Multiplexed qubit reading for error-correcting code

Abstract

Quantum device comprising a plurality of qubits, electrometers (100) coupled to qubits of the plurality, a voltage generation module (90) generating a plurality of voltages to excite said electrometers at frequencies, phases or amplitudes specific to each electrometer and a transmission line of an aggregated signal from the electrometers, said signal being, after being taken up by an amplifier (110), processed by a demodulation module (120) to provide demodulated signals.The plurality of qubits comprises qubits organized into a surface code for quantum error correction, including data qubits to ensure the preservation of quantum data and auxiliary qubits coupled to the electrometers (100). Modulations introduced by the voltage generation module (90) into the voltages of the plurality of voltages are dynamically adapted by a modulation assignment module (150) adapted to the code and as a function of said demodulated signal (125; 200) to adjust the read fidelity of the quantum device. Figure for the abstract: 5.

Description

Title of the invention: Multiplexed qubit reading for error-correcting code. Technical context.

[0001] The invention relates to the reading of quantum bits, or qubits. The reading technique involves multiplexing and the implementation of an error-correcting code.

[0002] The field of the invention is that of quantum computing, in particular based on quantum bits (qubits) constructed by technologies based on semiconductor materials, in particular of course silicon - we therefore speak of semiconductor qubits.

[0003] Semiconductor qubits have demonstrated operation compatible with temperatures on the order of 1 K and exhibit high operational fidelities, as described in Huang, JY, Su, RY, Lim, WH et al. High-fidelity spin qubit operation and algorithmic initialization above 1 K. Nature 627, 772-777 (2024). Furthermore, it is possible to control a large number of semiconductor qubits in parallel. Large-scale integration of these qubits is therefore a desirable goal.

[0004] Semiconductor qubits can operate by electrostatic potential trapping to isolate individual electrons, or holes, the information then being coded on the spin of the electron or hole - in this case, we speak of spin qubits.

[0005] A distinction is made between NISQ (noisy intermediate scale quantum computing) implementations, in which a small number (on the order of 10 to 100) of imperfect qubits are exploited, and LSQ (large scale quantum calculation) which involves error-correcting codes to realize more reliable logical qubits, in which errors are corrected efficiently.

[0006] LSQ computing requires the control of several thousand to several million qubits in a cryogenic environment. This cryogenic environment has a limited internal volume and a restricted number of cables passing to or from the outside of the enclosure (this is referred to as a wired connection bottleneck). Furthermore, the acceptable heat dissipation at the various stages of the cryostat is greatly limited by their temperature, which necessitates that the power consumption of the circuits responsible for controlling and reading the qubits, and which are therefore located closest to them in a low-temperature stage, be limited. It is therefore imperative to optimize these circuits.

[0007] Multiplexing techniques for electromagnetic signals are therefore developed, adapted to the signals to be passed through the cryogenic chamber. Control or readout circuits are also developed as close as possible to the qubits, possibly by distinguishing successive chambers of increasing temperatures around a central chamber containing the qubits.

[0008] For reading semiconductor qubits in particular, multiplexing techniques have been proposed. Some involve a form of reflectometry, in which the qubit is connected to a resonator. An incident signal is applied to the qubit to probe the frequency or amplitude variations of the LC resonator's resonance coupled to the different qubits to determine their states. By assigning each qubit a different resonant frequency, the information from each qubit is combined into a single cable, and then the signal is demodulated and processed outside the cryostat. However, the size of the inductances L of the LC resonators (100 pm² to 10 mm² per resonator and therefore per qubit) limits the possibilities of large-scale integration. [Jerger2012, Park2021, Abdo2018, Naaman2021, Bronn2022].

[0009] Another approach involves using wideband amplifiers, such amplifiers enabling frequency, phase, or amplitude multiplexing. [Morel2022] presents an implementation of this type of frequency multiplexing, as well as signal processing based on integrators and comparators. This approach is advantageous because the techniques for manufacturing qubits and this type of readout circuit are similar, allowing their cointegration at low temperature in a limited volume. The number of qubits read simultaneously is on the order of 10 to 50, and depends, among other things, on the amplifier bandwidth (typically around 50 MHz) and the desired readout fidelity (99.99% in 1 ps).

[0010] Regarding the amplifier, a distinction is made between R-TIAs, which have resistive feedback, and C-TIAs, which have capacitive feedback. C-TIAs can offer a higher bandwidth, typically 40 MHz for a power consumption of 200 pW [Razavi2000, Romanova2019, Schmidt2024]. This wide bandwidth can thus be divided into different ranges, each assigned to a respective single-electron transistor (SET), and frequency-division multiplexing of the qubit readout can be performed.

[0011] Phase and / or amplitude multiplexing was proposed by [Schmidt2023] using the same type of amplifiers. This technique increases the number of qubits per amplifier (typically by a factor of 5). Phase multiplexing introduces the concept of a constellation—a constellation being formed by the symbols associated with the 2N combinations of states of N qubits sharing the same frequency. [Schmidt2023] details the choice of phases / amplitudes applied to each qubits are separated to ensure maximum fidelity by isolating the 2N symbols. Therefore, read fidelity can vary for each state combination. In particular, the states 00..0 (all qubits in state 0) and 11..1 (all qubits in state 1) can easily be confused and require special care.

[0012] Quantum error correction (QEC) is a technique based on increasing the number of qubits used to encode a given amount of information. This encoding makes it possible to detect and correct errors. Errors in quantum computers are related to noise, decoherence, and imperfections in quantum gates.

[0013] Quantum error-correcting codes (QECs) aim to form a few perfect logical qubits from a large number of imperfect physical qubits. In the case of stabilizing error-correcting codes, the qubits are separated into a group of qubits carrying quantum information (data qubits) and a group of qubits used to create the logical qubit and obtain information about the errors that have occurred (ancilla qubits). The no-cloning theorem prevents direct measurement of the data qubits or duplication of their information. However, the ancilla qubits can be used to perform parity measurements on groups of data qubits. The parity information for each group can be decoded to estimate the errors that have occurred in the system and correct them without affecting the information held by the logical qubit.

[0014] Quantum error-correcting codes operate using several physical qubits whose joint state represents a logical qubit. The code is designed so that errors can be detected and corrected by measuring certain qubits within the code. Examples include repetition codes, Shor codes, Steane codes, and surface codes. Surface codes are error-correcting codes that use a two-dimensional lattice of qubits to encode logical qubits.

[0015] For example, [Tomita2014] presents a quantum error-correcting code named surface-17.

[0016] But until now, signal processing by reading circuits has not been addressed jointly with the exploitation of the data obtained by signal processing within the framework of a quantum error-correcting code.

[0017] More precisely, in the majority of quantum error-correcting codes, the reading of the qubits is assumed to be simultaneous and of identical fidelity for all qubits, without further evaluation of the consumption of the associated circuits and therefore of the practical feasibility.

[0018] On the other hand, designers of multiplexed readout circuits generally do not take into account the use that can be made of the signals read by their circuits when these are used. These designers also consider each signal as independent of others. Consequently, they do not take into account the expected correlations in these signals to optimize their circuits.

[0019] In addition to or instead of frequency multiplexing, phase multiplexing, amplitude multiplexing, or phase and amplitude multiplexing of the different single-electron transistors is also introduced. After demodulation by the frequency f, a complex number (I, Q) is obtained that depends on the combined state of the SETs. The set of possible coordinates forms a constellation.

[0020] This technique increases the number of SETs per transimpedance amplifier.

[0021] More generally, constellations with N SETs are created by choosing the N phases and amplitudes so as to disperse the points (I, Q) associated with one of the 2N combinations of states.

[0022] Since the distances between two points in the constellation are not all identical, certain combinations of states have greater or lesser read fidelity. Until now, the practice has been to define an average fidelity by assigning an identical weight to each combination of states.

[0023] The inventors wished to improve this practice and better control reading fidelity. Features of the invention and advantages

[0024] For this purpose, a quantum device is proposed comprising a plurality of qubits, electrometers coupled to qubits of the plurality, a voltage generation module generating a plurality of voltages to excite said electrometers with modulations specific to each electrometer and a transmission line of an aggregated signal from the electrometers, said signal being, after being taken up by an amplifier, processed by a demodulation module applying to the multiplexed information.

[0025] Several different frequencies can be used, each frequency being common to a plurality of qubits, which allows more qubits to be read, but the invention, in its generality, is implementable with a single frequency as well as with several frequencies.

[0026] Originally, the plurality of qubits includes qubits organized into a surface code for quantum error correction comprising data qubits to ensure the conservation of quantum data and auxiliary qubits coupled to electrometers, and modulations introduced by the voltage generation module in the voltages of the plurality of voltages being dynamically adapted by a modulation assignment module adapted to the correction code and as a function of said demodulated signal to adjust, and often maximize, a read fidelity of the quantum device.

[0027] Thus, in the invention currently under discussion, a situation is considered in which the probabilities of occurrence of these states are different from each other by several orders of magnitude, and the optimization of the frequencies, phases and amplitudes applied is modified compared to a case in which the probabilities of occurrence of the states would be similar to each other.

[0028] The invention is based on the principle, within the framework of a multiplexed reading, of dynamically using the determination of the state of a given set of qubits to continuously optimize the fidelity of the measurement of these qubits, fidelity being the probability of reading a correct result.

[0029] More specifically, the determination of the state of the set of qubits is carried out prior to its use by the quantum error-correcting codes, and a feedback loop is introduced between the reading of the qubits and the interpretation of the data, which reduces the electrical consumption and the reading time, without reducing the average reading fidelity.

[0030] The observation at the basis of the process used is that in the presence of errors to correct, all combinations of states - or syndromes, these being in finite number determined by the number of qubits and thus forming a list of possible syndromes - are not equiprobable.

[0031] Moreover, from knowledge of the system at a given time, it is possible to associate with each syndrome in the list of syndromes a probability of occurrence for the next measurement, having previously studied all possible errors on the qubits.

[0032] These two properties make it possible to maximize the average reading accuracy, by favoring the measurement of syndromes in which the system has the greatest probability of being in the next measurement. This is quite original and remarkable.

[0033] According to advantageous and optional features:

[0034] - A biasing of the electrometers (single-electron transistors) coupled to the qubits Auxiliary inputs can also be dynamically adjusted to regulate read fidelity. It is also proposed to use the symmetry of the single-electron SET transistors with respect to the IO> and LL> states to reset the syndrome to 00..0 after each measurement.

[0035] - A dynamic adaptation of the modulations can be performed between two readings successive readings of the quantum device. We therefore implement a feedback loop between the result of the last syndrome measurement and the choice of frequencies, phases and amplitudes, which we then optimize for the next reading based on knowledge of the last measured syndrome, via the determination of the probabilities of occurrence of the syndromes by the error-correcting code.

[0036] - The modulation allocation module can take into account knowledge acquired from the specific hardware characteristics linked to particular error rates of the qubits of plurality. Thus, the known hardware specificity of each qubit (data qubits and auxiliary qubits) is taken into account. For example, if one qubit has a higher error rate than the others, the desired measurement fidelity is increased for all syndromes involving a state change of that qubit. This memory of the individual hardware characteristics of the qubits can evolve over time. Two auxiliary qubits observing the same data qubit can be coupled to electrometers excited at different frequencies. In this way, auxiliary qubits can be grouped, reducing their correlations as much as possible, and the resulting groups of auxiliary qubits can be separated by assigning them different frequencies or connecting them to different amplifiers. This limits the number of symbols explainable by a single error, called first-order symbols, which are the most probable, per constellation.

[0037] - A characteristic dimension, typically a maximum width, measured in A Cartesian plane, for example the IQ output plane of a quadrature demodulation module, or a region of the plane, generally convex, associated with a quantum error syndrome in the code, can be modified by a decoding module of the demodulated information advantageously according to a probability of occurrence of said syndrome calculated, for example, by an error-correcting code module, and in any case at least according to a modulation assignment performed by the modulation assignment module based on said probability. Indeed, in one embodiment, the signal is demodulated at low temperature, and then thresholds are used (for example, with the region of interest ROI technique) to determine the state of the auxiliary qubits. This syndrome is then transmitted to the error-correcting code decoder for analysis and determination of the associated error.The thresholds are adjusted with respect to the probability ratios of occurrence of the corresponding states, to maximize the average reading accuracy.

[0038] - The module for decoding the demodulated information - information often represented in the complex plane – perhaps inside a cryostat, possibly multi-stage, maintaining the qubits at a cryogenic operating temperature. Interpreting the measurement directly at low temperature is indeed advantageous in terms of measurement noise and data transfer rate to the electronics located at a higher temperature. The modulation assignment module can nevertheless be outside the cryostat, in the same environment as the error-correcting code decoding module, and provide, by means of a command to the demodulated information decoding module, detection thresholds and, advantageously, constellations for the purpose of decoding the demodulated information.

[0039] - An error-correcting code decoding module can generate a list of The probabilities of syndromes for subsequent reading are determined by an analog signal provided by a demodulation module that processes the multiplexed signal and which may be a quadrature demodulation module. Indeed, while the previous method involves performing a firm demodulation, in another embodiment, a soft demodulation is first performed, solely in frequency, without thresholding in the IQ plane and therefore without symbol identification. The resulting complex numbers (I, Q) at different frequencies are then transmitted to the error-correcting code. This technique is advantageous because it provides the error-correcting code with information about the measurement uncertainty. If a complex number (I, Q) is too far from the expected symbols, the measurement can be repeated without repeating the syndrome extraction.

[0040] - The multiplexed signal demodulation module may be inside a cryostat maintaining the qubits at a cryogenic operating temperature, the error-correcting code decoding module being outside said cryostat.

[0041] - The code could be the surface-17 code. But this is just one example among others.

[0042] - Several different frequencies can be used, each frequency being common to a plurality of qubits, or specific to a qubit.

[0043] - Several electrometers in a group of electrometers can be excited at a common frequency and with phases or amplitudes specific to each electrometer in the group, the demodulation module performing quadrature demodulation by mixing with the common frequency to provide a demodulated signal, the modulations introduced by the voltage generation module including phase or amplitude modulations

[0044] Ultimately, we wish to adjust the distinguishability between combinations of states of the same group of auxiliary qubits according to their probability of occurrence. These probabilities of occurrence are estimated for the error-correcting code used and the error probabilities of the qubits and guide the choice of frequencies, phases, and amplitudes applied to each auxiliary qubit. We maximize the average read fidelity, defined as the sum of the read fidelities of each state F{ weighted by the corresponding probabilities of occurrence Pi. With 'V' being the number of auxiliary qubits. List of figures

[0045] Fig. 1 is a non-limiting illustration of a circuit for reading semiconductor qubits by electrometry.

[0046] Following [Fig.1], [Fig.2] shows a drain current as a function of the gate voltage of electrometers that can be used in the invention and are shown in [Fig.1].

[0047] Fig. 3 shows a simple way of distributing the states of a set of 2 qubits in the IQ plane, with phase modulations 0 and ji / 2.

[0048] Figure 4 shows an example of a surface-17 rotated error-correcting code (or rotated surface 17, "rotated" meaning "turned") which deals with 9 data qubits.

[0049] Figure 5 shows one embodiment of the invention.

[0050] Figure 6 shows a way of distributing the states of a set of 4 qubits in the IQ plane, used in different specific embodiments of the invention.

[0051] Fig. 7 shows a particular implementation of the invention, with the distribution of Fig. 6 and the error-correcting code of Fig. 4.

[0052] Fig. 8 shows another particular implementation of the invention, again with the distribution of Fig. 6 and the error-correcting code of Fig. 4.

[0053] Fig.9 shows an embodiment detail used in a specific embodiment, in relation to Fig.2.

[0054] [Fig. 10] shows an alternative embodiment of the invention to that of [Fig. 5].

[0055] Figure 11 shows another embodiment of the invention. Description related to the figures

[0056] [Fig.1] In [Fig.1], a quantum circuit with semiconductor qubits and qubit reading by electrometry is shown. It operates using a charge reading principle, with frequency multiplexing.

[0057] Semiconductor qubits are defined as electrons or holes placed in nanostructures close to a transistor. At a temperature below 4 K, a fixed number of charges can be isolated in quantum dots (QDs). For the application discussed here, two of these quantum dots are placed facing each other, but in two different regimes.

[0058] The first quantum dot serves as a qubit, containing a small number of electrons and holes, for example a single electron or a single hole. The spin of the electrons or holes can, for example, be used as a two-level system IO> and II>, but the techniques described here are applicable to other forms of semiconductor qubits.

[0059] The other quantum dot is used as a detector, and is operated in a regime called single-electron transistor (SET), for single-electron transistor [Williams2009, Gong2019, Morel2022].

[0060] The circuit in [Fig. 1] is built around spin qubits on a semiconductor, for example on silicon, placed in a cryostat at a temperature on the order of one kelvin (1 K). Each spin qubit is capacitively coupled to a single electron transistor (SET), placed in contact with it in the cryostat.

[0061] Qubits Q1, Q2 and Q3 have been represented, but the invention uses a larger number of qubits, for example on the order of tens, hundreds or more, grouped into different groups.

[0062] The associated SETs, one per qubit, are respectively referenced as SET SI, S2, and S3.... Each has one or more gates G, as well as a source S and a drain D, which are identified in the figure for SET SI. Depending on the spin of the qubit (i.e., its state, in the case of a spin qubit), the SET's conductance varies. This effect occurs through capacitive coupling between the respective quantum dots of the qubit and the SET.

[0063] The drains D of the SETs are connected to one or more constant (or possibly non-constant) potentials, and consequently, the SET delivers a current on its source S as a function of the spin of the qubit.

[0064] The SETs are voltage-excited by voltage generators, as shown in the left part of the figure. Each SET is excited separately. Different frequencies, f1, f2 and f3, generated by voltage generators are used.

[0065] In the embodiment presented, the voltage generators are placed at ambient temperature Tamb and output signals of a few mV at frequencies ranging from 1 MHz to approximately 100 MHz. Each generator is connected to the SETs by a transmission line that enters the cryostat. Alternatively, in another variant, the generators can be placed inside the cryostat.

[0066] The output currents of the SETs, appearing at their source S and which are on the order of nanoamperes (nA), are collected and summed into a total current Lut on a conducting line 50 in close proximity to the SETs, in the qubit cryostat. This line is common to several qubits, but not to all qubits—in which case another conducting line is present for the other qubits.

[0067] The Lut current is amplified by an amplification chain 110 (comprising one or more amplifiers), then read by a demodulation circuit.

[0068] Thus, frequency multiplexing may occur on the transmission line 50 during current collection. Phase and amplitude multiplexing may also occur.

[0069] Quadrature demodulation means are used to separate I and Q components which are then processed, for each frequency, by analog-to-digital converters.

[0070] The demodulation circuit can be placed at different temperatures, including ambient temperature.

[0071] There may be only one output cable from the coldest temperature stage for all the qubits, this output being able to be before or after the amplification chain 110, or between two successive segments thereof. The amplification chain 110 may indeed be placed at a temperature different from that of the qubits.

[0072] The amplification chain 70 includes a transimpedance amplifier (TIA), which converts the current Iout into a voltage Vout placed for example at the same temperature as the qubits.

[0073] The signal on the electromagnetic wave transmission line 60, before demodulation, but after conversion by the TIA is an output voltage.

[0074] The IQ demodulation extracts the complex I and Q components of the signal and transmits them to an analog-to-digital converter which places the amplitude and phase of the signal in the complex plane. These are presented as constellations of points called symbols corresponding to combinations of the states of the auxiliary qubits excited at the frequency.

[0075] [Fig.2] In [Fig.2], the drain current characteristic Ids (or source current) as a function of the gate voltage Vgs (taken between the gate and the source, or the gate and the drain) for a one-electron transistor.

[0076] By applying a small potential difference between the source and the drain of the transistor to an electron, and by varying, along the x-axis on [Fig.2], the voltage applied to the gate of the transistor to an electron, a succession of fine conductance peaks is observed - the drain-source current in nA is represented on the ordinates of [Fig.2] and it peaks at 1.0 nA - separated by areas of low conductance.

[0077] These peaks, known as Coulomb peaks, typically have an amplitude of 1 nA and a width of a few mV (2 to 3 mV in [Fig. 2]). The separation between two peaks is on the order of 10 mV to 100 mV (20 mV in [Fig. 2]).

[0078] The position of the peaks is imposed by the electrostatic environment of the quantum dot, which makes the one-electron transistor a very good local electrometer.

[0079] In particular, the charge state of the qubit shifts the Coulomb peak of the one-electron transistor, which induces a change in current Ld- On [Fig.2] we can see that the peaks for the IO> state and those for the ll> state are shifted by about 3 mV.

[0080] To maximize this effect, the gate voltage of the SET VSEt is biased at a position where the sensitivity to the charge state of the qubit is maximum. If the SET is sufficiently coupled to the qubit, which is typically the case in semiconductor qubits with high integrating power, the Coulomb peak is shifted by a value greater than its full width at half maximum. This results in maximum contrast between the two "0" states: Ion- 0 nA and "1": I0N ~ 1 nA. This is mentioned in [Fig.2] for a grid voltage between 0.44 V and 0.45 V, close to 0.443 V.

[0081] Reading the state of a qubit by electrometry involves several conversions. First, in the case of a spin qubit, there is an initial spin-to-charge conversion through a charge exchange with another quantum dot (QD) (Pauli spin blockade readout) or with a reservoir (Elzerman readout). Then, this charge state of the qubit influences the conductance of the single-electron transistor and modifies the measured output current Isd.

[0082] The state of the qubit IO> can correspond to the low current level "0" or the high current level "1" as needed, and conversely for the state ll>, which then corresponds to the other state. The reference qubit state that we wish to associate with the lowest current Ld = 0 nA is therefore chosen by the bias point VSEt.

[0083] A transimpedance amplifier (TIA) transforms a current into a voltage, with a typical gain on the order of 10⁶ to 10⁹ V / A. It allows the amplification of weak signals produced by SETs (0.1 to 10 nA) to voltages and noise levels compatible with measurement by room-temperature electronics. To increase their bandwidth and minimize their noise, it is advantageous to place these amplifiers at low temperatures, or even as close as possible to the qubits and single-electron SETs.

[0084] The principle of frequency multiplexing in a TIA transimpedance amplifier is based on the transmission on the signal extraction transmission line out of the cryostat of currents of different frequencies, these frequencies being between the lower limit and the upper limit of the bandwidth of the transimpedance amplifier.

[0085] With regard to the amplifier, in one embodiment a C-TIA is used and the bandwidth is divided into different ranges each assigned to a transistor with a respective one-electron SET, and frequency multiplexing of the reading is performed, for example a reading in 1 MHz per SET, i.e. about 40 SETs per C-TIA.

[0086] We typically aim for a fidelity greater than 99.99% for a reading time of 1 ps.

[0087] [Fig. 3] In addition to or instead of frequency multiplexing, phase multiplexing, amplitude multiplexing, or phase and amplitude multiplexing of the different single-electron transistors is also introduced in certain variants. For example, signals of the same frequency f but different phases 0A and 0B are applied to two SETs A and B. After demodulation by the frequency f, a four-dimensional complex number (I, Q) is obtained. possible values, depending on the combined state of SETs A and B. The set of these four coordinates forms a constellation.

[0088] Figure 3 shows the case of two-phase multiplexing: 0 and Φ / 2. The real part I is on the x-axis and the imaginary part Q on the y-axis. The symbols are in the upper right quadrant of the coordinate system (or at its boundary). Due to the spread of measurements caused by measurement noise during signal integration, they take the form of patches that are two-dimensional Gaussian distributions. A delimitation by ROI (region of interest) is represented by a dashed line, based on the measured intensity represented on a logarithmic scale by the color used.

[0089] This two-phase 0 and ^ / 2 multiplexing technique doubles the number of SETs per transimpedance amplifier, without loss of fidelity or increase in consumption of the TIA amplifier.

[0090] In one variant, quadrature amplitude modulation (QAM) is used, where the modulation amplitude varies in powers of 2 and where the phase alternates between 0, jt / 2, ir and 3jt / 2.

[0091] More generally, constellations with N SETs are created by choosing the N phases and amplitudes so as to maximize the distance between each point (I, Q) associated with one of the 2n combinations of states.

[0092] Since the distances between two points in the constellation are not all identical, certain combinations of states have a greater or lesser reading fidelity.

[0093] [Fig.4] Figure 4 shows the arrangement of the qubits used in the error-correcting code Surface error correction code 17. This is a surface error-correcting code. Surface codes are error-correcting codes that use characteristics of a qubit network to protect logical qubits from errors. A two-dimensional lattice of qubits is used to encode logical qubits. The qubits only interact with their nearest neighbors.

[0094] Here, the network consists of 9 data qubits numbered from 1 to 9 and 8 auxiliary qubits divided into two subgroups, one called subgroup "X" and the other subgroup "Z," and identified, with regard to the auxiliary qubits of the first subgroup, from XI to X4 and with regard to the auxiliary qubits of the second subgroup, from ZI to Z4. Each data qubit is connected to one or two auxiliary qubits "X" and to the same number of auxiliary qubits "Z." For example, data qubit 1 is connected to auxiliary qubits ZI and X2, and data qubit 5 is connected to auxiliary qubits X2, Z2, X3, and Z3. Each auxiliary qubit is connected to two or four data qubits. The data qubits are not connected to each other, and the auxiliary qubits are not connected to each other. The whole thing forms a two-dimensional lattice, hence the term "surface". The number of qubits, 9+8=17, justifies the name "surface 17".

[0095] For example, when an "X" error occurs on qubit 5, and no other errors occur simultaneously, the auxiliary qubits Z2 and Z3 are modified, while the other auxiliary qubits, Z1, XI, Z4, X2, X3, and X4, remain unchanged. This result is then interpreted as an "X" error on data qubit 5. This error is stored in memory, and the residual error is monitored until correction is required by applying the appropriate quantum gates.

[0096] Errors of type "X" are bit flips, while errors of type Z are phase flips. The correction procedures are known.

[0097] The error-correcting code algorithm periodically performs a measurement of the syndrome, namely the set of 8 states of the auxiliary qubits XI-X4 and Z1-Z4.

[0098] Then, after the measurement, a decoder determines the most probable error—if any—explaining the measured syndrome. This error may be the superposition of "X" and / or "Z" errors appearing simultaneously on several data qubits. However, given the low error rate per qubit, the highest probability is that there are no errors on any of the data qubits.

[0099] If there has likely been an error on one or more qubits, the decoder then determines the actions to be implemented to correct the identified error.

[0100] The error-correcting code is capable of correcting a number of simultaneous errors (in the sense of coexisting during measurement) less than a maximum number of errors specific to it. Surface 17, however, only corrects one error at a time. More sophisticated codes, however, make it possible to correct several errors simultaneously.

[0101] Reasoning in the case where there is no Z error and where the syndrome on the auxiliary qubits X is 0000, assuming an initial syndrome on the auxiliary qubits Z "0000", and a p=l% error rate "X" on each data qubit, we can calculate the probability of measuring each syndrome on the next read according to Table 1. [Tables 1] Syndrome (Z4Z3Z2Z1) Most probable interpretation on data qubits Probability "0000" No error 90.63% "0001" 1 1% "0010" 2 or 3 2% "0011" 1+2 or 1+3 0.02% "0100" 7 or 8 2% "0101" 4 1% "0110" 5 1% "YES" 1+5 or 2+4 or 3+4 0.03% "1000" 9 1% "1001" 1+9 0.01% "1010" 6 1% "1011" 1+6 0.01% "1100" 7+9 or 8+9 0.02% "1101" 4+9 0.01% "1110" 6+7 or 6+8 or 5+9 0.03% "1111" 4+6 0.01%

[0102] Thus, faced with a 0000 syndrome, the code estimates that the highest probability is that there was no Z error on the four data qubits.

[0103] Faced with a 0001 syndrome, the code estimates that the highest probability is that there has been a Z error on data qubit 1 and no other errors.

[0104] Faced with a 0101 syndrome, the code estimates that the highest probability is that there was a Z error on data qubit 4 and no other errors.

[0105] Faced with a 0110 syndrome, the code estimates that the highest probability is that there was a Z error on data qubit 5 and no other errors.

[0106] Faced with a 1000 syndrome, the code estimates that the highest probability is that there was a Z error on data qubit 9 and no other errors.

[0107] Faced with a 1010 syndrome, the code estimates that the highest probability is that there was a Z error on data qubit 6 and no other errors.

[0108] Faced with a 0010 syndrome, the code estimates that the highest probability is that there has been a Z error on data qubits 2 or 3, without it being possible at this stage to distinguish between data qubits 2 and 3, and no other errors.

[0109] Faced with a 0100 syndrome, the code estimates that the highest probability is that there has been a Z error on data qubits 7 or 8, without it being possible at this stage to distinguish between data qubits 7 and 8, and no other errors.

[0110] The syndromes mentioned above have a probability of occurrence of at least 1%, and include all syndromes associated with first-order errors.

[0111] Each syndrome has its own probability, and these probabilities differ by several orders of magnitude depending on whether the syndrome corresponds to 0 errors, 1 error, or 2 simultaneous errors on the data qubits. In the example presented, the read fidelity of the state "0000" has been maximized, because the error rate is low and therefore the syndrome is likely unchanged. Next, the fidelity associated with the errors of order 1 (“0001”, “0010”, “0100”, “1000”, “0101”, “0110” and “1010”) is maximized.

[0112] Some second-order errors are interpretable with sometimes a simple ambiguity (two or three possibilities - this is the case for syndromes 0011, 0111, 1100 and 1110) or even for syndromes 1001, 1011, 1101 and 1111 no ambiguity: they are associated respectively with the combination of an error on data qubit 1 and an error on data qubit 9, the combination of an error on data qubit 1 and an error on data qubit 6, the combination of an error on data qubit 4 and an error on data qubit 9, and the combination of an error on data qubit 4 and an error on data qubit 6.

[0113] For certain second-order errors, and for all third- and fourth-order errors, the error-correcting code incorrectly interprets the syndrome as originating from another, lower-order, and therefore more probable, error. These situations are not individually listed in Table 1. In this example, the total probability of occurrence for all these situations is 0.37%.

[0114] Other arrangements of physical qubits, different from the surface-17 code, can be used to construct a logical qubit.

[0115] The gates applied during syndrome extraction before measuring the state of the auxiliary qubits may include control-NOT (C-NOT) gates applied between the auxiliary qubit and each of the data qubits, which are four or two in number, hence the use of C-NOT gates, for example four in number. For the auxiliary qubits Z, it is possible not to use any other gates in addition to those thus indicated, and for the auxiliary qubits X, two Hadamard gates may be used in addition.

[0116] [Fig.5] The invention relates to a phase, frequency and amplitude multiplexed reading of a set of auxiliary qubits.

[0117] As shown in Figure 5, the system under consideration is a large set of data qubits and auxiliary qubits, the state of the auxiliary qubits 100 of which is regularly measured by electrometers, themselves connected to an amplification chain 110, which transmits the measured signals to a quadrature demodulator 120 (or more generally a demodulation module processing the multiplexed information provided by the amplification chain 110). This demodulator receives, for the purposes of demodulation, the frequencies that have been generated by sinusoidal voltage generators 90 to read the auxiliary qubits 100: f0, fb, etc. The sinusoidal voltage generators 90 perform radio frequency synthesis, forming voltages of the form + <p j avec 'cs           a>'furnis Pæ' a The allocation module, discussed later, uses one triplet per qubit. In the embodiment shown, the sinusoidal voltage generators 90 and the quadrature demodulator 120 are both located within the temperature range below 4 K, as are the qubits and the transimpedance amplifier of the amplification chain 110. Thus, the voltages are available in the environment of the quadrature demodulator 120, and there is no need to run a large number of cables through the cryostat wall. These voltages are used as references for demodulation. It is also possible, as disclosed in EP4016402A1, but this is optional, for the cryostat to have two stages. An internal stage at a lower temperature specifically houses the qubits, electrometers, and amplification chain, while the voltage generators and the demodulation module are located in a higher temperature stage, but below 4 K.It is also possible that the voltage generators are placed at room temperature as shown in [Fig. 1].

[0118] The sinusoidal voltage generators 90, in addition to producing sinusoidal voltages at different frequencies, provide, for each frequency, different phase shifts of the sinusoidal voltage, and also different amplitudes thereof, each combination being applied to the resonator of a given qubit. Thus, the principles of frequency, phase, and amplitude modulation are implemented to read a large number of qubits with a limited number of transimpedance amplifiers, or even a single transimpedance amplifier, if its bandwidth allows.

[0119] The frequency, phase, and / or amplitude modulation techniques presented previously are thus applied to a set of auxiliary qubits whose state is to be determined. The choice of optimal modulations is made outside the cryostat, at room temperature (approximately 300 K) in an allocation module 150. The allocation module 150 provides as many frequency, amplitude, phase triplets as there are auxiliary qubits to be read, here N. The frequency, amplitude, phase triplets are also provided by the allocation module 150 to a complex plane decoding module 130, which interprets the demodulated information. This module is located in the cryostat at less than 4 K and receives from the quadrature demodulator 120, for each frequency fi5, the intensities in the complex plane IQ determined by quadrature demodulation, in the form of an analog demodulated signal 125.These intensities are decoded using the constellations and detection thresholds associated with the frequency £ and provided within the framework of a setpoint 180 by the allocation module 150 to the decoding module in the complex plane 130. .

[0120] The decoding module in the complex plane 130 provides the decoded states forming a syndrome 200 to the error-correcting code decoding module 140 which is located outside the cryostat at room temperature.

[0121] And the error-correcting code decoding module 140 generates the list 145 of the probabilities of occurrence P of the different states of the auxiliary qubits. There are 2N of them. This list is transmitted to the allocation module 150 and used by it to decide the modulations to be performed, and more specifically to define the frequency, amplitude and phase triplets.

[0122] The measurement is repeated and allows observation of the appearance of errors on the data qubits.

[0123] The reading architecture thus defined offers free choice of frequencies, phases and amplitudes (fk, <pk, vk) appliquées à chaque qubit auxiliaire d’indice k, contrairement au cas d’un multiplexage base de réflectométrie pour lequel la fréquence est fixée par un résonateur.

[0124] Moreover, this allocation of frequencies, phases and amplitudes is modified whenever it is advantageous during a series of measurements, for example to isolate the signals relating to certain syndromes that one wishes to measure more precisely.

[0125] To minimize the reading error, the expected correlations between the states of the different auxiliary qubits for the same error on the data qubits are taken into account and the auxiliary qubits are grouped according to these correlations.

[0126] By spectrally separating two auxiliary qubits that observe the same data qubit in distant frequency bands, we minimize the number of points having a high probability of occurrence in the same constellation, at the same demodulation frequency.

[0127] Thus, for a given demodulation frequency, the probability of occurrence of the states 1100, 1010, 1001, 0110, 0101 and 0011 goes from ~p to ~p2, namely the probability of two independent errors.

[0128] A probability table of occurrence is established for each state. From a given syndrome, the probability of measuring each syndrome (the same syndrome, and also each of the other 2N-1 syndromes) is estimated during the next reading.

[0129] On this basis, the phase, amplitude and frequency assigned to each auxiliary qubit for the purpose of its reading are adjusted in order to maximize the average fidelity of reading the 2n syndromes, the fidelities of reading each syndrome being weighted by the probability of occurrence of the syndrome for the purpose of calculating the average fidelity.

[0130] The problem therefore amounts to considering as input parameters the 2N probabilities Pi obtained from knowledge of the error-correcting code used, and determining N frequency / phase / amplitude triplets (fk, <pk, vk) qui maximisent favg="E" exp,.

[0131] Furthermore, this optimization can take into account characteristics specific to each physical qubit, such as a higher error rate for a qubit of data or an auxiliary qubit, linked to the hardware implementation as it is known.

[0132] [Fig. 6] In [Fig. 6] a constellation obtained by modulating 4 SETs with phases (-3jt) / 8, (-ir) / 8, ir / 8 and 3ir / 8 is shown. The 24=16 states appear as two-dimensional Gaussian peaks – and therefore as essentially circular patches. State 0000 is centered on point 1=0 Q=0. A delimitation by ROI (region of interest) is shown in dashed lines, based on the expected intensity represented on a logarithmic scale by the color used, under the stated assumption that the 16 states are equiprobable (P = 1 / 16 for 0000, 0001, ..., 1111). The threshold in the IQ plane is a curvilinear curve in the (I, Q) plane, a straight line or a contour such as a circle or rectangle around the area of ​​the plane associated with one of the two states and therefore can be a circle as shown in the figure.

[0133] The states are not regularly spaced: 8 of them, including state 0000, but also states 0001, 0011, 0111, 1111, 1110, 1100 and 1000 are on a circle of large diameter centered on the point on the x-axis close to I = 1.4, and 8 others, including states 0010 and 0100, are on a circle of small diameter, about half the diameter of the large circle, and with the same center as the large circle.

[0134] This distribution gives, for example, better reading fidelity for the state

[1000] , which is on the large diameter circle and whose peak has no close neighbors, than for the state

[0100] , which is on the small diameter circle and is close to two other peaks of the constellation.

[0135] [Fig.7] We therefore use appropriate thresholds to distinguish the states associated with various probability distributions between two neighboring peaks, different from the 50%-50% distribution that was implicitly used in [Fig.6]. For this, the dimension in a plane of the region of interest associated with a syndrome is modified by the decoding module in the complex plane 130 according to the probability of occurrence of the syndrome provided by the list 145, and the assignment of the modulations made by the assignment module 150 on the basis of said probability.

[0136] Thus, between two states to be distinguished, the prior probability can be distributed, for example, as 20% for the first state and 80% for the second state. The threshold in the IQ plane is a circle whose center remains unchanged with respect to the choice made in connection with Figure 6, but with a radius adapted to maximize the average precision F^P^xFo + P^F!.

[0137] Figure 7 shows more precisely the phase-multiplexed read of the auxiliary qubits XI, X2, X3, and X4 within the surface-17 error-correcting code, for an error rate for Z-type errors p=l% on data qubits 1 to 9 and an initial syndrome

[0000] . As shown on the left side of the figure, The auxiliary qubit X3 has a phase of tt! 8, the auxiliary qubit X2 has a phase of -7, the auxiliary qubit X4 has a phase of and the auxiliary qubit XI has a phase of -3tf / 8.

[0138] The thresholds optimized for this case are represented by dashed lines in the complex plane shown on the right-hand side of the figure. The state

[0000] has the highest probability and is associated with a threshold in the form of a large-radius circle, followed by the states

[1000] ,

[1100] ,

[0001] , and

[0011] on the large circle and

[0100] ,

[0010] ,

[0110] on the small circle, which have thresholds in the form of circles of intermediate radii. The other states, with a lower probability, involve at least two independent errors and have thresholds in the form of circles of smaller radii. Thus, the states

[0100] ,

[0010] ,

[0110] have a decreased probability of being confused with another state, despite their position on the small circle.

[0139] [Fig.8] In Figure 8, we have represented, still within the framework of the surface correction code 17, and for an error rate for Z-type errors p=l% on data qubits 1 to 9 and an initial syndrome

[0000] , the phase-multiplexed read of a group of auxiliary qubits, some of which are of category X and others of category Z. Specifically, in Figure 9, these are XI, Z2, X3, and Z4. As shown on the left side of the figure, auxiliary qubit X3 has a phase of / 8. Auxiliary qubit Z2 has a phase of y. Auxiliary qubit XI has a phase of 3^7. Auxiliary qubit X4 has a phase of 3^7.

[0140] Since the auxiliary qubit group XI, Z2, X3 and Z4 does not contain any pair of auxiliary qubits observing the same type of error on the same data qubit, the probability of obtaining the states

[1100] and

[0011] (on the large circle) and,

[0110] (on the small circle) is decreased compared to the situation in [Fig.7], which improves the average fidelity of the measurement in the complex plane (right part of the figure).

[0141] The thresholds optimized for this case are again represented by dashed lines. The state

[0000] has the highest probability and is associated with a threshold in the form of a circle with a large radius, followed by the states

[1000] ,

[0100] ,

[0010] , and

[0001] , which have thresholds in the form of circles with intermediate radii. The other states, with lower probabilities, involve at least two independent errors and have thresholds in the form of circles with smaller radii, notably

[1100] ,

[0011] , and

[0110] , which are visible in [Fig. 7] for comparison.

[0142] It is preferable to group auxiliary qubits exhibiting the lowest possible correlations at the same frequency, in order to obtain a constellation with the fewest possible high probability states.

[0143] [Fig.9] Furthermore, after decoding in the complex plane of a syndrome and before the As a next step, it is advantageous to memorize this syndrome as a new reference state before a new syndrome extraction.

[0144] To achieve this, and as shown in [Fig. 9], the bias points of each single-electron transistor—the electrometers—are modified. These points are in state "1" in the result of the last decoding in the complex plane, so as to conventionally fix the relevant state as state "0". In this way, the next measurement systematically yields "00..0" when no parity change occurs and there is therefore no error detectable by the error-correcting code. The syndrome has thus been reset to "00..0".

[0145] In [Fig.9], compared to [Fig.2], the bias point of the gate of the transistor serving as an electrometer for the auxiliary qubit which has been identified as being in state 1 is placed at 0.44 V whereas it was previously at about 0.443 V. Thus, the biasing of the electrometers coupled to the auxiliary qubits is dynamically adapted to adjust said read fidelity: the distribution of the peaks in the complex plane is again that which is presented in [Fig.7] (right part of the figure) or [Fig.8] (right part of the figure).

[0146] Thus, in the specific case of syndromes with a very low probability of occurrence linked to several independent physical errors, the probability ratio with other states is taken into account to determine the optimal region of interest (ROI), as explained above. In some cases, these unlikely states can be ignored to maximize the overall fidelity of the measurement. As shown in [Fig. 5], in one embodiment, decoding in the complex plane is performed at low temperature, i.e., in the cryostat below 4 K, at the temperature at which the qubits are located.

[0147] In one embodiment, low-temperature demodulation is performed followed by the application of thresholds to determine the measured syndrome.

[0148] This method has the advantage of interpreting the measurement directly at low temperature (<4K), which is advantageous in terms of measurement noise and data transfer rate to the electronics placed at room temperature (approximately 300K).

[0149] [Fig. 10] However, according to a variant shown in [Fig. 10], flexible frequency demodulation is performed. The quadrature demodulator 120 is again in the low-temperature cryostat (<4 K) and provides the error-correcting code decoding module 140, which is still in the external environment (approximately 300 K), not with a syndrome but in the form of an analog signal, with a complex number (I, Q) for each frequency. The complex-plane decoding module 130 is eliminated. By removing the thresholding that this module 130 performs in the previous embodiment, the error-correcting code decoding module 140 is provided with richer information on the measurement accuracy, namely information including a distance between the actually measured value and the nearest expected value.

[0150] [Fig. 11] In [Fig. 11] a frequency matching is shown, with for example a single qubit per frequency. The figure has an upper and a lower part, on each of which the x-axis represents the frequencies f1, f2, f3... ([Fig. 1]) at which the excitations are generated by the sinusoidal voltage generators 90.

[0151] In the upper part of the figure, the frequencies are regularly spaced and the read fidelity is the same at all frequencies - the read fidelity is homogeneous over all the different qubits.

[0152] In the lower part of the figure, the separation between a particular frequency fk and neighboring frequencies has been increased. The frequencies fk_i and fk+[ are respectively closer to the frequencies fk.2 and fk+2, consequently, the latter being either left unchanged or shifted but less significantly. In any case, the frequencies fk2 and fk+2 are found in a more congested environment than fk, as the available frequency band is limited.

[0153] For an identical signal integration time for all qubits, the read fidelity is then better for the frequency fk and therefore for the associated qubit than for the frequencies fk+2, fk+b, fk_i, and fk2 and their associated qubits. Thus, there is better read fidelity for the qubit associated with the frequency fk than for the qubits associated with the other frequencies.

[0154] According to the invention, the allocation module 150 ([Fig.5] or [Fig.10]) dynamically adapts the allocated frequencies and their respective spacings under the constraint of the bandwidth of the amplification chain 110 ([Fig.5] or [Fig. 10]), to adjust the read fidelity of the qubits according to the priorities defined by the allocation module 150 in particular on the basis of the probabilities of occurrence P; of the different states of the auxiliary qubits.

[0155] Thus, at each reading stage, two or more states can be specifically separated, at least one of which is more easily discerned, to the detriment of other states for which the measurement may be less precise for reasons similar to those mentioned previously. The frequency sent to each transistor is then dynamically adapted to an electron instead of maintaining regularly spaced frequencies. References

[0156] [Park2021] Park et al., A fully integrated cryo-CMOS SoC for State manipulation, readout and high-speed gâte pulsing of spin qubits, IEEE Journal of solid State circuits, vol. 56, n° 11,3289-3306.

[0157] [Jerger2012] M. Jerger et al., Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits. Appl. Phys. Lett. 23 July 2012; 101 (4): 042604.

[0158] [Gong2019] M. J. Gong et al., "Design Considérations for Spin Readout Amplifiers in Monolithically Integrated Semiconductor Quantum Processors," 2019 IEEE Radio Frequency Integrated Circuits Symposium (RFIC), Boston, MA, USA, 2019, pp. 111-114.

[0159] [Rasavi2000] B. Razavi, "A 622 Mb / s 4.5 pA / / spl radic / Hz CMOS transimpedance amplifier [for optical receiver front-end]," 2000 IEEE International Solid-State Circuits Conférence. Digest of Technical Papers (Cat. No.00CH37056), San Francisco, CA, USA, 2000, pp. 162-163.

[0160] [Ramanova2019] A. Romanova, et al., A Review of Modem CMOS Transimpedance Amplifiers for OTDR Applications. Electronics 2019, 8, 1073.

[0161] [Tomita2014] Tomita, Yu, and Krysta M. Svore. "Low-Distance Surface Codes under Realistic Quantum Noise". Physical Review A 90, no. 6 (11 December 2014): 062320.

[0162] [Morel2022] fascicule EP4016402A1

[0163] [Abdo2018] fascicule WO2018 / 185542A1

[0164] [Naaman2021] WO2021 / 061776A1

[0165] [Bronn2022] US2022 / 0140927Al

[0166] [Williams2009] EP2075745A1

[0167] [Schmidt2023] demande de brevet FR2306530 du 22 juin 2023.

[0168] [Schmidt2024] demande de brevet FR2403977 du 17 avril 2024.

Claims

Demands

1. A quantum device comprising a plurality of qubits, electrometers (100) coupled to qubits of the plurality, a voltage generation module (90) generating a plurality of voltages to excite said electrometers with modulations specific to each electrometer, and a transmission line for an aggregated signal from the electrometers, said signal being, after being taken up by an amplifier (110), processed by a demodulation module (120), the quantum device being characterized in that the plurality of qubits comprises qubits organized into a code for quantum error correction comprising data qubits to ensure the preservation of quantum data and auxiliary qubits coupled to the electrometers (100), modulations introduced by the voltage generation module (90) being dynamically adapted by a modulation assignment module (150) adapted to the code as a function of said demodulated signal (125;200) to adjust the reading fidelity of the quantum device.;

2. Quantum device according to claim 1, characterized in that a polarization of the electrometers (100) coupled to the auxiliary qubits is also dynamically adapted to adjust said read fidelity.

3. Quantum device according to claim 1 or claim 2, characterized in that a dynamic adaptation of the modulations is performed between two successive readings of the quantum device.

4. Quantum device according to any one of claims 1 to 3, characterized in that the allocation module takes into account acquired knowledge of the material particularities related to particular error rates of the qubits of the plurality.

5. Quantum device according to any one of claims 1 to 4, characterized in that two auxiliary qubits observing the same data qubit are coupled to excited electrometers with distinct frequencies.

6. A quantum device according to any one of claims 1 to 5, characterized in that a characteristic dimension of a range or region of values ​​of at least one demodulated quantity, the range or region being associated with a given quantum error syndrome, is modified according to an occurrence probability (145) of said given syndrome and an allocation of modulations made on the basis of said probability.

7. Quantum device according to any one of claims 1 to 6, characterized in that a demodulated information decoding module (130) is inside a cryostat maintaining the qubits at a cryogenic operating temperature, the allocation module (150) being outside said cryostat and providing by a setpoint (180) to the demodulated information decoding module (130) detection thresholds for the purpose of decoding.

8. Quantum device according to any one of claims 1 to 7, characterized in that an error-correcting code decoding module (140) generates a list (145) of syndrome probabilities for later reading in view of an analog signal (125) which is communicated to it by a demodulation module (120).

9. Quantum device according to any one of claims 1 to 8, characterized in that the demodulation module (120) is inside a cryostat maintaining the qubits at a cryogenic operating temperature, the error-correcting code decoding module (140) being outside said cryostat.

10. Quantum device according to any one of claims 1 to 9, characterized in that the code is the surface-17 code or another surface code.

11. Quantum device according to any one of claims 1 to 10, characterized in that several different frequencies are used, each frequency being common to a plurality of qubits, or specific to a qubit.

12. Quantum device according to any one of claims 1 to 11, characterized in that several electrometers of an electrometer group are excited at a common frequency and with phases or amplitudes proper to each electrometer of the group, the demodulation module performing quadrature demodulation (120) by mixing with the common frequency to provide a demodulated signal, the modulations introduced by the voltage generation module comprising phase or amplitude modulations.

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