Operational quantum processing element

Abstract

An operational quantum processing element is disclosed. The operational quantum processing element includes a dopant dot embedded in a semiconductor substrate. A 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 an optimal linear hyperfine Stark coefficient. Additionally, aspects of the present disclosure are directed to methods of manufacturing such an operational quantum processing element.

Description

[Technical field]

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

[0002] Large-scale quantum processing systems are a promising technological revolution, with the potential to solve problems that are out of reach with classical machines. To date, several different structures, materials, and architectures have been proposed to implement quantum processing systems and create their basic units of information (quantum bits or qubits). A qubit can be understood as a quantum mechanical system that is encoded into two distinct energy levels.

[0003] Although semiconductor spin qubits have now reached a sufficiently high figure of merit to inspire error-correcting architectures for quantum information processing, there are still several outstanding challenges to be resolved before a viable quantum computing processor can be demonstrated in silicon.

[0004] However, several hurdles need to be overcome before such large-scale quantum computers can be commercially manufactured. One of these hurdles is the control of qubits. Several techniques have been proposed to control the state of qubits, but these techniques either do not scale effectively or result in faster decoherence. Manipulating spin-based qubits in semiconductors, and in particular performing fast operations on the spin states of qubits, is a key lever for building quantum gates. In particular, fast, individually addressable qubit operations are essential for scalable architectures.

[0005] Thus, 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 [Means for solving the problem]

[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, and a dopant dot comprising 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 with respect 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 operational quantum processing element, the method comprising: exposing a semiconductor substrate to atomic hydrogen H to form a monolayer of H to passivate a surface of the semiconductor substrate; selectively desorbing H atoms from the passivated surface by application of a suitable voltage and tunneling current to the STM tip to form a plurality of patches in the H monolayer, the distance between the plurality of patches and the orientation of the plurality of patches along a direction of the semiconductor lattice being selected to achieve a large linear hyperfine Stark coefficient; and incorporating at least one donor atom into each of the plurality of patches in the H monolayer to form a donor molecule.

[0008] The features and advantages of the invention will become apparent from the following description of embodiments thereof, given by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0009] [Figure 1A] 1 is a diagram illustrating an example of a spin qubit device 100 formed in a silicon substrate. FIG 1A is a top view of donor spin qubit device 100. FIG 1B is a diagram illustrating an example of a spin qubit device 100 formed in a silicon substrate. FIG 1A is a top view of donor spin qubit device 100. [Figure 1B] Figure 1 illustrates an example of a spin qubit device 100 formed in a silicon substrate. Figure 1B illustrates a cross-sectional side view. [Figure 2A]FIG. 2A shows a plot of the ESR spectral profile or resonance profile of a qubit excited by a Rabi frequency of 1 MHz. [Figure 2B] FIG. 2B shows a plot of spectator qubit error as a function of frequency detuning from the target qubit resonance. [Figure 3A] FIG. 3A is a diagram illustrating an example of a manipulation qubit device. [Figure 3B] FIG. 3B is a diagram showing another example of a manipulation qubit device. [Figure 4A] FIG. 13 shows the hyperfine Stark shift for an unmanipulated 2P donor dot system. [Figure 4B] FIG. 13 shows the hyperfine Stark shift for an unmanipulated 2P donor dot system. [Figure 4C] FIG. 13 shows the hyperfine Stark shift for an unmanipulated 2P donor dot system. [Figure 4D] FIG. 13 shows the hyperfine Stark shift for an unmanipulated 2P donor dot system. [Figure 5A] FIG. 1 shows the hyperfine Stark shifts for engineered 2P donor molecules of the present disclosure. [Figure 5B] FIG. 1 shows the hyperfine Stark shifts for engineered 2P donor molecules of the present disclosure. [Figure 5C] FIG. 1 shows the hyperfine Stark shifts for engineered 2P donor molecules of the present disclosure. [Figure 5D] FIG. 1 shows the hyperfine Stark shifts for engineered 2P donor molecules of the present disclosure. [Figure 6A] FIG. 1 shows the Stark coefficient as a function of donor interatomic distance and donor interaxis. [Figure 6B] FIG. 1 shows the Stark shift as a function of donor interatomic distance and donor interaxis. [Figure 6C] FIG. 1 shows electronic wave functions for 2P donor configurations along the

[0100] and

[0110] crystallographic directions. [Figure 7A]FIG. 1 shows an STM microscope image of the device. [Figure 7B] FIG. 3D rendering of STM topography showing the quantum dot on the left after P doping. [Figure 7C] A top view showing the positions of three donor atoms in the left quantum dot in a silicon crystalline substrate. [Figure 7D] FIG. 1 is a schematic energy diagram showing an electron-nuclear spin system. [Figure 7E] FIG. 1 shows the measured NMR spectrum for a 2P donor molecule. [Figure 7F] FIG. 1 shows the measured ESR spectrum for a 2P donor molecule. [Figure 8] 1 is a flow diagram illustrating an example method according to an aspect of the present disclosure. [Figure 9A] FIG. 13 shows a plot illustrating spectator qubit errors. [Figure 9B] 9B-D show example ESR spectra for a 2P donor quantum dot and the Rabi oscillations of the target and spectator qubits for a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz. [Figure 9C] 9B-D show example ESR spectra for a 2P donor quantum dot and the Rabi oscillations of the target and spectator qubits for a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz. [Figure 9D] 9B-D show example ESR spectra for a 2P donor quantum dot and the Rabi oscillations of the target and spectator qubits for a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz. [Figure 10A] FIG. 10A shows a plot of qubit error as a function of peak shift (Stark shift) and gate speed (Rabi frequency). [Figure 10B] FIG. 10B shows the qubit error for a Stark shift of 110 MHz as a function of the Rabi frequency. [Figure 11A] FIG. 11A shows the Stark shift as a function of electric field for an example 2P molecule with donors separated by 5.4 nm along the

[0110] direction. [Figure 11B] FIG. 11B shows a plot of T2* time due to charge noise as a function of electric field for a 2P donor configuration separated by 5.4 nm along

[0110] . [Figure 11C] FIG. 11C shows the electric field at −5 MV / m (peak 1106) and at 5 MV / m.

number

[0010] The reference to any prior art in the specification is not an admission or suggestion that this prior art forms part of the common general knowledge in any jurisdiction, or that this prior art would be understood by, considered relevant, and / or could reasonably be expected to be combined with other prior art by a person skilled in the art.

[0011] Overview One type of quantum computing system is based on the spin states of individual quantum processing elements, which may be localized electron spins, hole spins, or nuclear spins within a semiconductor chip. These electrons, holes, and / or nuclear spins are confined either in gate-defined quantum dots, called quantum bits or qubits, or on donor or acceptor atoms positioned within a semiconductor substrate.

[0012] Donor spin qubits in silicon are a promising platform for a universal quantum computer because they have the advantages of long coherence times and high-fidelity readout, single- and two-qubit gates, and scalability.

[0013] FIG. 1 shows an example of a spin qubit device 100 formed in a silicon substrate. FIG. 1A shows a top view of donor spin qubit device 100, and FIG. 1B shows a cross-sectional side view. Donor spin qubit device 100 may be used for quantum computers that include a plurality of these qubits. As shown in the drawing, qubit device 100 is formed as a structure including a semiconductor substrate 102 and a dielectric 104. In this example, the substrate is 28 silicon and the dielectric is silicon dioxide. An interface 107 is formed where substrate 102 and dielectric 104 meet. In this example, interface 107 is a Si / SiO2 interface. To form a qubit, a donor atom 108 is placed in substrate 102 inside region 109 under gate 106. Donor atom 108 may 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, qubit device 100 includes a single atom 108 embedded in a silicon crystal. However, the methods described herein may also be applied to qubit devices 100 that include clusters of two or more embedded atoms 108 .

[0014] The device 100 is then loaded with an electron 120 by the 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 the use of a potential well that is naturally formed by the coupling of a donor nucleus with an electron spin.

[0015] The gate electrode 106 is positioned over the region 109 and is operable to interact with the donor atoms 108. For example, the gate electrode 106 may 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. The electron wavefunction 121 is mediated by a local electric field applied to the gate electrode 106. For example, the local electric field applied to the gate electrode 106 may repel the electron wavefunction 121 away from or attract it to the donor 108.

[0016] In particular, AC electric fields can be used to control the quantum state of qubits associated with the nuclear spins, and furthermore, AC electric fields have a synergistic effect with an applied oscillating magnetic field.

[0017] A key component of a scalable quantum computer is the ability to individually address qubits to apply quantum gates. However, qubit addressability has been a challenge for donor spin qubit devices 100 because gates 106 have typically been implemented either via electron spin resonance (ESR) for nominally identical electron spins or nuclear magnetic resonance (NMR) for nominally identical nuclear spins, requiring a mechanism for distinguishability.

[0018] The addressability of individual donor qubits in silicon was first proposed through the donor Stark shift using the hyperfine or g-factor Stark shift of the qubit resonance. The Stark shift is the splitting of the degenerate spin states in the presence of an external electric field, while the qubit resonance is related to the energy gap separating 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. Any change in the g-factor therefore changes the qubit resonance. The donor Stark shift is achieved by the application of a local electric field. For example, the application of an electric field to the gate electrode 106 pulls the electron wavefunction 121 away from the donor 108. This 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 electron's spin momentum). This in turn affects the electron spin energy splitting and therefore the qubit resonance frequency.

[0019] In one of the first proposed methods, the Stark shift was implemented by applying a voltage to the gate 106 to create the required local electric field at the donor site 109. However, early experiments with single donors revealed that the Stark shift was much smaller than expected. The measured single-donor Stark effect was -1 ) are relatively small compared to the ESR linewidth, limiting the speed of single-qubit gate operation to the point where the gate fidelity is below the surface code error threshold (0.6-1%). Thus, these devices involve a trade-off between the speed and fidelity of the single-qubit gate: fast qubit gates result in substantial power broadening of the ESR peak linewidth, inducing interference errors with neighboring qubits, whereas slower driving results in qubit decoherence.

[0020] 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 oscillation between the low and high energy states of the qubit, and the Rabi frequency is the frequency at which the qubit oscillates between those two states. For example, it is the frequency at which an electron spin qubit oscillates between the spin-down state |↓〉 and the spin-up state |↑〉.

[0021] In some examples, Gaussian-shaped Rabi pulses may be used to improve qubit addressability because they have higher frequency selectivity compared to other pulse shapes, such as rectangular-shaped Rabi pulses.

[0022] FIG. 2A shows a plot 200 of the ESR spectral profile or resonance profile of a qubit excited by a 1 MHz Rabi frequency, a drive strength that can typically be obtained in an ESR qubit experiment. The x-axis shows the ESR frequency in MHz, and the y-axis shows the probability of electron spin-up. 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 is set to perform a π rotation of the qubit at zero frequency detuning. Here, frequency detuning is defined as the frequency shift between the target qubit, i.e., the qubit that is addressed, and the spectator qubit, i.e., the neighboring qubit that is not addressed.

[0023] For the example Rabi frequency with a rectangular pulse shape, the resonance peak exhibits significant power broadening with a full-width-half-maximum (FWHM) of about 1 MHz. For the example Rabi frequency with a Gaussian shape, the FWHM resonance is about 60 kHz. Thus, the linewidth of the resonance profile 204 for the Gaussian shaped Rabi pulse is smaller than the linewidth of the resonance profile 202 for the rectangular shaped Rabi pulse. Furthermore, the rectangular pulse induces significantly greater power broadening of the ESR peak than the Gaussian pulse.

[0024] 2B is a plot 220 of spectator qubit error as a function of frequency detuning from a target qubit resonance. The x-axis shows the spectator qubit frequency detuning in MHz, which 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.

[0025] Error profile 222 shows the error in a spectator qubit as a function of detuning from the target qubit resonance for a rectangular shaped Rabi pulse with a Rabi frequency of 1 MHz. Error profile 224 shows the error in a spectator qubit as a function of detuning from the target qubit resonance for a Gaussian shaped Rabi pulse with a Rabi frequency of 1 MHz. To achieve less than 1% qubit error for a rectangular shape (ignoring oscillations in the spectrum) requires a frequency shift of about 10 MHz, which reduces to about 600 kHz for a Gaussian shape. However, it is desirable to achieve a qubit error rate << 1%. To achieve this, even with Gaussian pulse shaping the spectator qubit would need to be detuned >> 1 MHz from the target qubit, which is not feasible.

[0026] Another approach to addressability is to ensure that each qubit has an inherently different resonance. To this end, multi-donor quantum dots can be used such that different quantum dots have different donor numbers and donor configurations. This approach does not rely on the Stark shift. Instead, this approach relies on different donor numbers and configurations that give rise to different electron spin resonances. While low errors are possible for some multi-donor quantum dots alone, it may be difficult to scale this approach to a large number of qubits due to the finite number of multi-donor dot configurations. In some cases, the error rate for this approach is about 10 for a two-electron spin qubit system consisting of 1P and 2P. -4 The error rate is calculated.

[0027] To overcome one or more of the problems identified above, aspects of the present disclosure provide a new manipulation qubit that combines the addressability method originally proposed with the multi-donor dot proposal. In particular, the manipulation qubits of the present disclosure include multiple donor atoms and a single electron shared between the donor atoms. These manipulation qubits extend the fidelity and speed of the qubit by manipulating a larger Stark coefficient in a pair of quantum dots. Furthermore, in a multi-donor quantum dot system, some aspects of the present disclosure may use the same donor configuration for each quantum dot. In such a system, a qubit may be uniquely addressed by applying a local electric field such that a Stark shift is generated in only that qubit. Another example may use different donor configurations for different multi-donor quantum dots in a quantum processing system.

[0028] The manipulation qubits of the present disclosure can be used as electron spin qubits, where quantum information is encoded in the spin of an electron shared between donor atoms. The manipulation qubits can also be used as nuclear spin qubits, where quantum information is encoded in the spin of any one of the donor atoms.

[0029] In particular, aspects of the present disclosure enable three types of qubit addressability: Addressing electron spin qubits by manipulating quantum processing elements with large Stark shifts. To avoid frequency concentration in the global field of large-scale devices, electron spin qubits are addressed by operating quantum processing elements with multiple donors that contribute more frequencies to the same electron. Addressing nuclear spin qubits using their ESR (electron spin resonance) peak for both readout and control.

[0030] FIG. 3A shows an example of an operational qubit device 300. To form the qubit device 300, two donor atoms 302A and 302B are placed in 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. The silicon substrate 304 is covered with a barrier material / dielectric 306, such as silicon dioxide. Additionally, a gate 308 and an antenna 310 may be located on top of the dielectric 306 in the region above the quantum dot 301. A voltage may be applied to the gate 308 to confine an electron 320 within the quantum dot 301. A magnetic field may be applied via the antenna 310 to control the electronic and nuclear spin states within the quantum dot 301. The electron 320 may be shared by the two donor atoms 302A, 302B.

[0031] FIG. 3B shows another example of an operational qubit device 350. It is similar to the device shown in FIG. 3A. The only difference is the placement of the gate. In FIG. 3A, gate 308 was shown as being placed on top of dielectric 306. In this example, one or more gates 312 are located in the semiconductor substrate 304. In some embodiments, one or more gates 312 are placed in the same plane as quantum dot 301. This in-plane gate 312 may be connected to the surface 306 of the substrate through a metal via (not shown). A voltage may be applied to the gate electrode 312 to confine one or more electrons 320 within the quantum dot 301.

[0032] In some devices, the in-plane gate electrode 312 is made of phosphorus-doped silicon (doping density of about 0.25 ML).

[0033] A large hyperfine Stark coefficient can be observed in such a manipulation qubit device 300, 350. This large hyperfine Stark coefficient results from the larger hyperfine coupling and electric dipole moment in the 2P donor dot compared to a single donor.

[0034] The quantum dot 301 with a single trapped 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.

[0035] 3A and 3B show a single quantum dot, it will be appreciated that this is by way of example only, in some embodiments, multiple quantum dots 301 and / or 350 may be arranged in a two- or three-dimensional structure to create a large-scale quantum processor.

[0036] 3A and 3B show a 2P donor molecule, the manipulation qubits of the present disclosure are not so limited. Instead, the manipulation qubits may include donor molecules that include three or more donor atoms.

[0037] Embodiments of the present disclosure manipulate 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, large linear hyperfine Start coefficients of ∼70 MHz / MVm can be achieved (assuming a Gaussian pulse shape), enabling single-qubit gate fidelity of >99.9998% for 2pi rotation gates with gate operation times of ∼0.5 μs.

[0038] These and other advantages of the qubit devices and control / operation techniques disclosed herein are described in detail in the following sections.

[0039] The position and orientation of the donor affect the Stark shift. As mentioned above, embodiments of the present disclosure relate to engineering the optimal Stark coefficient in mP donor molecular systems, such as 2P or 3P molecular systems. A large hyperfine Stark coefficient results from a larger hyperfine coupling and electric dipole moment in the donor molecule compared to single donor systems. The hyperfine Stark coefficient is a measure of the change in the hyperfine interaction between the donor electron and the nucleus due to an electric field. The unit of the hyperfine Stark coefficient is MHz / MVm-1.

[0040] In particular, the present inventors have demonstrated that specific positions and orientations of donor atoms within the donor molecule result in optimal Stark shifts for controlling and addressing these nuclear spin qubits.

[0041] 4A-4D show the hyperfine Stark shifts for an unmanipulated 2P donor dot system, and FIGS. 5A-5D show the hyperfine Stark shifts for engineered 2P donor molecules of the present disclosure.

[0042] In particular, FIG. 4A shows the electron spin resonance (ESR) spectrum for an unengineered 2P donor dot in native silicon with three resonant peaks. The x-axis shows the ESR frequency in GHz, and the y-axis plots the fraction of spin-up. Additionally, the nuclear spin states

[0043]

number

[0044] denote the left and right nuclear spins, respectively, of the two donor atoms in the dot, where the up and down arrows correspond to the up and down nuclear spin states of the donor atoms. In a 2P donor dot system, the donor atoms are sometimes called P1 and P2, respectively.

[0045] The lowest frequency peak in Figure 4A is

[0046]

number

[0047] is due to the two phosphorus donor nuclear spin states, while the highest frequency peak is

[0048]

number

[0049] belongs to a nuclear spin state. The middle peak is twice as high as the lowest and highest frequency peaks, and

[0050]

number

[0051] The nuclear spin states are degenerate within the peak linewidth with a FWHM of 72 MHz.

[0052] FIG. 4B shows the corresponding energy diagram of all spin states for an example 2P system. The four lower energy states correspond to the following all spin states:

[0053]

number

[0054] The four upper energy states correspond to the following total spin states:

[0055]

number

[0056] where

[0057]

number

[0058] represent the nuclear down and up spins, respectively, and ↓ and ↑ represent the electron spin down and spin up, respectively. Also shown in Figure 4B are the ESR resonance frequencies between the nuclear spin states in this example of an unmanipulated 2P donor dot.

[0059]

number

[0060] The degeneracy between the nuclear spin states is brought about by the electron wavefunctions overlapping equally on the two donors. The electric field in the device can destroy the degeneracy through the Stark effect by shifting the electron wavefunction closer to one of the donors. However, the Stark coefficient for this unmanipulated 2P quantum dot configuration is small (~1.7 MHz / MVm-1) and the subsequent Stark shift could not be measured. In this system, the nuclear spin and the electron spin cannot be addressed because the Stark shift is too small. Here

[0061]

number

[0062] Since the nuclear spin states are degenerate, all spin states

[0063]

number

[0064] is degenerate, and similarly all spin states

[0065]

number

[0066] is degenerate.

[0067] Figure 4C shows a schematic of the electronic wavefunction (blue / yellow ovals) across two phosphorus donor atoms P1 and P2. At zero electric field along the donor separation axis, the electron 20 is shared equally between donors P1, P2 (blue oval), whereas in the electric field used in the measurements (~4.3 MV / m) the electronic wavefunction is slightly more localized towards donor P1 (yellow oval), resulting in a small <7 MHz hyperfine Stark shift.

[0068] FIG. 4D shows the most likely donor configuration for this unengineered 2P quantum dot device that would produce the ESR spectrum shown in FIG. 4A. Here, the two phosphorus donors (402 and 404) are separated by 0.77 nm along the 0110 crystallographic axis, which corresponds to one unit on the x-axis, one unit on the y-axis, and zero units along the z-axis, respectively. For this example of an unengineered 2P molecule along the 0110 axis, the electric field available in the device (about 5.4 MV / m) would allow a maximum Stark shift of >7 MHz. However, because this field was not aligned directly along the donor axis but shifted by about 40°, the Stark shift would be smaller, about 5 MHz. This small Stark shift is insufficient to exceed the 72 MHz peak linewidth observed in these native silicon devices, so no Stark shift is observed in the ESR spectrum.

[0069] 5A is an ESR spectrum for an operational qubit device according to an embodiment of the present disclosure. The x-axis shows the ESR frequency in GHz, and the y-axis plots the spin-up fraction. For this operational qubit device, the ESR spectrum shows four resonant peaks, which are

[0070]

number

[0071] for each of the nuclear spin states, where

[0072]

number

[0073] The nuclear spin states are not degenerate. Because of this, the engineered 2P quantum dot has four unique electron spin resonances. The four ESR peaks may be fitted to a Gaussian function to extract a FWHM of 44 MHz as a result of a ±20 MHz chirp. This means that a so-called adiabatic inversion pulse can be used to measure the ESR spectrum, where the ESR frequency is swept linearly from -20 MHz to +20 MHz with respect to the carrier frequency.

[0074] The four resonances are also consistent with the 2P donor number, since each nuclear spin state (four in total for 2P) has a unique hyperfine interaction with the electron spin. Since the spectrum is centrosymmetric, the splitting between the first and second peaks in Figure 5A is the same size as between the third and fourth peaks. Thus, two hyperfine interactions can be extracted from the spectrum A1 = 189 MHz and A2 = 83 MHz, 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 is the time-dependent shift of the donor nuclear spins.

[0075]

number

[0076] This breaks the degeneracy between the states, giving rise to the four ESR transitions shown in FIG. 5A.

[0077] Stark shift

[0078]

number

[0079] Having broken the degeneracy of states, the four nuclear spin sates may now be addressed individually.

[0080]

number

[0081] Each of may be addressed by its corresponding individual ESR frequency.

[0082]

number

[0083] The ESR frequency for each of the nuclear spin states is shown on the x-axis of FIG. 5A.

[0084] Furthermore, an electron qubit may also be addressed to this donor configuration. The nuclear spins are in a degenerate state

[0085]

number

[0086] When an electric field is applied, the Stark shift makes these states non-degenerate, so that the ESR frequency now differs from that of non-Stark shifted qubits. Faster electronic addressability may be achieved with a very large Stark shift. This is because

[0087]

number

[0088] This effectively results in a large ESR frequency difference between the nuclear spin states. By maximizing the size of the Stark shift, the addressability of the electron spin for the 2P system is optimized.

[0089] In some embodiments, a plurality of manipulated multi-donor quantum dots are provided. In such embodiments, each of the multi-donor quantum dots may have a different number of donor atoms. In some embodiments, each of the multi-donor dots may have a different number of donor atoms. In other embodiments, the multi-donor quantum dots may have a combination of the same or different numbers of donor atoms. An electronic qubit of one of the plurality of multi-donor quantum dots may be addressed by applying a unique ESR frequency to that electronic qubit.

[0090] Figure 5B shows the relative energies of all the spin states and the ESR transitions between them. Again, the four lower energy states correspond to the following all spin states:

[0091]

number

[0092] The four upper energy states correspond to the following total spin states:

[0093]

number

[0094] Since there exists an optimal Stark shift for this example of an operational quantum processing element,

[0095]

number

[0096] The state of is lifted.

[0097] Figure 5C shows a schematic diagram of the electronic wave function (blue / yellow ovals) across two phosphorus donor atoms P1 and P2. At zero electric field along the donor separation axis, the electrons are shared equally between the donors (blue oval), whereas the electronic wave function at the electric field used in the measurements (~3.5 MV / m) is much more localized towards donor P1 (yellow oval), resulting in a large hyperfine Stark shift. The larger Stark shift in Figure 5C compared to Figure 4C is a result of the different donor configurations in the manipulated molecular qubits of the present disclosure.

[0098] In particular, the donor configuration indicates the donor separation and the orientation of the donors with respect to a crystal axis. In some examples, the donors may align their orientation with respect to a crystal axis. For example, a pair of adjacent donor atoms may be positioned along a crystal axis, such as

[0110] . In other examples, adjacent donors may not be aligned with respect to a crystal axis. Instead, the adjacent donors may be positioned at any position within the crystal lattice structure.

[0099] Figure 5D shows the most likely donor configuration for this example of an engineered 2P quantum dot device that would produce the ESR spectrum shown in Figure 5A and be associated with a total hyperfine coupling A1+A2. Here, the two donor atoms (502 and 504) are separated by 0.86 nm along the

[0130] crystallographic axis, which results in a total hyperfine interaction of 276 MHz. The theoretically determined value for the total hyperfine interaction of 276 MHz is in good agreement with the experimentally determined total hyperfine interaction of 272 MHz.

[0100] Table 1 below shows the different donor configurations with the closest match to the total hyperfine values ​​obtained from the ESR spectra, along with the values ​​of the linear Stark coefficient. From Table 1, it may be observed that the donor configuration along the

[0130] crystal axis has the largest Stark coefficient of 11.2 MHz / MVm-1, a factor two to three larger than most other configurations. This configuration corresponds to the configuration shown in FIG. 5D, which is an example of a donor configuration in which a donor molecular qubit can be engineered to produce a large Stark shift.

[0101] All other configurations would require unrealistic electric fields (>10 MV / m, shown in the last column of Table 1) to achieve the large Stark shifts observed and / or have larger differences between the predicted total hyperfine splitting and the experimental value.

[0102] [Table 1]

[0103] The inventors of the present disclosure have demonstrated that the precise 2P donor configuration as well as the orientation and size of the electric field play important roles in determining the size of the hyperfine Stark shift.

[0104] The ability to manipulate these larger hyperfine Stark shifts, beyond 110 MHz, may be used for faster fault-tolerant single-qubit gates addressable by global ESR fields. As shown in the ESR spectra of Figures 4A and 5A, initially the hyperfine Stark shifts are degenerate.

[0105]

number

[0106] Separating the peak into two non-degenerate peaks, while

[0107]

number

[0108] The nuclear spin state is not affected by the hyperfine Stark shift. It is therefore important to initialize the nuclear spins to the antiparallel state in order to control the ESR frequency through the hyperfine Stark shift. The phosphorus nuclear spin state in silicon is very stable, with a lifetime on the order of minutes, whereas operations on the electron spins can be performed on the order of microseconds. Thus, many operations can be performed on the electron spins without the need to reinitialize the nuclear spins.

[0109] 6A and 6B show the simulated hyperfine Stark shift for a single electron 120 in various 2P donor molecular configurations. In particular, FIG. 6A shows the Stark coefficient as a function of donor interatomic distance and donor interaxis, and FIG. 6B shows the Stark shift as a function of donor interatomic distance and donor interaxis.

[0110] The simulations in Figures 6A and 6B use an atomistic tight-binding model (nearest-neighbor only interaction model) to explore all 2P configurations in an 8a0 by 8a0 box in the device plane, which contains a total of 144 configurations (with 80 unique configurations due to symmetry about the <0110> axis), where a0 is the silicon atomic lattice constant 0.543 nm, and all 2P donor combinations within the domain of 8 x 8 atomic lattice sites were explored.

[0111] The x-axis in Figures 6A and 6B shows the distance between the two donor atoms in units of the silicon atomic lattice constant a0. The y-axis in Figure 6A shows the simulated Stark coefficient in units of MHz / (MV / m). The size 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. Furthermore, the Stark coefficient for Figure 6A is obtained at an electric field strength of 0 MV / m, whereas the Stark shift in Figure 6B is for an electric field of 5 MV / m. Both figures assume that the electric field is applied (θ=0°) along the inter-donor axis via one or more gates 308, 312. This inter-donor axis is the axis connecting the first donor with the second donor. Stark shift = Stark coefficient × electric field.

[0112] In this simulation, an electric field is applied (θ=0°) along the inter-donor axis via one or more gates 308, 312. This inter-donor axis is the axis connecting the first donor with the second donor.

[0113] Furthermore, FIG. 6A shows the simulation results for the Stark coefficient as a function of donor position in the XY plane, where the first donor is located at (0,0) (see 502) and the second donor is located at a distance r along the

[0100] ,

[0110] ,

[0120] , and

[0130] crystal directions. For each crystal axis, the Stark coefficient increases due to the increase in the electron-donor dipole moment with donor separation, resulting in a higher sensitivity to electric fields. Valley interference along the

[0110] and

[0130] directions causes oscillations of the Stark coefficient along these directions. In addition, it is observed that the presence of valley interference results in a non-monotonic increase in the linear hyperfine Stark coefficient. Along these crystal directions, the electron exists as a superposition over both donors, and its wave function has oscillations due to the presence of the underlying silicon crystal lattice. Here, the valleys indicate energy minima in the conduction band. There are six degenerate minima, also called valleys, in silicon, which for a single donor electron is an equal superposition over the six valleys. For two closely spaced donors, the electron wavefunction overlaps with both donors. The valley components of the electron wavefunction from each donor can interfere with each other constructively or destructively, changing the overall wavefunction depending on the exact donor separation and crystal orientation.

[0114] FIG. 6C shows the electronic wavefunctions for 2P donor configurations along the <0100> and <0110> directions to further illustrate valley interference. Along the <0100> (and equivalent) directions, the superposition of electronic wavefunctions constructively interferes with the separation between the 2P donors. However, when the donors are separated along the <0110> crystal direction, destructive interference can occur for a particular donor separation. In particular, both the X and Y valleys cause constructive and destructive interference of the electronic wavefunctions as a particular donor position changes, causing oscillations of the hyperfine Stark coefficients. This anisotropy of the electronic wavefunction interference comes from the anisotropy of the silicon effective mass, where each valley orbit has a smaller wavefunction envelope along the longitudinal direction and a larger radius along the lateral direction. This valley interference of the electronic wavefunctions can couple through the electron-donor dipole moment and the energies of the electronic antibonding states to produce oscillations of the hyperfine Stark coefficients in the

[0110] and

[0130] directions from their monotonic trends.

[0115] Figure 6B is a plot of the Stark shift for different 2P configurations for an electric field of 5 MV / m along the donor separation axis. The y-axis in this plot shows the Stark shift in MHz. The first donor is located at (0,0) and the second donor is positioned at a distance r along the

[0100] ,

[0110] ,

[0120] , and

[0130] crystallographic directions.

[0116] The shaded region 604 in FIG. 6B shows 2P donor configurations with a Stark shift of 110±5 MHz. For each configuration, this occurs when the second donor is located more than 8.5a0 (approximately 4.6 nm) away from the first donor. This result shows that the hyperfine Stark shift in 2P donors when separated by more than 4.6 nm is insensitive to dopant positioning along the crystal lattice. These donor configurations are easily patterned within ±1 lattice site accuracy of STM lithography. Furthermore, 2P donor configurations with smaller donor-to-donor separations show a larger variation in the Stark shift for an electric field of 5 MV / m because the size of the Stark shift is not limited by the total hyperfine interaction and is therefore more susceptible to variations in the hyperfine Stark coefficient.

[0117] As can be seen in Figure 6A, the hyperfine Stark coefficients for donor separations less than 2a0 ≈ 1 nm are generally limited to about 1 MHz / MVm-1 for most interdonor axes, which is comparable to the Stark shifts observed in single-donor systems (e.g., as shown in Figure 1). In contrast, a 2P donor configuration separated by 1.58a0 (0.86 nm) along the

[0130] direction has a linear hyperfine Stark coefficient of 11.2 MHz / MVm-1. This hyperfine Stark coefficient, which is 10 times larger for the same donor separation along a different crystallographic direction, is due to the presence of valley interference mentioned above.

[0118] However, this is not just a matter of inter-donor crystallographic directions, but also of inter-donor separation: extending the donor separation by a few lattice sites beyond 2a0 when viewed along the

[0110] and

[0120] directions results in a linear Stark coefficient higher than 70 MHz / MVm-1.

[0119] Such large zero-field linear Stark coefficients can result in a regime in which the Stark shift is limited by the size of the total hyperfine coupling due to relatively small electric fields. The total hyperfine coupling is maximum (679 MHz) for the 0.5a02P configuration (closest possible donor separation) and drops off rapidly toward about 110 MHz with increasing donor separation. For some example devices, an electric field of 5 MV / m is typically achievable, and for donor configurations with separations greater than about 8.5a0 (4.6 nm), the maximum Stark shift of these devices becomes limited by the total hyperfine interaction at this electric field.

[0120] Thus, by targeting the 6a0

[0110] 2P configuration, it is possible to engineer a hyperfine Stark shift of 105 MHz within a 7.6% tolerance due to the ±1 lattice site fabrication uncertainty. In particular, the 6a0

[0110] configuration has the second phosphorus donors separated by 6 lattice constants (a0) in the x and y directions. Since a0=0.543 nm, this translates to a separation of 4.6 nm along the

[0110] or about 8.5a0 separation along the

[0110] in atomic lattice units. This is just within region 604 in FIG. 6B. Furthermore, the 2P donor configuration with the smaller separation exhibits a larger variation in the Stark shift at an electric field of 5 MV / m because the total hyperfine interaction is larger, making the size of the Stark shift more sensitive to variations in the hyperfine Stark coefficient.

[0121] It is important to note that although the simulations in Figures 6A and 6B restricted the positions of the second donors to be along the

[0100] ,

[0110] ,

[0120] , and

[0130] crystallographic directions, the second donors may occupy any other lattice site or lattice orientation.

[0122] 7A-E show a 3P donor quantum dot system in which the donor molecule contains three donor atoms. In particular, FIG. 7A shows an STM microscope image of a device 700 containing a left quantum dot 702 and a right quantum dot 704 in isotopically pure silicon-28 with 120 ppm silicon-29. The quantum dots 702A and 702B may be tunnel-coupled to a charge sensor 706 (e.g., a single-electron transistor SET) and an electron reservoir 608 to load electrons onto the donor dots. 720 shows a magnified portion of the device 700 with the left (L) and right (R) quantum dots shown 10 nm apart. The left quantum dot 702 is an engineered quantum dot according to an embodiment of the present disclosure and contains three donor atoms. The left quantum dot 702 is an engineered 3P quantum dot. In this example, the right quantum dot 704 may be a manipulated dot or a conventional dot without departing from the scope of the present disclosure. The device 700 also includes gates 610A, 610B, and 610C, which may be used to control the electrochemical potential of the donor dots 704 and 706, while the SET gate 706 is primarily used to control the electrochemical potential of the SET. Image.

[0123] Figures 7B and 7C are schematic diagrams depicting a 3P donor system with one electron trapped in it. 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 an STM topography showing the left quantum dot after P doping, and Figure 7C is a top-view image showing the positions of the three donor atoms in a silicon crystalline substrate.

[0124] In this example, two donors (P1 and P2) are positioned along a crystal axis and separated by a distance along that axis. A third donor (P3) is positioned on another crystal axis and separated by a first distance from P1 and a second distance from P2. In some embodiments, the distance from P3 to each of P1 and P2 may be the same. The geometric orientation of the three donors in a 3P system includes the relative distances between the donors and the angles between the donors. Here, the orientation of the donor molecules is defined by the relative positions of the three donors.

[0125] FIG. 7D is a schematic energy diagram of an electron-nuclear spin system. Different Zeeman and hyperfine couplings for different spin configurations result in energy level splitting. The arrows indicate

[0126]

number

[0127] corresponds to the transition of

[0128] Figures 7E and 7F show the measured NMR and ESR spectra, respectively. These are the frequencies that allow the nuclei or electron spins to be individually addressed. The NMR spectrum has six peaks corresponding to a single nuclear spin flip in each electron spin state (indicated by the curved arrows in Figure 7D).

[0129]

number

[0130] Only the transition from is shown. Furthermore, 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. This spectral resolution does not allow for the observation of splitting due to nuclear-nuclear interactions. The ESR spectrum is annotated in the figure (indicated by vertical arrows in FIG. 7D) 2 3It is characterized by eight peaks corresponding to transitions between the =8 possible nuclear spin configurations.

[0131] Creation of 2P donors in specific configurations Once the donor configuration for the optimal Stark shift for addressing the nuclear spin qubit or electron spin qubit has been determined, the donor quantum dot qubit can be created. In one example, the Stark shift values ​​for different donor numbers and configurations (separation distances and orientations) can be determined. These values ​​may be stored in a lookup table or database. Depending on the type of addressability required and the corresponding optimal Stark shift value desired, a lookup in the lookup table / database may be performed to identify the number of donor atoms and their configuration. This information can then be used to operate the quantum processing device. In particular, the fabrication method according to aspects of this disclosure allows for precise placement of donor atoms in a silicon substrate to create an operation qubit.

[0132] FIG. 8 shows a flow diagram illustrating an example of a method 800 for operating a qubit device (eg, including multiple 2P molecules 300) with an optimal Stark shift for addressability according to an embodiment of the present disclosure.

[0133] First, a clean 2 × 1 surface of Si is prepared by heating it to near its melting point in ultra-high-vacuum (UHV). The surface has 2 × 1 unit cells and consists of rows of σ-bonded Si dimers, with the remaining dangling bonds on each Si atom forming weak π bonds with the Si atom of the other dimer containing it.

[0134] Next, in step 802 (i.e., monohydride deposition), the clean Si 2×1 surface is exposed to atomic H to break the weak Si π bonds and allow H atoms to bond with the Si dangling bonds. Under controlled conditions, a monolayer of H can be formed with one H atom bonded to each Si atom, filling the reactive dangling bonds and effectively passivating the surface.

[0135] Next, in step 804 (ie, hydrogen lithography), the STM tip is used to selectively desorb H atoms from the passivated surface by application of appropriate voltages and tunneling currents to form a pattern in the H resist.

[0136] It will be appreciated that H atoms can be desorbed from precise locations and in precise directions to position the donor molecule at precise locations to achieve a high Stark shift in the presence of an electric field. For example, if a donor molecule is to contain 12 lattice sites or two donor atoms spaced 4.6 nm apart along the

[0110] direction, one may use the STM tip to desorb six hydrogen atoms at one location along the row of dimers, and then desorb six additional hydrogen atoms along the same row of dimers, spaced 4.5 nm from the first location.

[0137] This process is repeated to create locations for other donor molecular sites, in this manner exposing areas of bare reactive Si atoms along the dimer rows, which then allow for the adsorption of reactive species directly onto the Si surface.

[0138] Returning to FIG. 8, in step 806 (i.e., PH3 dosing), phosphine (PH3) gas is introduced into the vacuum system through a controlled leak valve connected to a specially designed phosphine microdosing system. The phosphine molecules bind strongly to the exposed Si surface through holes in the hydrogen resist. As mentioned above, at a particular donor site, the phosphine molecule may bind to any one of the exposed silicon dimers.

[0139] Subsequent heating of the STM-patterned surface for crystal growth causes dissociation of the phosphine molecules, resulting in the incorporation of P into the exposed layer of Si. It is therefore the exposure of the STM-patterned H-passivated surface to PH that is used to generate the required donor molecules.

[0140] The hydrogen may then be desorbed in step 808, after which silicon may be blanket grown on the surface at room temperature in step 810. An alternative is to grow silicon directly through the hydrogen layer. The surface is then rapidly annealed.

[0141] Silicon is then grown on the surface at an elevated temperature, in one example about 50±5 nm of epitaxial silicon is grown at a temperature of 250° C.

[0142] After the required amount of silicon has been grown, a barrier may be grown. Finally, a microwave antenna may be aligned on the surface using electron beam lithography. Using etched registration markers, the antenna is aligned at a lateral distance of 300±50 nm from the embedded donor molecule, generating an oscillating magnetic field B1 perpendicular to the substrate at the location of the donor.

[0143] The gate may be positioned on the silicon substrate along with the antenna. Alternatively, the gate may be positioned in the same plane as the donor molecule. In such an example, the gate may be formed of Si:P during the H desorption step.

[0144] Optimal Stark shift for faster fault-tolerant single-qubit gates FIG. 9A shows the percentage of spectator qubit errors (dashed line 902), P(t), which is the probability of exciting an off-resonant qubit, as a function of nuclear spin

[0145]

number

[0146] as a function of the hyperfine Stark shift of the ESR peak and the target qubit Rabi frequency according to the Rabi equation given below.

[0147]

number

[0148] where

[0149]

number

[0150] is the magnetic field amplitude from the microwave antenna 210, δν is the offset from the peak resonant frequency (see below), and g e is the g-factor of the electron, and μ B is the Bohr magneton.

[0151] where δν is the hyperfine Stark shift (or more precisely, the Stark shift

[0152]

number

[0153] Non-Stark shift from the center of the ESR peak

[0154]

number

[0155] The spectator qubit error P(t) can be evaluated, and the probability of flipping the spectator qubit from spin down to spin up at time t=1 / 4γ, i.e., half a period of a Rabi cycle at the Rabi frequency of the detuned spectator qubit. The Rabi frequency of the target qubit is

[0156]

number

[0157] which is swept onto the y-axis of FIG. 3A.

[0158] The probability of exciting an off-resonant spectator qubit is proportional to the overlap of the target qubit ESR peak with the spectator qubit resonance frequency. This can be understood from equation (1) because the prefactor

[0159]

number

[0160] B on the y-axis of Figure 3A indicates the frequency f of the Rabi oscillation. ac This is because it is a Lorenzian with a full width at half maximum (FWHM) proportional to

[0161] Taking f=0 as the target qubit ESR frequency and f=δν as the spectator qubit ESR frequency separated by the Stark shift, it means that a larger Stark shift reduces the overlap of the Lorentzian and spectator qubit resonance frequencies. Thus, a larger hyperfine Stark shift leads to a lower spectator qubit error (as can be seen in Figure 9A). Conversely, an AC magnetic field strength B AC Increasing θ increases the Lorentzian FWHM (as well as increasing the target qubit Rabi frequency), leading to more overlap of the Lorentzians at the spectator qubit resonances and, consequently, a higher spectator qubit error rate.

[0162] FIG. 9A illustrates the qubit dephasing error T2 (shown by solid line 904). *9 also shows a qubit gate quality factor, which is measured at a length of 270 μs for a single phosphorus donor in silicon-28. The dephasing 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 dephasing error for a dephasing time of 270 μs is plotted for values ​​of 0.1% and 1.0% by solid lines 904. These solid lines form a lower limit for setting the target qubit Rabi frequency because otherwise the target qubit Rabi frequency could be set arbitrarily low to minimize spectator qubit error, which is shown by dashed lines 902 for error probabilities of 0.01%, 0.1%, and 1.0%. The shaded triangles 906 indicate the region where both the spectator qubit and dephasing qubit errors are within 1%, which is the approximate error rate threshold for the surface code.

[0163] 9A also shows how the performance of 2P and 1P donor configurations differs by plotting the size of the hyperfine Stark shift at an electric field of 5 MV / m for each configuration. The 1P donor, shown as dot 910, has the smallest hyperfine Stark shift, which limits how fast the Rabi frequency can be fault-tolerantly exercised relative to the target 1P donor electron spin when compared to the 2P donor.

[0164] We find that the hyperfine Stark shift for the 1P donor is too small to allow addressable fault-tolerant single-qubit operation. However, when the g-factor Stark shift is additionally included for a 1.5 T magnetic field (see dot 912), the combination of g-factor and hyperfine Stark shift is large enough to allow addressable fault-tolerant qubit operation at an electric field of 5 MV / m (5 MHz). For the 4.61 nm

[0110] 2P configuration (shown by dot 914), tight-binding simulations predict that the hyperfine Stark shift can be engineered to be an order of magnitude larger at 53 MHz, allowing qubit Rabi frequencies up to about 5.3 MHz, within the limit of 1% surface code fault tolerance. Experiments have also shown Stark shifts for other 2P donor configurations, such as the 0.77 nm <0110> (dot 916), 0.86 nm <0130> (dot 918), and 2.30 nm <0110> (dot 920) configurations respectfully shown previously in Figures 4D and 5D.

[0165] Although these configurations exhibit larger hyperfine Stark shifts than the 1P donor, the 4.61 nm 2P configuration (dot 914) is more suitable for large-scale architectures because it can achieve a larger Stark shift and the Stark shift is more robust to manufacturing tolerances.

[0166] Figures 9B-D show example ESR spectra for a 2P donor quantum dot, as well as the Rabi oscillations of the target and spectator qubits for a hyperfine Stark shift of 26 MHz and a Rabi frequency of 100 kHz. This position is indicated by an * in Figure 9A. Here, the target qubit has been rotated from down to up with 99.98% fidelity (in 5 μs), while there is about a 0.0015% probability that the spectator qubit will be erroneously rotated from down to up.

[0167] FIG. 10A is a plot of qubit error as a function of peak shift (Stark shift) and gate speed (Rabi frequency). Larger Stark shifts result in lower qubit addressability errors, with the optimal speed indicated by the red dashed region. FIG. 10B shows qubit error for a Stark shift of 110 MHz as a function of Rabi frequency. <0.01% error is possible for a Rabi frequency of 430 kHz, which is well below the 1% error threshold for surface codes.

[0168] Figure 11A shows the Stark shift as a function of electric field for an example 2P molecule with donors separated by 5.4 nm along the

[0110] direction. The points are obtained by tight-binding simulations of this 2P donor configuration for different electric fields along the donor axis. At zero electric field, the Stark shift is zero because the electron spin is shared equally between the donors and the Stark coefficient is approximately linear. The Stark coefficient at zero electric field is very large (84 MHz / MVm-1). By increasing the electric field, the electron spin becomes more localized to one donor. Beyond ±5 MHV / m the Stark shift saturates at ±114 MHz and the Stark coefficient is approximately 0 because the electrons are fully localized.

[0169] A large Stark coefficient is advantageous for qubit addressability, but can increase qubit dephasing due to charge noise. The sensitivity of electron spin coherence to charge noise may be estimated by performing simulations of the charge noise in an example device.

[0170] FIG. 11B shows the T2 due to charge noise as a function of electric field for a 2P donor configuration separated by 5.4 nm along

[0110] . *11A is a plot of the energy fluctuations of the electron spin qubit (curve 1102) over time. Curve 1104 is the standard deviation of the electron spin qubit energy fluctuations, which is obtained by taking the derivative of the hyperbolic tangent function fitted to the Stark shift data in FIG. 11A to obtain the standard deviation of the fluctuating electric field E σx The fluctuation of the qubit energy due to the charge noise is greatest when the Stark coefficient is at its maximum, so here we have T * Time is minimum. T2 * The black dotted line across =270μs represents the threshold where charge noise limits the qubit coherence time. This is because the longest measured coherence time for an electron spin in a single phosphorus donor in silicon is 270μs. Operating the electron spin qubit in the charge noise sweet spot (above + / -4.6MV / m) where the Stark shift saturates should ensure that qubit dephasing is not limited by charge noise.

[0171] FIG. 11C shows the results for electric fields of −5 MV / m (peak 1106) and 5 MV / m (peak 1108).

[0172]

number

[0173] 11C are plots of simulated ESR spectra for electron spins in a 2P molecule initialized to the -5MV / m state. See FIG. 11E, the electrons at -5MV / m are mostly localized on spin-down nuclei and the ESR peak is lower in frequency. At +5MV / m the electron spins are mostly localized on spin-up nuclei (see FIG. 11F) and the ESR peak is shifted up by 114 MHz. These provide two states for the electron spin qubit, where the -5MV / m state may be at the global ESR resonance frequency off and the +5MV / m state may be on resonance, or vice versa.

[0174] Although the manipulation qubits described herein refer to donor molecules, the manipulation qubits are not limited to donor molecules. Instead, the systems and methods of the present disclosure can be used to create manipulation qubits that include other multi-dopant molecules, such as multi-acceptor molecules. In such molecules, instead of confining a single electron, a single hole may be confined within the multi-acceptor molecule.

[0175] Additionally, although the quantum processing systems described herein are shown with gate electrodes for controlling the corresponding qubits, these gate electrodes may not always be necessary, and in other embodiments and examples, other control means may be used without departing from the scope of the present disclosure.

[0176] The present embodiments are therefore to be considered in all respects as illustrative and not restrictive.

[0177] Unless the context otherwise requires, as used herein, the term "comprise", as well as variations of that term, such as "comprising", "comprises", and "comprised", are not intended to exclude further additional elements, components, integers, or steps.

Claims

1. A semiconductor substrate; a dielectric material forming an interface with the semiconductor substrate; a dopant dot comprising a plurality of dopant atoms and one or more electrons / holes confined within said dopant dot; An engineered quantum processing element, 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. 10. The manipulated quantum processing element of claim 1 , wherein the distance between the dopant atoms and their orientations relative to each other and to the semiconductor substrate are manipulated to achieve an optimal linear hyperfine Stark coefficient.

3. The distance between the dopant atoms and the orientation of the dopant atoms within the semiconductor substrate are approximately 10 MHz / MVm －１ 3. The operated quantum processing element of claim 1 or 2, which is operated to achieve a linear hyperfine Stark coefficient of 1.

4. The operational quantum processing element of any one of claims 1 to 3, wherein the dopant dot comprises two donor atoms.

5. The operational quantum processing element of any one of claims 1 to 3, wherein the dopant dot comprises three donor atoms.

6. 6. The operational quantum processing element of claim 4 or 5, wherein the donor atom is a phosphorus atom.

7. 7. The operational quantum processing element of claim 1, wherein the distance between adjacent dopant atoms is at most 30 nanometers.

8. 8. The operational quantum processing element of claim 1, wherein the distance between adjacent dopant atoms is at most 6 nanometers.

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

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

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

12. The quantum processing element of 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 of claim 12 , wherein the dopant atoms are positioned along a [130] crystallographic axis of the semiconductor substrate.

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

15. 1. A method for manufacturing an operational quantum processing element, the method comprising: exposing a semiconductor substrate to atomic hydrogen H to form a monolayer of H and passivate a surface of the semiconductor substrate; selectively desorbing H atoms from the passivated surface by application of an appropriate voltage and tunneling current to the STM tip to form a number of patches in the H monolayer, the distance between the patches and the orientation of the patches along the direction of the semiconductor lattice being selected to achieve a large linear hyperfine Stark coefficient; and incorporating at least one donor atom into each of said plurality of patches in said H monolayer to form a donor molecule.

16. desorbing said hydrogen monolayer; The method of claim 15 further comprising blanket growing a layer of said semiconductor on said surface.

17. 17. The method of claim 15 or 16, wherein selectively desorbing H atoms further comprises desorbing H atoms to create one or more patches to create one or more in-plane gates.

18. 17. The method of claim 15 or 16, further comprising depositing one or more gates over the locations of the donor atoms.

19. The method of claim 18 , further comprising applying a voltage to the one or more gates to confine electrons within the donor molecules.

20. The method of any one of claims 15 to 19, wherein a distance between the plurality of patches in the semiconductor substrate is engineered to achieve a linear hyperfine Stark coefficient of about 10 MHz / MVm-1 or greater.

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