Engineered quantum processing elements

Abstract

Engineered quantum processing elements are disclosed. The engineered quantum processing element includes dopant dots embedded in a semiconductor substrate. The dielectric material forms an interface with the semiconductor substrate. The dopant dot includes a plurality of dopant atoms and one or more electrons / holes confined within the dopant dot. The geometric configuration of the plurality of dopant atoms relative to the semiconductor substrate is engineered to achieve optimal linear hyperfine Stark coefficients. In addition, aspects of the present disclosure are directed to methods of manufacturing such engineered quantum processing elements.

Description

Technical Field

[0001] Aspects of the present disclosure relate to quantum processing systems, and more particularly, to engineered quantum processing elements. Background Art

[0002] Large-scale quantum processing systems are expected to bring about a technological revolution and solve problems that classical machines cannot solve. To date, many different structures, materials, and architectures have been proposed to realize quantum processing systems and manufacture their basic information unit (quantum bit or qubit). A qubit can be understood as a quantum mechanical system encoded into two discrete energy levels.

[0003] Semiconductor spin qubits have now reached sufficiently high quality factors that error-correction architectures can be envisioned for quantum information processing, but several outstanding challenges remain to be addressed before viable quantum computing processors can be demonstrated in silicon.

[0004] However, many obstacles need to be overcome before such large-scale quantum computers can be commercially manufactured. One such obstacle is the control of qubits. To date, several techniques have been proposed to control the state of qubits, but these techniques either do not scale up efficiently or lead to faster decoherence. Manipulating spin-based qubits in semiconductors, especially fast manipulation of the spin state of qubits, is an important approach to building quantum gates. In particular, fast, individually addressable qubit operations are critical for scalable architectures.

[0005] Therefore, there is a need for a scalable qubit control system that can control multiple qubits simultaneously without adversely affecting the operation of the qubits. Summary of the invention

[0006] According to a first aspect of the present invention, there is provided an engineered quantum processing element, comprising: a semiconductor substrate; a dielectric material forming an interface with the semiconductor substrate; a dopant point comprising a plurality of dopant atoms and one or more electrons / holes confined within the dopant point, wherein the geometric configuration of the plurality of dopant atoms relative to the semiconductor substrate is engineered to achieve an optimal linear hyperfine Stark coefficient.

[0007] According to a second aspect of the present invention, there is provided a method for manufacturing an engineered quantum processing element, the method comprising: exposing a semiconductor substrate to atomic hydrogen H to form an H monolayer, and passivating the surface of the semiconductor substrate; selectively desorbing H atoms from the passivated surface by applying an appropriate voltage and tunneling current to the STM tip, thereby forming a plurality of patches in the H monolayer; wherein the distance between the plurality of patches and the orientation of the plurality of patches along the semiconductor lattice direction are selected to achieve a large linear hyperfine Stark coefficient; and combining at least one donor atom in each of the plurality of patches in the H monolayer to form a donor molecule. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Features and advantages 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:

[0009] FIG. 1 shows an example spin qubit device 100 formed in a silicon substrate. Figure 1A is a top view of donor spin qubit device 100, and Figure 1B It is a side cross-sectional view.

[0010] Figure 2A A graph showing the ESR spectral profile or resonance profile of a qubit excited by a 1 MHz Rabi frequency is shown.

[0011] Figure 2B is a plot of the spectator qubit error as a function of frequency detuned from the target qubit resonance.

[0012] Figure 3A An example engineered qubit device is shown.

[0013] Figure 3B Another example engineered qubit device is shown.

[0014] Figures 4A-4D The hyperfine Stark shift of an unengineered 2P donor dot system is shown.

[0015] Figures 5A-5D The hyperfine Stark shift of the engineered 2P donor molecules of the present disclosure is shown.

[0016] Fig. 6A The Stark coefficient is plotted as a function of the donor interatomic distance and the interdonor axis.

[0017] Figure 6B The Stark shift as a function of the donor interatomic distance and the interdonor axis is depicted.

[0018] Figure 6CThe electronic wave functions of the 2P donor configuration along the

[100] and

[110] crystal directions are shown.

[0019] Fig. 7A An STM micrograph of the device is shown.

[0020] Figure 7B It is a 3D rendering of the STM topography, showing the quantum dot on the left after P doping.

[0021] Figure 7C is a top-down image showing the positions of the three donor atoms in the left quantum dot in a silicon crystal substrate.

[0022] Fig.7D It is an energy diagram of the electron-nuclear spin system.

[0023] Fig. 7E and Figure 7F The measured NMR spectrum and the measured ESR spectrum of the 2P donor molecule are shown, respectively.

[0024] Figure 8 A flow chart illustrating an example method according to aspects of the present disclosure is shown.

[0025] Fig. 9A is a graph showing spectator qubit errors.

[0026] Figures 9B-9D Shown are the ESR spectra of a 2P donor quantum dot at a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz, as well as examples of Rabi oscillations of the target and spectator qubits.

[0027] Fig. 10A is a graph of qubit error as a function of peak shift (Stark shift) and gate speed (Rabi frequency).

[0028] Fig. 10B Shown is the qubit error as a function of the Rabi frequency at 110 MHz Stark offset.

[0029] Fig.11A The Stark shift as a function of the electric field is shown for an example 2P molecule with donors spaced 5.4 nm apart along the

[110] direction.

[0030] Fig. 11B is the charge noise as a function of the electric field for a 2P donor configuration spaced 5.4 nm apart along

[110] Time graph.

[0031] Fig. 11C is Graph of the simulated ESR spectra of the electron spin on the initialized 2P molecule in the state at -5MV / m electric field (peak 1106) and 5MV / m.

[0032] Fig.11E It is shown that at -5 MV / m the electrons are mainly localized on spin-down nuclei.

[0033] FIG. 11F shows that at +5 MV / m the electron spins are mainly localized on spin-up nuclei. DETAILED DESCRIPTION

[0034] The mention of any prior art in the specification is not an acknowledgement or implication that the prior art forms part of the common general knowledge in any jurisdiction, or that it could reasonably be expected that such prior art would be understood, regarded as relevant and / or combined with other prior art by a person skilled in the art.

[0035] Overview

[0036] One type of quantum computing system is based on the spin state of individual quantum processing elements, where the quantum processing elements can be electron spins, hole spins, or nuclear spins located in a semiconductor chip. These electrons, holes, and / or nuclear spins are confined in gate-defined quantum dots or positioned on donor or acceptor atoms in a semiconductor substrate and are called quantum bits or qubits.

[0037] Donor spin qubits in silicon are a promising platform for universal quantum computers due to their long coherence times and high-fidelity readout, single-qubit and two-qubit gates, and their advantages in scalability.

[0038] FIG. 1 shows an example spin qubit device 100 formed in a silicon substrate. Figure 1A is a top view of donor spin qubit device 100, and Figure 1Bis a side cross-sectional view. The donor spin qubit device 100 can be used in a quantum computer that includes a plurality of these qubits. As shown, the qubit device 100 is formed in a structure that includes a semiconductor substrate 102 and a dielectric 104. In this example, the substrate is 28Silicon, and the dielectric is silicon dioxide. An interface 107 is formed where the substrate 102 meets the dielectric 104. In this example, the interface 107 is a Si / SiO2 interface. To form a qubit, a donor atom 108 is located within the substrate 102 within a region 109 below the gate 106. The donor atom 108 can be introduced into the substrate using nanofabrication techniques, such as hydrogen lithography provided by a scanning tunneling microscope, or industry standard ion implantation techniques. In this example, the qubit device 100 includes a single atom 108 embedded in a silicon crystal. However, the methods described herein can be applied to qubit devices 100 that include clusters of more than one embedded atom 108.

[0039] Electrons 120 are then loaded onto the device 100 through the gate electrode 106. The physical state of the electron 120 is described by a wave function 121, which is defined as the magnitude of the probability of finding the electron at a particular location. Donor qubits in silicon rely on the use of the potential well naturally formed by the donor nucleus to confine the electron spin.

[0040] 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 interactions between the electrons 120 and the nuclei of the donor atoms 108. The electron wave function 121 is modulated by the local field applied to the gate electrode 106. For example, the local field applied to the gate electrode 106 can pull the electron wave function 121 away from or closer to the donor 108.

[0041] In particular, AC electric fields can be used to control the quantum state of qubits associated with the spins of the nuclei. Furthermore, AC electric fields work in conjunction with applied oscillating magnetic fields.

[0042] A key component of a scalable quantum computer is that qubits can be individually addressed to apply a quantum gate. However, qubit addressability has been a challenge for donor spin qubit devices 100 because gates 106 are typically implemented via electron spin resonance (ESR) on nominally identical electron spins or via nuclear magnetic resonance (NMR) on nominally identical nuclear spins, requiring a mechanism for distinguishability.

[0043] The addressability of individual donor qubits in silicon was originally proposed through donor Stark shift, which exploits the hyperfine or g-factor Stark shift of the qubit resonance. The Stark shift is the splitting of degenerate spin states in the presence of an external electric field, and the qubit resonance is related to the energy gap that separates the two spin states of the qubit, which allows the qubit to be addressed. The spin qubit resonance depends on the Zeeman splitting, which is linearly proportional to the g-factor. Therefore, any change in the g-factor will change the qubit resonance. The donor Stark shift is achieved via the application of a local electric field. For example, an electric field is applied to the gate electrode 106, pulling the electron wave function 121 away from the donor 108. The electric field reduces the hyperfine interaction (where the hyperfine interaction is the interaction between the electron spin and the nuclear spin of the donor) and also changes the electron spin g-factor (where the spin g-factor is a dimensionless magnetic moment that characterizes the spin momentum of the electron). This in turn affects the electron spin energy splitting, thereby affecting the qubit resonance frequency.

[0044] In one originally proposed approach, the Stark shift was achieved by applying a voltage to the gate 106 to create the desired local electric field at the donor site 109. However, initial experiments with a single donor showed that the Stark shift was much smaller than expected. The measured single donor Stark effect is comparable to (1MHz / MVm -1 )ESR linewidth, limiting the speed of single-qubit gate operation to a point where gate fidelity is at or just below the surface code error threshold (0.6-1%). Thus, in these devices, there is a trade-off between speed and fidelity of single-qubit gates. High-speed qubit gates result in substantial power broadening of the ESR peak linewidth, causing interference errors with neighboring qubits, while slower actuation results in qubit decoherence.

[0045] Pulse shaping of the Rabi amplitude can be used to improve qubit addressability by reducing the linewidth of the qubit resonance. The Rabi amplitude corresponds to the amplitude of the oscillation between the low and high energy states of the qubit, and the Rabi frequency is the frequency at which the qubit oscillates between the two states. For example, the frequency at which an electron spin qubit oscillates between the spin-down state |↓> and the spin-up state |↑>.

[0046] In some examples, a Gaussian-shaped Rabi pulse can be used to improve qubit addressability because it has higher frequency selectivity compared to other pulse shapes (such as rectangular-shaped Rabi pulses).

[0047] Figure 2AGraph 200 showing ESR spectral profiles or resonance profiles of qubits excited by a 1 MHz Rabi frequency, which is a drive strength typically available in ESR qubit experiments. The x-axis shows the ESR frequency in MHz, while the y-axis shows the electron spin-up probability. Resonance profile 202 corresponds to a qubit excited by a rectangular shaped Rabi pulse, and resonance profile 204 corresponds to a qubit excited by a Gaussian shaped Rabi pulse. In this example, the duration of the Rabi pulse has been set to perform a π rotation of the qubit at zero frequency detuning. Where frequency detuning is defined as the frequency offset between the target qubit (i.e., the qubit to be addressed) and the spectator qubit (i.e., the adjacent qubit not to be addressed).

[0048] For the example rectangular pulse shape Rabi frequency, the resonance peak shows a significant power broadening, where the full width at half maximum (FWHM) is approximately 1 MHz. For the example Gaussian shape Rabi frequency, the FWHM resonance is approximately 60 kHz. Therefore, the line width of the resonance profile 204 of the Gaussian shape Rabi pulse is less than the line width of the resonance profile 202 of the rectangular shape Rabi pulse. In addition, the power broadening of the ESR peak caused by the rectangular pulse is significantly greater than that of the Gaussian pulse.

[0049] Figure 2B 220 is a graph of spectator qubit error as a function of frequency detuned from the target qubit resonance. The x-axis shows the spectator qubit frequency detuned in MHz. This is the detuning of the qubit resonance of the spectator qubit from the qubit resonance of the target qubit. The y-axis shows the spectator qubit error.

[0050] Error profile 222 shows the error on the spectator qubit as a function of detuning from the resonance with the target qubit for a rectangular shaped Rabi pulse with a 1 MHz Rabi frequency. Error profile 224 shows the error on the spectator qubit as a function of detuning from the resonance with the target qubit for a Gaussian shaped Rabi pulse with a 1 MHz Rabi frequency. A frequency offset of approximately 10 MHz is necessary to achieve a qubit error below 1% for the rectangular shape (ignoring oscillations in the spectrum), dropping to approximately 600 kHz for the Gaussian shape. However, it is desirable to achieve a qubit error rate of << 1%. To achieve this, the spectator qubit must be detuned from the target qubit by >> 1 MHz - even with Gaussian pulse shaping, which is not feasible.

[0051] Another approach to achieve addressability is to ensure that each qubit inherently has a different resonance. To do this, multi-donor quantum dots can be used, so that different quantum dots have different donor numbers and donor configurations. This approach does not rely on the Stark shift. Instead, it relies on different donor numbers and configurations, resulting in different electron spin resonances. Although some multi-donor quantum dots may inherently exhibit low errors, this approach may be difficult to scale to large numbers of qubits due to the limited number of multi-donor dot configurations. In some cases, ~10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -4 The error rate.

[0052] To overcome one or more of the problems identified above, aspects of the present disclosure provide new engineered qubits that combine the originally proposed addressability approach with a multi-donor dot proposal. In particular, the engineered qubits of the present disclosure include multiple donor atoms and a single electron shared between the donor atoms. These engineered qubits extend the fidelity and speed of the qubit by engineering a larger Stark coefficient in a pair of quantum dots. In addition, in a multi-donor quantum dot system, some aspects of the present disclosure may utilize the same donor configuration for each quantum dot. In such a system, the qubit can be uniquely addressed by applying a local electric field to produce a Stark shift on the qubit. Other examples may use different donor configurations for different multi-donor quantum dots in a quantum processing system.

[0053] The engineered qubits of the present disclosure can be used as electron spin qubits, where quantum information is encoded in the electron spin shared between donor atoms. The engineered qubits can also be used as nuclear spin qubits, where quantum information is encoded in the spin of any one donor atom.

[0054] In particular, aspects of the present disclosure allow for three types of qubit addressability:

[0055] Addressing electron spin qubits by engineering quantum processing elements with large Stark shifts;

[0056] Addressing electron spin qubits by engineering quantum processing elements with multiple donors, thereby generating more frequencies for the same electron to avoid frequency crowding in the global field of large devices;

[0057] Addressing nuclear spin qubits by using the ESR (Electron Spin Resonance) peak for reading

[0058] Output and control both.

[0059] Figure 3AAn example engineered qubit device 300 is shown. To form the qubit device 300, two donor atoms 302A and 302B are located within a quantum dot 301 in a semiconductor substrate 304. In some examples, the donor atoms 302A, 302B are phosphorus atoms. In this example, the qubit 300 includes two donor atoms 302. On top of the silicon substrate 304 is a barrier material / dielectric 306 such as silicon dioxide. In addition, a gate 308 and an antenna 310 can be located on the dielectric 306 in the area above the quantum dot 301. A voltage can be applied to the gate 308 to confine the electron 320 in the quantum dot 301. A magnetic field can be applied via the antenna 310 to control the electron and nuclear spin states in the quantum dot 301. The electron 320 can be shared by the two donor atoms 302A, 302B.

[0060] Figure 3B Another example engineered qubit device 350 is shown. It is similar to the device shown in FIG. 3A. The only difference is the placement of the gate. Figure 3A 306. In this example, one or more gates 312 are located within the semiconductor substrate 304. In some embodiments, one or more gates 312 are placed in the same plane as the quantum dot 301. The in-plane gate 312 can be connected to the surface 306 of the substrate via a metal via (not shown). A voltage can be applied to the gate electrode 312 to confine one or more electrons 320 in the quantum dot 301.

[0061] In some devices, the in-plane gate electrode 312 is made of phosphorus-doped silicon (~0.25 ML doping density).

[0062] Large hyperfine Stark coefficients can be seen in such engineered qubit devices 300, 350. The large hyperfine Stark coefficients are a result of large hyperfine coupling and electric dipole moments in the 2P donor dots compared to a single donor.

[0063] The quantum dot 301 with a single confined electron is referred to herein as a donor molecule. When the donor atom is a phosphorus atom, the quantum dot 301 is referred to as an mP donor molecule, where m represents the number of phosphorus atoms in the donor molecule. m can be any number greater than 1.

[0064] It should be understood that although Figure 3A and Figure 3B A single quantum dot is shown, but this is just an example. In some embodiments, multiple quantum dots 301 and / or 350 may be arranged in a two-dimensional or three-dimensional structure to create a large quantum processor.

[0065] In addition, despite Figure 3A and Figure 3BA 2P donor molecule is shown, but the engineered qubits of the present disclosure are not limited thereto. Rather, the engineered qubits can include donor molecules comprising more than two donor atoms.

[0066] Various aspects of the present disclosure engineer not only the donor position but also the donor orientation within the mP donor molecule to achieve large linear hyperfine Stark coefficients. In 2P donor molecules, high linear hyperfine Stark coefficients as large as ∼70 MHz / MV m- can be achieved. 1 The linear hyperfine Stark coefficient (assuming Gaussian pulse shape) allows single-qubit gate fidelity of >99.9998% for a 2π rotating gate with ~0.5μs gate operation time.

[0067] These and other advantages of the disclosed qubit devices and control / operation techniques are described in detail in the following sections.

[0068] Position and orientation of donors affecting Stark shift

[0069] As described above, aspects of the present disclosure relate to engineering an optimal Stark coefficient in an mP donor molecule system (e.g., in a 2P or 3P molecule system). The large hyperfine Stark coefficient is a result of the large hyperfine coupling and electric dipole moment in the donor molecule compared to a single donor system. The hyperfine Stark coefficient is a measure of how the hyperfine interaction between the donor electron and the nucleus varies with the electric field. Its units are MHz / MVm- 1 .

[0070] In particular, the inventors have recognized that certain positions and orientations of donor atoms in donor molecules produce optimal Stark shifts for controlling and addressing these nuclear spin qubits.

[0071] Figures 4A-4D shows the hyperfine Stark shift of the unengineered 2P donor point system, and Figures 5A-5D The hyperfine Stark shift of the engineered 2P donor molecules of the present disclosure is shown.

[0072] In particular, Figure 4A The electron spin resonance (ESR) spectrum of an unengineered 2P donor site in natural silicon is shown - with three resonance peaks. The x-axis shows the ESR frequency in GHz, while the y-axis plots the spin-up fraction. In addition, the nuclear spin state and Represent the left and right nuclear spins of the two donor atoms in the dot, respectively. The upward and downward arrows correspond to the upward and downward nuclear spin states of the donor atoms. In the 2P donor dot system, the donor atoms can be referred to as P1 and P2, respectively.

[0073] Figure 4A The lowest frequency peak in Two phosphorus donor nuclear spin states, and the highest frequency peak belongs to nuclear spin state. The intermediate peak is twice as high as the lowest and highest frequency peaks and belongs to and Nuclear spin states, both of which are degenerate within the peak linewidth - with a FWHM of 72 MHz.

[0074] Figure 4B The corresponding energy diagram of the total spin state of the example 2P system is shown. The four lower energy states correspond to the total spin state and The four upward energy states correspond to the total spin state and in and represent nuclear spin down and spin up, respectively, and ↓ and ↑ represent electronic spin down and spin up, respectively. Figure 4B Also shown in FIG. 5 is the ESR resonance frequency between the nuclear spin states in the non-engineered 2P donor site in this example.

[0075] and The degeneration between nuclear spin states is a result of the electron wave function overlapping equally with both donors. The electric field in the device can break the degeneration caused by the Stark effect by moving the electron wave function closer to one of the donors. However, the Stark coefficient of this unengineered 2P quantum dot configuration is small (~1.7MHz / MVm- 1 ), and subsequently the Stark shift cannot be measured. In this system, the nuclear spin and the electron spin cannot be addressed because the Stark shift is too small. Here, and The nuclear spin state degenerates, and thus the total spin state and Degenerate, similarly, the total spin state and Degeneration.

[0076] Figure 4C Schematic diagram of the electron wave functions (blue / yellow ellipses) on two phosphorus donor atoms P1 and P2 are shown. Under zero electric field along the donor separation axis, the electron 20 is evenly shared between the donors P1, P2 (blue ellipses), while under the electric field used in the measurement (~4.3MV / m), the electron wave function is slightly more localized at the donor P1 (yellow ellipse), resulting in a small hyperfine Stark shift of <7MHz.

[0077] Figure 4D The most likely donor configuration for this unengineered 2P quantum dot device is shown, which would produce Figure 4A Here, the two phosphorus donors (402 and 404) are spaced 0.77 nm apart along the

[110] crystal axis. Wherein, the

[110] crystal axis corresponds to one unit on the x-axis, one unit on the y-axis, and zero units on the z-axis, respectively. For this example unengineered 2P molecule along

[110] , the available electric field in the device (~5.4MV / m) can allow a maximum Stark shift of >7MHz. However, since the electric field is not directly aligned along the donor axis, but offset by ~40°, the Stark shift will be smaller, at ~5MHz. This small Stark shift is not enough to exceed the 72MHz peak linewidth observed in these native silicon devices, so no Stark shift is observed in the ESR spectrum.

[0078] Figure 5A is an ESR spectrum of an engineered qubit device according to aspects of the present disclosure. The x-axis shows the ESR frequency in GHz, while the y-axis plots the spin-up fraction. For this engineered qubit device, the ESR spectrum shows four resonance peaks, representing and Each of the nuclear spin states. Here, The nuclear spin state is not degenerate. Therefore, the engineered 2P quantum dots have four unique electron spin resonances. The four ESR peaks can be fitted with a Gaussian function to extract a FWHM of 44MHz as a result of the ±20MHz chirp. This means that the ESR spectrum can be measured using so-called adiabatic inversion pulses, in which the ESR frequency is swept linearly from -20MHz to 20MHz relative to the carrier frequency.

[0079] The four resonances are also consistent with the number of 2P donors, since each nuclear spin state (4 in total for 2P) has a unique hyperfine interaction with the electron spin. The spectrum is symmetric about the center, so Figure 5A The splitting between the first and second peaks in the spectrum is the same size as the splitting between the third and fourth peaks. Therefore, two hyperfine interactions, A1 = 189 MHz and A2 = 83 MHz, can be extracted from the spectrum, which correspond to the hyperfine interactions between the electron spin and the first and second donor nuclear spins, giving a hyperfine Stark shift A1-A2 = 106 MHz. This hyperfine Stark shift breaks up the donor nuclear spins. and The degradation between states produces Figure 5A The four ESR transitions are shown in .

[0080] Due to Stark offset broken and The four nuclear spin states can now be addressed individually. c and Each of can be addressed by its corresponding individual ESR frequency. and The ESR frequency of each nuclear spin state is shown in Figure 5A on the x-axis.

[0081] Furthermore, for this donor configuration, electronic qubits can also be addressed. When an electric field is applied, these states become non-degenerate due to the Stark shift, so that the ESR frequency is now different from that of the non-Stark shifted qubit. Faster electronic addressability can be achieved by extremely large Stark shifts, which effectively yield Large ESR frequencies that differ between nuclear spin states. The addressability of electron spins on 2P systems is optimized by maximizing the size of the Stark shift.

[0082] In some embodiments, a plurality of engineered multi-donor quantum dots are provided. In such embodiments, the multi-donor quantum dots may each have a different number of donor atoms. In some embodiments, the multi-donor quantum dots may each have a different number of donor atoms. In other embodiments, the multi-donor quantum dots may have a combination of the same number or different numbers of donor atoms. An electronic qubit of one of the plurality of multi-donor quantum dots may be addressed by applying an ESR frequency specific to that electronic qubit.

[0083] Figure 5B The relative energies of the total spin states and the ESR transitions between them are shown. Likewise, the four low energy states correspond to the total spin states and The four upward energy states correspond to the total spin state and Due to the presence of an optimal Stark shift in this example engineered quantum processing element, and as well as and The degradation of the status is resolved.

[0084] Figure 5CSchematic diagram of the electron wave functions (blue / yellow ellipses) on two phosphorus donor atoms P1 and P2. Under zero electric field along the donor separation axis, the electrons are evenly shared between the donors (blue ellipses), while under the electric field used in the measurement (~3.5 MV / m), the electron wave functions are more localized at the donor P1 (yellow ellipse), resulting in a large hyperfine Stark shift. Figure 4C compared to, Figure 5C The larger Stark shift in is a result of the different donor configurations in the engineered molecular qubits of the present disclosure.

[0085] In particular, donor configuration refers to the donor spacing and the orientation of the donors relative to the crystal axis. In some examples, the donors can align their orientation relative to the crystal axis. For example, a pair of adjacent donor atoms can be positioned along a crystal axis such as

[110] . In other examples, adjacent donors may not be aligned relative to the crystal axis. Instead, they can be located at any position in the lattice structure.

[0086] Figure 5D The most likely donor configuration for this example engineered 2P quantum dot device is shown, which will produce Figure 5A The ESR spectrum shown in and is associated with the total hyperfine coupling A1+A2. Here, the two donor atoms (502 and 504) are separated by 0.86 nm along the

[130] crystal axis, which yields a total hyperfine interaction of 276 MHz. The theoretically determined value of the total hyperfine interaction of 276 MHz is in good agreement with the experimentally determined total hyperfine interaction of 272 MHz.

[0087] Table I below shows the different donor configurations that best match the total hyperfine values ​​obtained from the ESR spectra, as well as the values ​​of the linear Stark coefficient. From Table I it can be observed that the donor configuration along the

[130] crystal axis has a linear Stark coefficient of 11.2 MHz / MVm -1 This is a factor between two and three larger than most other configurations. This configuration corresponds to Figure 5D The configuration shown in , and is an example donor configuration that can be engineered for donor molecule quanta to produce a large Stark shift.

[0088] All other configurations require unrealistic electric fields (>10 MV / m, as shown in the last row of Table I) to achieve the observed large Stark shift, and / or have large discrepancies between the predicted total hyperfine splitting and the experimental values.

[0089] Table I identifies the most likely 2P donor configuration for the molecule in Figure 2e.

[0090]

[0091] The inventors of the present disclosure have recognized that the precise 2P donor configuration and the orientation and magnitude of the electric field play a key role in determining the magnitude of the hyperfine Stark shift.

[0092] The ability to engineer these larger hyperfine Stark shifts above 110 MHz can be used for faster fault-tolerant single-qubit gates that are addressable via global ESR fields. The peak is separated into two non-degenerate peaks, and and The nuclear spin state is not affected by the hyperfine Stark shift, e.g. Figure 4A and Figure 5A As shown in the ESR spectrum in . Therefore, it is important to initialize the nuclear spins to an antiparallel state to control the ESR frequency via the hyperfine Stark shift. Phosphorus nuclear spin states in silicon are very stable with lifetimes of several minutes, while operations on electron spins can be performed in microseconds. Therefore, many operations can be performed on electron spins without reinitializing the nuclear spins.

[0093] Fig. 6A and Figure 6B The simulated hyperfine Stark shift of a single electron 120 in various 2P donor molecule configurations is shown. In particular, Fig. 6A The Stark coefficient is plotted as a function of the donor interatomic distance and the interdonor axis, and Figure 6B The Stark shift as a function of the donor interatomic distance and the interdonor axis is depicted.

[0094] Fig. 6A and Figure 6B The simulations used an atomic tight-binding model (nearest neighbor interaction only) to look at all 2P configurations within an 8a0 by 8a0 box in the plane of the device, totaling 144 configurations (80 unique configurations due to symmetry about the

[110] axis), where a0 is the silicon atomic lattice constant of 0.543 nm, and all 2P donor combinations within the 8x8 atomic lattice site domain were looked at.

[0095] Fig. 6A and Figure 6B The x-axis in shows the distance between two donor atoms in units of a0 (silicon atom lattice constant). Fig. 6A The y-axis in shows the simulated Stark coefficient in MHz / (MV / m). The magnitude of the linear Stark coefficient is determined by the position of the second donor atom P2 relative to the first donor atom P1. Inset 602 shows the first donor at (X,Y)=(0,0) and the second donor at a distance r from the first donor atom. In addition, for Fig. 6A, the Stark coefficient is taken from the electric field strength of 0MV / m, and Figure 6B The Stark shift is for an electric field of 5 MV / m. Both figures assume that the electric field is applied along the inter-donor axis (θ=0°), which is the axis connecting the first donor to the second donor, via one or more gates 308, 312. Stark shift = Stark coefficient x electric field.

[0096] In this simulation, an electric field is applied via one or more gates 308, 312 along the inter-donor axis (θ=0°), which is the axis connecting the first donor to the second donor.

[0097] also, Fig. 6A The simulation results of the Stark coefficient as a function of the donor position in the XY plane are shown, where the first donor is located at (0,0) (see 502) and the second donor is placed at a certain distance r along the

[100] ,

[110] ,

[120] and

[130] crystal directions. For each crystal axis, the Stark coefficient increases with the donor spacing because the electron donor dipole moment increases, making it more sensitive to the electric field. Due to the valley interference along these directions, the Stark coefficient oscillates along the

[110] and

[130] directions. Due to the presence of valley interference, a non-monotonic increase in the linear hyperfine Stark coefficient is also observed. Along these crystal directions, the electron exists in a superposition between the two donors, and its wave function oscillates due to the underlying silicon lattice. Valley here means the energy minimum in the guide band. There are six degenerate minima, also called valleys, in silicon, and for a single donor electron, it is in equal superposition between the six valleys. For two closely spaced donors, the electron wave function overlaps with both donors. The trough components of the electron wave function from each donor can interfere with each other constructively or destructively, depending on the exact donor spacing and crystal orientation, thereby changing the overall wave function.

[0098] Figure 6CThe electron wave functions for 2P donor configurations along the

[100] and

[110] directions are shown to further explain the valley interference. Along the

[100] (and equivalent) directions, the electron wave function superposition constructively interferes with the spacing between 2P donors. However, if the donors are spaced along the

[110] crystal direction, some donor spacings may undergo destructive interference. In particular, as the position of a particular donor changes, both the X and Y valleys induce constructive and destructive interference of the electron wave functions, resulting in hyperfine Stark coefficient oscillations. This anisotropy of electron wave function interference originates from the anisotropy of the silicon effective mass, where each valley orbit has a smaller wave function envelope along the longitudinal direction and a larger radius along the transverse direction. This valley interference of the electron wave function can be coupled via the electron donor dipole moment and the energy of the electron antibonding state to produce oscillations of the hyperfine Stark coefficient in the

[110] and

[130] directions from a monotonic trend.

[0099] Figure 6B is a graph of the Stark shift for different 2P configurations along the donor spacing axis at 5 MV / m electric field. The y-axis in the graph shows the Stark shift in MHz. The first donor is located at (0,0) and the second donor is placed at a distance r along the

[100] ,

[110] ,

[120] and

[130] crystal directions.

[0100] Figure 6B The shaded area 604 shows a 2P donor configuration where the Stark shift is 110 ± 5 MHz. For each configuration, this occurs when the second donor is located more than 8.5a0 (~4.6nm) from the first donor. This result shows that when the 2P donor spacing exceeds 4.6nm, the hyperfine Stark shift on the 2P donor is insensitive to the dopant positioning along the lattice. These donor configurations are easily patterned within the ±1 lattice point accuracy of STM lithography. In addition, 2P donor configurations with smaller inter-donor spacing show larger Stark shift changes at 5MV / m electric field because the size of the Stark shift is not limited by the total hyperfine interactions and is therefore more susceptible to changes in the hyperfine Stark coefficient.

[0101] like Fig. 6A As shown, for donor spacings below 2a0≈1 nm, the hyperfine Stark coefficient is typically limited to approximately 1 MHz / MVm for most inter-donor axes. -1 , which is comparable to the Stark shift observed in a single donor system (e.g., as shown in Figure 1). In contrast, a 2P donor configuration spaced 1.58a0 (0.86nm) apart along the

[130] direction has a power of 11.2MHz / MVm -1This 10-fold larger hyperfine Stark coefficient for the same donor spacing along different crystallographic directions is due to the presence of the valley interference described above.

[0102] However, not only the crystallographic orientation of the donors is important, but also the spacing between them. Extending the donor spacing at several lattice sites to more than 2a0 yields frequencies above 70 MHz / MVm. -1 The linear Stark coefficient of , as seen along the

[110] and

[120] directions.

[0103] This large zero-electric-field linear Stark coefficient can lead to a situation where the Stark shift is limited by the size of the aggregate hyperfine coupling with relatively small electric fields. For the 0.5a0

[110] 2P configuration (the closest donor spacing possible), the Stark shift is maximum (679 MHz) and falls off rapidly towards ~110 MHz with increasing donor spacing. For some example devices, electric fields of 5 MV / m can be routinely achieved, and for donor configurations with spacings above approximately 8.5a0 (4.6 nm), the maximum Stark shift of these devices becomes limited by the aggregate hyperfine interactions in this electric field.

[0104] Thus, by targeting the 6a0

[110] 2P configuration, a hyperfine Stark shift of 105 MHz can be engineered within a tolerance of 7.6% due to the uncertainty in ±1 lattice site fabrication. Specifically, in the 6a0

[110] configuration, the second phosphorus donors are spaced 6 times the lattice constant (a0) apart in both the x- and y-directions. Since a0 = 0.543 nm, this calculates to a spacing of 4.6 nm along

[110] , or ~8.5 a0 along

[110] in an atomic lattice unit cell. This is exactly Figure 6B In addition, the 2P donor configuration with a smaller spacing exhibits a larger Stark shift variation at 5 MV / m electric field because the total hyperfine interaction is larger and thus the magnitude of the Stark shift is more susceptible to the variation of the hyperfine Stark coefficient.

[0105] although Fig. 6A and Figure 6B The simulations constrained the positions of the second donors to be along the

[100] ,

[110] ,

[120] , and

[130] crystal directions, but it is important to note that the second donors can occupy any other lattice site or lattice orientation.

[0106] 7A to 7E A 3P donor quantum dot system is shown, in which the donor molecule includes three donor atoms. In particular, Fig. 7AAn STM micrograph of a device 700 is shown, which includes a left (L) quantum dot 702 and a right (R) quantum dot 704 in isotopically pure silicon-28 and 120ppm silicon-29. Quantum dots 702A and 702B can be tunnel-coupled to a charge sensor 706 (such as a single electron transistor SET) and an electron storage 608 to load electrons onto a donor dot. 720 shows an enlarged portion of the device 700, wherein the left (L) and right (R) quantum dots are shown as being spaced 10nm apart. The left quantum dot 702 is an engineered quantum dot according to various aspects of the present disclosure and includes 3 donor atoms. The left quantum dot 702 is an engineered 3P quantum dot. In this example, the right quantum dot 704 can be engineered or can be a conventional dot without departing from the scope of the present disclosure. The device 700 also includes a left gate 710A, a middle gate 710B and a right gate 610C, which can be used to control the electrochemical potential of the donor sites 704 and 706. However, the SET gate 706 is mainly used to control the electrochemical potential of the SET.

[0107] Figure 7B and Figure 7C Schematic diagram of a 3P donor system in which one electron is confined. The positions of the three donor atoms are labeled I1, I2, I3 (730, 732, 734), and the electron wave function is labeled S. In particular, Figure 7B is a 3D rendering of the STM topography, showing the left quantum dot after P doping, and Figure 7C is a top-view image showing the locations of three donor atoms in a silicon crystal substrate.

[0108] In this example, two donors (P1 and P2) are positioned along a crystal axis and are spaced a certain distance along the axis. A third donor (P3) is positioned on another crystal axis and is spaced a first distance from P1 and a second distance from P2. In some embodiments, the distances of P3 to P1 and P2, respectively, may be the same. The geometric orientation of the three donors in the 3P system includes the relative distances between the donors and the angles between them. The orientation of the donor molecules is defined by the relative positions of the three donors.

[0109] Fig.7D is an energy diagram of an electron-nuclear spin system. The energy levels split due to different Zeeman and hyperfine couplings of different spin configurations. The arrows correspond to and Transition.

[0110] Fig. 7E and Figure 7FThe measured NMR spectrum and the measured ESR spectrum are shown respectively. These frequencies allow the nuclear or electron spins to be addressed individually. The NMR spectrum has 6 peaks corresponding to a single nuclear spin flip in each electron spin state (e.g. Fig.7D ). Fig.7D Only indicate from In addition, the NMR spectrum has another peak corresponding to the transition when the quantum dot is ionized and all spins are driven at the same frequency. The spectral resolution does not allow the observation of splitting by nucleus-nucleus interactions. The ESR spectrum is characterized by 8 peaks, corresponding to the 2 3 = Transitions between 8 possible nuclear spin configurations (e.g. Fig.7D ) as indicated by the vertical arrow in the figure.

[0111] Making 2P donors in specific configurations

[0112] Once the donor configuration is determined for the optimal Stark offset for addressing a nuclear spin qubit or an electron spin qubit, the donor quantum dot qubit can be manufactured. In one example, Stark offset values ​​for different donor quantities and configurations (separation distances and orientations) can be determined. These values ​​can be stored in a lookup table or database. Depending on the type of addressability required and the corresponding optimal Stark offset value required, a lookup can be performed in the lookup table / database to identify the number of donor atoms and their configuration. This information can then be used to engineer quantum processing devices. In particular, using a manufacturing method according to aspects of the present disclosure allows donor atoms to be precisely placed in a silicon substrate to create engineered qubits.

[0113] Figure 8 A flow chart illustrating an example method 800 for engineering a qubit device (eg, including a plurality of 2P molecules 300 ) having an optimal Stark shift for addressability, according to aspects of the present disclosure, is shown.

[0114] Initially, a clean Si 2×1 surface is formed in ultra-high vacuum (UHV) by heating to near the melting point. This surface has a 2×1 unit cell and consists of rows of σ-bonded Si dimers, with the remaining dangling bonds on each Si atom forming weak π bonds with the other Si atom of the included dimer.

[0115] Next, in step 802 (i.e., monohydride deposition), the clean Si 2×1 surface is exposed to atomic H to break the weak Siπ bonds, thereby allowing H atoms to bond to Si dangling bonds. Under controlled conditions, a H monolayer can be formed, with one H atom bonding to each Si atom, thereby satisfying the reactive dangling bonds, effectively passivating the surface.

[0116] Next, at step 804 (ie, hydrogen lithography), the STM tip is used to selectively desorb H atoms from the passivated surface by applying appropriate voltages and tunneling currents, thereby forming a pattern in the H resist.

[0117] It will be appreciated that the H atoms are desorbed from precise locations and in precise directions, allowing the donor molecule to be placed in precise locations to achieve a high Stark shift in the presence of an electric field. For example, if the donor molecule includes two donor atoms spaced 12 lattice sites or 4.6 nm apart along the

[110] direction, then the STM tip can be used to desorb six hydrogen atoms at one location along a dimer column, and then six additional hydrogen atoms along the same dimer column at 4.5 nm from the first location.

[0118] This process is repeated to create locations for additional donor molecule sites. In this way, regions of bare reactive Si atoms are exposed along the dimer columns, allowing subsequent adsorption of reactive species directly to the Si surface.

[0119] Back to Figure 8 In step 806 (i.e., PH3 dosing), phosphine (PH3) gas is introduced into the vacuum system via a controlled leak valve connected to a specially designed phosphine micro-dosing system. Phosphine molecules are strongly bonded to the exposed Si surface via the holes in the hydrogen resist. As noted above, at a specific donor site, the phosphine molecule can bond to any exposed silicon dimer.

[0120] Subsequent heating of the STM patterned surface for crystal growth causes the phosphine molecules to dissociate and result in the incorporation of P into the exposed Si layer. Thus, the STM patterned H-passivated surface is exposed to PH3, which is used to generate the required donor molecules.

[0121] The hydrogen can then be desorbed at step 808, followed by overgrowing the surface with silicon at room temperature at step 810. An alternative approach is to grow silicon directly through the hydrogen layer. The surface is then rapidly annealed.

[0122] Silicon is then grown on the surface at an elevated temperature. In one example, approximately 50 ± 5 nm of epitaxial silicon is grown at a temperature of 250°C.

[0123] Once the desired amount of silicon has been grown, the barrier can be grown. Finally, the microwave antenna can be aligned on the surface using electron beam lithography. By using etched registration marks, the antenna is aligned at a lateral distance of 300 ± 50 nm from the buried donor molecules to generate an oscillating magnetic field B1 orthogonal to the substrate at the donor location.

[0124] The gate can be positioned on the silicon substrate together with the antenna. Alternatively, the gate can be located in the same plane as the donor molecules. In such an example, the gate can be formed from Si:P during the H desorption phase.

[0125] Optimal Stark shift for faster fault-tolerant single-qubit gates

[0126] Fig. 9A The spectator qubit error percentage is shown (on dashed line 902), which is the probability P(t) of exciting a deviating resonant qubit, which is the nuclear spin The hyperfine Stark shift of the ESR peak is a function of the target qubit Rabi frequency, according to the Rabi equation given below:

[0127]

[0128] in B ac is the magnetic field amplitude from the microwave antenna 210, δv is the offset from the peak resonant frequency (see below), ge is the electronic g-factor, and μB is the Bohr magneton.

[0129] Here δv corresponds to the hyperfine Stark shift (or more precisely, the shift from Stark The center of the ESR peak is shifted to the non-Stark The magnitude of the frequency shift of the center of the ESR peak). The spectator qubit error P(t) can be evaluated, as well as the probability that the spectator qubit flips from spin down to spin up at time t = 1 / 4γ, i.e., half the period of the Rabi cycle at the detuned spectator qubit’s Rabi frequency. The target qubit’s Rabi frequency is equal Its Figure 3A Sweep on the y-axis.

[0130] The probability of exciting an off-resonance spectator qubit is proportional to the overlap of the target qubit ESR peak with the spectator qubit resonant frequency. This can be understood from equation (1) because the prefactor is Lorenzian, and its full width at half maximum (FWHM) is Figure 3A B on the y-axis ac Proportional, Figure 3A The frequency f of the Rabi oscillation is shown.

[0131] Taking f = 0 as the target qubit ESR frequency, and taking f = δv as the spectator qubit ESR frequency separated by the Stark shift, means that a larger Stark shift reduces the overlap of the Lorenzian and spectator qubit resonance frequencies. Therefore, a larger hyperfine Stark shift leads to lower spectator qubit errors (e.g. Fig. 9A Conversely, increasing the AC magnetic field strength B AC , increasing the Lorentzian FWHM (and increasing the target qubit Rabi frequency), leading to more Lorentzian overlap at the spectator qubit resonance, and therefore higher spectator qubit error rate.

[0132] Fig. 9A The quantum shift phase error is also shown (as shown by solid line 904), which has been measured for a single phosphorus donor in silicon-28 to be as long as 270 μs. The phase shift error is estimated from the qubit gate quality factor, as the ratio of the gate time divided by the coherence time, which depends on the Rabi frequency. The phase shift error for a 270 μs phase shift time is plotted by solid line 904 for 0.1% and 1.0% values. These form a lower limit for setting the target qubit Rabi frequency, as otherwise the target qubit Rabi frequency can be set arbitrarily low to minimize spectator qubit errors, which are indicated by dashed line 902 for 0.01%, 0.1%, and 1.0% error probabilities. The shaded triangle 906 represents the region where both the spectator qubit and phase shift qubit errors are within 1% (approximately the error rate threshold for the surface code).

[0133] Fig. 9A How different 2P and 1P donor configurations perform is also shown by plotting the magnitude of the hyperfine Stark shift for each configuration at 5 MV / m electric field. The 1P donor, shown as point 910, has the smallest hyperfine Stark shift, which limits how fast the Rabi frequency can be for fault-tolerant execution of a target 1P donor electron spin compared to a 2P donor.

[0134] We note that the hyperfine Stark shift for the 1P donor is too small for addressable, fault-tolerant single-qubit operation. However, if the 1.5 T magnetic field additionally includes a g-factor Stark shift (see point 912), the combined g-factor and hyperfine Stark shift are large enough (5 MHz) to allow addressable, fault-tolerant qubit operation at 5 MV / m electric field. For the 4.61 nm

[110] 2P configuration (indicated by point 914), tight-binding simulations predict that the hyperfine Stark shift can be engineered to be orders of magnitude larger at 53 MHz, allowing qubit Rabi frequencies up to ≈5.3 MHz and within the surface code fault tolerance limit of 1%. Experiments also indicate Stark shifts for other 2P donor configurations, such as Figure 4D and Figure 5D The 0.77 nm

[110] (point 916), 0.86 nm

[130] (point 918) and 2.30 nm

[110] (point 920) configurations shown previously, respectively.

[0135] Although these configurations show larger hyperfine Stark shifts than the 1P donor, the 4.61 nm

[110] 2P configuration (point 914) is more optimal for large architectures because it can achieve larger Stark shifts and the Stark shift is more robust to manufacturing tolerances.

[0136] Figures 9B-9D The ESR spectrum of a 2P donor quantum dot and examples of Rabi oscillations of the target and spectator qubits are shown at a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz. Fig. 9A Here, the target qubit has been rotated from bottom to top with 99.98% fidelity (in 5 μs), while the probability that the spectator qubit is incorrectly rotated from bottom to top is ∼0.0015%.

[0137] Fig. 10A is a graph of qubit error as a function of peak offset (Stark offset) versus gate speed (Rabi frequency). Larger Stark offsets result in lower qubit addressability errors, with the optimal speed shown by the red dashed region. Fig. 10B The qubit error for a 110MHz Stark offset as a function of the Rabi frequency is shown in . For a 430kHz Rabi frequency, errors of <0.01% are possible, well below the 1% error threshold for surface codes.

[0138] Fig.11A The Stark shift as a function of electric field is shown for a 2P molecule with donors spaced 5.4 nm apart along the

[110] direction, for example. Each point is taken from a tight-binding simulation of this 2P donor configuration at different electric fields along the donor axis. At zero electric field, the Stark shift is zero because the electron spins are equally shared between the donors and the Stark coefficient is approximately linear. At zero electric field, the Stark coefficient is extremely large (84 MHz / MVm -1 ). By increasing the electric field, the electron spin becomes more localized at one of the donors. Above ±5 MHV / m, the Stark shift saturates to ±114 MHz and the Stark coefficient ≈ 0, since the electron is fully localized.

[0139] Although a large Stark coefficient is beneficial for qubit addressability, it may increase the dephasing of the qubits caused by charge noise. By performing simulations of charge noise in an example device, the sensitivity of electron spin coherence to charge noise can be estimated.

[0140] Fig. 11B is the charge noise-induced function of the electric field for a 2P donor configuration spaced 5.4 nm apart along

[110] . Curve 1104 is the standard deviation of the electron spin qubit energy fluctuations, which is obtained by fitting to Fig.11A The hyperbolic tangent function of the Stark shift data in is derived and multiplied by the standard deviation E of the fluctuating electric field obtained from the charge noise simulation. σx The quantum bit energy fluctuations caused by charge noise are largest where the Stark coefficient is largest, so Time is the smallest here. The dashed black line shows the threshold for charge noise to limit the qubit coherence time, since 270 μs is the longest measured coherence time for electron spins on a single phosphorus donor in silicon. Operating the electron spin qubit in the charge noise sweet spot of Stark shift saturation (above + / - 4.6 MV / m) should ensure that the quantum shift phase is not limited by charge noise.

[0141] Fig. 11C is The simulated ESR spectra of the electron spins on the 2P molecule initialized in the state under -5MV / m electric field (peak 1106) and 5MV / m (peak 1108). At -5MV / m, the electrons are mainly localized on the spin-down nuclei (see Fig.11E ), and the frequency of the ESR peak is lower. At +5MV / m, the electron spins are mainly localized on the spin-up nuclei (see Figure 11F), and the ESR peak is shifted upward by 114MHz. These provide two states for the electron spin qubit, where the -5MV / m state can be offset from the global ESR resonance frequency and the +5MV / m state can be in resonance, and vice versa.

[0142] Although the engineered qubits described herein refer to donor molecules, they are not limited to donor molecules. Instead, the systems and methods of the present disclosure can be used to create engineered qubits that include other multi-dopant molecules, such as multi-acceptor molecules. In such molecules, instead of confining a single electron, a single hole can be confined in a multi-acceptor molecule.

[0143] Furthermore, although the quantum processing systems described herein have been shown to have gate electrodes for controlling the respective qubits, these may not always be necessary. In other embodiments and examples, other control means may be used without departing from the scope of the present disclosure.

[0144] S53334180:AXD:ALK:glg

[0145] The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

[0146] As used herein, the term "comprise" and variations of the term, such as "comprising", "comprises" and "comprised", are not intended to exclude other additions, components, integers or steps, unless the context requires otherwise.

Claims

1. An engineered quantum processing element comprising: Semiconductor substrates; a dielectric material forming an interface with the semiconductor substrate; A dopant dot comprises a plurality of dopant atoms and one or more electrons / holes confined within the dopant dot, wherein a geometric configuration of the plurality of dopant atoms relative to the semiconductor substrate is engineered to achieve an optimal linear hyperfine Stark coefficient.

2. The engineered quantum processing element of claim 1, wherein: The distances between the plurality of dopant atoms and the orientations of the plurality of dopant atoms relative to each other and the semiconductor substrate are engineered to achieve an optimal linear hyperfine Stark coefficient.

3. The engineered quantum processing element according to claim 1 or 2, wherein: The distances between the plurality of dopant atoms and the orientations of the plurality of dopant atoms within the semiconductor substrate are engineered to achieve approximately tens of MHz / MVm or more -1 The linear hyperfine Stark coefficient of .

4. The engineered quantum processing element according to any one of claims 1 to 3, wherein: The dopant dots include two donor atoms.

5. The engineered quantum processing element according to any one of claims 1 to 3, wherein: The dopant dots include three donor atoms.

6. The engineered quantum processing element according to any one of claims 4 to 5, wherein: The donor atom is a phosphorus atom.

7. An engineered quantum processing element according to any one of claims 1 to 6, wherein: The distance between neighboring dopant atoms is up to 30 nanometers.

8. The engineered quantum processing element according to any one of claims 1 to 7, wherein: The distance between neighboring dopant atoms is up to 6 nanometers.

9. The engineered quantum processing element of claim 8, wherein: The distance between adjacent dopant atoms is between 3 and 5 nanometers.

10. The engineered quantum processing element of claim 9, wherein: The adjacent dopant atoms are positioned along a [110] crystal axis of the semiconductor substrate.

11. The quantum processing element of claim 10, having a Stark shift of approximately 105 MHz and an electric field of 5 MV / m.

12. The quantum processing element according to any one of claims 1 to 8, wherein: The distance between the dopant atoms is between 0.5 and 1 nanometer.

13. The quantum processing element according to claim 12, wherein: The dopant atoms are positioned along a [130] crystal axis of the semiconductor substrate.

14. A quantum processing system comprising a plurality of engineered quantum processing elements according to any one of claims 1 to 13.

15. A method for manufacturing an engineered quantum processing element, the method comprising: exposing a semiconductor substrate to atomic hydrogen H to form a H monolayer and passivate a surface of the semiconductor substrate; selectively desorbing H atoms from the passivated surface by applying an appropriate voltage and tunneling current to the STM tip, thereby forming a plurality of patches in the H monolayer; wherein the distances between the plurality of patches and the orientations of the plurality of patches along the direction of the semiconductor lattice are selected to achieve a large linear hyperfine Stark coefficient; as well as At least one donor atom is incorporated in each of the plurality of patches in the H monolayer to form a donor molecule.

16. The manufacturing method according to claim 15, further comprising: desorbing the hydrogen monolayer; A layer of the semiconductor is overgrown on the surface.

17. The manufacturing method according to any one of claims 15 or 16, wherein: Selectively desorbing H atoms further comprises: desorbing H atoms to create one or more patches, wherein the one or more patches are used to create one or more in-plane gates.

18. The manufacturing method according to any one of claims 15 or 16, further comprising: One or more gate electrodes are deposited over the locations of the donor atoms.

19. The manufacturing method according to claim 18, further comprising: A voltage is applied to the one or more gates to trap electrons in the donor molecules.

20. The manufacturing method according to any one of claims 15 to 19, wherein: The distance between the plurality of patches within the semiconductor substrate is engineered to achieve approximately tens of MHz / MVm or more -1 The linear hyperfine Stark coefficient of .

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