Method for initializing and / or reading the quantum state of a qubit of a quantum processor

Abstract

The invention relates to a method for initializing and / or reading the quantum state of at least one qubit (3) of an electron spin bus of an NV quantum processor (2), wherein an adiabatic electromagnetic pulse (7) is generated to invert the spin of the at least one qubit (3) and is fed into the quantum processor (2), characterized in that an adiabatic sech / tanh pulse (7) is used to invert the spin, as well as a quantum computer system (1) with an NV quantum processor with a strong coupling drive, comprising multiple qubits (3) and an inversion device (4) for initializing and / or reading the quantum state of the qubits (3), which is designed to carry out the method.

Description

[0001]

[0002] Method for initializing and / or reading out the quantum state of a qubit of a quantum processor

[0003] The application relates to a method for initializing and / or reading out the quantum state of at least one, in particular several, qubits of a quantum processor, in particular an electron spin bus. A further subject matter of the invention is a quantum computer system with a quantum processor, in particular an NV quantum processor with a strong-coupling drive, comprising several qubits and an inversion device for initializing and / or reading out the quantum state of the qubits.

[0004] Goiter, D. Andrew; Wang, Hailin; Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond. Physical Review Letters, 2014, Vol. 112, No. 11, p. 116403 describes: Rabi oscillations and adiabatic passage of single electron spins in a diamond nitrogen void are demonstrated using two Raman-resonant optical pulses tuned to the respective dipole opto-transitions. It is shown that the optical spin control is nuclear-spin selective and can be robust against rapid decoherence, including radiative decay and spectral diffusion, of the underlying optical transitions. A direct comparison between the Rabi oscillation and the adiabatic passage, as well as a detailed theoretical analysis, provide significant physical insights into the connections and differences between these coherent spin processes and also explain the role of spectral diffusion in these processes.Optically controlled coherent spin processes enable the use of nitrogen vacancy-excited states to mediate coherent spin-phonon coupling, thus opening up the possibility of combining optical control of both spin and mechanical degrees of freedom.

[0005] Whaites, OT, et al. Adiabatic dynamical-decoupling-based control of nuclear spin registers. Physical Review Research, 2022, Vol. 4, No. 1, p. 13214 describes: The use of nuclear spins around electron spin qubits as quantum registers and long-lasting memories opens the way for new applications in quantum information and biological sensing. Therefore, there is a need for generic and robust forms of nuclear register control. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, a technique is demonstrated in which adiabatic gates are generated from dynamical decoupling protocols, which simultaneously extend coherence. This pulse-based adiabatic control is illustrated for nuclear spins around NV centers in diamond. A closed-form expression is derived from Landau-Zener theory and shows that it reliably describes the dynamics. Through the

[0006] NC-2024-1716 1Identification of Robust Floquet States shows that the technique enables polarization, one-shot flips, and state storage for nuclear spins. These results lead to a control paradigm that combines dynamic decoupling with adiabatic evolution.

[0007] The use and manipulation of spins as quantum states in spin-based quantum processors allows information to be stored and processed in the form of spin states, leading to an exponential increase in computing power compared to classical computers. This ability to utilize superposition and entanglement within spin states enables quantum computers to solve problems that are inaccessible to traditional computers.

[0008] Spin inversion is a crucial process in quantum computing, particularly in the initialization of qubits (quantum bits). This technique reverses the spin of an electron or nucleus acting as a qubit from one state to another. This is essential for bringing the qubits into a defined initial state required for quantum operations.

[0009] Similarly, after the calculations, in which one or more quantum gates are applied to the qubits, the populations are transferred, i.e., inverted, from one spin manifold to another to read out the result of the calculation.

[0010] Spin is an intrinsic quantum mechanical property of quantum mechanical systems, such as electrons, and is described as intrinsic angular momentum. For example, each electron can assume one of two possible spin states: "spin-up" or "spin-down." This property is crucial for the functioning of qubits in spin-based quantum computers.

[0011] An electron spin bus is a concept in quantum computing based on the use of spin-based qubits. In an electron spin bus, electrons are used as carriers of quantum information to connect different qubits. Here, an electron spin acts as a bus qubit, connected to a limited number of nuclear spins that serve as client qubits. This allows for the formation of local processing units that can be interconnected via electron-electron or electron-nuclear couplings. This is particularly important for scaling quantum computers and implementing complex quantum mechanical algorithms. By using electron spins as qubits, an electron spin bus enables increased coherence of quantum information. This coherence is crucial for maintaining the quantum mechanical properties necessary for quantum computing.Improved coherence leads to fewer errors in quantum operations and allows for longer computation times without decoherence.

[0012] Up to now, a rectangular pulse from a control field has been used to invert the spins during the initialization of such quantum processors. After initialization, the qubits are coherently manipulated with microwaves or high-frequency radiation, and the spin state is then measured with a photon counter. The fidelity, which indicates the similarity of two states, is determined by rectangular pulses in the microwave range.

[0013] The spin inversions achieved with NC-2024-1716 are, however, significantly reduced by even small fluctuations in the external magnetic field, for example, due to thermal or other changes in the setup or the control field. This is because the application of a rectangular pulse only completely inverts the spin if the pulse is in resonance with the spin precession around the external magnetic field, and if the pulse amplitude is chosen precisely so that the rotation angle is 180°. Even minor deviations therefore do not result in a complete inversion and thus reduce fidelity.

[0014] The object of the present invention is therefore to realize an inversion of spins in a quantum processor that is robust against small fluctuations of the external magnetic fields and the magnetic control field.

[0015] This task is solved in a device of the type mentioned above by generating an adiabatic electromagnetic pulse to invert the spin of the at least one qubit and feeding it into the quantum processor.

[0016] An adiabatic inversion can be achieved using an adiabatic electromagnetic pulse. In an adiabatic inversion, a time-dependent magnetic field can be applied to the spin, rotating it beyond a resonance point. This technique has proven effective in achieving high fidelity in the inversion, even in environments with strongly fluctuating fields, particularly external magnetic fields. The adiabatic pulse can invert the spin magnetization over a defined bandwidth, independent of the pulse intensity, as long as it exceeds a certain threshold. The adiabatic pulse satisfies the adiabatic condition, which, in a coordinate system rotating with the instantaneous frequency of the pulse, takes the form...

[0017]

[0018] exhibits this. In this coordinate system, the vector of the effective external magnetic field B acting on the spin can be rotated 180° around the y-axis from z to -z over the duration of the adiabatic pulse. Here, da / dt is the rotational speed of the effective field vector B. e ft around the y-axis, y the gyromagnetic ratio and B e tf(t) is the vector of the effective field of the bed at the respective time t.

[0019] Under the influence of the adiabatic pulse, the rotation of the bed is slow compared to the precession of the magnetization around B. e tf, so that the magnetization can adiabatically follow this vector.

[0020] This adiabatic inversion of magnetization can occur independently of the pulse amplitude, since above a certain threshold of amplitude it is independent of the precession frequency, which is proportional to the size of the bed and thus to the pulse amplitude and to external magnetic fields.

[0021] Compared to rectangular pulses, an adiabatic pulse can produce an essentially rectangular inversion profile in the frequency domain, a larger bandwidth and / or better stability.

[0022] NC-2024-1716 3 Amplitude fluctuations of the control pulses are achieved. The essentially rectangular inversion profile can exhibit a magnetization that is essentially uniform within the limits of the frequency range.

[0023] In particular, an adiabatic pulse can achieve a flatter inversion profile with steeper flanks compared to a similar rectangular pulse.

[0024] For initialization, particularly in an NV quantum processor, the cores of the NV centers can first be initialized to a state |0>. Subsequent initialization of the electron spin with the adiabatic pulse can only invert one electron transition. Since adiabatic pulses add an uncontrolled complex phase factor, they cannot be used for coherent rotations of electron or nuclear spins on the Bloch sphere. Therefore, the adiabatic electromagnetic pulse cannot be used to apply quantum gates to the qubits.However, when controlling nuclei strongly coupled to the NV center by high-frequency pulses, this cannot have a detrimental effect, because when applying further quantum gates to the nuclei, although an uncontrolled phase is added as a global phase factor, this does not affect the computation result, since that phase factor does not affect the values ​​of the diagonal of the density matrix and it cannot be measured.

[0025] Furthermore, the adiabatic pulse can be used to read out the populations of the individual nuclear configurations by selectively selecting the electron for a specific nuclear configuration, in particular m s = -1 to m s = 0, which is inverted by an adiabatic pulse. Since only populations can be read out in this way, an uncontrolled phase factor of the adiabatic pulse is not measurable.

[0026] According to a further development of the invention, an adiabatic sech / tanh pulse is used for spin inversion. An adiabatic sech / tanh pulse can achieve complete inversion over an adjustable frequency and amplitude range. A robust inversion, in particular an electron spin bus inversion, can be achieved with a sech / tanh pulse. Complex phase factors introduced by a sech / tanh pulse do not affect the results of subsequent calculations using quantum gates, since these phase factors do not affect the values ​​of the diagonal of the density matrix. A sech / tanh pulse can exhibit a sech-shaped (hyperbolic secant) amplitude modulation and a tanh-shaped (hyperbolic tangent) frequency modulation.

[0027] A sech / tanh pulse can be used in particular for the inversion of the electron spin bus of an NV processor with a strong coupling drive, as it has the greatest selectivity among the adiabatic pulses.

[0028] Furthermore, a microwave pulse can be used as the adiabatic electromagnetic pulse. A microwave pulse can achieve a particularly effective inversion for the initialization and / or readout of quantum states. Preferably, the adiabatic electromagnetic pulse lies in a frequency range of 1 GHz to 300 GHz.

[0029] It is possible that the adiabatic pulse is set to a predetermined frequency and amplitude range before being transmitted to the quantum processor. By setting the adiabatic pulse to a

[0030] NC-2024-1716 4. Within a predefined frequency and amplitude range, which has been predefined and optimized for the respective application, an application-specific adjustable inversion can be achieved. In this way, individual states or state ranges can be selectively inverted, while other states remain unaffected even by fluctuations in the external magnetic fields or the magnetic control field. Preferably, qubits of the electron spin bus are inverted to transfer populations of nuclear spins of the quantum processor from one spin manifold to another for the purpose of initialization and / or readout. Inverting the qubits of the electron spin bus enables the simple and effective inversion of the nuclear spins of the quantum processor that serve as client qubits.

[0031] Furthermore, the adiabatic electromagnetic pulse can induce an ODMR inversion in the quantum processor. In optically detected magnetic resonance (ODMR), the electron spin of a crystal defect or an NV center can be optically pumped as a double resonance technique to initialize and / or read out the spin. Such an ODMR inversion can enable the optical measurement of populations during readout in which uncontrolled phase factors do not appear. A disruptive influence of uncontrolled phase factors introduced by the adiabatic pulse can thus be avoided. An essentially rectangular ODMR inversion spectrum can be achieved with an adiabatic electromagnetic pulse.

[0032] It is possible to inject the adiabatic electromagnetic pulse, in the form of a laser pulse, into the quantum processor. By injecting the adiabatic electromagnetic pulse as a laser pulse, the inversion, and thus the initialization and / or readout, of the spin of the at least one qubit can be performed in a simple manner. Mechanical contact with the quantum processor is not required for initialization and / or readout.

[0033] It can be advantageous if the adiabatic electromagnetic pulse interacts with an NV electron, acting as the electron spin bus of the quantum processor, to invert its spin bus. The NV electron can be a nitrogen vacancy center with a negative charge. The NV electron of the electron spin bus can be configured as a bus qubit of an NV quantum processor with a strong-coupling drive. In the strong-coupling drive, the dynamics of the quantum mechanical system can be strongly coupled to external fields or other quantum mechanical systems.

[0034] Furthermore, several strongly coupled nuclei can be inverted directly or indirectly, particularly via an electron spin bus, by the adiabatic electromagnetic pulse as qubits of the quantum processor. The quantum processor can, in particular, be an NV quantum processor. By achieving a strong coupling regime with the strongly coupled nuclei as qubits of the quantum processor, the robustness of quantum operations against disturbances and noise can be improved. This can, in particular, increase the reliability of computations with the quantum processor. In the case of indirect inversion, the strongly coupled nuclei can be assigned as client qubits to the bus qubits of an electron spin bus.

[0035] NC-2024-1716 5During initialization, an initialization pulse and during readout, a readout pulse with a different pulse shape than the initialization pulse can be used, wherein the pulse shape of the readout pulse is, in particular, a time inversion of the pulse shape of the initialization pulse. The readout pulse can have a pulse shape that has the same amplitude as the pulse shape of the initialization pulse, but an inverted sign of the frequency. The initialization pulse can cause such an inversion that a transfer from the population with quantum number m s = 0 into the m s = -1 manifold occurs. The readout pulse can cause an inversion such that a transfer from the population with quantum number m s = -1 to m s = 0 is achieved.

[0036] It is possible for the adiabatic pulse to have a length of 15 ps and / or a bandwidth of less than or equal to 2 MHz and / or a maximum amplitude of essentially 1.5 MHz. By giving the adiabatic pulse a bandwidth of less than or equal to 2 MHz, inversion over a state width above 2 MHz can be avoided. In this way, high selectivity can be achieved, since only states lying within half the bandwidth around a center frequency, which defines the middle of the bandwidth, are inverted. The bandwidth of less than or equal to 2 MHz allows for the targeted inversion of individual or a few quantum mechanical states and can still allow fluctuations around the center frequency to be compensated for. This is because the splitting of the electron transitions with respect to the hyperfine interaction with 14N nitrogen is approximately...2 MHz, so that selectivity through this bandwidth is more important for NV quantum processors than realizing the largest possible bandwidth.

[0037] In a quantum computer system of the type mentioned above, it is proposed to solve the above problem by designing the inversion device to carry out the previously described method, thereby yielding the advantages described in connection with the method.

[0038] According to a further development of the invention, the inversion device comprises a function generator, in particular an adjustable one, for generating the adiabatic electromagnetic pulse. An adiabatic electromagnetic pulse for inverting the spin of the at least one qubit can be easily generated by means of a function generator, in particular an adjustable one, such as an arbitrary waveform generator (AWG). In particular, the frequency, amplitude, and / or pulse shape of the adiabatic electromagnetic pulse can be set with an adjustable function generator and thus adapted to the respective application.

[0039] The following section explains embodiments, further developments, and examples of the invention in more detail with reference to the accompanying drawings. The figures show:

[0040] Fig. 1 shows a sketch of the structure of the quantum computer system according to the invention.

[0041] Fig. 2 shows the amplitude and frequency modulation of a sech / tanh pulse as an example of an adiabatic electromagnetic pulse.

[0042] Fig. 3 shows the inversion of the spin of a qubit by the adiabatic electromagnetic pulse and

[0043] NC-2024-1716 6Fig. 4 shows the comparison of an ODMR spectrum of a rectangular pulse and the sech / tanh pulse.

[0044] Figure 1 shows the basic structure of the quantum computer system 1 according to the invention. This system comprises a quantum processor 2 in the form of an NV quantum processor, which has NV centers that serve as qubits 3. The quantum processor 2 has several qubits 3.

[0045] For initialization, the spins of these qubits 3 are inverted. This is done using an inversion device 4. The inversion device 4 comprises a function generator 5 and a laser 6. The function generator 5 is coupled to the laser 6 in such a way that it generates an adiabatic electromagnetic pulse 7 and shines it into the quantum processor 2.

[0046] The adiabatic electromagnetic pulse 7 interacts with the qubits 3 of the quantum processor 2 in such a way that their spins are inverted and thus initialized.

[0047] To perform the calculations, the quantum computer system 1 also includes a device 8 for applying quantum gates to the qubits 3 of the quantum processor 2. The device 8 allows the qubits 3 to be coherently manipulated using microwaves or high-frequency radiation. The quantum gates, which essentially correspond to individual computational operations, result in coherent rotations of the spin of the qubits 3 on the Bloch sphere, which is not possible with the adiabatic electromagnetic pulse 7 of the inversion device 4.

[0048] To read out the calculation result, another adiabatic electromagnetic pulse 7 is fed into the quantum processor 2 using the inversion device 4. This second adiabatic electromagnetic pulse 7, used for reading out the result, differs in frequency from the first adiabatic pulse 7, which was used for initialization. While the amplitude of both pulses 7 can be the same, the second adiabatic pulse 7 has the opposite sign with respect to its frequency.

[0049] The second adiabatic pulse 7 causes an ODMR inversion, allowing the quantum states of the qubits 3 to be determined from the emitted photon signal 9. The quantum computer system 1 includes a photon counter 10, which detects this photon signal 9 and makes it available for further processing. In this way, the spins are read out as the quantum states of the qubits 3.

[0050] Figure 2 shows the amplitude and frequency modulations of a sech / tanh pulse 11 as an example of an adiabatic pulse 7 with respect to time t. It can be seen that the time course of the amplitude A of the sech / tanh pulse 11 follows the form of a hyperbolic secant. The time course of the frequency F of the sech / tanh pulse 11, on the other hand, follows a hyperbolic tangent. The frequency F of the sech / tanh pulse 11 exhibits a zero crossing, while the amplitude A of the sech / tanh pulse 11 maintains positive values.

[0051] Due to this specific form of amplitude and frequency modulation, and because the electromagnetic sech / tanh pulse 11 fulfills the adiabatic condition, it can act as an adiabatic stimuli under its influence.

[0052] NC-2024-1716 7 electromagnetic pulse 7 a rotation of the effective magnetic field bed slowly relative to the precession of the magnetization M of the qubit 3 around B eft, so that an adiabatic inversion of the spin of qubit 3 can occur, as shown in Fig. 3.

[0053] Figure 3 shows the time course of the adiabatic inversion of the spin of qubit 3. The representation is in a coordinate system that rotates with the instantaneous frequency of pulse 7. In this coordinate system, the effective field B is measured over the duration of pulse 7. e The tf, which the spin sees, is rotated from the z-axis to the -z-axis. The z-component of Bett is the difference between the irradiated frequency, which varies over time during pulse 7, and the fixed resonant frequency of the magnetic transition of qubit 3. The x-component is proportional to the time-dependent amplitude A of pulse 7 (the so-called Bl field). Due to the tuned time dependencies of the frequency offset and the Bl field, the magnetization M is adjusted over the duration of the adiabatic pulse B. eThe function is rotated from z to -z. For the sech / tanh pulse 7, this is achieved using the sech function for the amplitude A and a tanh function for the frequency F.

[0054] Since the rotation of the bed is slow compared to the precession of the magnetization M by a certain time, the magnetization M follows the vector of the bed adiabatically. This adiabatic inversion of the magnetization M is independent of the pulse amplitude A, since above a certain threshold of amplitude A it is independent of the precession frequency, which is proportional to the size of B. e ft is.

[0055] Furthermore, the bandwidth D of the inversion can be adjusted by the parameter range of the frequency F. Figure 4 shows the inversions using a rectangular pulse corresponding to the prior art (Figure 4a) and using an adiabatic sech / tanh pulse 7 according to the invention (Figure 4b). The intensities I of the respective ODMR spectra are shown against the frequency F. The intensity I of the ODMR spectrum indicates the strength of the inversion, with a low intensity I of the ODMR spectrum indicating a strong inversion, while a high intensity I of the ODMR spectrum indicates a weak or non-existent inversion.

[0056] The rectangular pulse leading to the spectrum in Fig. 4a has a duration of 432 ns. The adiabatic pulse 7 leading to the spectrum in Fig. 4b has a duration of 15 ps and a maximum amplitude of approximately 1.5 MHz.

[0057] The inversion using the rectangular pulse (Fig. 4a) results in an essentially Gaussian ODMR spectrum. In this spectrum, the edges of the inverted region exhibit a gradual roll-off extending over a wide frequency range. The region of strong inversion around the center frequency F M It is therefore comparatively small. With increasing distance from the center frequency F M The strength of the inversion decreases steadily, but also fluctuates far from the center frequency F. M still strong. This is particularly evident in Fig. 4a in the low frequency range, where the inversion increases again.

[0058] In contrast, the inversion using the adiabatic pulse 7 (Fig. 4b) exhibits a substantially rectangular inversion profile with steep edges. Within the set bandwidth D of 2 MHz around the center frequency F MThe adiabatic pulse 7 leads to a generally constant degree of inversion.

[0059] NC-2024-1716 8 increasing distance to the center frequency F M The strength of the inversion drops off abruptly and remains far from the center frequency F. M consistently at a very low level.

[0060] In this way, high selectivity can be achieved, since only states within half the bandwidth D around the center frequency F are inverted. M lay.

[0061] This inversion achievable with the adiabatic pulse 7 leads to high fidelity, since the inversions are not reduced by small fluctuations of the external magnetic field or the control field, but rather a broad plateau area around the center frequency F. Mwith a consistently strong inversion. Even with shifts in the frequency domain, the inversions in the bandwidth D around the center frequency F are maintained. M The spin states lying on the surface are therefore inverted without changing the inversion strength.

[0062] By means of the quantum computer system 1 according to the invention and the method according to the invention for initializing and / or reading out the quantum state, an inversion of spins in a quantum processor can be realized which is robust against fluctuations of the external magnetic fields and the magnetic control field.

[0063] NC-2024-1716 9 REFERENCE MARK LIST

[0064] 1 quantum computer system

[0065] 2 quantum processors

[0066] 3 Qubit

[0067] 4 Inversion device

[0068] 5 Function Generator

[0069] 6 lasers

[0070] 7 adiabatic electromagnetic pulse

[0071] 8 Device

[0072] 9 photon signal

[0073] 10 photon counters

[0074] 11 sech / tanh-Puls

[0075] A Amplitude

[0076] effective magnetic field

[0077] D bandwidth

[0078] F Frequency

[0079] F M Medium frequency

[0080] I Intensity

[0081] M Magnetization, which precesses around the effective field t time

[0082] x, y, z axes

[0083] NC-2024-1716 10

Claims

PATENT CLAIMS 1. Method for initializing and / or reading out the quantum state of at least one qubit (3) of an electron spin bus of an NV quantum processor with Strong Coupling Drive, wherein an adiabatic electromagnetic pulse (7) is generated to invert the spin of the at least one qubit (3) and fed into the quantum processor (2), characterized in that an adiabatic sech / tanh pulse (7) is used to invert the spin.

2. Method according to one of the preceding claims, characterized in that a microwave pulse is used as the adiabatic electromagnetic pulse (7).

3. Method according to one of the preceding claims, characterized in that the adiabatic pulse (7) is set to a predetermined frequency and amplitude range before being introduced into the quantum processor (2).

4. Method according to one of the preceding claims, characterized in that qubits (3) of the electron spin bus are inverted in order to transfer populations of nuclear spins of the quantum processor (2) from one spin manifold to another for the purpose of initialization and / or readout.

5. Method according to one of the preceding claims, characterized in that the adiabatic electromagnetic pulse (7) causes an ODMR inversion in the quantum processor (2).

6. A method according to any one of the preceding claims, characterized in that the adiabatic electromagnetic pulse (7) is irradiated into the quantum processor (2) in the form of a laser pulse.

7. A method according to any one of the preceding claims, characterized in that the adiabatic electromagnetic pulse (7) interacts with an NV electron as the electron spin bus of the quantum processor (2) to invert it.

8. Method according to one of the preceding claims, characterized in that several strongly coupled nuclei are directly or indirectly inverted by the adiabatic electromagnetic pulse (7) as qubits (3) of the quantum processor (2).

9. Method according to claim 8, characterized in that several strongly coupled nuclei are indirectly inverted by the adiabatic electromagnetic pulse as qubits (3) of the quantum processor (2) via an electron spin bus.

10. Method according to one of the preceding claims, characterized in that an initialization pulse and a readout pulse with a different pulse shape than the initialization pulse are used during initialization, or wherein an initialization pulse and a readout pulse with a different pulse shape than the initialization pulse are used during initialization. NC-2024-1716 11 Readout uses a readout pulse with a different pulse shape than the initialization pulse, where the pulse shape of the readout pulse is a time inversion of the pulse shape of the initialization pulse.

11. Method according to one of the preceding claims, characterized in that the adiabatic pulse (7) has a length of 15 ps and / or a bandwidth of less than or equal to 2 MHz and / or a maximum amplitude of substantially 1.5 MHz.

12. Quantum computer system (1) with an NV quantum processor with strong coupling drive, comprising several qubits (3) and an inversion device (4) for initializing and / or reading out the quantum state of the qubits (3), characterized in that the inversion device (4) is configured to carry out the method according to one of claims 1 to 10.

13. Quantum computer system (1) according to claim 12, characterized in that the inversion device (4) has a function generator (5) or an adjustable function generator for generating the adiabatic electromagnetic pulse (7).

14. Quantum computer system (1) comprising at least one qubit (3) and an inversion device (4) designed and configured to perform a procedure comprising the step of: - Initializing and / or reading out a quantum state of the at least one qubit (3). NC-2024-1716 12

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