrature component, Q, but differ significantly in their respective in-phase, I, components such that a connecting line 15 joining the centroids is parallel to the in-phase, I, axis of the graph 1 of Figure 2. Note in real devices, it often happens that the line 16 between the |0) and |1) centroids is not exactly aligned on the / -axis such that the mean of a 0-measurement and the mean of a 1-measurement often do not have the same value of Q. Reference

[17] shows an example of this. To simplify classification, the IQ voltages may be rotated along the axis between the "0"- and "l"-centroids, restoring the symmetry as seen in Fig.2. A simple process of quantum state discrimination may be implemented as follows. A discrimination threshold 16 corresponding to a specific in-phase voltage value, I = IDiscr, bisects the connecting line 15 joining the two centroids. This discrimination threshold defines a demarcation between the two data clouds, 2 and 4, of readout measurement data. Any individual phasor (data point) residing in a first zone 18 of in-phase, I, voltage values that are less than the discrimination threshold: I <IDiscr (to the left of the discrimination line) may be deemed to have been the result of performing a readout measurement resulting in the wavefunction collapse: l^) -> 10), and can be assigned a quantum state measurement outcome value of “0”. By contrast, a phasor (data point) residing in a second zone 20 of in-phase, I, voltage values that are greater than the discrimination threshold: I >IDiscr (to the right of the discrimination line) may be deemed to have been the result of performing a readout measurement resulting in the wavefunction collapse: -> 11), and can be assigned a quantum state measurement outcome value of “1”. In this way, each of the “soft” in-phase voltage values, I, may be mapped to a “hard” binary value (“0” or “1”) subject to this use of the discrimination line 16. This mapping process may be referred to in the art as a “hardening map” for generating a “hard” binary measurement outcome value, of “0” or “1 ”, from a “soft” readout measurement data value, I. The accuracy of the discrimination threshold is dependent upon the accuracy and quality of the statistics of the measurement data clouds themselves. In other words, a suitable discrimination threshold value is dependent upon an accurate position for each of the two centroids (“X”) of the two readout measurement data clouds, 2 and 4, which, in turn, is improved by having access to good readout statistics / histograms. In other examples, where the distribution of the data clouds of readout measurement phasor data, AROeieRO, is not as conducive to the use of a simple discrimination line 16, a machine learning (ML) algorithm may be trained in order to be able to generate a value of a probability that a given soft readout measurement data value (phasor) arose from either the wavefunction: l^) = |1) or from the wavefunction: |^) = |0). Based on the value of that probability, a quantum state discrimination may be applied to each “soft” in-phase voltage value, ( / , Q), to map that value to a “hard” quantum state measurement outcome value, such as a one-bit binary value (“0” or “1 ”). References

[13] to

[17] below, give examples of using machine learning to assist quantum state discrimination in the readout of qubits. In particular, Fig. 2 of reference

[17] is an example of a process of preparing a qubit in the states |0) and |1) and performing repeated qubit readout measurements upon it many times so as to generate data clouds of readout data providing readout statistics / histograms of the form shown in Figure 2 of the present application. The readout statistics / histograms in reference

[17] are used to calibrate a discriminator kernel in an ML algorithm for improved quantum state discrimination upon the qubit. In general, qubit readout measurements can be repeated to generate “readout histograms” for use in a process of “quantum state assignment”, or “quantum state discrimination”, such as discussed in references [4], [5], [6] and others. As described above, this is the process of assigning a particular qubit readout measurement result to a post-measurement quantum state. This may correspond to converting the particular qubit readout measurement value, which is a value within a continuum of possible analogue readout measurement values, into a single one-bit binary value representative of a quantum state measurement outcome value. While the above discussion is made in terms of superconducting qubits, it is reiterated that superconducting qubits have been singled out for discussion purely to aid understanding of the matters at hand. In general, the task of quantum state assignment / discrimination is applicable to the measurement of any qubit regardless of the physical implementation of the qubit in question. This is because the act of conducting a physical measurement of a qubit state is inherently noisy. Any given measurement process (referred to as a “shot”) repeated many times on a given qubit state will, in general, not reproduce exactly the same physical measurement value each time (i.e., each “shot”). Instead, repeated measurements (“shots”) will build up a “readout histogram” of data defining a distribution of physical measurement values clustered around a notional modal value. Traditional error decoding approaches often rely on the binarization (single-bit) or “hardening” of readout data discussed above, which can ignore valuable information embedded in the “soft” analogue qubit readout signal. Common error decoding approaches with access to analogue information often rely on binarized (single-bit) quantum state measurement outcome data as input to the decoder. The process of converting analogue to binary outcomes inevitably leads to a loss of information that reduces decoder performance. It has been shown that exploiting soft (analogue) measurement information before it is converted into hard (single-bit) information can improve decoding performance. For example, see references [1] and [2] below. Thus, as noted above, “soft” (analogue) qubit readout measurement information is a valuable resource not only use in for making improvements in the process of quantum state discrimination, but also in quantum error correction codes (QEC). Furthermore, “soft” measurement probability values, e.g., such as those associated with “readout histograms” discussed above associated with quantum state discrimination processes, are an important part of many quantum computation processes and can assist in managing and / or decoding errors that arise during quantum computations, from noise sources such as those discussed above. For example, see references [1] and [2] below. However, this management and / or decoding process often requires the contemporaneous provision of both the “hard” quantum state measurement outcome values and the associated probabilities associated with the quantum state discrimination. The inventors have realised that this can cause bottlenecks in the transmission of the required data between components of a quantum computing system. The inventors have realised that this problem may be addressed by an appropriate and versatile compression system that is sympathetic to these circumstances. At its most general, the invention provides a system (and method) for compressing qubit state readout measurement data that combines both quantum state measurement outcome (“hard”) data resulting from application of a quantum state discrimination process to analogue (“soft”) measurement information, together with a compressed amount of probability information associated with the analogue (“soft”) measurement information. By applying compression to an appropriate choice of some of, but not all of, the probability information, the inventors have found that significant benefits can achieved including (but not limited to) easing the issue of data transmission bottlenecks and / or reducing data storage space requirements, while retaining much (or all) of the most beneficial “soft” information needed to achieve a greater benefit from in quantum error correction coding. In a first aspect, the invention provides a quantum computing system comprising: a plurality of quantum devices for encoding information using quantum computational states; a readout system for performing a readout measurement operation upon quantum devices from amongst the plurality of quantum devices to produce readout measurement data describing analogue readout measurement values; a data compressor for compressing the readout measurement data by: acquiring data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation; performing quantum state discrimination upon the readout measurement data thereby generating respective quantum state measurement outcome values; producing compressed measurement outcome data comprising the quantum state measurement outcome values and data describing probabilities, from amongst the acquired data describing probabilities, which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data. The readout measurement values may be generated / created originally in an analogue form (e.g., by the measurement apparatus) and subsequently converted into a digital form of representation. The data describing analogue readout measurement data may therefore be in a digital form (e.g., multi-bit data; bytes of data, etc.). In this way, a significant reduction in the size of a data set associated with readout measurement results may be achieved without suffering a significant concomitant reduction in the information contained within the data set. Quantum state discrimination applied to the readout measurement values may comprise assigning to a given readout measurement value, a single-integer binary value selected from two pre-set single-integer binary values (single-bit e.g., 1 or 0). The result is a quantum state measurement outcome. Single-bit (hard) quantum state measurement outcome data values are conducive to being represented by small data items (e.g. a binary single-integer representation, 0 or 1, of a quantum state via a single bit) in contrast to probabilities having multi-bit values (i.e., not a single-integer representation) which may fall anywhere within an extended range of values from those representing 0.0 (zero; representing the maximal improbability) to those representing 1.0 (one; representing the maximal probability) typically require a greater bit depth in order to be accurately described in base-2 (e.g., a byte). By focussing the compressive step upon probabilities contained within the data set, a significant degree of compression can be achieved and, simultaneously, the benefits of retaining probability values are effectively retained by selecting extremal probabilities for exclusion from the compressed data set. It is to be noted that the acquired data describing probabilities may be in any suitable form that encodes probability values. For example, the data may describe a given probability value as an integer that encodes probability information or may describe a given probability value as a non-integer (e.g., floatingpoint) number. Encoding probabilities in integers would be readily understood by the person skilled in the art, and is common practice in computer sciences, but for the avoidance of doubt it is to be understood that, for example, a probability value may be encoded as an integer selected from an interval of integers whereby each integer from the interval is assigned to represent a respective unique, normalised probability value selected from within the continuous interval of real non-integer numbers: [0,1]. The acquiring of a respective probability may comprise providing probabilities some of which do fall within a pre-set range of extremal probabilities, and some of which do not, and subsequently selecting from the provided probabilities those probabilities that do not fall within a pre-set range of extremal probabilities such that probabilities within the pre-set range of extremal probabilities are excluded from the acquired probabilities. For example, a respective probability may be acquired for each readout measurement value occurring as a result of performing the readout measurement operation. Alternatively, the acquiring of a respective probability may comprise providing only those probabilities which do not fall within a pre-set range of extremal probabilities (i.e., none of the probability values provided to the decoder is an “extremal” probability because none has a value close enough to 0 or 1 to be considered “extremal”), such that probabilities within the pre-set range of extremal probabilities are excluded from the acquired probabilities. For example, a respective probability may be acquired for only those readout measurement values having a non-extremal (“moderate”) probability of occurring as a result of performing the readout measurement operation. The quantum computing system may comprise a data transmission system for transmitting the compressed measurement outcome data and / or may comprise a data storage system for storing the compressed measurement outcome data. The data transmission system may comprise a bus (or databus) configured within the quantum computing system for transferring data between components of the quantum computing system. The data transmission system may provide an “internal” data transmission channel in this sense (i.e., “internal” to the quantum computing system). The components of the quantum computing system may be connected (or connectable) in communication with the data compressor (e.g., communicatively connected by a communication link between them) for receiving data transmissions of the compressed measurement outcome data. The components may comprise data processing components (e.g., classical computer processors) configured for performing quantum error correction decoding to identify errors in the quantum information encoded in one or more of the plurality of quantum devices of the quantum computing system, and to generate corrections thereto. The quantum computing system may comprise such a decoding system for receiving the compressed measurement outcome data transmitted by the data transmission system, the decoding system being configured for executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices. The data transmission system may be configured for enabling data transmission / communications between the quantum computing system and an external computer(s). In this sense, the data transmission system may be configured to form a part of an overall data transmission channel, in use, a part of which is external to (but connectable to) the quantum computing system. The quantum computing system may comprise a distributed quantum computing system comprising, as a first component, the plurality of quantum devices, the readout system, and the data compressor, and further comprising the decoding system as a second component separate to, and separated from, the first component. In this case, the data transmission system may be configured for interfacing / communicating with an external wireless data transmission apparatus or network, such as a wired network such as an Ethernet, or an optical transport network (OTN), an optical local-area or wide-area network (LAN or WAN), or other wireless (but non-optical) telecommunications apparatus / network. The appropriate choice and configuration of the data transmission system may be made according to the nature of the physical separation between the first and second components of the distributed quantum computing system and the wireless data transmission apparatus or network available for use. For example, the first and second components may reside in different location within a building housing data centre network, or the like, such that the data transmission system may comprise one or more data centre optical interconnects. Alternatively, the first and second components may reside in different buildings within a city or within different cities such that the data transmission system may comprise a wider area national optical telecommunications network. Of course, the characteristics and performance of the data transmission system configured within the non-distributed quantum computing system, or the characteristics and performance of the wireless data transmission apparatus or network available for use by the distributed quantum computing system impose their own constraints on the maximum bit rate at which the compressed measurement outcome data may be transmitted. For example, in relation to a non-distributed quantum computing system, as an example of what may be considered a channel that is "internal" to the quantum computing system, data rates of between 10Gbps to 20Gbps or more may be achieved using an Advanced extensible Interface (AXI) bus. As another example, a high-speed interface known as the Peripheral Component Interconnect Express, PCIe, such as the PCI Express 5.0, is a common motherboard interface for peripheral connections and may provide data rates of between 100Gbps and 1000Gbps. In relation to a distributed quantum computing system, for example, a Gigabit ethernet restricts transmissions to data rates of 1 Gbps, or a data rate of 10Gbps in the case of the WGigabit ethernet. These maximum data-rates typically apply to a single cable and are typically only achievable over 10s of metres (e.g., components in different rooms but not different cities). Thus, by providing an intelligent means for compressing measurement outcome data, a suitably high flow of qubit readout information may be achieved using existing data transmission architectures without having to resort the expense and engineering difficulties of adding extra capacity to existing architectures. For example, the data rate provided by one 1Gbps Ethernet cable, or one internal data bus, may be boosted by adding a second Ethernet cable to the transmission channel, or by adding a second internal bus to the data transmission system. However, this increases the cost of the system. In the case of adding a second Ethernet cable, it requires both the receiver and sender to have two such cables making it harder to implement networking for the system. Same considerations apply to adding a second internal bus because these cost space on a processor (e.g., an FPGA or actual silicon on an ASIC or new PCIe slots). In general, this apparently simple solution, of using a second Ethernet cable, or of adding additional internal busses, increases the complexity and cost of building and maintaining the system. The compression of measurement outcome data disclosed herein also assists in permitting one to scale up the number of quantum devices for encoding information using quantum computational states such as is expected to occur when as the number of qubits within quantum computers grows. It is possible that useful quantum systems will involve a minimum of 1000 logical qubits, and a million physical qubits. The bandwidth requirements for transmitting measurement outcome data from such systems may well exceed the bandwidths of single cables and interconnects, and reductions in bandwidth requirements, enabled by the present invention, may lead to less cabling or fewer internal interconnects being needed. This may help reduce the cost and complexity of the quantum computing systems in question. The way in which the invention provides the benefits of making it easier to transmit qubit readout information (soft information) over limited bandwidth channels (whether “internal” or “external” channels), also provides a synergy with quantum error correction (QEC) decoding performance improvements. In particular, by excluding “extremal” probabilities from the compressed data to be transmitted, and selecting the non-extremal probabilities for transmission, the most important probabilities (soft information) for use in QEC decoding are retained. It is known in the art that such probabilities may be used to determine / update the “edge weights” in hyper-graph-based QEC decoding algorithms (e.g., belief propagation decoding, minimum-weight-perfect-matching decoding etc.), and that the non-extremal probabilities are the ones that matter most in this context, thereby making decoding less resourceintensive by requiring fewer edge weights be updated. The application of quantum state discrimination to (soft) readout measurement values to generate respective (hard) quantum state measurement outcome data may correspond to applying what is known in the art as a “hardening map” to the analogue (soft) readout measurement values, as discussed in references cited below. The application of quantum state discrimination to a(soft) readout measurement value may comprise comparing the readout measurement value to a pre-set threshold value (e.g., a “thresholding” process) and determining a 1 -bit binary value for the resulting quantum state readout measurement outcome value according to the comparison. For example, if the comparison reveals that a (soft) readout measurement value exceeds the pre-set threshold value, then the quantum state readout measurement outcome value may be set to a first pre-set binary value (e.g., “1”), else if the comparison reveals that a (soft) readout measurement value does not exceed the pre-set threshold value, then the quantum state readout measurement outcome value may be set to a second pre-set binary value (e.g., “0”), that is distinct from the first pre-set value. The application of quantum state discrimination to a(soft) readout measurement value may comprise comparing to a pre-set threshold value (e.g., a “thresholding” process), a probability of a given readout measurement value having occurred as a result of performing the readout measurement operation and determining a 1 -bit binary value for the resulting quantum state readout measurement outcome value according to the comparison. In this way, a mapping of a (soft) readout measurement value may comprise applying a process of quantum state discrimination to a probability of a given readout measurement value having occurred as a result of performing the readout measurement operation. For example, if the comparison reveals that a probability exceeds the pre-set threshold value, then the quantum state readout measurement outcome value may be set to a first pre-set binary value (e.g., “1”), else if comparison reveals that the probability does not exceed the pre-set threshold value, then the quantum state readout measurement outcome value may be set to a second pre-set binary value (e.g., “0”), that is distinct from the first pre-set value. Alternatively, the application of quantum state discrimination to a (soft) readout measurement value may comprise applying to the readout measurement value a machine learning (ML) algorithm trained for applying a process of quantum state discrimination, such as is readily available to the person skilled in the art (e.g., as discussed in references

[13] to

[17] below cited below). The acquiring of the respective probabilities of each of the readout measurement values occurring as a result of performing the readout measurement operation, may comprise acquiring pre-prepared data from a data store of the quantum computing system, or from an external data store with which the quantum computing system is configured to retrieve such data. The respective probabilities may be acquired from data describing the statistical distribution of a plurality of repeated readout measurement results associated with a given quantum device (e.g., a qubit). This data may be generated by performing a plurality (e.g., -100,000) of repeated readout measurements upon a given quantum device and storing the readout measurement values (e.g., in a digital form describing analogue values) in a data store. The statistical distribution may be normalised by the total number of the plurality of repeated readout measurement results, such that the statistical distribution describes a distribution of probabilities of a given readout measurement value occurring as a result of performing the readout measurement operation. The distribution of probabilities may define a probability density function. Here, the term “normalised” includes a reference to the result of dividing a frequency of occurrence of each readout measurement value described the statistical distribution, by the total number of readout measurements performed. The statistical distribution may describe a frequency of occurrence (or a probability) of measurement values falling within a respective one of a finite number of bins each spanning a respective unique finite range of possible measurement values. Here, the term “histogram” includes a reference to a chart that plots the distribution of a numeric variable's values as a series of bars. Each bar typically covers a range of numeric values called a bin or class; a bar's height indicates the frequency of occurrence of data points with a value within the corresponding bin. Accordingly, the statistical distribution may describe a histogram, e.g., a “readout histogram” such as described herein. The quantum computing system may comprise a quantum state discrimination unit configured to apply a quantum state discrimination process in respect of each of the (soft) readout measurement values thereby to provide a respective probability of each of the readout measurement values occurring as a result of performing the measurement operation. The quantum state discrimination unit may be configured to determine a probability of each of the (soft) readout measurement values according to a probability density function. The quantum state discrimination unit may be configured to perform a calibration process for generating data describing the probability density function. The calibration process may comprise repeatedly preparing and measuring a selected quantum device (e.g. a qubit) has been prepared in a selected quantum state of the computational bases (e.g., quantum state |0) or 11)), repeatedly applying the measurement operation upon quantum device, and repeatedly evaluating a corresponding probability of each of the (soft) readout measurement values occurring as a result of performing the measurement operation. The resulting distribution of probabilities may be used to provide the probability density function. Alternatively, the quantum state discrimination unit may be configured to apply a machine learning algorithm which is trained to apply the quantum state discrimination process and to thereby produce the probability of each (soft) readout measurement value occurring as a result of performing the measurement operation. The application of quantum state discrimination to the readout measurement values to generate respective quantum state measurement outcome values may map a (soft) readout measurement probability value to an integer representation (e.g., 0 or 1) for a quantum state of a quantum device, amongst the plurality of quantum devices, via a single bit. So-called “soft” information is preserved in terms of the probabilities, from amongst the acquired probabilities, which do not fall within a pre-set range of extremal probabilities. This preserved information may be described, for each probability, as a binary digit (multi-bit) having a bit depth that is selected by the user as appropriate to achieve a desired balance between achieving an acceptable level of accuracy whilst also achieving an acceptable level of compression enabling viable rates of data transmission from the data transmission system. The pre-set range of extremal probabilities may be pre-set by the user with this balance in mind. A probability may be considered to be extremal, for example, if the value of the probability differs from a value of 0.5 by more than 0.25. For example, for a first pre-set range of extremal probabilities, the probabilities, p, in the range: pLower <p <Pupper may be considered to be extremal probabilities, if the lower bounding probability ofthe range, PLower^ is itself in the range: 0.75 <pLower <1.0. The upper bounding probability ofthe range, pUpper, may be a value in the range: 0.75 <pUpper <1.0. For example, the value of pUpper may be set to Pupper = l-°, and the value of pLower may be varied by the user as appropriate. Alternatively, for a second pre-set range of extremal probabilities, or in addition to the first pre-set range of extremal probabilities, for example, probabilities, p, in the range: pLower <p <pUpper may be considered to be extremal probabilities, if the upper bounding probability ofthe range, pUpper, is itself in the range: 0.0 <pUpper <0.25. The lower bounding probability ofthe range, pLower, may be a value in the range: 0.0 <pLower <0.25. For example, the value of pLower may be set to pLower = 0.0, and the value of pUpper may be varied by the user as appropriate. One example, but not the only example, ofthe benefits that flow from preserving some ofthe probabilities (soft information) is its subsequent use in error correction decoding. Such decoding is generally performed using a decoding graph (or decoding hypergraph) with weighted edges. For example, many surface code decoding algorithms work by grouping “defects” (non-trivial stabiliser check outcomes) on a decoding graph. The “soft information” contained in the preserved probabilities may be used, according to the invention, to adjust the edge weights to account for confidence in quantum state measurement outcomes, thereby increasing the accuracy ofthe decoder. This may also aid the speed ofthe decoder because only those probabilities, from amongst the acquired probabilities, which do not fall within a preset range of extremal probabilities are considered for this purpose by the decoder, resulting in fewer edge weights to update and any edges that correspond to readout measurements having associated probabilities which do fall within a pre-set range of extremal probabilities mean (by virtue of their extremal probability value) that one can ascribe to them a high level of confidence of being associated with a given qubit quantum state to which they are classified. Edge weights forthose measurements have little need of update. The compression scheme can also be used in the case where the input to the decoder is in the form of soft detection events (or “defect probabilities”). The mapping from measurement probabilities (e.g., probabilities from or for quantum state discrimination unit) to defect probabilities may be performed using a Soft XOR using known techniques readily available to the person skilled in the art (e.g., see Appendix. A.1.7 in reference [1] below, and Appendix. C.1 in reference [2] below). In other words, the compression according to the invention may provide only the soft information (e.g., classification probabilities) needed to update those edges in the decoding graph where the probability of a soft measurement error (i.e., a mistake in classification) is high, while effectively setting to zero the classification error probability for those measurements where the soft probability falls within a pre-set range of extremal probabilities, and is compressed away. There are fewer computations that need to be made by the decoder: as only a small number of soft probabilities are provided to the decoder, only a few edges need to be updated, and the edges that are updated are the ones where the change is the most significant. This makes the decoding process simpler, therefore faster. The pre-set range of extremal probabilities may comprise two sub-ranges of extremal probabilities separated from each other by a contiguous intermediate range of non-extremal probabilities, wherein the data compressor is arranged to compress the readout measurement data by performing quantum state discrimination upon the readout measurement values having a respective probability, from amongst the acquired probabilities, falling within any of the two sub-ranges thereby generating respective quantum state measurement outcome data values. In his way, an intermediate range of “moderate” probability values may separate two different “extremal” probability sub-ranges. In other words, the pre-set range of extremal probabilities may be discontinuous, rather than continuous. One extremal sub-range of the two sub-ranges may comprise probability values that are lower than any probability value in the other extremal sub-range of the two sub-ranges and lower than any probability value in the intermediate range of probabilities. One extremal sub-range of the two sub-ranges may comprise probability values that are higher than any probability value in the other extremal sub-range of the two sub-ranges and higher than any probability value in the intermediate range of probabilities. For example, the pre-set range of extremal probabilities may be split into a “tail” of low probability values and a “tail” of high probability values at opposite respective ends of the intermediate range of “moderate” probability values. The pre-set range of extremal probabilities may be contiguous with an adjacent range of probabilities which encompasses all of the probabilities from amongst the acquired probabilities that are not encompassed by the pre-set range of extremal probabilities. For example, the pre-set range of extremal probabilities may define a single “tail” of high probability values or a single “tail” of low probability values. The pre-set range of extremal probabilities, or each one of the two sub-ranges as appropriate, may extend: from an uppermost probability value of 1 (unity) to a lowermost probability value exceeding 0 (zero); and / or, from a lowermost probability value of 0 (zero) to an uppermost probability value exceeding 0 (zero). Each of the respective quantum state measurement outcome data values within the compressed measurement outcome data may be represented by a single bit, and each of the probabilities within the compressed measurement outcome data is represented by a plurality of bits. The bit depth of the plurality of bits may be the same for each of the probability values or may differ as between different probability values. For example, probability values within a pre-set or user-defined sub-interval within the intermediate probabilities may be represented using a bit depth that is greater than a bit depth used to represent other intermediate probability values that are not in the sub-interval. The data compressor may be configured to compress the measurement data by applying quantum state discrimination to each readout measurement value produced by the readout system, thereby to generate said respective quantum state measurement outcome data values (e.g., in 1 -bit binary form) such that the compressed measurement outcome data comprises quantum state measurement outcome data corresponding to each readout measurement value produced by the readout system. The data compressor may be configured to generate the compressed measurement outcome data such that the quantum state measurement outcome data values provide an array of values in which each quantum state measurement outcome value is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated. The quantum state measurement outcome data values may be arranged to form an array ordered according to the ascending or descending order of the value of the respective probability, from amongst the provided probabilities, with which they are associated. The quantum state measurement outcome data values may be arranged to form an array ordered in the same order as the order of the values of the respective probabilities, from amongst the provided probabilities, with which they are associated. The order of the values of the respective probabilities, from amongst the provided probabilities, may be the same order as the order in which the corresponding readout measurements occurred. The data compressor may be configured to generate, in respect of each of the quantum state measurement outcome data values, a respective further data item having: a first value if the associated probability value falls within said pre-set range; or, a second value, distinct from the first value, if the associated probability value falls outside said preset range. For example, the further data item may serve as a “flag” to indicate when an associated probability value is extremal or not extremal (i.e., “moderate”). Each further data item may be represented by a single bit. For example, a bit value of “0” for the further data item may indicate that an associated probability is extremal, and a value of “1” for the further data item may indicate that the associated probability is not extremal (i.e., “moderate”), or vice versa. The data compressor may be configured to generate the compressed measurement outcome data such that the respective further data items form an array of values in which each further data item is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated. The further data items may be arranged to form an array ordered according to the ascending or descending order of the value of the respective probability, from amongst the provided probabilities, with which they are associated. The further data items may be arranged to form an array ordered in the same order as the order of the values of the respective probabilities, from amongst the provided probabilities, with which they are associated. The order of the further data items may be the same order as the order in which the corresponding readout measurements occurred. The data compressor may be configured to acquire the probabilities by obtaining data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation and by applying a data compression (e.g., a lossy compression or otherwise) to at least some of the obtained data thereby to provide said acquired probabilities. In this way, a preprocessing may be applied to probability values that have been initially obtained, with the aim of acquiring probability values that are in a compressed form, or otherwise require a lower data transmission (and / or data storage) overhead. The processing the obtained probabilities, before they are incorporated into the compressed measurement outcome data as the acquired probabilities, may comprise an intermediate step of applying a compression function to the data describing the obtained probabilities. A compression method such as would be readily available to the skilled person may be employed. The compression may be a lossy compression. Examples include, but are not limited to, reducing the number of bits used (e.g., bit depth) to represent some or each of the probability values incorporated within the resulting acquired probabilities. Examples include, but are not limited to, “binning” some or all of the obtained probability values into a to a respective one of a pre-set finite number of distinct probability “bins” such that some or all of the binned probabilities acquires a value corresponding to the probability represented by the bin in question. This may reduce the number of distinct probability values incorporated within the resulting acquired probabilities. For example, each probability amongst the acquired probabilities may be described according to a respective one of finite number of contiguous probability sub-intervals (e.g., a “bin” width), wherein: a width of each of the probability sub-intervals is common to all of the probability sub-intervals; or a respective width of one or more of the probability sub-intervals differs from a width of one or more other probability sub-intervals amongst said probability sub-intervals. Put in other words, all bin widths may share the same size or, alternatively, not all bin widths may share the same size. Wider bin widths increase the compression applied, and therefore a choice of the width of a given probability bin may be set according to preferences or advantages as appropriate. As an example, the width of a given probability bin for non-extremal (“moderate”) probability values may be set to be narrower than the width of any probability bin for an extremal probability value. As an example, the width of a given probability bin may be set to increase (or decrease) according to the proximity of the bin in question to the nearest bin to it that is associated with an extremal probability. This would mean that the widths of probability bins associated with non-extremal (“moderate”) probabilities that are located furthest from extremal probabilities would be narrower (or wider) than those located closer to extremal probabilities. This permits the resolution / granularity of the acquired probabilities to be higher (or lower) for the more / most moderate probability values as compared to the extremal probabilities. The data compressor may be configured to generate the compressed measurement outcome data comprising a composite array comprising the array of quantum state measurement outcome data values and the array of respective further data items. The composite array may comprise an array of 2-bit elements in which one bit of each 2-bit element comprises a quantum state measurement outcome data value and one bit of each 2-bit element comprises a said further data item. The data compressor may be configured to generate the compressed measurement outcome data comprising two separate arrays comprising the array of quantum state measurement outcome data values as one of the two arrays and comprising the array of respective said further data items as one of the two arrays. The quantum computing system may comprise a quantum state discrimination unit configured to apply a quantum state discrimination process in respect of each of the readout measurement values thereby to provide a respective said probability of each of the readout measurement values occurring as a result of performing the readout measurement operation. The readout measurement operation may comprise a syndrome measurement operation and the compressed measurement outcome data may comprise syndrome data representative of an error state of other quantum devices amongst the plurality of quantum devices. The quantum computing system may comprise a data transmission system for transmitting the compressed measurement outcome data. The quantum computing system may comprise a decoding system for receiving the compressed measurement outcome data from the data compressor and for executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices. In a second aspect, the invention may comprise a distributed quantum computing system comprising, as a first component, the quantum computing system disclosed herein according to the first aspect of the invention, and further comprising, as a second component separated from the first component, a decoding system for receiving the compressed measurement outcome data transmitted by the data transmission system, the decoding system being configured for executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices. In the distributed quantum computing, the decoding system may be configured to determine a correction for an error state by decoding the syndrome data using the quantum error correction algorithm. A syndrome (also referred to as syndrome data) is a collection of values (e.g. measurement values, generally based on qubit measurements, in particular syndrome qubit measurement) representative of an error state of physical data qubits in the quantum computer. Syndrome data may be obtained by measuring a plurality of syndrome qubits (e.g. surface code stabiliser measurements). The syndrome data may also comprise additional data, such as a bitstring (or similar) describing whether each quantum device is in a leaked or unleaked state. Many quantum error correction codes involve measuring stabilisers and detecting changes in stabiliser measurement values between successive measurement rounds. Each pair of successive measurements is referred to as a detector. In the absence of errors, the parity of measurements associated with the detector should be consistent (i.e. both should have the same value). A defect occurs if the measurement values of a detector disagree (i.e. are different). A defect may represent the end of a chain of errors in a decoding graph (the chain of errors may span both space-like and time-like dimensions of the decoding graph). In other words, defects are non-trivial syndrome values, and they may correspond to a change in value of a syndrome qubit measurement outcome between successive rounds of syndrome measurement. A decoding system (also referred to herein as a decoder) is a classical computing system that decodes syndromes and provides one or both of (i) possible error locations (i.e. which data qubits may have experienced an error), and (ii) a correction for the qubit error state. It is possible to determine a correction during decoding without determining error locations, and the correction may be a single bit representing whether a logical error has occurred. The correction can generally be tracked by a classical computer (e.g. by the decoder or a control system) and does not generally need to be applied to the quantum devices. The decoder may be a dedicated hardware device (e.g. implemented using an FPGA or ASIC or similar) or it may be a software component implemented using a CPU. The quantum error correction algorithm may implement a surface code (e.g. planar code) error correction procedure. Alternatively, the quantum error correction algorithm may be any other error correction algorithm that utilises a decoding hypergraph (e.g. a decoding graph), such as other topological quantum error correction algorithms. The decoding system may be configured to determine said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to respective probabilities from amongst the probabilities within the compressed measurement outcome data. A decoding hypergraph may be a decoding graph, and the hyperedges may be edges. A hypergraph is a generalisation of a graph in which edges (“hyperedges”) can be connected to more than two nodes (graphs are a specific type of hypergraph in which each edge connects to two nodes). The methods of the present invention apply equally to decoding hypergraphs. Accordingly, any reference herein to decoding graphs and edges should be understood to also encompass decoding hypergraphs and hyperedges respectively. Decoding hypergraphs (especially decoding graphs) are used in many error correction codes (such as topological error correction codes including the surface code) to facilitate decoding of the syndrome by pairing (or grouping) “defects” in the syndrome (these defects generally provide an indication of end points of chains (or hyperchains) of errors on physical data qubits in the error correction code). A decoding hypergraph is a hypergraph (in the mathematical sense) comprising hyperedges representing error mechanisms, and nodes (or vertices) representing differences in successive syndrome measurements (or more generally, a decoding hypergraph comprises nodes representing detectors, which are measurement results that sum to zero (e.g. modulo 2 sum) during perfect (i.e. error-free) operation of the quantum computing system). The decoding system may comprise a transmitter system for transmitting the quantum error correction data to the first component of the distributed quantum computing system for use in correcting errors in the quantum computing system associated with the quantum devices thereof. The first component of the distributed quantum computing system may comprise a receiver system for receiving quantum error correction data from the second component of the distributed quantum computing system, for use by the first component of the distributed quantum computing system in correcting errors associated with quantum devices thereof. The quantum computing system according to any aspect of the invention, may comprise a data storage system for storing the compressed measurement outcome data. In a further aspect, the invention may provide a decoder comprising a computing system configured for receiving compressed measurement outcome data generated by a quantum computing system, the compressed measurement outcome data comprising: quantum state measurement outcome values generated by the quantum computing system by applying a quantum state discrimination process upon readout measurement values produced by performing a readout measurement operation upon quantum devices thereof which encode information using quantum computational states; and, data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data; wherein the decoder is configured to execute a quantum error correction algorithm to determine a correction for an error state of one or more said quantum devices using said quantum state measurement outcome values and said data describing probabilities. The decoder may be configured to determine said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to respective probabilities from amongst said probabilities within the compressed measurement outcome data. The decoder may comprise a transmitter system for transmitting quantum error correction data describing said correction for an error state to the quantum computing system according to the invention in its first aspect for use in correcting errors in the quantum computing system associated with quantum devices thereof. In a third aspect, the invention may provide a method for compression of data generated by a quantum computing system comprising a plurality of quantum devices that encode information using quantum computational states and comprising a readout system that performs a readout measurement operation upon quantum devices from amongst the plurality of quantum devices to produce readout measurement data describing analogue readout measurement values; wherein the data compression method comprises: acquiring data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation; performing quantum state discrimination upon the readout measurement data thereby generating respective quantum state measurement outcome data values; producing compressed measurement outcome data comprising the quantum state measurement outcome data values and data describing probabilities, from amongst the acquired data describing probabilities, which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data. The method may include providing the compressed measurement outcome data to a data transmission system for transmission therefrom. The method may comprise providing the compressed measurement outcome data to a data storage system for storing the compressed measurement outcome data. In the method, the pre-set range of extremal probabilities my comprise two sub-ranges of extremal probabilities separated from each other by a contiguous intermediate range of non-extremal probabilities, and the method includes compressing the readout measurement data by performing quantum state discrimination upon the readout measurement values having a respective probability, from amongst the acquired probabilities, falling within any of the two sub-ranges thereby generating respective quantum state measurement outcome data. According to the method, the pre-set range of extremal probabilities may be contiguous with an adjacent range of probabilities which encompasses all of the probabilities from amongst the acquired probabilities that are not encompassed by the pre-set range of extremal probabilities. The pre-set range of extremal probabilities may extend: from an uppermost probability value of 1 (unity) to a lowermost probability value exceeding 0 (zero); and / or, from a lowermost probability value of 0 (zero) to an uppermost probability value exceeding 0 (zero). Each of the respective quantum state measurement outcome data values within the compressed measurement outcome data may be represented by a single bit, and each of the probabilities within the compressed measurement outcome data is represented by a plurality of bits. The method may comprise compressing the measurement outcome data by performing quantum state discrimination upon each readout measurement value produced by the readout system, thereby to generate said respective quantum state measurement outcome data such that the compressed measurement outcome data comprises quantum state measurement outcome data corresponding to each readout measurement value produced by the readout system. The method may comprise generating the compressed measurement outcome data such that the quantum state measurement outcome data values provide an array of values in which each quantum state measurement outcome value is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated. The quantum state measurement outcome data values may be arranged to form an array ordered according to the ascending or descending order of the value of the respective probability, from amongst the provided probabilities, with which they are associated. The quantum state measurement outcome data values may be arranged to form an array ordered in the same order as the order of the values of the respective probabilities, from amongst the provided probabilities, with which they are associated. The order of the values of the respective probabilities, from amongst the provided probabilities, may be the same order as the order in which the corresponding readout measurements occurred. The method may comprise generating, in respect of each of the quantum state measurement outcome data values, a respective further data item having: a first value if the associated probability value falls within said pre-set range; or, a second value, distinct from the first value, if the associated probability value falls outside said preset range. In the method, each further data item may be represented by a single bit. The method may comprise generating the compressed measurement outcome data such that the respective further data items form an array of values in which each further item is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated. The further data items may be arranged to form an array ordered according to the ascending or descending order of the value of the respective probability, from amongst the provided probabilities, with which they are associated. The further data items may be arranged to form an array ordered in the same order as the order of the values of the respective probabilities, from amongst the provided probabilities, with which they are associated. The order of the further data items may be the same order as the order in which the corresponding readout measurements occurred. The method may comprise acquiring said probabilities by obtaining data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation and by applying a data compression to at least some of the obtained data thereby to provide said acquired probabilities. According to the method each probability amongst said acquired probabilities may be described according to a respective one of finite number of contiguous probability sub-intervals, wherein: a width of each of the probability sub-intervals is common to all of the probability sub-intervals; or a respective width of one or more of the probability sub-intervals differs from a width of one or more other probability sub-intervals amongst said probability sub-intervals. The method may comprise generating the compressed measurement outcome data comprising a composite array comprising the array of quantum state measurement outcome data values and the array of respective further data items. The composite ordered array may comprise an array of 2-bit elements in which one bit of each 2-bit element comprises a quantum state measurement outcome data value and one bit of each 2-bit element comprises a further data item. The method may comprise generating the compressed measurement outcome data comprising two separate arrays comprising the array of quantum state measurement outcome data values as one of the two arrays, and comprising the array of respective further data items as one of the two arrays. The method may comprise, by a quantum state discrimination unit, applying a quantum state discrimination process in respect of each of the readout measurement values thereby to provide a respective said probability of each of the readout measurement values occurring as a result of performing the readout measurement operation. According to the method, the readout measurement operation may comprise a syndrome measurement operation and the compressed measurement outcome data comprises syndrome data representative of an error state of other quantum devices amongst the plurality of quantum devices. The method may comprise providing a decoding system for receiving the compressed measurement outcome data from the data compressor and, by the decoding system, executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices. In a fourth aspect, the invention may provide a method for distributed quantum computing using a distributed quantum computing system comprising a first component and a second component separated from the first component and comprising a decoding system, the method comprising: by the first component, implementing the quantum computing as disclosed herein with reference to the third aspect of the invention; and, by the second component, receiving the compressed measurement outcome data transmitted by the data transmission system and, by the decoding system, executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices. The method for distributed quantum computing may comprise, by the decoding system, determining a correction for an error state by decoding the syndrome data using the quantum error correction algorithm. The method for distributed quantum computing may comprise, by the decoding system, determining said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to the respective probabilities from amongst the probabilities within the compressed measurement outcome data. The invention may provide a method for distributed quantum computing comprising, by the second component, transmitting the quantum error correction data to the first component of the distributed quantum computing system for use in correcting errors in the first component of the distributed quantum computing system associated with the quantum devices thereof. The invention may provide a method for distributed quantum computing comprising, by the first component, receiving quantum error correction data from the second component of the distributed quantum computing system, for use by the first component of the distributed quantum computing system in correcting errors associated with quantum devices thereof. In a fifth aspect, the invention may provide a decoding method comprising: receiving compressed measurement outcome data generated by a quantum computing system, the compressed measurement outcome data comprising: quantum state measurement outcome values generated by the quantum computing system by applying a quantum state discrimination process to readout measurement values produced by performing a readout measurement operation upon quantum devices thereof which encode information using quantum computational states; and, data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data; wherein the decoding method further comprises executing a quantum error correction algorithm to determine a correction for an error state of one or more said quantum devices using said quantum state measurement outcome values and said data describing probabilities. The decoding method may further comprise determining said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to respective probabilities from amongst said probabilities within the compressed measurement outcome data. The decoding method may comprise transmitting quantum error correction data describing said correction for an error state to the quantum computing system according to the first aspect of the invention for use in correcting errors in the quantum computing system associated with quantum devices thereof. In a further aspects, the invention may provide: a computer program comprising code which, when run on a computer, causes the computer to perform the method of the third aspect and / or the method of the fourth aspect; a non-transitory computer readable storage medium storing a computer program comprising code which, when run on a computer, causes the computer to perform the method of the third aspect and / or the method of the fourth aspect; and a computer system programmed to perform the method of the third aspect and / or the method of the fourth aspect. The computer or the computer system may comprise a quantum computing system. The term “computer system” includes the hardware, software, and data storage devices for embodying a system or carrying out a method according to the above-described aspects. For example, a computer system may comprise a central processing unit (CPU) and / or a quantum processing unit (QPU), input means, output means and data storage. The computer system may have a monitor to provide a visual output display. The data storage may comprise RAM, disk drives or other computer readable media. The computer system may include a plurality of computing devices connected by a network and able to communicate with each other over that network. The methods of the above aspects may be provided as computer programs or as computer program products or computer readable media carrying a computer program which is arranged, when run on a computer, to perform the method(s) described above. The term “computer readable media” includes, without limitation, any non-transitory medium or media which can be read and accessed directly by a computer or computer system. The media can include, but are not limited to, magnetic storage media such as floppy discs, hard disc storage media and magnetic tape; optical storage media such as optical discs or CD-ROMs; electrical storage media such as memory, including RAM, ROM and flash memory; and hybrids and combinations of the above such as magnetic / optical storage media. The invention includes the combination of the aspects and preferred features described except where such a combination is clearly impermissible or expressly avoided. Summary of the Figures Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures in which: Figure 1 schematically illustrates process of measurement applied to a qubit. Figure 2 schematically illustrates readout histograms (probability density functions) for readout measurement values obtained by applying a process of readout measurement of a quantum state of a Transmon qubit; Figure 3 schematically illustrates a data cloud of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state 10), alongside a readout histogram (probability density function) for readout measurement values obtained by applying a process of readout measurement of the quantum state of a Transmon qubit, and a histogram of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated with a quantum state |0); Figure 4 illustrates, for a Transmon qubit repeatedly prepared in a quantum state |0) and subject to a readout measurement, on 100,000 separate occasions, a histogram of the frequency of occurrence of respective probabilities that a given readout measurement value arose as the result of applying the readout measurement operation to a quantum state |0); Figure 5 schematically illustrates a data cloud of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state 11), alongside readout histograms (probability density functions) for readout measurement values obtained by applying a process of readout measurement of the quantum state of a Transmon qubit, and a histogram of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0); Figure 6 illustrates, for a Transmon qubit repeatedly prepared in a quantum state |1) and subject to a readout measurement, on 100,000 separate occasions, a histogram of the frequency of occurrence of respective probabilities that a given readout measurement value arose as the result of applying the readout measurement operation to a quantum state |0); Figure 7 schematically illustrates two data clouds of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state : 0 = (|0) + |1)) / V2, alongside readout histograms (probability density functions) for readout measurement values obtained by applying a process of readout measurement of the quantum state of a Transmon qubit, and a histogram of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0); Figure 8 illustrates, for a Transmon qubit repeatedly prepared in a quantum state: 0 = (|0) + |1)) / V2, and subject to a readout measurement, on 100,000 separate occasions, a histogram of the frequency of occurrence of respective probabilities that a given readout measurement value arose as the result of applying the readout measurement operation to a quantum state |0); Figure 9 schematically illustrates an input to, and a compressed output of, a data compressor for compressing the measurement outcome data according to a first example; Figure 10 schematically illustrates an input to, and a compressed output of, a data compressor for compressing the measurement outcome data according to a second example; Figure 11 schematically illustrates an input to, and a compressed output of, a data compressor for compressing the measurement outcome data according to a third example; Figure 12 schematically illustrates an input to, and a compressed output of, a data compressor for compressing the measurement outcome data according to a fourth example; Figure 13 schematically illustrates a quantum computer system; Figure 14 schematically illustrates a distributed quantum computer system; Figure 15 schematically illustrates steps in a method of data compression. These steps may form non-transitory instructions in a computer-readable medium which, when executed by a quantum computing system, cause the quantum computing system to carry out the method of according to the invention; Figure 16 illustrates a relationship between a compression control parameter in a method of data compression, and the consequential degree of binarization of qubit readout measurement values; Figures 17(A) and 17(B) illustrate a relationship between: (A) a compression control parameter in a method of data compression on qubit readout measurement outcome data from qubits of a quantum computing system, and the consequential logical qubit error probability in the quantum computing system subject to QEC decoding using the compressed measurement outcome data; and (B) a compression ratio in compressed qubit readout measurement outcome data from qubits of a quantum computing system, and the consequential logical qubit error probability in the quantum computing system subject to QEC decoding using the compressed measurement outcome data. Detailed Description of the Invention Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference. Figure 3 shows in schematic form a data cloud 2 of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state |0). Each measurement value is represented as a voltage phasor possessing an “in-phase” ( / ) component and a “quadrature” (Q) component, as discussed above. A small sample of these readout measurement values (phasors) is shown in the form of black dots (“•”) to indicate a variation in measurement values. The notional position (marked by an “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside is indicated alongside a second notional position (also marked by an “X”) where that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside if the qubit in question had been prepared in the quantum state |1). This second notional position is not attended by a data cloud given that the qubit in question has, in fact, been prepared in the quantum state 10), and this fact is indicated by the square border surrounding the “ket” symbol “|0)” in Figure 3, for the prepared quantum state. A readout histogram 6 defines a probability density function for the distribution of the values obtained for the “in-phase” ( / ) component of the readout voltage phasors obtained as analogue readout measurement values after applying the process of readout measurement to the prepared quantum state of the Transmon qubit. This probability density function may be obtained by dividing, into a finite number of finite-width bins, the continuous range of possible analogue values of the “in-phase” ( / ) component of the readout voltage phasors, accumulating statistics of this “in-phase” ( / ) component over many (e.g., 100,000) repeated measurements of the qubit when repeatedly prepared in the quantum state |0) so as to populate the histogram, and finally dividing the population of each bin by the total number of measurement repeats (e.g., by 100,000) in order to convert the population of each bin into a probability that a readout measurement result will fall into that bin. The result is a probability density function, in histogram form. Concentric circles (a, b, c, d, and e) are shown upon the data cloud 2, each being centred upon the notional position (marked by an “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside. Each circle demarcates a contour of constant data cloud density and, therefore a respective position 24 of constant probability upon the probability density function 6. Successive concentric circles differ in radius by an amount corresponding to a fixed proportion of the height of the probability density function, such that the five concentric circles separate six successive intervals of probability. Each one of the six intervals of probability has a width equal to that of each one of the other five intervals of probability which define six probability bins (a’, b’, c’, d’, e’ and f) of equal width in a histogram 26 of the frequency of probability occurrence for respective probabilities. Each probability bin covers a respective finite range of probabilities that a given readout measurement value, amongst the 100,000 measurement values, arose as the result of applying the readout measurement operation to a quantum state |0). For example, in the schematic representation of Figure 3, the six probability bins cover the following respective bin ranges of probability, P: Bin f: 0 <P <1 / 6 Bina’: 1 / 6 <P <2 / 6 Bin b’: 2 / 6 <P <3 / 6 Bin c’: 3 / 6 <P <4 / 6 Bind’: 4 / 6 <P <5 / 6 Bine’: 5 / 6 <P <1 Each bar of the frequency of probability occurrence histogram has a height (“Frequency (%)”) indicating the relative frequency of occurrence of probabilities in these respective probability bins. Clearly, Bin e’ possesses the tallest histogram bar indicating that the great majority of readout measurement values possess an “in-phase” ( / ) component which, according to the probability density function 6, has a high probability of arising as the result of applying the readout measurement operation to a quantum state |0). This corresponds to the strong clustering of the readout measurement values (phasors) shown in the form of black dots (“•”) in Figure 3, around the notional position (marked by an “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside. However, a wider spread of the readout measurement values (phasors) is also shown and a differing number of these fall within one of the bins a’, b’, c’, d’ and f according to the degree of noise present during the act of readout measurement. It is noted that the frequency of occurrence of probabilities in the bins d’, c’, b’, and a’ successively fall, in that order, indicating that the occurrence of low probabilities falls as the position of readout measurement values (phasors) moves away from the notional noise-free phasor position (“X”). However, the frequency of occurrence of probabilities in Bin f is slightly larger than that in Bin a’. This may arise due to a state preparation error: if the true state of the wavefunction was 1^) = a|0) + / ?11) where p is non-zero, the measurement has a finite probability of collapsing the state into the |1) basis state. Note that an initial state preparation of state |0) cannot naturally collapse to state |1) but may be excited to state |1) by an excitation process. As such, excitation to state |1) requires an interaction with the environment, such as noise from the surroundings or an error in a measurement pulse from the qubit readout system. Thus, the initially prepared quantum state |0) of the Transmon may be excited into the quantum state |1) of the Transmon thereby permitting the act of readout measurement to induce a collapse of the wavefunction of the Transmon as follows: Target state preparation: \ip) = 10) -> Actual state preparation: \ip) = <z|0) + / ?|1) -> collapse: |1) Accordingly, the frequency of occurrence of probabilities in Bin f may be caused to rise, and this is the cause of the minor secondary peak 12 in the probability density function defined by the readout histogram 6. This secondary peak has a peak (in probability) that falls within the probability interval defined by Bin f: 0 <P <1 / 6. A threshold is defined as being at the boundary between Bin d’ and Bin e’, of the histogram 26 of the frequency of probability occurrence, demarcates “extremal” probabilities of the histogram from nonextremal probabilities referred to here as the “moderate” region of the histogram. Bin e’: 5 / 6 <P <1, is deemed to define “extremal” probabilities - in this example, those probabilities being closest to an extreme end of the probability interval: [0,1], and including an interval end point. A probability value falling within a given probability bin may be counted as an occurrence of a probability having a value corresponding to the mid-point of the probability bin in question. Figure 4 illustrates a histogram of the frequency of occurrence of respective probabilities, P(z = 0), for a true Transmon qubit that was repeatedly prepared in a quantum state |z) = |0) and subject to a readout measurement, on 100,000 separate occasions. This histogram shows the relative frequency (expressed as a % on a logarithmic scale) of occurrence of probabilities that a given readout measurement value (“in-phase” ( / ) voltage component) arose as the result of applying the readout measurement operation to the Transmon when in the quantum state |z) = |0). Here, the probability interval [0, 1] of the histogram is divided into 32=25 separate bins of equal bin width. This means that each probability bin can be represented by a respective one of the 32 distinct binary numbers that can be represented by a 5-bit binary number, from decimal 0 to decimal 31, as indicated at the upper horizontal axis of Figure 4. In this case, a probability Pt value falling within the ith probability bin (i = 0 to 31) may be counted as an occurrence of a probability having a value determined by the decimal value, i, of the binary number representation of the probability bin in question, such that: Pt = i / 31. In this example, a threshold is positioned to demarcate “extremal” probabilities of the histogram, for which: Pt >30 / 31, i. e.,i = 30 or 31, from a “moderate” region of non-extremal probabilities for which: Pt <30 / 31, i. e., i = 0 to 29. It is to be noted that the ordinate axis of the histogram of Figure 4 expresses relative frequency of occurrence of probabilities on a logarithmic scale. This means that the height of the histogram bar for the most frequent of the extremal probabilities is of the order of between 100x and 10,000x higher than any of the other histogram bars, especially those in the “moderate” region. This means that when compression is applied to the readout measurement data associated with extremal probabilities, as described in more detail below, the compression rate is very high. Figure 5 shows in schematic form a data cloud 4 of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state |1). Each measurement value is represented as a voltage phasor possessing an “in-phase” ( / ) component and a “quadrature” (Q) component, as discussed above. A small sample of these readout measurement values (phasors) is shown in the form of black dots (“•”) to indicate a variation in measurement values. The notional position (marked by an “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside is indicated alongside a second notional position (also marked by an “X”) where that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside if the qubit in question had been prepared in the quantum state |0). This second notional position is not attended by a data cloud given that the qubit in question has, in fact, been prepared in the quantum state 11), and this fact is indicated by the square border surrounding the “ket” symbol “|1)” in Figure 5, for the prepared quantum state. A readout histogram 8 defines a probability density function for the distribution of the values obtained for the “in-phase” ( / ) component of the readout voltage phasors obtained as analogue readout measurement values after applying the process of readout measurement to the prepared quantum state of the Transmon qubit. In a manner directly analogous to that discussed above with reference to Figure 3, this probability density function may be obtained by dividing, into a finite number of finite-width bins, the continuous range of possible analogue values of the “in-phase” ( / ) component of the readout voltage phasors, accumulating statistics of this “in-phase” ( / ) component over many (e.g., 100,000) repeated measurements of the qubit when repeatedly prepared in the quantum state |1) so as to populate the histogram, and finally dividing the population of each bin by the total number of measurement repeats (e.g., by 100,000) in order to convert the population of each bin into a probability that a readout measurement result will fall into that bin. The result is a probability density function, in histogram form. However, the concentric circles (a, b, c, d, and e) that are centred upon the notional position (marked by the left-hand “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside when the Transmon is prepared in the quantum state 10), show little overlap with the data cloud 4 associated with readout measurement of the Transmon when prepared in the quantum state |1). As noted above, each one of the six probability bins (a’, b’, c’, d’, e’ and f) in the histogram 28 of the frequency of probability occurrence covers a respective finite range of probabilities that a given readout measurement value, amongst the 100,000 measurement values, arose as the result of applying the readout measurement operation to a quantum state |0), rather than a quantum state |1). Given that the Transmon was prepared in the quantum state 11), this means that each bar of the frequency of probability occurrence histogram 28 has a height (“Frequency (%)”) indicating very different relative frequencies of occurrence when compared to the histogram 26 of Figure 3. Bin f possesses the tallest histogram bar indicating that the great majority of readout measurement values possess an “in-phase” ( / ) component which, according to the probability density function 6, has a low probability of arising as the result of applying the readout measurement operation to a quantum state |0). This is, of course, because the state was not initially prepared in the quantum state |0), although some unintended relaxation process to the quantum state |0) may occur thereby populating Bin e’, permitting the act of readout measurement to induce a collapse of the wavefunction of the Transmon as follows: \ip) = |1) -> relaxation process: \ip) = |0) For a |1) -> |0) transition, the mechanism may be as follows. A qubit in an excited state naturally tends to relax from the excited state |1) into the ground state |0). The initial state can thus be a pure |1) state, and it is a natural relaxation event (also known in the literature as an “amplitude damping” or “T1 -event”) that causes it to decay to the |0) state. As a result of the different processes having very different probabilities, a 11) —> |0) relaxation transition is common whereas a 10) —> |1) excitation transition is relatively rare. Consequently, although not shown in figures 2, 3, 5 and 7, the respective readout histograms may possess secondary peak, 10 and 12, of different sizes. Often the |0)-state readout histogram may show a relatively small secondary peak, while the |l)-state readout histogram may show a larger secondary peak. This corresponds to the strong clustering of the readout measurement values (phasors) shown in the form of black dots (“•”) in Figure 5, around the notional position (marked by the right-hand “X”) that one would expect a perfectly noise-free qubit readout measurement value (phasor) to reside arising from readout measurement of a Transmon initially prepared in the quantum state |1). A degree of readout noise present during the act of readout measurement populates the frequency of occurrence of probabilities in the bins a’, d’, c’, b’, and e’. Accordingly, the frequency of occurrence of probabilities in Bin e’ may be caused to rise, and this is the cause of the minor secondary peak 10 in the probability density function defined by the readout histogram 8. This secondary peak has a peak (in probability) that falls within the probability interval defined by Bin e’: 5 / 6 <P <1. A threshold located at the boundary between Bin a’ and Bin f, of the histogram 28 of the frequency of probability occurrence, demarcates “extremal” probabilities of the histogram from non-extremal probabilities referred to here as the “moderate” region of the histogram. Bin f: 0 <P <1 / 6, is deemed to define “extremal” probabilities - in this example, those probabilities being closest to an extreme end of the probability interval: [0,1], and including an interval end point. Figure 6 illustrates a histogram of the frequency of occurrence of respective probabilities, P(z = 0), fora true Transmon qubit that was repeatedly prepared in a quantum state |z) = |1) and subject to a readout measurement, on 100,000 separate occasions. This histogram shows the relative frequency (expressed as a % on a logarithmic scale) of occurrence of probabilities that a given readout measurement value (“in-phase” ( / ) voltage component) arose as the result of applying the readout measurement operation to the Transmon when in the quantum state |z) = |0) (i.e., not the state of qubit preparation). Here, as in Figure 4, the probability interval [0, 1] of the histogram is divided into 32=25 separate bins of equal bin width. In this example, a threshold is positioned to demarcate “extremal” probabilities of the histogram, for which: Pt <1 / 31, i. e.,i = 1 or 0, from a “moderate” region of non-extremal probabilities for which: Pt >1 / 31, 1.e.,i = 2 to 31. The ordinate axis of the histogram of Figure 5 expresses relative frequency of occurrence of probabilities on a logarithmic scale. Figure 7 schematically illustrates two data clouds, 2 and 4, of many (100,000) qubit readout measurement values of a Transmon qubit prepared in a quantum state : 0 = (|0) + |1)) / V2, alongside readout histograms (probability density functions), 6 and 8, for readout measurement values obtained by applying a process of readout measurement of the quantum state of a Transmon qubit, and a histogram 29 of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0). Figure 8 illustrates a histogram of the frequency of occurrence of respective probabilities for a true Transmon qubit that was repeatedly prepared in a quantum state W = (|0) + |1» / V2 and subject to a readout measurement on 100,000 separate occasions. The histogram shows the frequency of occurrence of respective probabilities that a given readout measurement value arose as the result of applying the readout measurement operation to a quantum state |0). Because of the superposition of both the |0) and the |1) state, there exists an equal probability that a given readout measurement operation will cause either one of the following two wavefunction collapses: |^) = (|0) + |1)) / V2 -> collapse: |0) l^) = (|0) + |1» / V2 collapse: |1) As a result of this, the histogram of frequency of occurrence of probabilities has two thresholds each of which is positioned to demarcate “extremal” probabilities of the histogram, for which: P <1 / 63, 1. e. ,i = 1 or 0, and Pt >62 / 63, 1. e.,i = 62 or 63. Each probability bin of the histogram is represented by a respective one of the 64 distinct binary numbers that can be represented by a 6-bit binary number, from decimal 0 to decimal 63, as indicated at the abscissa axis of Figure 8. In this case, a probability Pt value falling within the ith probability bin (i = 0 to 63) may be counted as an occurrence of a probability having a value determined by the decimal value, i, of the binary number representation of the probability bin in question, such that: Pt = i / 63. A “moderate” region in Figure 8 is the region of the histogram located in between the two thresholds demarcating “extremal” probabilities. This “moderate” region comprises two overlapping moderate regions of the type discussed above with reference to Figure 4 and Figure 6 whereby each one of the two overlapping moderate regions extends from a respective one of the thresholds. The ordinate axis of the histogram of Figure 8 expresses relative frequency of occurrence of probabilities on a logarithmic scale. The qubit measurements at the extreme probability values of i = 0 or 63 are two orders of magnitude more frequent than any other individual measurement probability value. Binarized quantum state measurement outcome values of “0” representing |0) and “1” represent |1) (i.e., from quantum state discrimination) are about equally likely on average. In other examples, the bin widths of successive probability bins of the histogram of frequency of occurrence of probabilities, may differ in width at different bin locations within the probability interval: [0,1], In such an event, one may use a pre-defined function which maps any given probability value P to a corresponding probability bin. A pre-defined function may be used which maps any given probability value P to a corresponding integer representation of that probability. For example, the integer probability I may be given via I = ftP) where f can be the trivial function: ftP) = round^P * 31), and its inverse function is: P(T) = / / 31. One may use any other invertible function ftP) with values in the range [0,max_int] to encode the probability. Given a sequence of qubit readout measurements, one may represent the probability of obtaining a particular readout measurement, z, as a result of applying a readout operation upon a qubit in a given initial state \j) = |0) i.e., j = 0, as an N-bit unsigned integer, Pi. The probability of obtaining the given readout measurement z = z; at index i given the initial state \j) = |0) i.e., j = 0, is then given by: P(z = W = 0) = P. / (2N — 1) The N-bit unsigned integer probability values, Pi, are thereby mapped to normalised probability values, P(z = zt\j = 0), in the interval [0,1]. The probability of obtaining the same analogue readout measurement z = z; at index i given the initial state \j) = |1) i.e., j = 1, is given by: P(z = zf | j = 1) = 1 - P(z = zf | j = 0) = 1 - Pi I (2^-^ Hence only the probabilities associated with the \j) = |0) state need to be stored and used. For a sequence with m measurements, one may have an array of readout measurement probabilities, Pi, of length m as follows: [Po,’Pl’P2,-Pi -Pm-lV Here, the probabilities are TV-bit unsigned integers from the following integer interval: {0,..., 2W - 1}. In order to map a given (soft) readout measurement value, zit to obtain a 1 -bit (i.e., hardened) value from the array of readout measurement probability values, noted above, one may apply a quantum state discrimination process whereby a given readout measurement value, zit having a probability value: Pi <(2W-1 - 1), is assigned an appropriate one of two possible 1-bit binary values (i.e., one of 0 or 1), otherwise it is assigned the other one of the two possible 1 -bit binary values (i.e., 1 or 0) given that the probability value in question thereby satisfies: pL >(2W-1 - 1). When performing readout measurements upon qubits with a good readout accuracy (e.g., >90% readout fidelity), most qubit readout measurement operations return a readout result in which one can have a high level of confidence. This translates into readout measurement probability values, P, being close to P = 1.0 or P = 0.0 or in the case of an / V-bit unsigned integer representation of readout measurement probability values, p, being close to p = 2W - 1 or p = 0. Whatever the representation of probabilities, the effect upon the histogram of frequency of probability occurrence is to skew (or bias) the distribution of the frequency of occurrence of the possible readout measurement probabilities towards the two extremes of pL « 0 or P « 0.0 and p « 2W - 1 or P « 1.0. The inventors have realised that the storing and / or transmission of non-binarized (soft) information about the qubit readout measurement probability at either extreme is not necessary, as all the information about that measurement outcome can be represented in the binary outcome 0 or 1. In other words, it is an acceptable approximation to deem the qubit readout measurement probability implicitly to be either pL = 0 (P = 0) or pt = 2N - 1 (P = 1). A method of compression has therefore been developed by the inventors for compression of data generated by a quantum computing system comprising a plurality of quantum devices (e.g., qubits, qutrits or qudits) that encode information using quantum computational states. The method relates to quantum computing system comprising a readout system that performs a readout measurement operation upon the quantum devices to produce measurement data describing readout measurement values. The data compression method comprises applying quantum state discrimination to the readout measurement values thereby generating respective quantum state measurement outcome data values (i.e., hard information), and acquiring a respective probability of each readout measurement value occurring as a result of performing the readout measurement operation. The applying of quantum state discrimination to the readout measurement values may be performed according to any suitable thresholding process whereby a given readout measurement value is compared to a pre-set discrimination threshold such that the quantum state measurement outcome value is set to one of two 1 -bit values: “0” or “1” according to the comparison. An example of the discrimination threshold 16 shown in Figure 2, Figure 3, Figure 5 and Figure 7. Probability values of each readout measurement value occurring as a result of performing the readout measurement operation, may be acquired from data defining a readout histogram (i.e., defining a probability density function) associated with the quantum device in question. Such readout histogram data may be a pre-prepared readout histogram data, and this may be generated according to any suitable known method as would be readily available to the person skilled in the art, such as disclosed elsewhere herein for example. The method includes producing compressed measurement outcome data comprising the quantum state measurement outcome data values and “moderate” probability values, from amongst the acquired probabilities, which do not fall within a pre-set range of “extremal” probabilities. In other words, those probability values (within the pre-set range of extremal probabilities) are excluded from the compressed measurement outcome data thereby reducing the size of the data set without a loss of relevant information. The relevant information is preserved in “hard” form (i.e., quantum state measurement outcome data values) for those readout measurement events having associated “extremal” probabilities which implicitly provide a sufficiently high level of confidence that the quantum state measurement outcome value accurately represents the true quantum state of the qubit that had been subjected to the readout measurement event in question. If the compressed measurement outcome data is then sent to a data transmission system employing a data transmission channel having a given data transmission bandwidth, for transmission therefrom, the rate of transmission of information may be improved since less data is required to convey the same amount of information via the transmission channel. Furthermore, if the compressed measurement outcome data is then sent to a data storage system for storing the compressed measurement outcome data, then more information may be stored in a given storage space. In addition, if the compressed measurement outcome data is then sent to a quantum error correction (QEC) decoder employing a decoding graph (or hypergraph) algorithm that uses the probabilities to compute weights for graph edges, the nature of compression of the data permits an immediate efficiency in the computational overhead in implementing the decoding algorithm, for reasons discussed above relating to provision of those probabilities of significance, and exclusion of those probabilities of little significance or practically no significance. The decoder may not directly use the probabilities p as the edge weights but may update the edge weights w according to some known function w(p) - see Appendix E.2 in reference [2] below (https: / / arxiv.org / pdf / 2403.00706) for an example. Example 1 Figure 9 shows an example of data compression according to an embodiment of the invention. Here, the method includes acquiring a set 30a of m probability values: P^Z=D = [Po,.Pl / P2,-Pi •••Pm—l^’j = 1 each respective one being a probability of a respective one of m readout measurement values occurring as a result of performing a qubit readout measurement operation. This data may be acquired from data defining a readout histogram (i.e., defining a probability density function) associated with the qubit in question, of the type such as, for example, the readout histograms (probability density functions), 6 and 8, shown in Figure 7. As noted above, Figure 7 schematically illustrates qubit readout histograms for a Transmon qubit in a quantum state : 0 = (|0) + |1)) / V2, alongside a histogram 29 of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0). Figure 8 also illustrates, for real Transmon qubit readout measurements, a histogram of the frequency of occurrence of probabilities that a given readout measurement value arose as the result of applying the readout measurement operation to a quantum state |0). Here, the probabilities are binned into one of 64 probability bins of equal bin width, ranging from the probability bin i = 0 to the probability bin i = 63. Each bin label represents a readout measurement probability having a value determined by the decimal value, pi = i, of the binary number representation of the probability bin in question, such that the normalised readout measurement probability, Pit over the interval [0,1], is given by: Pt = i / 63. In general, in respect of readout measurement results applied to qubit in a quantum state 0 = (a10) + P |1», for which quantum state discrimination may yield a discrimination of a measurement-induced 5 wavefunction collapse of the form: \ip) = (or|0) + ^|1)) -> collapse: |0) with probability \a\2 or \ip) = (<z|0) + ^|1)) -> collapse: 11) with probability | / ?|2 The compression algorithm may be as follows. Algorithm: for a qubit in a state comprising a superposition of 10) and 11), using probabilities of collapse to a 11) state upon measurement. Inputs: A length-m array of readout measurement probabilities, pit each an IV-bit un-signed integer: P^Z=D = [Po,.Pl,.P2, -Pi •••Pm—j = 1 A “cut-off length”, L, which is an (IV - l)-bit un-signed integer. Process: Let c: length-m array containing 2 bits per element Let s: empty array (IV bits per element) For each measurement probability pt in p(z = j) = [p0, Pi,, P2, - Pi - Pm-i]T for fixed j, do: If Pi <A: #(i.e., from within an “extremal” region, low “extremal” probabilities) cl = 0 #(“extremal” probability) cl = 0 #(i.e., discriminated state “0” representing |0)) elif pj >(2W - 1 — L): #(i.e., from within an “extremal” region, high “extremal” probabilities) cl = 0 #(“extremal” probability) cl = 1 elif p£ >(2W-1 - 1): #(i.e., discriminated state “1” representing |1)) c?= 1 #(from within the “moderate” region) cl = l#(quantum state-discrimination threshold applied: discriminates to # state “1” representing |1)) elif pi <(2W-1 - 1): cf = 1 #(from within the “moderate” region) f = 0#(quantum state-discrimination threshold applied: discriminates to s.appendfe) # state “0” representing 0)) #(i.e., the outcome probability from the readout histogram or # probability density function) Return (c,s) Outputs: Array c - A 2-bit array of length m. Array s - A collection, with maximum size m, of A / -bit “moderate” measurement probabilities pL. Here, the algorithm has the following inputs and outputs, schematically shown in Figure 9. The inputs, 30a and 30b, to the algorithm comprise the following: A length-m array 30a, p(z = 1), of readout measurement probabilities, pit each an / V-bit unsigned integer: p(z = 1) = [p0,<Pi,<P2, -Pi -Pm-i]T ■ For example, let N = 6 such that each measurement probability value, pit may be represented by a 6-bit integer representing one of 26 = 64 separate probability bins, as shown in Figure 8. Each probability bin has a width of 1 / 64 and any probability within the kth range: k k + 1 — <kth probability <;k = 0to 63 64 64 is assigned an IV-bit un-signed integer value having a respective one of 64 different discrete IV-bit integer values which, in decimal, represent: k = Oto 63 representing a normalised probability of: fc / 64. For example: 000000; 000001; 000010;... 111110; 111111, provide 6-bit integer values representing: 0; 1; 2;... 62; 63 in decimal. A “cut-off length”, L, 30b which represents a size of any pre-set range of extremal probabilities that are to be excluded from probabilities contained within the compressed data. It is an (IV - 1)-bit un-signed integer. For example, if N = 6 then the cut-off length value, L, may be represented by a 5-bit integer varying in size from a minimum value: L = 2° = 1 (or 00000 in binary) representing a minimum range size of one probability bin of probabilities spanned by the histogram shown in Figure 8, to a maximum value: L = 25 = 32 (or 11111 in binary) representing a maximum range size of one half of the probability bins spanned by the histogram of Figure 8. In the example shown in Figure 8, L = 21 = 2 (or 00010 in binary). In the example, two separate pre-set ranges of extremal probabilities are defined, and the same cut-off length is applied to each one of these two extremal probability ranges, those being: pre-set range #1 of extremal probabilities: bins k = 0 and k = 1; pre-set range #2 of extremal probabilities: bins k = 62 and k = 63. This means that any of the probability values, pit within length-m array 30a, p(z = 1), that have a value falling within bins k = 0 and k = 1, or within bins k = 62 and k = 63 will be excluded from the outputs of the compression process. The pre-set range of “extremal” probabilities extends from an uppermost probability value of 1 (unity) such as encompassed by the uppermost probability bin “63” of Figure 8, for example, to a lower probability value exceeding zero such as encompassed by the probability bin “62” of Figure 8, and from a lowermost probability value of zero such as encompassed by the lowermost probability bin “0” of Figure 8 to an upper probability value exceeding zero as encompassed by the probability bin “1” of Figure 8. The outputs, 31 a and 31 b, to the algorithm comprise the following: A 2-bit array, [cf, c*], 31a of length m. The first bit, c°, is a flag to indicate whether or not a given readout measurement probability pL of the input array 30a of readout measurement probabilities, is “extremal” from within a pre-set range of extremal probabilities, or is non-extremal and from within the “moderate” region, such that: cf = 0^ “extremal”; CP = 1 => “moderate”. The second bit, cl, gives the (“hard”) quantum state measurement outcome value such that: cl = state |0); cl = 1 => state 11)). An N-bit collection 31 b with maximum size m, of measurement probabilities pt for the cases where the probability is from within the “moderate” region: cf = 1 “moderate”. These moderate probabilities can be considered to be “soft” data because they are not 1 -bit values. Measurement probabilities pL for the cases where the probability is from within an “extremal” region: cf = 0 “extremal”, are excluded from the collection 31b. The exclusion of these extremal probabilities can be considered to be a partial “hardening” of the data because all information about the qubit readout measurement value is limited to the “hard” (binarized) quantum state entry cl (i.e., 1-bit value) within the 2-bit array 31a. For example, measurement probabilities plt p2, pm_lt at least are excluded from the N-bit collection 31b, and each one of those measurement probabilities has associated with it an entry within the 2-bit array 31a in which c° = 0. By contrast, measurement probabilities p0, pm_3, pm-2, are included within the N-bit collection 31b, and each one of those measurement probabilities has associated with it an entry within the 2-bit array 31a in which c° = 1. In this example of the method of compression, the pre-set range of extremal probabilities comprises two sub-ranges of “extremal” probabilities separated from each other by a contiguous intermediate range of non-extremal (“moderate”) probabilities, and the method includes compressing the measurement outcome data by applying quantum state discrimination upon the readout measurement values having a respective probability, from amongst the acquired probabilities, falling within any of the two sub-ranges thereby generating respective quantum state measurement outcome data. The pre-set range of extremal probabilities is contiguous with an adjacent range of “moderate” probabilities which encompasses all of the probabilities from amongst the acquired probabilities that are not encompassed by the extremal probabilities. The acquiring of a respective probability prior to data compression may comprise providing only those probabilities which do not fall within a pre-set range of extremal probabilities (none is an “extremal” probability) such that probabilities within the pre-set range of extremal probabilities are excluded from the acquired probabilities, or may comprise providing probabilities spanning the full range of probabilities (some are “extremal” probabilities and some are not) and then filtering those provided probabilities to acquire the probabilities which do not fall within a pre-set range of extremal probabilities, for use in data compression. To further illustrate this, consider the notional scenario schematically illustrated in Figure 7, showing the histogram 29 of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0). This notional histogram has six probability bins (a’ to e’ and f). Each one of the measurements denoted by a dot (“•”) is assigned a probability according to the readout histogram (probability density function), 6 or 8, associated with the two possible collapsed (post-measurement) states of the qubit. Consider seven selected measurement events resulting in qubit readout measurement values (analogue / “soft”) annotated as i = 0 to 6 on Figure 7. Assume that qubit readout measurements are made and resulting measurement probabilities are defined to describe the probability that a given readout measurement value arose as a result of the initial superposition quantum state of the qubit collapsing into the |0) eigenstate upon measurement. Extremal probability values are deemed to be those falling within bin “ f ” or bin “ e’ ”, which correspond respectively to measurement values falling within the inner circle “e” or outside the outer circle “ a ” of the data cloud 2 associated with the |0) eigenstate, whereas “moderate” probability values are deemed to be those falling within any of bins “ a’ ” to bin “ d’ ” which correspond respectively to measurement values falling between the circles “ a ” to “ e ” of the data cloud 2. One can see that measurement events i = 0 and 5 fall between the circles “ a ” to “ e ” of the data cloud 2 and are deemed “moderate” and have cf = 1 “moderate”. By contrast, measurement events i = 1,2,3,4 and 6 fall within the circle “ e ” or outside the circle “ a ” of the data cloud 2 and are deemed “extremal” as indicated by c? = 0 => “extremal”. In addition, measurement events i = 0,1,2,3,5 and 6 fall to the left of the quantum state discrimination threshold 16 and so the eigenstate of the qubit is assumed to have collapsed into the |0) eigenstate as indicated by the value of the second bit, c^, which gives the (“hard”) quantum state measurement outcome such that: c* = 0 => state |0). However, measurement event i = 4 falls to the right of the quantum state discrimination threshold 16 and so the eigenstate of the qubit is assumed to have collapsed into the |1) eigenstate as indicated by the value of the second bit, c^, which gives the (“hard”) quantum state measurement outcome such that: = 1 state 11)), as shown below, with j = 1. Input: Outputs: P(2=j) p(z = D Po Po [1.0] Pl — [0,0] Pl — [0,0] Pl — [0,0] Compress > Pl Pl [1,1] Ps Ps [1,0] P6 — [0,0] The algorithm may employ different values of cut-off length “L" at opposite ends of the probability histogram (e.g., opposite ends of Figure 8). Typically, when we only consider P(z = 0) or P(z = 1), the probability histogram distributions may look approximately symmetric, and a sensible cut-off, L, may be the same for both “extremal” regions, as shown in Figure 8. However, one may define a first cut-off length Llt for one of the two “extremal” regions, and a second cut-off length L2, for the other of the two “extremal” region, in which L1 L2. In general, the value of “j” may be fix in advance of implementing the algorithm. This fixes in advance what the probabilities, pit represent. For example, one may either select j = 1, in which case the probability values represent the probability that measurement of the state gave a “1” outcome, or we may select j = 0, in which case the probability values represent the probability that measurement of the state gave a “0” outcome. In this way, a reduction in the size of the output data set is achieved by a careful selection of the probability information contained within it resulting in a compression of the data size. Each readout measurement value produced by the readout system is subjected to quantum state discrimination (i.e., is binarized in to a 1 -bit binary value) thereby to generate a respective quantum state measurement outcome value (1 -bit). The compressed measurement outcome data thereby comprises quantum state measurement outcome data (1 -bit) derived from each readout measurement value produced by the readout system. Each of the respective quantum state measurement outcome data values within the compressed measurement outcome data is represented by a single bit, c^, and each of the probabilities, Pi, within the compressed measurement outcome data is represented by a plurality of bits. In respect of each of the quantum state measurement outcome data values in 1 -bit form, cl, the further 1 -bit data item, c°, is provided having a first value of “0” (zero) if the associated probability value is deemed “extremal” or a distinct second value of “1” (one) if the associated probability value is “moderate”. The compressed measurement outcome data is arranged such that the respective further 1 -bit data items, c°, form an array of values in which each further item is arranged in association with the respective probability, pt, with which it is associated. As can be seen from Figure 9, the compressed measurement outcome data comprises a composite array comprising the array of 2-bit elements [c?,^] of binarized (“hard”) quantum state measurement outcome data values, c^, in 1 -bit form and the array of respective further data items c°. Consequently, much of the data may be in 1 -bit form. Example 2 Figure 10 shows an example of data compression according to an embodiment of the invention. Here, as in Example 1, the method includes acquiring a set 30a of m probability values, but in this case the probabilities are for a measurement-induced collapse of the qubit state to a post-measurement state |0): P^ = j) = [P0 / P1 / P2, -Pi-Pm-lV ■] = 0 Each respective probability is a probability of a respective one of m readout measurement values occurring as a result of performing a qubit readout measurement operation. This data may be acquired from data defining a readout histogram (i.e., defining a probability density function) associated with the qubit in question, of the type such as, for example, the readout histograms (probability density functions), 6 and 8, shown in Figure 3 or Figure 5. The inputs, 30a and 30b, to the algorithm similar to those disclosed above regarding Example 1: namely, a length-m array 30a, p(z = 0), of readout measurement probabilities, pit and a “cut-off length”, L, 30b. As noted above, Figure 3 and Figure 5 schematically illustrates qubit readout histograms for a Transmon qubit in a pre-measurement state having a high probability of undergoing a measurement-induced collapse to a quantum state: = 10) on / ' = |1) respectively, alongside a histogram, 26 or 28 of the frequency of occurrence of individual probabilities that a respective readout measurement value is associated to a quantum state |0). Figure 4 and Figure 6 also each illustrate, for real Transmon qubit readout measurements, a histogram of the frequency of occurrence of probabilities that a given readout measurement value arose as the result of the readout measurement operation inducing a collapse of the qubit state to a quantum state |0). Here, the probabilities are binned into one of 32 probability bins of equal bin width, ranging from the probability bin i = 0 to the probability bin i = 31. Each bin label represents a readout measurement probability having a value determined by the decimal value, pL = i, of the binary number representation of the probability bin in question, such that the normalised readout measurement probability, Pit over the interval [0,1], is given by: Pt = i / 31. The compression algorithm may be as follows. Here, j = 0 in Figure 10. The probabilities, “pj” represent the probability that the measurement operation results in a collapse to state “|0)” of the qubit, the “0” eigenstate, as a consequence of being measured. Algorithm: Inputs: A length-m array of readout measurement probabilities, pit each an N-bit un-signed integer, describing a probability that a readout measurement value arose from a measurement-induced collapse of a qubit state to a state |0): P(Z = 0) = [P0 / P1 / P2, -Pi -Pm-lV A “cut-off length”, L, which is an (N - l)-bit un-signed integer. Process: Let cO: length-m array containing 1 bit per element Let cl: maximum length-m array containing 1 bit per element Let s: empty array (N bits per element) For each measurement probability pL in p(z = 0) = [P0 / P1 / P2, - Pi -Pm-i\T do: If Pi >(2W-1-1): #(i.e., from within an “extremal” region, high “extremal” probabilities) cf = 0 #(“extremal” probability) cl = no entry #(i.e., state “0” representing |0) is assumed) elif Pi >(2W-1-1): cf= 1 #(from within the “moderate” region) f = 0 #(quantum state-discrimination threshold applied: discriminates to # state “0” representing |0)) elif pi <(2W 1 - l):c? = 1 #(from within the “moderate” region) cl = l#(quantum state-discrimination threshold applied: discriminates to s.appendfe) # state “1” representing |1)) #(i.e., the outcome probability from the readout histogram or # probability density function) Return (cO, cl,s) Outputs: Array cO - A 1 -bit array of length m. Array cl - A 1 -bit array of maximum length m. Array s - A collection, with maximum size m, of A / -bit “moderate” measurement probabilities pL. Here, the algorithm has the following inputs and outputs, schematically shown in Figure 10. The output data set comprises: A 1 -bit array 130a of length m in which each element of the array is the further 1 -bit data item, cf, having a first value of “0” (zero) if the associated probability value is deemed “extremal” or a distinct second value of “1” (one) if the associated probability value is “moderate”. A 1 -bit collection 310b with maximum size m, which contains the quantum state measurement 5 outcome data values in 1 -bit form, c^. An N-bit collection 31 b with maximum size m, of measurement probabilities pL for the cases where the probability is from within the “moderate” region: cf = 1 “moderate”. The number of elements of the second two collections, 310b and 31 b, sum to m. In other words, where an entry is absent from the 1 -bit collection 310b, an associated entry is present in the N-bit collection 31 b, 10 and vice versa. 15 Note that the algorithm of Example 2 actually involves the transmission of less data than the algorithm of Example 1. It will be readily appreciated that if the qubit to be measured is in a state |1) and the readout measurement probabilities, pit each describe a probability that a readout measurement value arose from a measurement-induced collapse of the qubit state to the state 11), then the algorithm of Example 2 may be adjusted to reposition the location of “extreme” probabilities. Here, j = 1 in Figure 10. The probabilities, “pf represent the probability that the measurement operation results in a collapse to state “|1)” of the qubit, the “1” eigenstate, as a consequence of being measured. Algorithm: Inputs: A length-m array of readout measurement probabilities, pit each an N-bit un-signed integer, describing a probability that a readout measurement value arose from a measurement-induced collapse of a qubit from some pre-measurement state to a post-measurement state |1): p(z = 1) = [P0 / P1 / P2, -Pi - Pm-1]T A “cut-off length”, L, which is an (N - l)-bit un-signed integer. Process: Let cO: length-m array containing 1 bit per element Let cl: maximum length-m array containing 1 bit per element Let s: empty array (N bits per element) For each measurement probability pL in p(z = 1) = [P0 / P1 / P2, - Pi -Pm-i\T do: If Pz <i: #(i.e., from within an “extremal” region, low “extremal” probabilities) c° = 0 #(“extremal” probability) cl = no entry #(i.e., state “0” representing |0) is assumed) elif pt >(2W-1 - 1): cf = 1 #(from within the “moderate” region) cl = l#(quantum state-discrimination threshold applied: discriminates to # state “1” representing |1)) elif pi <(2^-1): c° = 1 #(from within the “moderate” region) cl = 0 #(quantum state-discrimination threshold applied: discriminates to # state “0” representing |0)) s.append(pj) #(i.e., the outcome probability from the readout histogram or # probability density function) Return (cO, cl,s) Outputs: Array cO - A 1 -bit array of length m. Array cl - A 1 -bit array of maximum length m. Array s - A collection, with maximum size m, of N-bit “moderate” measurement probabilities pt. In either implementation of Example 2, the result is to generate the compressed measurement outcome data comprising two separate arrays, 130a and 130b, comprising the array of quantum state measurement outcome data values, cl, as one of the two arrays, and comprising the array of further data 5 items, cf, as one of the two arrays. The method may comprise, by a quantum state discrimination unit, applying a quantum state discrimination process in respect of each of the readout measurement values thereby to provide a respective said probability of each of the readout measurement values occurring as a result of performing the readout measurement operation. The readout measurement operation is performed on a qubit in some pre-measurement quantum state that induces a collapse of the quantum 10 state to either a post-measurement state |0) or state |1). Each pre-measurement quantum state is unknown and is not a “prepared” quantum state, and hence the probability values are used to measure the confidence in a given quantum state measurement outcome value obtained by applying quantum state discrimination to readout values. Example 3 15 Figures 11 and 12 show an example of data compression according to an embodiment of the invention. Here, once more, the method includes acquiring a set 30a of m probability values: P^ = j) = [P0 / P1 / P2, -Pi-Pm-lV '] = 0 each respective one being a probability of a respective one of m readout measurement values occurring as a result of performing a qubit readout measurement operation. This example algorithm is applicable in circumstances where a histogram of the frequency of occurrence of measurement probabilities is such as is shown schematically in Figure 3 (histogram 26) and in Figure 5 (histogram 28). The inputs, 30a and 30b, to the algorithm comprise those disclosed above regarding Example 1: namely, a length-m array 30a, p(z = 0), of readout measurement probabilities, pit and a “cut-off length”, L, 30b. In each case, a single “cut-off” zone of “extremal” probabilities is present. In the example of Figure 11, which applies in cases where a histogram 28 of the type shown in Figure 5 arises, the single zone of “extremal” probabilities occupies the lowest probability bin including probability values of zero or otherwise very low. This corresponds to a circumstance in which a qubit happens to be in some pre-measurement state that typically collapses to state |1) upon measurement. This is because the probability values in question describe the probability that the qubit readout measurement result arose from a measurement operation having been performed on a qubit to cause it to collapse to the |0) state (not the state |1)) and therefore the high frequency (%) of occurrence of extremely low measurement probability values attests to the measured qubit rarely being in a state |0) (namely, it is frequently in state |1)). In this case, when an element ct of the 1 -bit output array [cj of length m has the value: ct = 0, this value may be interpreted to mean that the qubit resides in a defective state. Outputs from the algorithm comprise: A 1 -bit array, [q], of length m. A value q = 0 is assigned if the associated probability value, pit is deemed “extremal”. A value q = 1 is assigned if the associated probability value, pit is “moderate”. A value of q = 0 may be interpreted as a defect (i.e., it is a state 11), and not a state 10)), as discussed in more detail above. An N-bit collection with maximum size m, of measurement probabilities pt for the cases where the probability value, pit is “moderate”. This example of the algorithm may be as follows: Algorithm: Inputs: A length-m array of readout measurement probabilities, pt, each an N-bit un-signed integer, describing a probability that a readout measurement value arose from a measurement-induced collapse of a premeasurement qubit to a state |0): P(Z = 0) = [p0 / PvP2, -Pi A “cut-off length”, L, which is an (N - l)-bit un-signed integer. Process: Let c: length-m array containing 1 bit per element Let s: empty array (N bits per element) For each measurement probability pL in p(z = 0) = [P0 / P1 / P2, - Pi -Pm-i\T do: If Pi <L: #(i.e., from within an “extremal” region, low “extremal” probabilities) Ci = 0 #(“extremal” probability: interpreted as a quantum state else: Ci = 1 #measurement outcome “1” meaning qubit in state |1)) #(from within the “moderate” region) s.append(pj) #(i.e., the outcome probability from the readout histogram or Return (c,s) Outputs: Array c - A 1 -bit array of length # probability density function) m. Array s - A collection, with maximum size m, of A / -bit “moderate” measurement probabilities pL. Alternatively, in the example of Figure 12, which applies in cases where a histogram 26 of the type shown in Figure 3 arises, the single zone of “extremal” probabilities occupies the highest probability bin including probability values of unity (1) or close to that value. This corresponds to a circumstance in which a qubit is in some pre-measurement state and is cause to collapse to a |0) by the measurement process. This is because the probability values in question describe the probability that the qubit readout measurement result arose from a measurement operation caused the qubit to collapse to the |0) state and therefore the high frequency (%) of occurrence of extremely high measurement probability values attests to the measured qubit frequently collapsing to a state |0). In this case, when an element cL of the 1 -bit output array [q] of length m has the value: cL = 0, this value may be interpreted to mean that the qubit resides in a non-defective state 10>, i.e., correct. Outputs from the algorithm then comprise: A 1 -bit array, [q], of length m. A value q = 0 is assigned if the associated probability value, pit is deemed “extremal”. A value q = 1 is assigned if the associated probability value, pit is “moderate”. A value of q = 0 may be interpreted as a |0) non-defective state, as discussed in more detail above. An N-bit collection with maximum size m, of measurement probabilities pL for the cases where the probability value, pit is “moderate”. This example of the algorithm maybe as follows: Algorithm: Inputs: A length-m array of readout measurement probabilities, pit each an N-bit un-signed integer, describing a probability that a readout measurement value arose from a measurement-induced collapse of a premeasurement qubit state to a state |0): P(Z = 0) = [P0 / P1 / P2, -Pi -Pm-lV A “cut-off length”, L, which is an (N - l)-bit un-signed integer. Process: Let c: length-m array containing 1 bit per element Let s: empty array (N bits per element) For each measurement probability pL in p(z = 0) = [P0 / P1 / P2, - Pi -Pm-i\T do: If Pi >(2W-1-L): #(i.e., from within an “extremal” region, high “extremal” probabilities) ct = 0 #(“extremal” probability: interpreted as a binarized measurement #outcome state “0” meaning qubit in state |0)) else: Ci = 1 #(from within the “moderate” region) s.appendfe) #(i.e., the outcome probability from the readout histogram or # probability density function) Return (c,s) Outputs: Array c - A 1 -bit array of length m. Array s - A collection, with maximum size m, of A / -bit “moderate” measurement probabilities pt. In the data format described above, with reference to Figure 11 and Figure 12, the value of “j" is pre-set and provided to the decoder in advance to be able to interpret the data it receives. It is to be noted that the readout measurement operation may comprise a syndrome measurement 5 operation and the compressed measurement outcome data may comprise syndrome data representative of an error state of other quantum devices amongst the plurality of quantum devices. Figure 13 schematically illustrates a quantum computer system according to an example of the invention. In this example, the quantum computer system is a non-distributed system in which the components of the system are comprised within the same device 32. Figure 14 schematically illustrates an alternative 10 example of the invention in which the quantum computer system is a spatially distributed quantum computer system whereby some parts of the system are comprised within a first component part of the system 32A while other parts of the system is comprised within second component part of the system 32B. The first and second components parts are configured in communication via a data transmission channel 50. In both examples, the elements of the quantum computing system are common to both examples with the possible exception of the data transmission channel 50 which may be selected for longer-distance data transmission (e.g., between buildings) as opposed to within a closed device. The quantum computing system 32 comprises controller 33 for controlling a plurality of quantum devices 36 arranged in a qubit register 34 for encoding information using quantum computational states. The quantum devices may be qubits, such as Transmon qubits, neutral atom qubits, trapped ion qubits or any other qubit type available to the person skilled in the art for encoding information using quantum computational states. In the present examples, the quantum devices take the form of Transmon qubits for ease of illustration, but it is to be noted that the invention is not limited to use with Transmon qubits. The controller is arranged to control the qubits 36 in the qubit register 34 in such a way as necessary to implement a quantum computing task desired by a user to be implemented by the quantum computing system 32. The quantum computing system 32 also comprises a qubit readout device 38 for performing a readout measurement operation upon quantum devices from amongst the plurality of quantum devices to produce readout measurement data 40 (“soft”) describing analogue readout measurement values. The readout data may be in digital form in the computing system, of course. The compressor 42 is configured to acquire from the qubit readout device 38 the qubit readout measurement values, and therewith to generate associated probability data describing respective probabilities of the readout measurement values. For each received qubit readout measurement result, the compressor generates a respective probability of the analogue readout measurement value having occurred as a result of performing the readout measurement operation upon a qubit in some premeasurement quantum state, and hereby causing the qubit’s quantum state to collapse to a given postmeasurement quantum state, of |0) or 11), as appropriate. These probabilities may be derived from a “readout histogram” (probability density function) 52 as discussed herein, or by other available means such as by employing a Machine Learning algorithm suitably trained for this purpose, as discussed in references cited below. The compressor 42 is configured to binarize the received readout measurement values thereby generating respective quantum state measurement outcome values in 1 -bit binary form, according to any of the algorithms (such as any of: Examples 1, Example 2, Example 3) so as to produce compressed measurement outcome data 53 as descried above in detail. This compressed data comprises the binary / binarized quantum state measurement outcome values (“hard” data) and data (“soft” data) describing probabilities, from amongst the acquired probabilities, which do not fall within a range of extremal probabilities that is pre-set within the compressor by the user, as desired (see inset 54). As a result, data describing “moderate” probabilities is included within the compressed data but probabilities within the pre-set range of “extremal” probabilities are excluded from the compressed measurement outcome data, and the size of the data is lower as a result. The compressed data 53 is transmitted to a QEC decoder unit 46 for use in determining quantum error corrections using, for example, a code employing graph edges weighted according to the “moderate” probabilities included within the compressed data. Known QEC decoders are not discussed in detail here, and reference is made to prior art cited in references listed below for examples such as are readily available to the person of ordinary skill in the art. Error corrections 48 generated by the QEC decoder unit 46 are output to the controller 33 for use in correcting errors associated with the quantum computation tasks involving the qubits 36. In addition, a data store 43 is provided and the compressor may store the compressed data 53 in the data store as desired, for later use. Compression provided by the compressed data 53 allows more data to be stored within a store 43 of given storage capacity. In the example shown in Figure 13, transmission of compressed data 53 from the compressor to the QEC decoder 46 takes place via a transmission channel 44, such as a data bus, built within the quantum computing device 32 when in non-distributed form. In the example shown in Figure 14, transmission of compressed data 53 from the compressor to the QEC decoder 46 takes place via a transmission channel 50, such as a fibre-optic network data transmission line, built between the first component 32A and the second component 32B of the quantum computing device when in distributed form. Compression provided by the compressed data 53 allows more data to be transmitted via a transmission channel 50 of a given transmission rate / capacity. Figure 15 schematically illustrates steps in a method of data compression according to the invention. These steps may form instructions in a computer-readable medium which, when executed by a quantum computing system 32 or 32A / B, cause the quantum computing system to carry out the method of according to the invention. The steps comprise at least the following: Step 1: Acquiring a respective probability of each analogue readout measurement value; Step 2: Apply quantum state discrimination to the analogue readout measurement values to produce quantum state measurement outcome values; Step 3: Produce compressed measurement outcome data comprising the quantum state measurement outcome values and non-extremal (“moderate”) probabilities. Figure 16 illustrates a relationship between the “cut-off size”, L, which is an input to the compression algorithm and serves as the compression control parameter, and the consequential proportion of the total number of qubit readout measurement values that become binarized as result from each choice of the “cut-offside”, L. Here, the probabilities are represented by 6-bit unsigned integers (N = 64) in which all probabilities are binned within one of 64 probability bins, such as shown in Figure 8. A minimal cut-off size can be seen to map 99% of measurements to binary outcomes, and increasing the length gives higher rates of compression. Effects of compression on decoding: The Minimum Weight Perfect Matching (MWPM) decoder is a popular choice for decoding error syndromes in Surface Code quantum error correction. Using a “soft” MWPM decoder that uses the measurement probabilities to update edge weights in the decoding graph, one can obtain the results shown in Figures 17(A) and 17(B). The accuracy of QEC decoding that results from using the compressed data is indicated in Figures 17(A) and 17(B). Figure 17(A) shows a relationship between the “cut-off size”, L, and the consequential logical qubit error probability in the quantum computing system subject to MWPM decoding using the compressed qubit readout measurement outcome data. Increasing the cut-off size makes decoder performance marginally fall but a small cut-off size is very close in performance to the original soft decoder without compression applied. Figure 17(B) shows a relationship between a compression ratio in compressed qubit readout measurement outcome data from qubits of a quantum computing system, and the consequential logical qubit error probability in the quantum computing system subject to MWPM decoding using the compressed qubit readout measurement outcome data. The logical error rate vs the compression ratio (original size / compressed size) for 6-bit “soft” probability values is shown. It can be seen that a compression ratio of close to 3.0 can be achieved without significant accuracy loss. A cut-off size of L = 1 does not affect logical error rates significantly, but offers a significant amount of data compression. With a soft decoder tailored to use the compressed data, it is possible to improve decoding speed while retaining a good accuracy of decoding. Bi nary / binarized measurement outcomes do not require the corresponding edge weights to be changed in the decoding graph. By using the compression scheme, only those edges that are affected by uncertain measurements (with “moderate” probabilities) need to be updated by the decoder. This reduces the number of necessary graph operations. The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof. While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention. For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations. Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described. Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps. It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / -10%. While the above disclosure refers to single-bit quantum state measurement outcome values, one skilled in the art will appreciate that additional bits could be used, e.g. when using qutrits / qudits and / or when detecting leakage. References A number of publications are cited above in order to more fully describe and disclose the invention and the state of the art to which the invention pertains. Full citations for these references are provided below. The entirety of each of these references is incorporated herein. [1] Johannes Bausch et al.: Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network, 9 Oct. 2023, arXiv:2403.00706v2 [quant-ph] 30 Aug 2024, https: / / arxiv.org / pdf / 2310.05900 [2] Hany Ali et al.: Reducing the error rate of a superconducting logical qubit using analog readout Information, 30 Aug 2024, arXiv:2310.05900v1 [quant-ph] 9 Oct 2023, https: / / arxiv.org / pdf / 2403.00706 [3] Jonathan Y. Huang et al.: High-fidelity spin qubit operation and algorithmic initialization above 1 K: Nature, Vol 627, pp772, 28 March 2024. [4] Johannes Heinsoo et al.: Rapid high-fidelity multiplexed readout of superconducting qubits, arXiv:1801.07904v1 [quant-ph] 24 Jan 2018, https: / / arxiv.org / pdf / 1801.07904 [5] Riste et al.: Initialization by measurement of a two-qubit superconducting circuit, arXiv:1204.2479v1 [cond-mat.mes-hall] 11 Apr 2012, https: / / arxiv.org / pdf / 1204.2479 [6] Walter et al.: Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits, arXiv:1701.06933v2 [quant-ph] 25 Jan 2017 [7] A.M. Zagoskin: Quantum Engineering. Cambridge University Press, 2011. Page 264, eq. 5.165. ISBN 978-0-521-11369-4 [8] Pattison et al.: Improved quantum error correction using soft information, arXiv:2107.13589v1 [quant-ph] 28 Jul 2021, https: / / arxiv.org / pdf / 2107.13589 [9] Neereja Sundaresan et al.: Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders, Nature Communications, (2023) 14:2852, https: / / doi.Org / 10.1038 / S41467-023-38247-5

[10] D’Anjou etal.: Soft Decoding of a Qubit Readout Apparatus'. arXiv:1405.6060v3 [quant-ph] 23 Dec 2014, https: / / arxiv.org / pdf / 1405.6060

[11] Raveendran et al.: Soft syndrome iterative decoding of quantum LDPC codes and hardware architectures, EPJ Quantum Technology, volume 10, Article number: 45 (2023).

[12] Varbanov et al.: Neural network decoder for near-term surface-code experiments, arXiv:2307.03280v2 [quant-ph] 23 Oct 2023, https: / / arxiv.org / pdf / 2307.03280

[13] Magesan et al,: Machine learning for discriminating quantum measurement trajectories and improving readout. arXiv:1411.4994v2 [quant-ph] 24 Nov 2014, https: / / arxiv.org / pdf / 1411.4994

[14] Krenn et al.: Artificial intelligence and machine learning for quantum technologies, PHYSICAL REVIEW A 107, 010101 (2023)

[15] Seif et al.: Machine learning assisted readout of trapped-ion qubits, arXiv:1804.07718v2 [quant-ph] 1 May 2018, https: / / arxiv.org / pdf / 1804.07718

[16] Ryan et al.: Tomography via Correlation of Noisy Measurement Records, arXiv: 1310.6448v3 [quant-ph] 20 Dec 2013, https: / / arxiv.org / pdf / 1310.6448

[17] Corcoles et al.: Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits, Phys. Rev. Lett. 127, 100501 — Published 31 August 2021, https: / / link.aps.Org / accepted / 10.1103 / PhysRevLett. 127.100501

Claims

1. A quantum computing system comprising:a plurality of quantum devices for encoding information using quantum computational states;a readout system for performing a readout measurement operation upon quantum devices from amongst the plurality of quantum devices to produce readout measurement data describing analogue readout measurement values;a data compressor for compressing the readout measurement data by:acquiring data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation;performing quantum state discrimination upon the readout measurement data thereby generating respective quantum state measurement outcome values;producing compressed measurement outcome data comprising the quantum state measurement outcome values and data describing probabilities, from amongst the acquired data describing probabilities, which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data.

2. A quantum computing system according to any preceding claim wherein the pre-set range of extremal probabilities comprises two sub-ranges of extremal probabilities separated from each other by a contiguous intermediate range of non-extremal probabilities, wherein the data compressor is arranged to compress the readout measurement data by performing quantum state discrimination upon the readout measurement values having a respective probability, from amongst the acquired probabilities, falling within any of the two sub-ranges thereby generating respective quantum state measurement outcome values.

3. A quantum computing system according to claim 1 wherein the pre-set range of extremal probabilities is contiguous with an adjacent range of probabilities which encompasses all of the probabilities from amongst the acquired probabilities that are not encompassed by the pre-set range of extremal probabilities.

4. A quantum computing system according to any preceding claim wherein the pre-set range of extremal probabilities extends:from an uppermost probability value of 1 (unity) to a lowermost probability value exceeding 0 (zero); and / or,from a lowermost probability value of 0 (zero) to an uppermost probability value exceeding 0 (zero).

5. A quantum computing system according to any preceding claim wherein each of the respective quantum state measurement outcome values within the compressed measurement outcome data is represented by a single bit, and each of the probabilities within the compressed measurement outcome data is represented by a plurality of bits.

6. A quantum computing system according to any preceding claim wherein the data compressor is configured to generate the compressed measurement outcome data such that the quantum state measurement outcome values provide an array of values in which each quantum state measurement outcome value is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated.

7. A quantum computing system according to claim 6, wherein the data compressor is configured to generate, in respect of each of the quantum state measurement outcome values, a respective further data item having:a first value if the associated probability value falls within said pre-set range; or,a second value, distinct from the first value, if the associated probability value falls outside said pre-set range.

8. A quantum computing system according to claim 7 wherein each further data item is represented by a single bit.

9. A quantum computing system according to claim 7 or claim 8 wherein the data compressor is configured to generate the compressed measurement outcome data such that the respective further data items form an array of values in which each further data item is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated.

10. A quantum computing system according to any preceding claim wherein the data compressor is configured to acquire said probabilities by obtaining data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation and by applying a data compression to at least some of the obtained data thereby to provide said acquired probabilities.

11. A quantum computing system according to any preceding claim wherein each probability amongst said acquired probabilities is described according to a respective one of finite number of contiguous probability sub-intervals, wherein:a width of each of the probability sub-intervals is common to all of the probability sub-intervals; or a respective width of one or more of the probability sub-intervals differs from a width of one or more other probability sub-intervals amongst said probability sub-intervals.

12. A quantum computing system according to any preceding claim comprising a quantum state discrimination unit configured to apply a quantum state discrimination process in respect of each of the readout measurement values thereby to provide a respective said probability of each of the readout measurement values occurring as a result of performing the readout measurement operation.

13. A quantum computing system according to any preceding claim wherein the readout measurement operation comprises a syndrome measurement operation and the compressed measurement outcome data comprises syndrome data representative of an error state of other quantum devices amongst the plurality of quantum devices.

14. A quantum computing system according to any preceding claim comprising a data transmission system for transmitting the compressed measurement outcome data.

15. A quantum computing system according to any preceding claim comprising a decoding system for receiving the compressed measurement outcome data from the data compressor and for executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices.

16. A distributed quantum computing system comprising, as a first component, the quantum computing system according to claim 14, and further comprising, as a second component separated from the first component, a decoding system for receiving the compressed measurement outcome data transmitted by the data transmission system, the decoding system being configured for executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices.

17. A distributed quantum computing system according to claim 16 wherein the decoding system is configured to determine said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to respective probabilities from amongst said probabilities within the compressed measurement outcome data.

18. A distributed quantum computing system according to any of claims 16 to 17 wherein the decoding system comprises a transmitter system for transmitting the quantum error correction data to the first component of the distributed quantum computing system for use in correcting errors in the quantum computing system associated with quantum devices thereof, and wherein the first component of the distributed quantum computing system comprises a receiver system for receiving quantum error correction data from the second component of the distributed quantum computing system, for use by the first component of the distributed quantum computing system in correcting errors associated with quantum devices thereof.

19. A quantum computing system according to any preceding claim further comprising a data storage system for storing the compressed measurement outcome data.

20. A decoder comprising a computing system configured for receiving compressed measurement outcome data generated by a quantum computing system, the compressed measurement outcome data comprising:quantum state measurement outcome values generated by the quantum computing system by applying a quantum state discrimination process upon readout measurement values produced by performing a readout measurement operation upon quantum devices thereof which encode information using quantum computational states; and,data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data;wherein the decoder is configured to execute a quantum error correction algorithm to determine a correction for an error state of one or more said quantum devices using said quantum state measurement outcome values and said data describing probabilities.

21. A decoder according to claim 20 configured to determine said correction using a decoding graph or a decoding hypergraph with weighted edges weighted according to respective probabilities from amongst said probabilities within the compressed measurement outcome data.

22. A decoder according to claim 20 or claim 21 wherein the decoder comprises a transmitter system for transmitting quantum error correction data describing said correction for an error state to the quantum computing system according to claim 14 for use in correcting errors in the quantum computing system associated with quantum devices thereof.

23. A method for compression of data generated by a quantum computing system comprising a plurality of quantum devices that encode information using quantum computational states and comprising a readout system that performs a readout measurement operation upon quantum devices from amongst the plurality of quantum devices to produce readout measurement data describing analogue readout measurement values; wherein the data compression method comprises:acquiring data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation;performing quantum state discrimination upon the readout measurement data thereby generating respective quantum state measurement outcome values;producing compressed measurement outcome data comprising the quantum state measurement outcome values and data describing probabilities, from amongst the acquired data describing probabilities, which do not fall within the pre-set range of extremal probabilities such that datadescribing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data.

24. A method according to claim 23 wherein the pre-set range of extremal probabilities comprises two sub-ranges of extremal probabilities separated from each other by a contiguous intermediate range of non-extremal probabilities, and the method includes compressing the readout measurement data by performing quantum state discrimination upon the readout measurement values having a respective probability, from amongst the acquired probabilities, falling within any of the two sub-ranges thereby generating respective quantum state measurement outcome data.

25. A method according to claim 23 wherein the pre-set range of extremal probabilities is contiguous with an adjacent range of probabilities comprising which encompasses all of the probabilities from amongst the acquired probabilities that are not encompassed by the pre-set range of extremal probabilities.

26. A method according to any of claims 23 to 25 comprising generating the compressed measurement outcome data such that the quantum state measurement outcome values provide an array of values in which each quantum state measurement outcome value is arranged in association with the respective probability, from amongst the acquired probabilities, with which it is associated.

27. A method according to claim 26 comprising generating, in respect of each of the quantum state measurement outcome values, a respective further data item having:a first value if the associated probability value falls within said pre-set range; or,a second value, distinct from the first value, if the associated probability value falls outside said pre-set range.

28. A method according to any of claims 23 to 27 comprising acquiring said probabilities by obtaining data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation and by applying a data compression to at least some of the obtained data thereby to provide said acquired probabilities.

29. A method according to any of claims 23 to 28 wherein each probability amongst said acquired probabilities is described according to a respective one of finite number of contiguous probability subintervals, wherein:a width of each of the probability sub-intervals is common to all of the probability sub-intervals; or a respective width of one or more of the probability sub-intervals differs from a width of one or more other probability sub-intervals amongst said probability sub-intervals.

30. A method according to any of claims 23 to 29 comprising providing the compressed measurement outcome data to a data transmission system for transmission therefrom.

31. A method according to any of claims 23 to 30 comprising providing a decoding system for receiving the compressed measurement outcome data from the data compressor and, by the decoding system, executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices.

32. A method for distributed quantum computing using a distributed quantum computing system comprising a first component and a second component separated from the first component and comprising a decoding system, the method comprising:by the first component, implementing the quantum computing of claim 30; and,by the second component, receiving the compressed measurement outcome data transmitted by the data transmission system and, by the decoding system, executing a quantum error correction algorithm using data from the compressed measurement outcome data thereby to generate quantum error correction data which describes a correction for an error state of the quantum devices.

33. A method according to claim 32 comprising, by the second component, transmitting the quantum error correction data to the first component of the distributed quantum computing system for use in correcting errors in the first component of the distributed quantum computing system associated with quantum devices thereof; and, by the first component, receiving quantum error correction data from the second component of the distributed quantum computing system, for use by the first component of the distributed quantum computing system quantum computing system in correcting errors associated with quantum devices thereof.

34. A decoding method comprising:receiving compressed measurement outcome data generated by a quantum computing system, the compressed measurement outcome data comprising:quantum state measurement outcome values generated by the quantum computing system by applying a quantum state discrimination process to readout measurement values produced by performing a readout measurement operation upon quantum devices thereof which encode information using quantum computational states; and,data describing respective probabilities of readout measurement values occurring as a result of performing the readout measurement operation which do not fall within a pre-set range of extremal probabilities such that data describing probabilities within the pre-set range of extremal probabilities are excluded from the compressed measurement outcome data;wherein the decoding method further comprises executing a quantum error correction algorithm to determine a correction for an error state of one or more said quantum devices using said quantum state measurement outcome values and said data describing probabilities.

35. A computer program comprising code which, when run on a computer, causes the computer to perform the method of any of claims 23 to 34; or a non-transitory computer readable storage medium storing a computer program comprising code which, when run on a computer, causes the computer toperform the method of any of claims 23 to 34; or a computer system programmed to perform the method of any of claims 23 to 34.s

Images