Systems and methods for qubit initialization and control

Abstract

A method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate, the method comprising: i) loading electrons onto the multi-donor quantum dot in a spin down state; ii) executing a zero or one electronic reset pulse; iii) applying an RF signal to drive at least one EDSR transition; and iv) repeating steps ii)-iii) N times to achieve the predetermined target spin state.

Description

Technical Field

[0001] Aspects of the present disclosure relate to advanced processing systems, and in particular, to quantum processing systems and methods and systems for initializing and / or controlling processing elements. Background Art

[0002] The developments described in this section are known to the inventors. However, unless otherwise stated, it should not be assumed that any developments described in this section qualify as prior art simply by virtue of their inclusion in this section, or that those developments are known to a person of ordinary skill in the art.

[0003] Large-scale quantum processing systems are expected to bring about a technological revolution, potentially solving problems that cannot be solved by classical machines. To date, many different structures, materials, and architectures have been proposed to realize quantum bits (or qubits) and corresponding quantum control and processing systems.

[0004] Many obstacles need to be overcome before such large-scale quantum computers can be manufactured commercially. Accurately measuring the state of qubits at any given time in a quantum processing device is one of such basic requirements. Different types of sensors and qubit measurement and initialization techniques have been proposed in the art. However, some of these techniques may be prone to errors. Therefore, there is a need for improved techniques for measuring qubit states and / or initializing qubits in quantum processing systems. Summary of the invention

[0005] According to a first aspect of the present invention, a method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate is provided, the method comprising the following steps: i) loading electrons onto the multi-donor quantum dot in a spin-down state; ii) performing a zero or one electron reset pulse; iii) applying an RF signal to drive at least one EDSR transition; and iv) repeating steps ii)-iii) N times to achieve the predetermined target spin state.

[0006] According to a second aspect of the present invention, a method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate is provided, the method comprising the following steps: i) determining an initialization pulse sequence based on the predetermined target spin state, the initialization pulse sequence comprising at least one electron reset pulse and at least one EDSR transition; ii) loading electrons onto the multi-donor quantum dot in a spin-down state; iii) applying the initialization pulse sequence; and iv) repeating step iii) N times to achieve the predetermined target spin state.

[0007] According to a third aspect of the present invention, a method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate is provided, the method comprising the following steps: i) loading electrons onto the multi-donor quantum dot in a spin-down state; ii) performing an ESR measurement to determine a total nuclear spin state; and determining that the total nuclear spin state of the multi-donor quantum dot is not the target spin state; iii) determining and performing an initialization pulse sequence; wherein the initialization pulse sequence comprises at least one ESR spin reset pulse and at least one EDSR transition; performing an ESR measurement to determine the total nuclear spin state; and initializing nuclear spins based on the determination that the total nuclear spin state of the multi-donor quantum dot is the target spin state; and returning to step iii) based on the determination that the total nuclear spin state of the multi-donor quantum dot is not the target spin state.

[0008] According to a fourth aspect of the present invention, there is provided a quantum processing element, which is configured to initialize a predetermined target spin state in a multi-donor quantum dot, the quantum processing element comprising: a semiconductor substrate and a dielectric material forming an interface with the semiconductor substrate; a multi-donor quantum dot embedded in the semiconductor substrate, the multi-donor quantum dot comprising at least two donor atoms, the at least two donor atoms sharing at least one electron; and a control element for controlling the multi-donor quantum dot; wherein the electron is loaded onto the multi-donor quantum dot in a spin-down state; and wherein the control element is configured to: apply an RF signal to drive at least one EDSR transition; and apply at least one electron spin reset pulse; thereby achieving the target spin state and initializing the quantum dot. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Advantages and features of the present invention will become apparent from the following description of embodiments given by way of example only with reference to the accompanying drawings, in which:

[0010] Figure 1A Shown is a top view of an embodiment of a donor spin qubit device formed in a silicon substrate using donor atoms.

[0011] Figure 1B Shows Figure 1A Cross-sectional side view of the device.

[0012] Figure 2A An embodiment of a multi-donor quantum dot device is shown.

[0013] Figure 2B A further embodiment of a multi-donor quantum dot device with an in-plane gate is shown.

[0014] Figure 2C Another example of a multi-donor quantum dot device is shown.

[0015] Figure 3A Eight possible transitions between spin states of 2P quantum dots driven by electron spin resonance (ESR) or electron dipole spin resonance (EDSR) are shown.

[0016] Figure 3B Shows Figure 3A ESR and EDSR frequencies of the 2P quantum dots for spin-up transitions.

[0017] Figure 4A Twelve possible EDSR transitions for 3P quantum dots are shown.

[0018] Figure 4B Shows Figure 4A The frequency of the EDSR spin-up transition of 3P quantum dots.

[0019] Figure 5A is a flow chart illustrating an example method for initializing a multi-donor qubit device using EDSR.

[0020] Figure 5B is a flow chart illustrating an alternative example method for initializing a multi-donor qubit device using EDSR.

[0021] Fig. 6A The electron spin-up fraction as a function of the nuclear spin configuration of the first example 2P quantum dot system is shown before the initialization protocol has been performed.

[0022] Figure 6B The electron spin-up fraction as a function of the nuclear spin configuration of the first example 3P quantum dot system is shown before the initialization protocol has been performed.

[0023] Fig. 7A Shown are ESR measurement results after an initialization protocol has been performed on a first example 2P quantum dot system.

[0024] Figure 7B Shown are ESR measurement results after an initialization protocol has been performed on a first example 3P quantum dot system.

[0025] Figure 7C Shows the result Figure 6B The first peak of the example 3P device Similar results for the initialization of three different initialization pulse sequences.

[0026] Fig. 8A and 8B The Rabi-chevron experimental results of the first example 2P and 3P quantum dot systems are shown respectively.

[0027] Fig.9A An EDSR energy diagram of a first example 3P quantum dot system is shown.

[0028] Fig. 9B Shows the corresponding Fig.9A A graph of the measured EDSR spectra for 12 different transition frequencies of a first example 3P quantum dot system is shown.

[0029] Fig. 9C It shows that when the initial state The inversion probabilities of the EDSR transitions corresponding to the first, second, and third nuclear spins, respectively, at the beginning.

[0030] Fig.9D is a graph showing the dependence of the Rabi frequency on the square root microwave power.

[0031] Fig. 10A shows that applying an initialization sequence to initialize the nuclear spin state to the target state The ESR spectrum is then measured.

[0032] Fig. 10B shows that applying an initialization sequence to initialize the nuclear spin state to the target state The ESR spectrum is then measured.

[0033] Fig. 10C It shows the process starting from the initial state (i) and transitioning to the target state Initialization fidelity.

[0034] Fig. 10D It shows the process starting from the initial state (i) and transitioning to the target state Initialization fidelity.

[0035] Fig.11A The electron spin-up fraction as a function of the nuclear spin configuration for the second example 2P quantum dot system is shown before the initialization protocol has been performed.

[0036] Fig. 11B Shown are ESR measurement results after an initialization protocol has been performed on a second example 2P quantum dot system.

[0037] Fig. 12A The electron spin-up fraction as a function of the nuclear spin configuration for the second example 3P quantum dot system is shown before the initialization protocol has been performed.

[0038] Fig. 12B Shown are ESR measurement results after an initialization protocol has been performed on a second example 3P quantum dot system.

[0039] Fig.13AShown is the electron spin-up fraction as a function of the nuclear spin configuration for an example 4P quantum dot system before the initialization protocol has been performed.

[0040] Fig. 13B Shown are ESR measurement results after an initialization protocol has been performed on an example 4P quantum dot system.

[0041] Fig.14A The amplitude and direction of the AC electric field applied to an example 3P quantum dot are shown.

[0042] Fig. 14B The Rabi frequency for an electric field of 33.6 kV / m is shown. DETAILED DESCRIPTION

[0043] The spin states of electrons or atomic nuclei in semiconductor materials are good candidates for carrying quantum information and acting as quantum bits (or qubits) for quantum computing systems. To perform quantum computing, three important steps are required—initialization of the qubits, control of the qubits, and readout of individual qubits. Some aspects of the present disclosure provide new and improved techniques for qubit initialization and control.

[0044] One type of quantum computing system is based on the spin state of individual qubits, where the qubits are electron and / or nuclear spins located inside a semiconductor quantum chip. These electron and / or nuclear spins are confined in gate-defined quantum dots or on donor atoms located in a semiconductor substrate. The inherent weak magnetic coupling of donor qubits in silicon to the environment results in high coherence times. Single-qubit and double-qubit operations above the error correction threshold have been demonstrated using AC magnetic fields.

[0045] FIG. 1 illustrates an example spin qubit device 100 formed in a silicon substrate using donor atoms. Figure 1A is a top view of qubit device 100 . Figure 1B 1 is a cross-sectional side view. Qubit device 100 can be used in a quantum computer including a plurality of these qubits. As shown, qubit device 100 is formed in a structure including semiconductor substrate 102 and dielectric 104. In this example, the substrate is isotopically purified silicon (Silicon-28) and the dielectric is silicon dioxide. In other examples, the substrate can be silicon (Si). An interface 107 is formed where substrate 102 and dielectric 104 meet. In this example, it is Si / SiO 2interface. To form a qubit, donor atoms 108 are located within substrate 102 within region 109 below gate 106. Donor atoms such as phosphorus atoms 108 may be introduced into the substrate using nanofabrication techniques (e.g., hydrogen lithography provided by a scanning tunneling microscope or industry standard ion implantation techniques). In this example, qubit device 100 includes a single atom 108 embedded in a silicon-28 crystal. However, the methods described herein may be applied to qubit devices 100 that include clusters of more than one embedded atom 108.

[0046] Electrons 120 are loaded onto the device 100 via gate electrode 106. The physical state of the electron 120 is described by a wave function 121 - which is defined as the probability amplitude of finding the electron at a particular location. Donor qubits in silicon rely on confining the electron spin using the potential well naturally formed by the donor nucleus.

[0047] The gate electrode 106 is located above the region 109 and is operable to interact with the donor atoms 108. For example, the gate electrode 106 can be used to induce an AC electric field in the region between the interface 107 and the donor atoms 108 to modulate the hyperfine interaction between the electrons 120 and the nuclei of the donor atoms 108, wherein the hyperfine interaction is the interaction between the electron spin and the nuclear spin of the donor atom.

[0048] Figure 2A A multi-donor quantum dot device 200 is shown. To form the qubit device 200, two donor atoms 202A and 202B are located within a quantum dot 201 in a semiconductor substrate 204. In some examples, the donor atoms 202A, 202B are phosphorus atoms. In this example, the qubit 200 includes two donor atoms 202, which are generally referred to herein as 2P quantum dots. On top of the silicon substrate 204 is a barrier material / dielectric 206, such as silicon dioxide. In addition, a gate 208 and an antenna 210 can be located on the dielectric 206 in the region above the multi-donor quantum dot 201. A voltage can be applied to the gate 208 to confine the electrons 220 in the quantum dot 201. The electrons 220 can be shared by the two donor atoms 202A, 202B.

[0049] Figure 2B Another example of a multi-donor quantum dot device 250 is shown. This is similar to Figure 2A The only difference is the location of the gate. Figure 2A In FIG. 1 , the gate is shown as being placed on top of dielectric 206. Figure 2BIn some embodiments, the gate is located within the semiconductor substrate 204. In some embodiments, one or more gates 212 are placed in the same plane as the donor dots. The in-plane gate can be connected to the surface of the substrate via a metal via (not shown). In some examples, a multi-donor quantum dot device can include a plurality of gates located on the surface (e.g., Figure 2A in the semiconductor substrate (such as Figure 2B The gate in the figure).

[0050] A voltage may be applied to the gate electrode 212 to confine one or more electrons 220 in the quantum dot 201. In a 2P quantum dot with one electron, there are three spins (two nuclear spins from the donor and the spin of the electron). Therefore, each of the three spins can be considered a qubit.

[0051] Figure 2C Another example of a multi-donor quantum dot device 270 is shown. To form the qubit device 270, three donor atoms 202A, 202B, and 202C are located within a quantum dot 201 in a semiconductor substrate 204. In some examples, the donor atoms 202A, 202B, and 202C are phosphorus atoms. In this example, the qubit 270 includes three donor atoms 202, which are generally referred to herein as 3P quantum dots. Electrons 220 can be shared by the three donor atoms 202A, 202B, and 202C.

[0052] In other examples, there may be m donor atoms—where m is an integer. In some examples, there may be up to 10 donor atoms in a quantum dot device. In the case where there are m donor atoms that are phosphorus atoms, a multi-donor quantum dot may be referred to as an mP quantum dot. In a general quantum dot system with m donors and one electron, there are a total of m+1 spins, and therefore m+1 possible qubits.

[0053] The spin of the electron 220 in the 2P quantum dot 201 is strongly coupled to the nuclear spins of the two donor atoms via hyperfine interactions. The hyperfine interaction is the interaction between the electron spin and the nuclear spin of the donor atom. The frequency coefficient of the hyperfine interaction is tens to hundreds of MHz, depending on the donor configuration in the quantum dot. Therefore, the operating frequency of the electronic qubit will change due to different nuclear spin configurations. For example, in 2P quantum dots, there are four nuclear spin configurations, namely: Wherein the first arrow indicates the nuclear spin state of the first donor 202A and the second arrow indicates the nuclear spin state of the second donor 202B, or vice versa. This change in qubit operation frequency in multi-donor quantum dots poses a significant challenge to single qubit operations of electron spins.

[0054] A key component of a scalable quantum computer is individually addressable qubits to apply quantum gates. However, qubit addressability has been a challenge for spin qubit devices because quantum gates typically require a mechanism that is distinguishable in the frequency domain.

[0055] One particular part of qubit addressability is the initialization protocol. Preparing qubits into a well-defined initial state is a key requirement among the key requirements for performing any quantum computation. Existing multi-qubit initialization methods for donor quantum dot devices are inefficient and can be difficult to scale up.

[0056] One option to control the nuclear spins of donor atoms is to use nuclear magnetic resonance (NMR). In particular, NMR allows control of the nuclear spins if they are individually addressable. Thus, NMR can be used to initialize the nuclear spins to any desired configuration. However, this comes with limitations and requires more hardware.

[0057] NMR operates at a very different operating frequency band than ESR (10-100 MHz instead of 20-40 GHz for ESR). Therefore, broadband operation requires a transmission line (not shown) to deliver the signal. Therefore, the requirement for broadband operation introduces performance limitations because different instruments are required for the radio frequency range. Other disadvantages of using NMR include limitations on instruments that deliver radio frequency (RF) signals, which are usually addressed by using two separate instruments - again introducing hardware overhead.

[0058] Another current technique is to use post-selection. This is where an electronic qubit is addressed using a single frequency corresponding to one of the nuclear spin configurations. The measurement is repeated many times and the results are averaged. The data is then filtered with respect to one nuclear spin configuration corresponding to the selected single qubit frequency, and all measurements made when the nuclear spin was not in the correct configuration are discarded. This avoids the requirement to initialize the quantum system to the desired initial state. However, the efficiency of this post-selection method is very low. It introduces at least 2 m times the time overhead, where m is the number of donors in the system.

[0059] Frequency multiplexing is another approach used. Instead of addressing the qubit with one frequency, this approach uses frequencies corresponding to each nuclear spin configuration to address the qubit. Thus, the electronic qubit can be addressed regardless of the initial nuclear spin configuration. Again, this approach is very inefficient because efficient qubit operation benefits from maximizing the available RF drive power. However, the total RF power will have a thermal effect and is therefore limited by the cooling power of the refrigerator used to contain the device. Therefore, through multiplexing, only 2% of the total power is needed. -mA small fraction of the power is used to drive the qubit, and the rest of the power is dissipated and generates heat. Lower power at the qubit drive frequency slows down the qubit's qubit operation speed, i.e., how quickly an operation can be performed. Ultimately, this will limit the quantum gate fidelity.

[0060] Some aspects of the present disclosure propose and demonstrate an initialization protocol for multi-donor spin qubits in semiconductors, which can be used in quantum computations in current and future implementations of quantum processing / computing systems. The initialization protocol according to some aspects of the present disclosure can initialize the m+1 spins of a multi-donor point system to a specific state as a prerequisite for any computational step. The initialization protocol provides many advantages over known techniques. The nuclear configuration can be initialized to a specific configuration with high fidelity by a series of pulses within the ESR frequency band, allowing the electronic qubit to operate efficiently at a single frequency using maximum drive power, with zero hardware overhead and minimal time overhead.

[0061] According to some other aspects of the present disclosure, a mechanism for controlling the Rabi frequency is provided, enabling qubit initialization and control to be faster and more efficient than previously known techniques. In particular, some aspects of the present disclosure control the Rabi frequency by changing the angle of the electric field applied to the quantum device.

[0062] Electron spin resonance (ESR) and EDSR in multi-donor quantum dots.

[0063] Figure 3A An energy level diagram of an example 2P quantum dot is shown.

[0064] For 2P quantum dots, there are 2 2 = 4 possible nuclear spin configurations, namely: For a 2P quantum dot with one electron, there are a total of 8 spin states. They are:

[0065]

[0066] The first single-line arrow represents the electron spin. For a general multi-donor quantum dot system with m donors and one shared electron, there are a total of 2×2 m total spin state. Figure 3A The eight total spin states arranged in relative energies are shown in . The four total spin states corresponding to spin-down electrons have lower energies than the four total spin states corresponding to spin-up electrons.

[0067] Figure 3AAlso shown are eight possible transitions between spin states driven by electron spin resonance (ESR) or electron dipole spin resonance (EDSR). In particular, there are four possible EDSR transitions - labeled EDSR1-EDSR4, and there are four possible ESR transitions - labeled ESR1-ESR4.

[0068] ESR is a direct means of driving electrons between two spin states. 0 In the case of an AC magnetic field, the electron spin energy level is no longer degenerate. The two spin states |↑>, |↓> are separated by an energy difference ΔE. Therefore, by applying an AC magnetic field, the electron spin can be changed from the spin-down state |↓> to the spin-up state |↑>, or vice versa. ESR is due to the interaction between the intrinsic magnetic moment of the electron and the external magnetic field B. 0 Produced by coupling.

[0069] In particular, ESR is the transition between opposite electron spin states but the same nuclear spin configuration. For example, in a 2P system, the four ESR transitions are:

[0070]

[0071] On the other hand, EDSR in donor systems is due to the modulation of the hyperfine coupling of the electron spin and nuclear spin of the donor atoms in the system. EDSR is mediated by an electric field that simultaneously flips one of the electron spin and nuclear spin in a multi-donor system. For a 2P system, there are four possible EDSR transitions, such as Figure 3A as shown in .

[0072] Figure 3B Shows Figure 3A The frequency of the ESR and EDSR spin-up transition of the 2P quantum dot. For example, in order to convert the 2P quantum dot system from the spin state Excitation to spin state For example, a single frequency corresponding to an ESR frequency (ESR4) of approximately 40.7 GHz may be applied to gate 208. The ESR frequency (ESR4) is shown as Figure 3B The vertical peak 302D in the ESR and EDSR frequencies are proportional to the applied magnetic field and can vary over a wide range.

[0073] EDSR pulses can be generated using an on-chip microwave antenna (gate 208) or using a gate electrode (210 or 212) with a single tone similar to ESR. EDSR transitions are electron-nuclear trigger transitions that can be performed via modulating the hyperfine interaction between nuclear spins and electron spins. Modulation of the hyperfine interaction can be achieved by applying an electric field that moves the electron wave function away from the donor nucleus.

[0074] To drive one of the EDSR transitions, the hyperfine interaction must be modulated at a frequency corresponding to the energy between the two allowed states. Figure 3A In FIG. 4 , four EDSR transitions are shown—each with a different corresponding drive frequency, such as Figure 3B As shown in the peaks 1, 2, 3, and 4. Figure 3B Four ESR peaks are also shown in FIG. 3 , where each ESR transition corresponds to a different driving frequency as shown by peaks 302A, 302B, 302C, and 302D.

[0075] Figure 4A The EDSR energy diagram of 3P quantum dots is shown. For 3P quantum dots, there are 2 3 =8 nuclear spin configurations and a total of 16 spin states. For the example 3P quantum dot, the hyperfine coupling of the first nuclear spin is 201 MHz, the hyperfine coupling of the second nuclear spin is 77 MHz, and the hyperfine coupling of the third nuclear spin is 42 MHz. The eight nuclear spin states are shown by relative energy levels. The bottom row of states corresponds to eight nuclear spin states with spin-down electrons, and the top row corresponds to eight nuclear spin states with spin-up electrons. There are 12 EDSR transitions (1-12), shown as connecting lines between the top and bottom states (EDSR transitions 5, 6, 7, and 8 flip the spin state of the first nuclear spin flip, EDSR transitions 2, 3, 10, and 11 flip the spin state of the second nuclear spin, and EDSR transitions 1, 4, 9, and 12 flip the spin state of the third nuclear spin. Figure 4A There are also eight ESR transitions in the equation (not shown). ESR transitions only flip the electron spin, and the nuclear spin is not affected. Therefore, ESR transitions follow Figure 3A Connect the bottom state to the top state directly above it.

[0076] Different NMR frequencies are required to resolve the three nuclear spins individually. The NMR frequencies are related to the hyperfine interactions by the following equation −

[0077]

[0078] The nuclear Zeeman depends on the static magnetic field and the ± depends on whether the electron spins are up or down. The addressable frequency of each nuclear spin depends on their environment. The frequencies of addressing nuclear spins are in the MHz range, while the EDSR and ESR frequencies are in the GHz range. Therefore, no transmission lines are needed for broadband operation. Figure 4BA graph of the EDSR spectrum of 3P quantum dots is shown (ESR spectrum not shown). The x-axis is frequency in GHz, and the y-axis shows the spin-up probability of the nuclear spin. The frequencies of all 12 EDSR transitions to the electron spin-up state are shown. The order of magnitude of all EDSR transitions (1-12) is tens of GHZ, more specifically in the range of 40-41 GHz. The ESR transitions are also in the range of 40-41 GHz, but are not shown. Therefore, the operation of both ESR and EDSR requires a narrow frequency range; therefore, there are no specific performance requirements for the transmission line; and no additional frequency generator equipment is required.

[0079] This EDSR driving protocol can be applied to mP QDs, or any multi-donor QDs with up to 10 donor atoms.

[0080] Initialization protocol

[0081] According to some aspects of the present disclosure, hyperfine-based EDSR can be used to drive electron-nuclear transitions in multi-donor qubits in silicon. The initialization protocol disclosed herein is a deterministic and high-fidelity initialization protocol for nuclear spin configuration. Therefore, it allows quantum gate operations to be performed on donor electron qubits at a single frequency, and thus eliminates the need for NMR, frequency multiplexing, or post-selection of electron qubit operations. In summary, EDSR-based polarization constitutes a powerful tool to operate multi-qubit systems within a single quantum dot to expand qubit counts.

[0082] Figure 5A 5 is a flow chart illustrating an example initialization protocol 500A according to some aspects of the present disclosure. The initialization protocol 500A consists of a series of EDSR pulses alternating with at least one ESR pulse to produce a target state. In one example, the target state can be a total spin down state. The total spin down state can then be used as the initial state for quantum measurements or operations on qubits. For example, in a 2P quantum dot system, the initial target state can be In other examples, the target state can be any spin state of the multi-donor quantum dot system.

[0083] The method 500A begins at step 502 where an initialization pulse sequence that depends on a target state is determined. The initialization pulse sequence is independent of the initial state.

[0084] For the example 2P quantum dot system, the following are examples of pulse sequences used to achieve different predetermined target states - see Figure 3A .

[0085]

[0086]

[0087] Table A: Example pulse sequence for initialization

[0088] The ESR of 2P quantum dots ALL Includes the following ESR transitions: ESR1, ESR2, ESR3, and ESR4—See Figure 3A .ESR ALL Pulses can be performed in two ways. One is to perform ESR ALL The pulse method is to apply all ESR1, ESR2, ESR3 and ESR4 pulses in sequence. Another method for performing ESR ALL The best approach is to use frequency multiplexing (standard RF technology) to apply the ESR pulses simultaneously - this approach saves time. It will be appreciated that the ESR for multi-donor quantum dot systems ALL All ESR transitions will be included.

[0089] Next, at step 504, electrons are deterministically loaded onto the multi-donor quantum dots in a spin-down state. In some examples, electrons are loaded onto the mP quantum dots by applying a voltage to a gate electrode. The voltage may be applied to Figure 2A At least one of the surface gate electrodes 208 and 210 in Figure 2B or Figure 2C In-plane gate electrode 212.

[0090] In the example 2P system, the electron 220 is deterministically loaded in the spin-down state. Therefore, the system can be in one of four total spin states: —See also Figure 3A For the initialization protocol 500A, no initial state needs to be determined.

[0091] In some examples, multiple electrons can be loaded onto a multi-donor quantum dot system, and the spins of the unpaired electrons can be used as electron spin qubits in the device.

[0092] Next, at step 506, a zero or one electron spin reset pulse is performed. If a zero electron reset pulse is desired, nothing needs to be done and the method can proceed to step 508. The electron spin reset pulse can be performed using an ESR pulse or by unloading and loading electrons on the quantum dot, or alternatively, the electron spin reset pulse can be performed by applying a voltage to the gate electrode. To drive the ESR transition using an electron spin reset pulse, an RF signal is applied to at least one of the gate electrode or the transmission line. The ESR transition flips the electron spin while leaving the nuclear spin unchanged. For example, to self-spin state Transition to spin state exist Figure 3A ESR2 can be used in

[0093] Next, at step 508, an RF signal is applied to the gate electrode or transmission line to drive at least one EDSR transition. The applied signal corresponds to an EDSR transition that brings the total spin state closer to the target state. The EDSR transition is driven to perform a controlled SWAP gate on one of the nuclear spins from spin-up to spin-down or vice versa while sliding the electron spins.

[0094] For example, if the initial state is the lowest energy spin state Then the EDSR signal can correspond to the EDSR4 transition to produce the state Here, the EDSR4 transition drives the controlled SWAP gate on the second nuclear spin and the electron spin. In another example, if the initial state is the lowest energy spin state The RF signal applied to the gate electrode or transmission line can correspond to the state generated Here, the EDSR3 transition drives the controlled SWAP gate at the first nuclear spin.

[0095] Next at step 510, steps 506 and 508 are repeated N times to achieve the target state with high probability. Therefore, due to the high fidelity of the process and the very high probability that one or more EDSR signals have achieved the target state, the target state has been achieved. Here, N is an integer greater than or equal to one. In principle, steps 506 and 508 can be repeated as many times as needed. The device can be designed to have a large EDSR efficiency, and therefore a high fidelity, so that it should be possible to achieve initialization where N=1.

[0096] Method 500A is an unconditional initialization protocol because the protocol works without any feedback during the process - i.e., there is no need to measure the spin state during the initialization protocol. Therefore, for any mP quantum dot system, only a subset of the total number of transitions may result in a robust process where there is a high probability that the target state will be achieved. For example, in the 2P quantum dot system at step 510, the total spin down target state is achieved and the system has been initialized. The qubit device is now ready to perform quantum operations. The probability of achieving the target state can be increased via device design and can be effective (probability is about 1).

[0097] For example, if the target state is Then, an initialization pulse sequence is determined at step 502 to achieve the target state. According to Table A, the initialization sequence is as follows:

[0098] i. Electronic reset pulse

[0099] ii.EDSR4

[0100] iii.EDSR1

[0101] iv. Electronic reset pulse

[0102] v.EDSR2

[0103] vi. Electronic reset pulse

[0104] It will be appreciated that the pulse sequence corresponding to each target state is designed to achieve that target state regardless of the initial state. In the case of, method 500A is used, in step 502, according to the target state is To determine the initialization pulse sequence. For example, see pulse sequences i-vi above.

[0105] Next, at step 504, electrons are loaded onto the 2P quantum dots in the spin-down state. Next, at step 506, a zero electron reset is performed when the electrons are in the spin-down state. Next, at step 508, an RF signal is applied to drive the EDSR4 and EDSR1 transitions. In this case, the EDSR4 transition is applicable / valid. If the state is Then the EDSR1 transition will apply. At the end of step 508, the spin state is Next, at step 510, steps 506 and 508 are repeated N times to achieve the target state with high probability. Therefore, returning to step 504, an electron reset pulse is performed. The electron spin reset pulse is performed using ESR conversion, unloading and loading electrons or by a voltage applied to the gate electrode. The spin state is now Next, at step 508, an RF signal is applied to drive the EDSR2 to transition—thereby generating a spin state Returning to step 506 again, an electron spin reset pulse is performed to produce the final target state

[0106] Similarly, the example initialization pulse sequence can be used to robustly transform any initial spin state to a target state

[0107] Figure 5B is a flow chart illustrating an alternative deterministic series of method steps 500B of an example initialization protocol in accordance with some aspects of the present disclosure.

[0108] Method 500B begins at step 520, where electrons are deterministically loaded onto a multi-donor quantum dot in a spin-down state. In some examples, electrons are loaded onto the mP quantum dot by applying a voltage to a gate electrode. The voltage may be applied to Figure 2A At least one of the surface gate electrodes 208, 210 in Figure 2B In-plane gate electrode 212.

[0109] Next, at step 522, an ESR measurement may be performed to determine if the system is in the target state. If the spin state is determined to be the target state, then at step 524, the nuclear spins of the multi-donor quantum dot system are initialized.

[0110] For example, in a 2P quantum dot, at step 522, an ESR measurement is performed, and the result of the ESR measurement is that the total spin configuration is If this is the target state—then the nuclear spin is initialized and method 500B terminates at step 524 .

[0111] However, if the total spin state determined at step 522 is not the target state, method 500B proceeds to step 526. At step 526, an initialization pulse sequence is calculated that will transform the initial state to the target state. The initialization pulse sequence consists of one or more ESR transitions / electron spin reset pulses and one or more EDSR transitions. The initialization pulse sequence corresponds to a sequence of ESR and EDSR transitions, for example, Figure 3A and Figure 4A The transitions shown transform a known initial state into a known target state.

[0112] Returning to the example of the 2P quantum dot system, if the total spin state is determined to be and this is not the target state, then an initialization pulse sequence including ESR, EDSR and electron spin reset pulse is calculated and then executed at step 526 .

[0113] For the example 2P quantum dot system, the target state can be the total spin down state Therefore, the calculation of the initial state of the transformation to pulse sequence.

[0114] Transform to A possible initialization pulse sequence is shown in Figure 3A :

[0115] i) Reset electronics: to

[0116] ii) EDSR3: to

[0117] iii) Reset electronics: to

[0118] iv) EDSR1: to

[0119] v) Reset electronics: to

[0120] Once the initialization pulse sequence is calculated, the sequence is executed. An RF signal is applied to a gate electrode (e.g., gates 208, 210, and / or 212) or a transmission line to drive an EDSR transition. In this example, the applied signal corresponds to an EDSR transition that brings the total spin state closer to the total spin down state. The EDSR transition is driven to perform a controlled SWAP gate on one of the nuclear spins.

[0121] The electron spin reset pulse can be performed by performing an ESR transition. Alternatively, the electron spin reset pulse can be performed by unloading and loading electrons on the quantum dots. Alternatively, the electron reset pulse can be performed by applying a voltage to the gate electrode. In one example, step (i) can be performed using an ESR transition, step (iii) can be performed by unloading and loading electrons on the multi-donor quantum dots, and step (v) can be performed by applying a voltage pulse to the gate electrode. In other example initialization pulse sequences, different methods and combinations thereof can be used to perform the electron reset.

[0122] Once the initialization pulse sequence has been performed, method 500B proceeds again to step 522 where an ESR measurement is performed to determine the overall spin state—and therefore whether the target state has been achieved.

[0123] Returning to the example of 2P quantum dots, at step 522, an ESR measurement is performed and it is determined that the total spin state is Since this is the target spin state in this example, the method terminates at step 524 and the nuclear spin has been initialized.

[0124] After the initialization protocol is completed, the multi-donor quantum dot system is initialized and ready for qubit operations. Although methods 500A and 500B have been explained as starting from the initial state Initially, the protocol will succeed regardless of the initial spin state.

[0125] In some examples, the initialization protocol 500B can be executed multiple times to ensure that the state is initialized with high fidelity. Therefore, the initialization protocol is robust to errors.

[0126] In another embodiment, the initialization protocol can be used in a quantum processing system including a plurality of multi-donor quantum dots.

[0127] Experimental Results

[0128] Fig. 6A and Figure 6BThe experimental results for the first example 2P and 3P quantum dot systems are shown, respectively. The ESR peak amplitude measured over time is a direct measure of the efficiency of the initialization protocol. Without applying the initialization protocol, the system has a similar probability of being in any one nuclear spin configuration.

[0129] Fig. 6A The electron spin-up fraction as a function of the nuclear spin configuration for the first example 2P quantum dot system is shown. The first example 2P quantum dot system has the following hyperfine interactions: A 1 =65MHz and A 2 =103MHz. There are four peaks at a specific frequency, which correspond to the four possible nuclear spin configurations of the 2P quantum dot system. The height of each peak corresponds to the probability that the system is in that nuclear spin configuration.

[0130] Figure 6B The electron spin-up fraction as a function of the nuclear spin configuration for the first example 3P quantum dot system is shown. The 3P quantum dot system has the following hyperfine interactions: A 1 =42MHz, A 2 =77MHz and A 3 =201MHz. There are eight peaks at a specific frequency, which correspond to the eight possible nuclear spin configurations of the 3P quantum dot system. The height of each peak corresponds to the probability that the system is in that nuclear spin configuration.

[0131] With a successful initialization protocol, all ESR peaks except one are expected to be significantly suppressed. Initialization to the target for the example 2P quantum dots was performed using an initialization protocol similar to that disclosed herein. (For the example 3P quantum dots ) of this result in Fig. 7A Figure 7B Shown in.

[0132] Fig. 7A 5 shows an ESR measurement after initialization protocol 500A has been performed on a first example 2P quantum dot system, showing the frequency in GHz relative to the measured electron spin up fraction. Thus, it can be seen that the 2P quantum dot system is in a nuclear spin state

[0133] Figure 7B 5 shows an ESR measurement after an initialization protocol 500A has been performed on a first example 3P quantum dot system, showing the frequency in GHz relative to the measured electron spin up fraction. It can be seen that the 3P quantum dot system is in a nuclear spin state

[0134] Figure 7Cis a graph showing the EDSR peak amplitude of 3P quantum dots. In particular, the graph shows the spin-up fraction on the y-axis and the frequency of the EDSR pulse on the x-axis. The BG in the graph refers to the background measurement, where frequencies far from any resonance are purposely applied to see how the measurement changes over time, and as a reference for different peak heights.

[0135] Since there are a large number of EDSR transitions (1-8) for 3P, there are potentially several different valid initialization protocols. Here, three different initialization pulse sequences are shown - 702 (for large hyperfine spins), 704 (for medium hyperfine spins), and 706 (for small hyperfine spins), all of which lead to the first The three pulse sequences correspond to the initialization of the The pulse sequences involve initializing different nuclear spins—for example, pulse sequence 702 for a qubit initially in a state with a large hyperfine value, pulse sequence 704 for a qubit initially in a state with a medium hyperfine value, and pulse sequence 706 for a qubit initially in a state with a small hyperfine value.

[0136] After initializing the nuclear spin configuration using the initialization protocol disclosed herein, the electronic qubit can be addressed at a single frequency. The initialization protocol produces a stable electronic qubit, allowing coherent control of the qubit.

[0137] By applying an AC electric field to the gate electrode, the electronic qubit can be The total spin state and The total spin states are driven between each other - this gives rise to Rabi oscillations, which constitute the oscillatory behavior of the secondary system.

[0138] Fig. 8A and Figure 8B The Rabi-Chevron experimental results of the first example 2P and 3P quantum dot systems are shown respectively. The x-axis is the duration, and the y-axis is the frequency. For the 2P quantum dot system, coherent Rabi oscillations were observed at about 39.0826 GHz (as shown in the lighter color part of the chart). For the 3P quantum dot system, coherent Rabi oscillations were observed at about 40.40225 GHz.

[0139] Fig.9A The EDSR energy diagram of the first example 3P quantum dot system is shown. Figure 4A As discussed, for 3P quantum dots, there are 12 EDSR transitions (1-12), shown as connecting lines between the top and bottom states. These EDSR transitions correspond to angular momentum conservation electron-nuclear trigger transitions. There are also eight perpendicular ESR transitions (not shown).

[0140] Different NMR frequencies are needed to individually address the three nuclear spins: I 1 ,I 2 and I 3 These frequencies are determined directly from the measured ESR spectra of 3P quantum dots. As mentioned above, the addressable frequencies of individual nuclear spins depend on their environment - so these NMR frequencies are different from Figure 4A Four of these transitions (EDSR transitions 4, 5, 8, and 9) correspond to the first nuclear spin I 1 , where the second and third nuclear spins remain unchanged, for example, and Four of these transitions (EDSR transitions 2, 3, 10, and 11) correspond to the second nuclear spin I 2 The remaining four transitions (EDSR transitions 1, 6, 7, and 12) correspond to the third nuclear spin I 3 A flip in which the first nuclear spin and the second nuclear spin remain unchanged.

[0141] Fig. 9B A graph of measured EDSR spectra corresponding to 12 different transition frequencies of a first example 3P quantum dot is shown. The x-axis shows the frequency in GHz, and the y-axis shows the electron spin-up fraction. For each of the 12 EDSR transitions (1-12), the center frequency value is shown. Thus, Fig. 12B The frequency (in GHz) that drives each of the 12 EDSR transitions is shown. Each of the 12 EDSR transitions is labeled at the top of the graph.

[0142] In order to characterize 3P quantum dots, it is necessary to measure the EDSR spectrum. To ensure that all EDSR transitions are captured in this measurement, a pulse sequence of randomized nuclear configurations is introduced. First, electrons are loaded onto 3P quantum dots with random spin states by rapidly pulsing the 0→1 charge transition line across the quantum dots. Next, an electron-core SWAP gate is performed by applying 4 EDSR transitions corresponding to the same nuclear spin. This drives the nuclear spin to a random initial state. For example, EDSR transitions 4, 5, 8, and 9 are applied to affect the first nuclear spin state. The process is then repeated for the remaining nuclear spins. For example, an electron-core SWAP gate is performed by applying 4 EDSR transitions (i.e., EDSR transitions 2, 3, 10, and 11) that affect the second nuclear spin. Similarly, EDSR transitions 1, 6, 7, and 12 are applied to perform another electron-core SWAP gate for the third nuclear spin. After executing this pulse sequence, the nuclear spin configuration is randomized and initialized.

[0143] Next, the electrons are reinitialized to the spin-down state |↓> using a voltage applied to the gate. Next, an adiabatic reversal EDSR pulse is applied, where the pulse frequency is swept adiabatically around the expected EDSR frequency. This flips the electrons to the |↑> manifold conditioned on a random initial nuclear spin configuration. Fig. 12B The measured EDSR spectrum shown matches the calculated EDSR value determined using hyperfine coupling obtained from ESR measurements.

[0144] The EDSR initialization protocol relies on a controlled SWAP gate between the electron and nuclear spins and is implemented using an adiabatic inversion pulse. Therefore, the initialization fidelity achieved depends strongly on the efficiency of the adiabatic inversion pulse, i.e., the efficiency of flipping the electron spins conditional on the initial nuclear spin configuration. To characterize the inversion efficiency, Landau-Zener interferometry is performed on three of the EDSR transitions (one transition for each nuclear spin). In this experiment, EDSR transitions 9, 11, and 12 are used. First, the system is initialized to Next, an adiabatic inversion pulse at the target EDSR transition is applied. In particular, the frequency is swept linearly around the transition frequency (chirp)—see, for example, Fig. 12B The frequencies of transitions 9, 11 and 12 are shown. The reversal rate is given by the Landau-Zener equation:

[0145]

[0146] In addition, with the drive strength f r The inversion rate depends largely on the frequency sweep rate ω / τ (τ is the inversion pulse duration and ω is the frequency width of the sweep) compared to the inversion rate ω / τ (τ is the inversion pulse duration and ω is the frequency width of the sweep).

[0147] Fig. 9C It shows that when the initial state The reversal probabilities of EDSR transitions 9, 11, and 12 corresponding to the flipping of the first, second, and third nuclear spins at the beginning, respectively. The x-axis shows the pulse duration (τ) in milliseconds (ms), and the y-axis shows the electron spin-up probability. The electron spin-up probability is measured at a microwave output power of 0 dBm. Dashed lines 902A, 902B, and 902C are fits of equation 1 for each of the three EDSR transitions 9, 11, and 12, respectively. From the fitted data, the corresponding Rabi frequency f can be obtained r,i The Rabi frequency of EDSR transition 9 is 6.47 kHz, the Rabi frequency of EDSR transition 11 is 23.78 kHz, and the Rabi frequency of EDSR transition 12 is 11.12 kHz.

[0148] Fig.9D is a graph showing the dependence of the Rabi frequency on the square root microwave power for each of the three EDSR transitions 9, 11 and 12. On the x-axis is the square root power, The y-axis is the Rabi frequency in kHz. For each EDSR transition, the Rabi frequency depends linearly on the square root power of the microwave output. The gradient of each line 908A (corresponding to transition 9), 908B (corresponding to transition 11), and 908C (corresponding to transition 12) is different for each nuclear spin. This linear dependence is expected.

[0149] Based on the microwave induced electric field (E) being equal at all three transition frequencies and donor positions, different gradients represent different dipole moments of each donor, coupling them to electric actuators with different strengths. The first-order coupling strength is given by the amplitude of the Stark shift produced by the electric field, i.e., δAi=ηiE. The Stark shift is the splitting of energy levels due to an external electric field. Where ηi is the Stark coefficient, which is a measure of how the electric field E splits for each of the hyperfine couplings.

[0150] The Stark coefficient for each donor nuclear spin can be determined using an atomic tight binding model. The Stark coefficient for each donor nuclear spin is shown in inset 906. These coefficients are related to the measured Rabi frequency f r,i The combination constrains both the direction and amplitude of the AC electric field at the qubit location. Therefore, both the direction and amplitude of the AC electric field can be obtained. In this example, the amplitude of the AC electric field is |E| = 33.6 ± 0.5 kV / m (at 0 dBm). This is consistent with the electric field simulated using finite element modeling of the antenna - for example Figure 2A In some examples, the gate 208 in the plane can be connected via an in-plane gate—e.g. Figure 2B or Figure 2C The AC electric field is applied by the gate 212 in the circuit.

[0151] With future redesign of the device architecture, microwave pulses could be applied to the in-plane gate electrodes, generating stronger and more localized fields and allowing faster and even coherent operation.

[0152] Finally, according to the Landau-Zener calibration curve ( Fig. 9C ), the optimal pulse duration can be determined while managing the trade-off between device heating and pulse duration that incurs initialization protocol overhead.

[0153] In one example, it was observed that when the microwave power exceeded 0 dBm, more frequent device instability was also observed. In addition, the pulse and pulse duration contribute to the overhead of the initialization protocol. At 0 dBm, I 2 and I 3The reversal rate approaches unity for τ>4ms, but is only 1 Therefore, in this example, τ=5 ms is selected for the actual initialization sequence to avoid the sequence duration being too long.

[0154] Fig. 10A and Fig. 10B The nuclear spin states are shown and Initialization sequence. Fig. 10A and Fig. 10B Also shown is the ESR spectrum measured after applying the initialization sequence.

[0155] In order to initialize from a random nuclear configuration to a nuclear spin configuration The electron spins are initialized to the spin-down state |↓> and four EDSR pulses are applied. In this example, EDSR pulses corresponding to EDSR transitions 4, 5, 8, and 9 are applied. This sequence transfers spin-down polarization from electrons to nuclear spins I 1 , unconditionally affecting the states of the other two nuclear spins. Repeat the electron spin initialization—that is, flip the electron from |↑> to |↓>. Then apply EDSR pulses corresponding to EDSR transitions 2 and 3 to initialize spin I 2 (Spin I 1 Already in To end the nuclear initialization sequence, the electrons are initialized again, and an EDSR pulse corresponding to EDSR transition 1 is applied to initialize the spin I 3 (Spin I 1 and I 2 Already in The pulse sequence is Fig.13A 1002. After completing this initialization process using the EDSR, the ESR spectrum can be measured. Fig.13A The measured ESR spectrum is shown. The x-axis shows the frequency in GHz, and the y-axis shows the electron spin-up fraction. The measured ESR spectrum has a main peak at the lower end of the frequency region shown. This peak corresponds to when the nuclear spin is in Therefore, the ESR spectrum confirms that the nuclear spin has been successfully initialized to the predetermined

[0156] For the spin-up state The initialization process for nuclear spins is similar, although now the electrons are initialized in the spin-up state |↑> before each EDSR step. Fig. 10B1004. In some examples, electrons can be initialized in the spin-up state |↑> by applying an ESR inversion pulse at all 8 ESR frequencies simultaneously.

[0157] Fig. 10B 1 shows an ESR spectrum measured after the initialization process has been performed. The x-axis shows the frequency in GHz, and the y-axis shows the electron spin-up fraction. The measured ESR spectrum has a main peak at the higher end of the frequency region shown. This peak corresponds to when the nuclear spin is in Therefore, the ESR spectrum confirms that the nuclear spin has been successfully initialized to the predetermined state.

[0158] To further investigate and quantify the initialization fidelity, a series of repeated random initialization sequences interleaved with nuclear state readouts were performed to determine the nuclear configuration before and after initialization. Interleaving means performing an initialization sequence followed by a readout—this can be repeated multiple times. First, the nuclear spin configuration of the 3P quantum dots is randomized. Next, the first nuclear readout sequence is performed by inverting and reading out the electron spin at each of the eight ESR frequencies and averaging 60 times. This is followed by l initialization attempts and then the second nuclear readout sequence. Knowing the nuclear configuration before and after initialization allows the use of a Markov chain model in order to construct a normalized transition probability matrix M. The initialization fidelity from initial state i to final state j is then expressed by the matrix element M j,i Given.

[0159] Fig. 10C It shows the process starting from the initial state (i) and transitioning to the target state The x-axis is the number of initialization attempts l ranging from 0 to 10. The y-axis shows the initialization fidelity. In particular, the initialization fidelity from each of the 7 possible initial states to the target state is shown. The initialization fidelity as a function of the number of initialization attempts l, excluding the case where i = j, i.e. when the initial state is already in the target state). Similarly, Fig. 10D The process from each of the 7 possible initial states to the target state is shown. Initialization fidelity as a function of the number of initialization attempts l (excluding the following case: = j, i.e. when the initial state is already in the target state).

[0160] The curves are normalized by the probability of starting and staying in the target state (i=j case), which eliminates about 5% of the errors in state readout and electronic initialization. The seven different initial configurations can be classified by the state i of the nuclear spin 1 From Figure 12C, it can be observed that 1 has the lowest reversal rate, because η1 Smaller.

[0161] Therefore, since Fig. 10C and Fig. 10D Both, I 1 The fidelity of the flipping is lower for l < 5. Averaging different initial nuclear spin configurations (black dashed lines) allows the determination of the overall effective initialization fidelity. and Both, the overall effective initialization fidelity was determined to be for l>5 replicates And each initialization trigger is By optimizing the inversion efficiency of the EDSR and performing higher fidelity electron spin initialization, the single excitation fidelity can be further improved to >99%.

[0162] Fig.11A The electron spin-up probability as a function of the nuclear spin configuration for a second example 2P quantum dot system with the following hyperfine interactions is shown: 1 =33MHz and A 2 =77MHz. The dots represent experimental data, while the solid line represents the fit. The x-axis depicts δf in MHz, and the y-axis represents the spin-up probability. There are four spin-up probability peaks 902A-902D at specific frequencies corresponding to the four nuclear spin configurations of the second example 2P quantum dot system. In particular, peaks 1102A, 1102B, 1102C, and 1102D respectively show that the nuclear spin is in and The height of each of the peaks 1102A-D corresponds to the probability that the system is in that nuclear spin configuration, and as Fig.11A It can be seen that all four probabilities are about the same height.

[0163] Before applying the initialization protocol, the probability of the nuclear spin existing in any of the four nuclear spin states is substantially equal.

[0164] Fig. 11B 5 shows an ESR measurement after having performed an initialization protocol 500A according to the method on a second example 2P quantum dot system. In particular, Fig. 11B The spin-up probability at different frequencies is shown. The probability of the state has a peak value of 1104, while the probability of the nuclear spin being in any other state is almost zero. Therefore, it can be seen that the second 2P quantum dot system has been initialized to the nuclear spin state

[0165] Fig. 12AThe electron spin-up fraction as a function of the nuclear spin configuration for a second example 3P quantum dot system with the following hyperfine interactions is shown: 1 =12MHz, A 2 =15MHz and A 3 =119 MHz. There are eight peaks corresponding to the eight nuclear spin configurations of the second example 3P quantum dot system at a specific frequency. The height of each of the peaks corresponds to the probability that the system is in that nuclear spin configuration. Before applying the initialization protocol, the probability that the nuclear spin exists in any of the eight nuclear spin states is substantially equal. Peak 1202 shows that the nuclear spin is in The probability of the state.

[0166] Fig. 12B 5 shows an ESR measurement after having performed the initialization protocol 500A according to the method on a second 3P quantum dot system, showing the ratio of the measured electron spin up fraction in GH z Therefore, it can be seen that the second 3P quantum dot system has been initialized to the nuclear spin state —See peak 1204.

[0167] Fig.13A The electron spin-up fraction of the 4P quantum dot system as a function of the nuclear spin configuration is shown. The 4P quantum dot system has the following hyperfine interactions: A 1 =30MHz, A 2 =68MHz, A 3 =97MHz and A 4 =180MHz. There are 16 peaks at a specific frequency, which correspond to the 16 nuclear spin configurations of the 4P quantum dot system. The height of each peak corresponds to the probability that the system is in that nuclear spin configuration. Before applying the initialization protocol, the probability that the nuclear spin exists in any of the 16 nuclear spin states is essentially equal. Peak 1302 shows that the nuclear spin is in The probability of the state.

[0168] Fig. 13B 5 shows an ESR measurement after having performed the initialization protocol 500A according to the method on a 4P quantum dot system, showing the ratio of the measured electron spin up fraction in GH z Therefore, it can be seen that the 4P quantum dot system has been initialized to the nuclear spin state —See peak 1304.

[0169] Electrical control of electron and nuclear spins

[0170] Electrical control of the spins is desirable for qubit manipulation. An oscillating electric field can be applied locally or globally to a multi-donor quantum dot system. For example, one or more surface gate electrodes—such as Figure 2A The AC electric field can be applied via the gate 210 and / or gate 208 in the plane. In other embodiments, the AC electric field can be applied via the in-plane gate—e.g. Figure 2B The AC electric field is applied by gate 212 in the qubit. Electrical control of the nuclear spin can deterministically polarize the nuclear spin. This electrical control of the nuclear spin can be used for a variety of purposes. For example, performing two qubit gate operations, creating a local magnetic field, etc.

[0171] The inventors have found that by changing the direction of the oscillating electric field, the driving strength of the EDSR can be varied. This is because changing the direction of the electric field affects the coupling between the electron spin and the electric field, thereby changing the strength of the EDSR signal required to initialize or control the corresponding mP qubit. In addition, the inventors have found that in a specific direction of the electric field, the driving strength of the EDSR can be changed. m P qubits are used to optimize the driving strength of EDSR.

[0172] From the derivation of the Rabi frequency of the EDSR driver, an estimate of the AC electric field radiated from the antenna at a point location can be found. A hyperfine coupled donor electron system, such as a 3P system with electrons, has a static spin Hamiltonian of the form:

[0173] H 0 =ω n I z +ω e S z +AI·S (2)

[0174] where ω n (ω e ) is the donor nuclear (electron) Larmor frequency, I(S) is the nuclear (electron) spin operator, and A is the hyperfine constant. EDSR causes nuclear electron spin trigger transition and the related I z +S z = 0 subspace has Hamiltonian;

[0175]

[0176] When an AC electric field is applied, the field couples to the spin levels via the Stark effect. For systems with more than one donor atom, the lack of spherical symmetry produces a finite dipole moment, and thus they have a linear Stark shift. For small AC electric fields, the linear Stark shift will be the dominant term, so the AC electrical drive (at I z +S z =0 subspace can be expressed as:

[0177]

[0178] Here, η is the linear Stark coefficient and ε is the amplitude of the AC electric field. 0 Using the rotating wave approximation and choosing an appropriate energy source, the complete Hamiltonian of the system can be expressed as:

[0179]

[0180] where ω 0 is the characteristic split H 0 And approximate value Therefore the Rabi frequency of the driver at the resonant frequency is

[0181] Since the donors are in close proximity, the AC electric field is the same at all donor locations. This means that the Stark coefficient is proportional to the Rabi frequency, where the constant of proportionality is the amplitude of the AC electric field.

[0182] For a small electric field ε, the hyperfine constant A of donor i i (∈) can be written as first order:

[0183]

[0184] Here, ΔA i (∈) is the hyperfine Stark shift of donor i, and is defined as is the Stark coefficient vector of donor i. Therefore, the response of the electric field to the electron density at the donor site depends on the direction of the field. The Stark coefficient is

[0185] Therefore, changing the angle of the applied AC electric field can optimize the Rabi frequency of each nuclear spin configuration. By doing so, the speed and efficiency of the initialization protocol can be improved.

[0186] Using an atomistic tight-binding modeling tool, the best-matching donor configuration was determined under a directionally varying electric field. Fig.14A The amplitude and direction of the AC electric field applied to an example 3P quantum dot are shown.

[0187] Since the points have a planar configuration, the dipoles are only valid along the xy plane, and therefore both the x and y components of the electric field are considered. The linear assumption of the Stark shift is valid for electric fields up to 100 kV / m. These simulations show that for Fig.14A The electric field applied at an angle of 24.20° to the vertical gives a Stark coefficient proportional to the Rabi frequency observed in the experiment. From this, the AC electric field amplitude was determined to be 33.6 kV / m at 0 dBm.

[0188] Fig. 14B The Rabi frequency for an electric field of 33.6 kV / m is shown. At the previously mentioned angle of 24.2, the calculated Rabi frequency agrees well with the experiment, as shown in Table B.

[0189] <![CDATA[f r,1 (kHz)]]> <![CDATA[f r,2 (kHz)]]> <![CDATA[f r,3 (kHz)]]> experiment 6.47 23.78 11.12 simulation 5.92 23.81 11.3

[0190] Table B: Comparison of Rabi frequency between experiment and NEMO-3D simulation at 0 dBm.

[0191] Furthermore, although the quantum processing systems described herein have been shown to have gate electrodes and transmission lines for controlling corresponding qubits, these may not always be necessary. In other embodiments and examples, other control means may be utilized without departing from the scope of the present disclosure.

[0192] The present embodiments are therefore to be considered in all respects as illustrative and not restrictive.

[0193] As used herein, the term "comprise" and variations such as "comprising", "having" and "consisting of" are not intended to exclude further additions, components, integers or steps, unless the context requires otherwise.

[0194] The reference to any prior art in this specification is not an acknowledgement or suggestion that the prior art forms part of the common general knowledge in any jurisdiction, or that it could reasonably be expected that the prior art would be understood, regarded as relevant and / or combined with other pieces of prior art of the skilled person.

Claims

1. A method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate, the method comprising: i) loading electrons onto the multi-donor quantum dots in a spin-down state; ii) performing a zero or one electronic reset pulse; iii) applying an RF signal to drive at least one EDSR transition; and iv) repeating steps ii)-iii) N times to achieve the predetermined target spin state.

2. The method of claim 1, further comprising determining an initialization pulse sequence that depends on the predetermined target spin state and applying the pulse sequence before performing step (i).

3. A method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate, the method comprising: i) determining an initialization pulse sequence depending on the predetermined target spin state, the initialization pulse sequence comprising at least one electronic reset pulse and at least one EDSR transition; ii) loading electrons onto the multi-donor quantum dots in a spin-down state; iii) applying said initialization pulse sequence; iv) repeating step iii) N times to achieve the predetermined target spin state.

4. The method according to any one of claims 2 or 3, wherein: The initialization pulse sequence is configured to achieve the target spin state independent of an initial spin state.

5. The method according to claim 4, wherein: Each target spin state has an associated initialization pulse sequence.

6. The method according to any one of claims 2 to 5, wherein: The initialization pulse sequence is determined based on the initial spin state and the target spin state.

7. The method according to any one of claims 1 to 6, further comprising the following steps: performing an ESR measurement to determine the total spin state of the multi-donor quantum dot; Based on a determination that the total spin state of the multi-donor quantum dots is not in the target spin state, steps (ii)-(iii) are repeated until the target spin state is achieved.

8. A method for initializing a predetermined target spin state of a multi-donor quantum dot in a semiconductor substrate, the method comprising: i) loading electrons onto the multi-donor quantum dots in a spin-down state; ii) performing ESR measurements to determine the total nuclear spin state; According to the determination that the total nuclear spin state of the multi-donor quantum dot is not the target spin state: iii) determining and executing an initialization pulse sequence; wherein the initialization pulse sequence comprises at least one ESR spin reset pulse and at least one EDSR transition; iv) performing an ESR measurement to determine the total nuclear spin state; terminating the method based on a determination that the total nuclear spin state of the multi-donor quantum dot is the target spin state; Based on the determination that the total nuclear spin state of the multi-donor quantum dots is not the target spin state, return to step iii).

9. The method according to any one of claims 1 to 8, wherein: The target spin state is a total nuclear spin down state.

10. The method according to any one of claims 1 to 9, wherein: An RF signal for driving the at least one EDSR transition is applied to the transmission line.

11. The method according to any one of claims 1 to 9, wherein: The RF signal for driving the at least one EDSR transition is applied to at least one gate electrode of a plurality of gate electrodes.

12. The method according to any one of claims 1 to 11, wherein: The multi-donor quantum dot includes at least two phosphorus atoms.

13. The method according to any one of claims 1 to 12, wherein: Donor-based quantum dots are 2P quantum dots.

14. The method according to any one of claims 1 to 12, wherein: The multi-donor quantum dots are 3P quantum dots.

15. The method according to any one of claims 1 to 12, wherein: The multi-donor quantum dots have 4-10 phosphorus donor atoms.

16. The method according to claim 5, wherein: The multi-donor quantum dot is a 2P quantum dot, and the predetermined target spin state is a spin state The initialization pulse sequence comprises: i) Electronic reset pulse ii) EDSR4 iii) EDSR1 iv) Electronic reset pulse v)EDSR2 vi) Electronic reset pulse.

17. The method according to claim 5, wherein: The multi-donor quantum dot is a 2P quantum dot, and the predetermined target spin state is a spin state The initialization pulse sequence comprises: i) Electronic reset pulse ii)ESR1, ESR2, ESR3, ESR4 iii) EDSR4 iv) EDSR1 v) Electronic reset pulse vi) EDSR3 vii) Electronic reset pulse.

18. The method according to claim 5, wherein: The multi-donor quantum dot is a 2P quantum dot, and the predetermined target spin state is a spin state The initialization pulse sequence comprises: i) Electronic reset pulse ii) EDSR4 iii) EDSR1 iv) Electronic reset pulse v)ESR1, ESR2, ESR3, ESR4 vi) EDSR2 ix) Electronic reset pulse.

19. The method according to claim 3, wherein: The multi-donor quantum dot is a 2P quantum dot, and the predetermined target spin state is a spin state The initialization pulse sequence comprises: i) Electronic reset pulse ii)ESR1, ESR2, ESR3, ESR4 iii) EDSR4 iv) EDSR1 v) Electronic reset pulse vi)ESR1, ESR2, ESR3, ESR4 vii) EDSR3 viii) Electronic reset pulse.

20. A quantum processing element, the quantum processing element being configured to initialize a predetermined target spin state in a multi-donor quantum dot, the quantum processing element comprising: A semiconductor substrate and a dielectric material forming an interface with the semiconductor substrate; A multi-donor quantum dot, wherein the multi-donor quantum dot is embedded in the semiconductor substrate, the multi-donor quantum dot comprises at least two donor atoms, and the at least two donor atoms share at least one electron; as well as A control element, the control element is used to control the multi-donor quantum dots; wherein the electrons are loaded onto the multi-donor quantum dots in a spin-down state; and Wherein, the control element is configured as: applying an RF signal to drive at least one EDSR transition; and applying at least one electron spin reset pulse; Thereby achieving the target spin state and initializing the quantum dot.

21. The quantum processing element according to claim 20, wherein: The control element includes at least one gate electrode.

22. The quantum processing element according to claim 20, wherein: The control element includes a transmission line for applying the RF signal to drive at least one EDSR transition.

23. The quantum processing element according to any one of claims 20 to 22, wherein: The donor atoms of the multi-donor quantum dots are phosphorus atoms, and the semiconductor substrate is a silicon substrate.

24. The quantum processing element according to any one of claims 20 to 23, wherein: The at least one gate electrode is fabricated within the semiconductor substrate.

25. The quantum processing element according to any one of claims 20 to 23, wherein: The at least one gate electrode is patterned on the semiconductor surface.

26. A quantum processing element, the quantum processing element being configured to initialize a predetermined target spin state in a multi-donor quantum dot, the quantum processing element comprising: A semiconductor substrate and a dielectric material forming an interface with the semiconductor substrate; A multi-donor quantum dot, wherein the multi-donor quantum dot is embedded in the semiconductor substrate, the multi-donor quantum dot comprises at least two donor atoms, and the at least two donor atoms share at least one electron; as well as A control element, the control element is used to control the multi-donor quantum dots; wherein the electrons are loaded onto the multi-donor quantum dots in a spin-down state; and Wherein, the control element is configured to execute the method according to any one of claims 1-19.

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