Quantum Processing Systems

Abstract

A quantum processing system is disclosed. In one embodiment, the quantum processing system includes: a plurality of donor atoms positioned in a silicon crystal substrate, each donor atom being positioned at a donor site; and a plurality of conductive control electrodes, the plurality of conductive control electrodes being arranged around the donor atoms to operate the donor atoms as quantum bits. At least two pairs of nearest adjacent donor atoms among the plurality of donor atoms are arranged along the [110] direction of the silicon crystal substrate and are configured to operate as quantum bits.

Description

Technical Field

[0001] Aspects of the present disclosure relate to advanced processing systems and methods for operating the same, and more particularly, to quantum processing systems controllable to perform error-corrected quantum computing. Background Art

[0002] The developments described in this section are known to the inventors. However, unless otherwise stated, it should not be assumed that any developments described in this section are considered prior art simply because they are included in this section, or that those developments are known to a person of ordinary skill in the art.

[0003] Large-scale quantum processing systems hold the promise of a technological revolution, with the prospect of solving problems that are impossible with classical machines. To date, many different structures, materials, and architectures have been proposed to implement quantum processing systems and fabricate their basic information units (or qubits).

[0004] For example, one way to make qubits is to use the nuclear or electron spins of ionized phosphorus donor atoms in silicon, so that each phosphorus donor atom then acts as a qubit (or quantum bit). 31 Due to the addressability and long coherence of the P spins, this fabrication technique provides a near-perfect encoding of the qubit state. In addition, qubits fabricated in this way have demonstrated the second-longest lifetime and benefit from a semiconductor host that enables electrical addressing and high precision.

[0005] However, in order to begin to see the computational advantages that quantum processing systems can provide, basic quantum circuits (or quantum gates) need to be made, which is not easy. For example, in the case of a single donor atom in silicon, creating a two-qubit gate requires precise control of the electron-electron exchange interaction between two neighboring donor atoms and the hyperfine interaction between the electron and nuclear spin of the same donor atom. Normally, electron-electron exchange occurs via the Heisenberg exchange interaction, a quantum mechanical effect that occurs between identical particles.

[0006] Although the Heisenberg exchange interaction is an attractive way for qubits to interact (because it provides compact routing for quantum processors), achieving this interaction consistently and controllably across multiple silicon-based qubits is often problematic. This is because of quantum interference effects inherent in the silicon band structure and the valley degrees of freedom present in silicon. Basically, the crystal structure of silicon causes the donor-bound electron charge to be distributed in the space around the donor at a frequency k. μThe valley frequency oscillates at a frequency of 0.81 k0 (called the valley frequency), which is incommensurate with the lattice frequency k0. Notably, two-electron interference occurring at the valley frequency between two electrons bound to two donor atoms has been predicted to cause the exchange coupling between the two donor atoms to oscillate as a function of the inter-donor position, strongly modulating the hydrogen molecular-like exponential decay. For changes in the donor position of only a few lattice sites, the exchange can vary by up to 5 orders of magnitude, which is critical for quantum computers and simulators. Variations in the magnitude of the exchange can degrade the precision of two-qubit gates, prevent the required large-scale qubit synchronization, and destroy many-body effects.

[0007] Additionally, wave function engineering options have been proposed, where the electronic valley content of silicon is modified by coupling to interface states or by using strained silicon. However, concerns remain regarding the complex fabrication processes involved in these techniques and the impact of interface traps, roughness, or strain inhomogeneities on exchange changes, electronic coherence, and device reliability.

[0008] Therefore, an improvement is desired which is compatible with existing device manufacturing techniques and in which exchange coupling can be stabilized. Summary of the invention

[0009] According to a first aspect of the present disclosure, a quantum processing system is provided, comprising: a plurality of donor atoms positioned in a silicon crystal substrate, each donor atom being positioned at a donor site; a plurality of conductive control electrodes, the plurality of conductive control electrodes being arranged around the donor atoms to operate the donor atoms as quantum bits; wherein at least two pairs of nearest adjacent donor atoms among the plurality of donor atoms are arranged along a

[110] direction of the silicon crystal substrate and are configured to operate as quantum bits.

[0010] In some embodiments, each pair of nearest neighbor donor atoms has an exchange coupling value, and a maximum variation in exchange coupling values ​​between pairs of donor atoms is less than a predetermined factor.

[0011] In some embodiments, the predetermined factor is ten.

[0012] In addition, the silicon crystal substrate may include multiple donor sites arranged along the

[110] direction, each site including multiple positions, and wherein a first donor atom is located at a first position among the multiple positions at the first donor site, and a second donor atom is located at a second position among the multiple positions at the second donor site, and wherein the first position is different from the second position.

[0013] In certain embodiments, each donor site includes six locations.

[0014] Furthermore, when the first donor atom is located at any of a plurality of positions at the first donor site and the second donor atom is located at any of a plurality of positions at the second donor site, two-dimensional protection is provided to the exchange coupling J from valley interference.

[0015] Furthermore, the distance between donor atoms in a pair of donor atoms may be at least 10 nm, and in some embodiments between 10 nm and 25 nm.

[0016] The quantum processing system may further include a plurality of control gates arranged around the donor atoms to create a detuned field to increase the exchange coupling value between at least 90% of the donor atom pairs to a specific exchange coupling value.

[0017] According to a second aspect of the present disclosure, a quantum processing system is provided, comprising: a plurality of donor atoms positioned at donor sites in a silicon crystal substrate; a plurality of conductive control electrodes, the plurality of conductive control electrodes being arranged around the donor atoms to operate the donor atoms as quantum bits; wherein at least one pair of nearest adjacent donor atoms is arranged in one of a plurality of possible mutually inequivalent donor-donor positions along the

[110] direction of the silicon crystal substrate, wherein each inequivalent donor-donor position is associated with an exchange coupling value, and a variation in the exchange coupling value with respect to the plurality of possible inequivalent donor-donor positions is less than a predetermined factor.

[0018] The plurality of non-equivalent donor-donor locations may include 10 configurations.

[0019] Furthermore, when at least one pair of nearest neighbor donor atoms is arranged in any of a plurality of possible inequivalent donor-donor positions, the exchange coupling J is provided with two-dimensional protection against valley interference.

[0020] According to a third aspect of the present disclosure, there is provided a quantum processing system, comprising: a plurality of quantum bits, the plurality of quantum bits being created by positioning donor atoms along a

[110] direction in a silicon crystal substrate so that the difference in magnitude of exchange coupling between pairs of donor atoms is less than a predetermined factor; and a plurality of control gates, the plurality of control gates being arranged around the donor atoms to create a detuned field to increase the exchange coupling values ​​between at least 90% of the donor atom pairs to a specific exchange coupling value.

[0021] In certain embodiments, a pair of control gates in the plurality of control gates are arranged to control a pair of qubits to create a detuned electric field.

[0022] Furthermore, the quantum processing system of the third aspect may include a plurality of conductive control electrodes arranged around the donor atoms to operate the donor atoms as quantum bits.

[0023] According to a fourth aspect of the present disclosure, a structure for use in a quantum processing system is provided, the structure comprising: a silicon crystal substrate comprising a plurality of donor atom sites arranged along a

[110] direction of the silicon crystal substrate, each donor atom site comprising a plurality of possible positions for positioning the donor atom; a plurality of donor atoms, each donor atom being positioned in a corresponding donor atom site of the plurality of donor atom sites in any one of the plurality of possible positions; wherein the donor atoms closest to each other in the

[110] direction interact with each other, and each pair of nearest adjacent donor atoms has an exchange coupling value, and wherein the maximum variation in the exchange coupling values ​​between the plurality of pairs of nearest adjacent donor atoms is less than a predetermined factor. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1A It is a schematic diagram of the unit cell of a bulk silicon crystal in real space.

[0025] Figure 1B-Figure 1D The different planes and directions in the silicon unit cell lattice are shown. In particular, Figure 1B The

[100] direction and plane are shown, Figure 1C The

[110] direction and plane are shown, and Figure 1C The

[111] direction and plane are shown.

[0026] Figure 2 yes Figure 1A Schematic diagram of a silicon crystal in reciprocal space.

[0027] Figure 3 is a schematic diagram of a 2×1 silicon surface with multiple rows of silicon dimers.

[0028] Figure 4A Schematic diagram of a 2D array of single electron spins bound to donor atoms in a silicon substrate.

[0029] Figure 4B is a diagram showing the exchange interaction between two donor atoms.

[0030] Figure 5A is a schematic diagram of the donor atomic sites in the

[100] direction and the

[110] direction relative to a specific donor atomic site.

[0031] Figure 5B is the STM image of the quasi-particle wave function of the exchange-coupled donor pair.

[0032] Figure 5C Depicted Figure 5B The STM image of , which is filtered around the valley frequency kμ ~ 0.81*k0, shows the in-plane y-valley interference.

[0033] Figure 5D It is from passing through Figure 5C The phase difference extracted from the fitting of the lines cut by the two donor atoms shown in Graph of the curve.

[0034] Figure 5E It is shown that for d tar =12nm, relative to θ tar Plotted normalized envelope weight j μv Graph of the curve.

[0035] Fig. 5F is a graph showing the exchange interaction values ​​of donor atoms positioned in the

[100] direction.

[0036] Figure 5G is a graph showing the exchange interaction values ​​for the donor atom positions in the

[110] direction.

[0037] Figure 5H is a graph showing the ratio of the minimum and maximum exchange interaction values ​​in the

[100] and

[110] directions for various inter-donor distances.

[0038] Figure 6 is a graph showing the percentage of qubits tuned to the maximum exchange interaction value for a given tunability factor in the

[100] and

[110] directions.

[0039] Figure 7 is a schematic diagram of an exemplary structure according to aspects of the present disclosure.

[0040] Fig. 8A Shown is a tunable 2-qubit gate with a control gate placed on top of a silicon substrate.

[0041] Figure 8B Shown is a tunable 2-qubit gate with a control gate placed coplanar with the two qubits.

[0042] Figure 9A-9B is a schematic diagram of processing steps for placing donor atoms in a silicon substrate in the

[110] direction (or

[001] plane) according to aspects of the present disclosure.

[0043] Fig. 10A Schematic diagram of H desorption at two adjacent donor sites along the

[110] direction.

[0044] Fig. 10B is an image of two donor atoms positioned in the silicon substrate along the

[110] direction.

[0045] Figure 11A-11B is a schematic diagram of the architecture of a quantum processor according to aspects of the present disclosure.

[0046] Although the present invention is susceptible to various modifications and alternative forms, specific embodiments are shown in the drawings by way of example and are described in detail. However, it should be understood that the drawings and specific embodiments are not intended to limit the present invention to the specific forms disclosed. The present invention will cover all modifications, equivalents and substitutions within the spirit and scope of the present invention as defined by the appended claims. DETAILED DESCRIPTION

[0047] Overview

[0048] This section describes the known properties of silicon and the problems associated with placing donor atoms in silicon substrates to fabricate advanced processing systems such as quantum processing systems.

[0049] Silicon has a crystal structure with cubic symmetry. Each silicon crystal is characterized by a unit cell that repeats in the x, y and z directions. Figure 1A A unit cell 100 of silicon is shown, which includes eight silicon atoms at the eight corners of a cubic structure. The crystal planes and directions of the silicon unit cell 100 are generally described using the Miller index. According to this index, the directions are defined using the x, y, and z directions. For example, the direction

[110] defines the direction of a vector that is orthogonal to the xy plane or surface of a facet. Three principal crystal directions are defined using this index:

[0050]

[100] direction,

[110] direction and

[111] direction, such as Figure 1B , 1C and as shown in 1D.

[0051] Furthermore, it should be understood that the band structure of silicon is complex. It has the following properties: when the crystal momentum (k) is zero, the energy of the electronic states in the conduction band is not minimized, but at non-zero values ​​of k μ is minimized, the non-zero value k μ is about 81% of the paths that reach the Brillouin zone boundary, such as Figure 2 A reciprocal lattice cell 200 of silicon having a first Brillouin zone is shown in FIG.

[0052] Silicon is usually considered to have six degenerate valleys in its conduction band, since it has cubic symmetry and there are six equivalent minima in the structure. In conventional electronics, the presence of multiple valleys does not usually affect the transport properties in a profound way. However, valley physics plays a key role in quantum electronics, because interference between different valleys complicates the manipulation of the spins of donor atoms placed in the silicon substrate.

[0053] In general, each silicon atom in the lattice structure 100 is bonded to four other silicon atoms - two below and two above. This is the most stable state of silicon because all of its possible bonds are satisfied. However, the silicon atoms on the substrate surface are only bonded to the two silicon atoms below because they lack any atoms bonded above. Therefore, the surface Si atoms have two bonding sites available above (called dangling bonds). In order to reduce the number of dangling bonds, adjacent silicon atoms on the surface are bonded to each other so that each surface silicon atom has one available dangling bond. When adjacent surface atom pairs are bonded to each other in this way, they are pulled toward each other and out of their cubic lattice positions, thereby forming multiple rows of silicon atom pairs known as dimer rows. Figure 3 A 2x1 silicon surface 300 is shown with multiple rows of dimers 302. The figure also shows dangling bonds 304 on each silicon atom.

[0054] As mentioned above, by placing donor atoms (e.g., phosphorus atoms) 28 Some quantum processing systems are made in Si structures. This manufacturing generally involves exposing the silicon surface to atomic hydrogen so that the hydrogen atoms can bond to the surface Si atoms (using dangling bonds 304), thereby forming a monolayer of hydrogen atoms on the surface. Thereafter, a scanning tunneling microscope (STM) tip is used to selectively desorb hydrogen atoms, thereby exposing dangling bonds in precisely selected locations (for example, 6 hydrogen atoms can be desorbed at a specific location to expose 3 silicon dimers). Then, phosphorus donor atoms are introduced, for example by means of phosphine gas (PH3), so that exactly one phosphorus atom is strongly bonded to the dangling bonds exposed at each exposure location (for example, a phosphorus donor atom can be strongly bonded to any one of the three silicon dimers in a specific location). Thereafter, the phosphorus electron pairs bound to the donor atoms embedded in the silicon crystal can interact with each other (via exchange coupling J) to form quantum bit pairs, which can be controlled to perform certain circuit operations.

[0055] Figure 4A is 28 Schematic diagram of a 2D array 400 of single electron spins bound to donor atoms 402A, 402B ... 402N in Si, where 2-qubit operations occur between nearest neighbors (eg, donor atoms 402A and 402B) using the Heisenberg exchange interaction. Figure 4B Shows Figure 4A An exchange interaction 410 is shown between the two donor atoms 402A and 402B.

[0056] An important feature of the exchange coupling between donor atoms is the oscillation of the exchange coupling, in which the donor separation changes on the order of the lattice constant due to the aforementioned multi-valley silicon conduction band. Interference between these valleys can lead to rapid oscillations in the exchange interaction and can lead to exchange gate errors and out-of-sync quantum processors. Another problem with donor-based qubits is the randomness or uncertainty of the accuracy of the donor placement, which occurs because the donor atom can bond to any of the three exposed silicon dimers at a specific site, depending on how the PH3 molecule positions itself during CVD within the exposed dimer array. These two features lead to inherent randomness in the exchange coupling J generated between the two qubits, which in turn leads to exchange gate errors and out-of-sync quantum processors.

[0057] In the past decade, many researchers have studied the effects of these features on the exchange coupling between neighboring donor atoms, and have found that in a one-dimensional positional scheme, the exchange coupling between two neighboring donor atoms is not affected by valley interference along the

[100] crystal direction. However, this assumes that the donor atoms can be precisely positioned and in a perfect linear arrangement. This is incompatible with the prior art dopant positioning using STM lithography, where dopants are randomly incorporated into a sheet of 3 dimers, resulting in a two-dimensional uncertainty in the relative positions of neighboring donor atoms. Some studies have considered random 3D donor placement errors and have also concluded that there is no region in space including along

[100] where valley-induced exchange changes are limited and exchange is stable.

[0058] Based on these studies, when fabricating donor-based qubits, researchers typically position the phosphorus donors in the silicon surface along the

[100] direction.

[0059] However, contrary to common sense and practice, the present inventors have discovered a dopant placement scheme in which exchange is not affected by in-plane valley interference and therefore is not affected by in-plane (2D) random variations in dopant positions.

[0060] In particular, the inventors of the present application have proposed a donor-based quantum processing system in which donor atoms are located at donor sites arranged in the

[110] direction. This quantum processing system takes into account actual donor positioning errors or variations and exhibits an exchange variation of less than 10 times. Therefore, the proposed donor-based quantum processing system achieves exchange uniformity while retaining batch-reproducible donor properties.

[0061] The donor atoms in the presently disclosed quantum processing system are arranged based on customized exchange calculations and analysis that rely on the actual positions of the donor atoms in the silicon plane, which is achievable using STM technology.

[0062] The following sections describe experimental results, silicon substrates with donor atoms placed in the

[001] plane, processes for fabricating donor-based qubits in the

[001] plane, and quantum processing systems using donor-based qubits in the

[001] plane.

[0063] Test results

[0064] The existence of valley-induced J oscillations inevitably constrains the design of quantum architectures. First, due to Figure 4B A direct consequence of the decay of the exchange exponent due to the envelope portion shown in is the need to place the donor atoms within a precision of about 2 nm (i.e., the electron Bohr radius), otherwise the exchange coupling J will vary by more than an order of magnitude. This threshold is critical because it is often difficult to tune exchange coupling variations of this order or any larger order by any known tuning scheme, which ultimately affects the uniformity of the qubits in a particular quantum processing system, and therefore the ability to control and address such qubits in synchronized operation, which may be required in large-scale quantum processing.

[0065] STM lithography generally meets this requirement because it is possible to randomly incorporate a single donor atom within a sheet of three hydrogen-desorbed dimers along the

[110] direction using STM. However, even with STM, it is difficult to predict or force the donor atom to bond to a specific silicon atom among the six exposed silicon atoms, and in fact, assuming chemical reactions between dangling bonds and PH3 molecules, the donor atom randomly bonds to any of the six exposed silicon atoms. Therefore, two neighboring donor atoms can have up to 12 non-equivalent donor-donor sites.

[0066] Figure 5A A donor atom site 502 and two other donor atom sites 504 and 506 are shown, wherein donor atom site 504 is in the

[100] direction from donor atom site 502, and donor site 506 is in the

[110] direction from donor atom site 502. In addition, each donor site 502, 504, and 506 includes 6 possible locations where a donor atom 508 can be placed. Figure 5A For the target distance d tar The angle with the target is θ tar , donor atoms 508 in sites 502, 504, and 506 are bonded to silicon atoms in the intermediate silicon dimer. Figure 5A The open circle in the figure indicates the target location in both directions.

[0067] The inventors performed low-temperature STM on exchange-coupled donors to directly image and measure the valley phase interference between two donor atoms at the wave function level. This is done by filtering the STM image around the valley frequency kμ~0.81*k0 to extract the valley phase difference between the two donors. To achieve. Figure 5B-5D The y-valley interference and valley phase difference of a donor-donor site adjacent to a donor atom are shown.

[0068] In particular, Figure 5B is an STM image of the quasi-particle wave function of the exchange-coupled donor pair 510. Point 512 indicates the precise location of the two donors, and point 514 indicates the location of the silicon atom at the 2×1 reconstructed surface. Figure 5C Shows Figure 5B The STM image 510 of is filtered around the valley frequency kμ ˜0.81*k0, showing in-plane y-valley interference. The crosses 522 indicate the locations of the donor sites. Figure 5D It is from passing through Figure 5C The phase difference extracted from the fitting of the cut lines of the two donor atoms shown in If Close to π, the y valley interferes destructively between the two donors, which may affect the exchange coupling J.

[0069] From these images, the valley phase interference between the donors was directly quantified. This is the first time that valley interference between two phosphorus atoms in silicon has been directly observed and quantified. From these observations, the inventors have constructed a predictive model for the magnitude of the exchange change using only experimentally measured parameters as input. This model is the Phenomenological Effective Mass Model (P-EM) and it can be expressed as

[0070]

[0071] Among them, Δφ u is the valley phase difference between adjacent donors in valley μ, Δφ v is the valley phase difference between adjacent donors in valley v, a and b are the anisotropic envelope Bohr radii, is the relative position between the two donors, μ indicates the valley where the first electron is exchanged between the two donors, and v indicates the valley where the second electron is exchanged between the two donors.

[0072] In this equation, the first part (i.e., ) includes the envelope or orbital term, and this part affects the exchange value (J) in a smooth, slowly varying manner. The second part (i.e., cos(Δφ u ±Δφ v )) includes valley interference terms, which affect the exchange value (J) in a rapidly changing manner.

[0073] Figure 5E It is shown that for d tar =12nm, relative to θ tar Plotted normalized envelope weight j μv 540. In this graph, it can be seen that the six different envelope terms (j xx 、j xy 、j xz 、j yy 、j yz and j zz ) evolves smoothly because they do not contain any valley interference, but their ratio is not constant and varies by several orders of magnitude. This is a direct result of the anisotropic and exponential nature of the donor envelope. It can be seen in graph 540 that along the

[100] direction, j yz Item and j zz and j yy degenerate, and largely dominates any term for electron exchange in the x-valley. yz 、j zz and j yy The degeneracy between arises from symmetry, since the product between the y and z orbitals is equal along the

[100] direction.

[0074] However, along the

[110] direction, j zz The universality of is maximized. Therefore, in this direction, j zz Compared with the degenerate term j xz and j yz Therefore, placing the donor along the

[110] direction leads to a finite Δφ x or Δφ y , which may vary specifically according to the configuration obtained from one pair to another, and therefore according to the destructive j xz and j yz However, their effects on the exchange value can be ignored because j zz Dominate in this direction.

[0075] Fig. 5F is a graph 550 showing the relationship between the linear relationship of the linear relationship between ... tar =0°), both of which can be placed in one of the 6 possible positions in the donor site, and Figure 5G is a graph 560 showing the relationship between the

[110] direction (ie, where θ tar=45°), each of which can be placed in one of the 6 possible positions of the donor site. In both cases, the average distance between the donor atoms is 12 nm (i.e., d tar =12 nm). Each of these graphs shows the normalized J value calculated based on the phenomenological effective mass (P-EM) theoretical model of equation (1).

[0076] exist Fig. 5F As can be seen in the graph 540, for the distance change caused by different positions from 11 nm to 13 nm, the change in the normalized J value in the

[100] direction for each of the 12 different positions is approximately 100 times or two orders of magnitude. For example, the difference between the lowest exchange coupling value (Jmin) and the highest exchange coupling value (Jmax) is greater than 100 times. This change in the normalized J value can be explained by the curve graph 540 and the P-EM model. yy 、j zz and j yz The degeneracy and dominance of the terms along the

[100] direction means that the sum expressed in Eq. 1 can be simplified to these terms, which involve only Δφ y and Δφ z , and the latter is zero in the xy plane. Therefore, Δφ y It is only important along the

[100] direction. The normalized J value for a position that is perfectly aligned in the

[100] direction leads to the construction of a y-valley, Δφ y = 0 and maximized J. However, when the donor atoms are misaligned or not fully aligned along the

[100] direction, Δφ y is finite, and thus, for these locations, the normalized J value of this configuration is reduced by more than two orders of magnitude. This means that when the donor is placed along the

[100] direction, only the x-valley interference (i.e., ) does not affect the exchange, thereby providing one-dimensional protection for the exchange to prevent valley interference from dopant placement errors.

[0077] On the other hand, Figure 5G It can be seen that the normalized J value at each of the 10 different positions in the

[110] direction changes by less than a factor of 10 for the change caused by different distances from 11 nm to 13 nm. For example, the lowest exchange coupling value (J min ) and the maximum exchange coupling value (J max ) is less than a factor of 10. This can again be explained by the graph 540 and the P-EM model of equation (1). Placing the donor along the

[110] direction results in a finite Δφ x or Δφ y′, which can vary depending on the positional differences between the donor atom pairs. However, due to the zz In the

[110] direction, where the address is dominant, both values ​​have negligible impact on the J value. As a result, the possible exchange values ​​(J) obtained for two donors along the

[110] axis are more constrained and vary by less than an order of magnitude, as shown in graph 560. When the donor is placed along the

[110] direction, or The fact that neither affects exchange provides two-dimensional protection for the exchange coupling, J, against valley interference from dopant placement errors, where placing the donor in the

[100] direction does not provide such two-dimensional protection.

[0078] Figure 5H 5 is a graph 570 showing the ratio of Jmin / Jmax values ​​plotted at target locations in the

[100] direction and the

[110] direction for a wide range of target distances between neighboring donor atoms from 10 nm to 25 nm. As shown in the graph, the values ​​in the

[110] direction show limited variation (10 times or less) over a wide range of distances, approaching the envelope limit at target distances above 12 nm because of the in-plane valley interference Δφ x and Δφ y does not affect the exchange value. On the contrary, the value in the

[100] direction remains well below 500 times over the entire range, because j yy 、j yz and j zz The degeneracy between holds for all distances.

[0079] It is therefore clear that the variation in exchange coupling values ​​around the

[110] direction is consistently much lower (at least an order of magnitude lower) than around the

[100] direction, and is limited to within a factor of 10 for a wide range of distances providing a large range of usable exchange values ​​for quantum computing purposes.

[0080] Demonstrating that the

[110] direction is optimal and can minimize valley-induced exchange changes facilitates the construction of robust and consistently executed 2-qubit gates and reveals key information for quantum computing architectural strategies, where, for example, robust two-qubit operations need to be achieved.

[0081] Furthermore, Figure 6is a graph 600 showing the percentage of qubits tuned to a maximum value for a given tunability factor. For an actual tunability factor of 3, consistent with the proposed donor qubit tuning scheme for distances of 15 nm and greater, if the donor is aligned along

[100] , approximately 50% of the qubits will be tuned, as shown in the dashed profile at 602. However, for the same factor as shown in the solid profile at 604, this percentage exceeds 90% along

[110] , reaching the minimum yield of globally controlled stable quantum machines with efficient quantum error correction to be achieved. For donors in the

[100] direction, this percentage can be achieved with a tunability factor of approximately 100, as shown at 606 (which is not realistic).

[0082] Therefore, envelope-restricted exchange changes along the

[110] direction constitute a valuable asset for larger-scale quantum computations, since small changes in the J value mean that at least 90% of the qubits in the

[110] direction can be expected to be tuned to the maximum exchange interaction value, such that at least 90% of the qubits in a quantum processing system can exhibit coherence and can be uniformly controlled.

[0083] Donor qubits in silicon

[0084] Figure 7 An exemplary highly schematic structure 700 for a quantum processing system according to aspects of the present disclosure is shown.

[0085] Structure 700 includes a silicon crystalline substrate 702 and a plurality of donor atoms 704 positioned in the silicon crystalline substrate in the

[001] plane. In particular, Figure 7 The donor atoms are shown positioned in the same plane around the

[110] or [-110] direction (which are equivalent crystal directions) within the donor atom sites 706. Each donor site 706 includes six possible locations where the donor atom 704 can be placed, and Figure 7 As can be seen in Figure 2, the donor atom can occupy any of the six possible positions.

[0086] In structure 700, a 2-qubit operation occurs between nearest neighboring donor atoms (e.g., donor atoms 704A and 704B or donor atoms 704B and 704C) using a Heisenberg exchange interaction. The value of the exchange interaction between donor atom pairs 700 can be such that the maximum change in the exchange interaction value across the entire structure 700 is within a predetermined factor (e.g., a factor of 10).

[0087] Tuning donor qubits in silicon in the

[110] direction (or

[001] plane)

[0088] In some embodiments, to further reduce Figure 7The change in the exchange interaction value of the donor atom pair shown in can be used to electrically tune the exchange coupling magnitude to the maximum exchange interaction value using a tuning circuit.

[0089] To achieve this, in some cases a J-gate can be used between two donor atoms to tune the J coupling to a specific value (e.g. Figure 5D J shown max ). Alternatively, Gate A may be used.

[0090] In other embodiments, a swap gate may be utilized. FIG8 illustrates a tunable 2-qubit gate. In particular, Fig. 8A A tunable 2-qubit gate 800 is shown having two qubits 806 and 808, with control gates 802 and 804 placed on top of a silicon substrate 805, and Figure 8B A tunable 2-qubit gate 810 is shown having two qubits 806 and 808 with control gates 802 and 804 placed in a plane (ie, the

[110] plane).

[0091] In operation, control gates 802 and 804 create an electric field (called a detuned field) between the two qubits, which enhances the exchange coupling between the qubits. In particular, the detuned field causes part of the charge from one qubit to transition to the other qubit. The charge configuration of the system is represented as (M, N), where M indicates the number of electrons on the first donor atom and N is the number of electrons on the second donor atom. When electrons bound to one donor are pulled toward the other donor by the detuned electric field, the exchange coupling J can go from a smaller value in the (1, 1) state toward a larger value that is designed to be in the (2, 0) state (because there is a large spatial overlap of the wave functions in the latter). The detuned field can be adjusted from the top gate (see Fig. 8A ) or from an in-plane gate (see Figure 8B ) to apply this electric field. Placing detuned gates on both sides of the donor qubit eliminates the need for sensitive tunnel barrier control via the J-gate. In addition, this design relaxes the more stringent engineering requirements of the Kane architecture for donor separation and gate width, leading to a reduction in the overall gate density in the quantum processing system.

[0092] As above Figure 6 As shown in , by tuning donor atoms at least 10 nm apart using a tuning factor of 5, at least 90% of the qubit pairs can be tuned to have substantially the same exchange interaction when they are positioned in the

[110] direction.

[0093] Fabricating donor qubits in silicon in the

[001] plane

[0094] FIG. 9 summarizes the various processing steps (steps ak) for placing donor atoms in a silicon substrate in the

[001] plane.

[0095] A clean Si 2×1 surface was formed in ultra-vacuum (HUV) by heating to near the melting point. The surface has a 2×1 unit cell and consists of multiple rows of σ-bonded Si dimers, where the remaining dangling bonds on each Si atom form weak π bonds with another Si atom of the dimer it comprises.

[0096] Processing step (a) (i.e., monohydride deposition) involves exposing the clean Si 2×1 surface to atomic H to break weak Siπ bonds, thereby allowing H atoms to bond to Si dangling bonds. Under controlled conditions, a monolayer of H can be formed with one H atom bonded to each Si atom, satisfying the reactive dangling bonds, effectively passivating the surface; see step (a).

[0097] Next, at process step (b) (ie, hydrogen desorption), the STM tip is used to selectively desorb H atoms from the passivated surface by applying appropriate voltage and tunneling current, thereby forming a pattern in the H resist; see step (b).

[0098] It will be appreciated that the H atoms are desorbed from the precise location where the donor atoms are to be placed and according to aspects of the present disclosure, the H atoms are desorbed in such a way as to create a location where the donor atoms are to be placed along the

[110] direction.

[0099] A particularly advantageous feature of dimer rows formed on the surface of the silicon substrate is that these rows are oriented in the

[110] direction, as shown in FIG. 9 , and thus, to create the positions of two nearest neighbor donor atoms in the

[110] direction, the STM tip is used to desorb six hydrogen atoms at one position along the dimer row, and then desorb six additional hydrogen atoms along the same dimer row at a specific distance (e.g., about 10-25 nm, and more preferably about 12-15 nm) from the first position (see Fig. 10B ). The process is then repeated to create sites for additional donor atoms along the

[110] direction. In this way, regions of bare reactive Si atoms are exposed along the dimer rows, allowing subsequent active reactive species to adsorb directly onto the Si surface. Fig. 10B Shown is an image of two donor atoms positioned in a silicon substrate in the

[110] direction using STM.

[0100] Back to Fig. 9A At step (c) (i.e., PH3 metering), phosphine (PH3) gas is introduced into the vacuum system via a controlled leak valve connected to a specially designed phosphine micrometering system. Through the holes in the hydrogen resist, the phosphine molecules are firmly bonded to the exposed Si surface; see step (c). As mentioned above, at a specific donor site, the phosphine molecule can bond to any of the three exposed silicon dimers.

[0101] Subsequent heating of the STM patterned surface for crystal growth results in the dissociation of the phosphine molecules and incorporation of P into the first Si layer; see step (d). Thus, the STM patterned H passivated surface is exposed to PH3, which is used to produce the desired P array.

[0102] The hydrogen can then be desorbed at step (e) before overgrowing the surface with silicon at room temperature at step (f).An alternative is to grow silicon directly through the hydrogen layer, as shown in step (g).

[0103] At step (h), the surface is rapidly annealed.

[0104] Then, as shown in step (i), silicon is grown on the surface at an elevated temperature. Then, as shown in step (j), a barrier is grown. Finally, as shown in step (k), a conductive gate may be aligned on the surface.

[0105] By manufacturing a silicon substrate with donor atoms in this manner (i.e., arranged along the

[110] direction), the value of the exchange coupling can be managed so that error-corrected quantum computing can be achieved without the use of strained silicon. Therefore, the structures, architectures, and processing systems disclosed herein are relatively easier to manufacture than quantum processing systems in which the donor atom pairs are positioned along the

[100] direction.

[0106] U.S. Patent 7,097,708, "Substituted donor atoms in silicon crystal for quantum computer," describes some aspects of fabrication processes that can be used to fabricate the devices described herein, and is incorporated herein by reference in its entirety.

[0107] Quantum processor based on donor qubits in silicon in the

[110] direction

[0108] As previously described, multiple donor atoms are arranged in a two-dimensional matrix in the

[001] plane (or along the

[110] direction) in silicon. In some variations of quantum processors, qubits can be encoded in donor sites that include multiple donor atoms arranged in a cluster. In this case, the qubit is encoded using a combination of quantum properties of the donor atoms in the cluster.

[0109] The data qubit elements are encoded in a first plurality of donor atoms, and the remaining donor atoms are arranged to facilitate quantum error correction. The qubits encoded on the second plurality of donor atoms are also referred to herein as "helper" qubits.

[0110] The data and auxiliary qubits are encoded in the nuclear spins of the corresponding donor atoms. Since at least 90% of the donor atom pairs in the

[001] plane can be tuned to a uniform exchange value, in a quantum processor according to aspects of the present disclosure, the donor electrons and nuclear spins can be rotated simultaneously using a global magnetic field that can be applied externally to the entire architecture. This provides substantial advantages for architectures that require local (for each qubit) application of a magnetic field.

[0111] The control structure is arranged in silicon to interact with the data qubits and the auxiliary qubits. The arrangement of the control structure allows multiple qubits to be controlled simultaneously. In particular, the qubits can be controlled simultaneously in a pattern distributed on a matrix. The structure can be controlled to load electrons to each donor atom and on multiple donor atoms simultaneously or to unload electrons from each donor atom and on multiple donor atoms simultaneously.

[0112] Reference now Fig.11A , showing an exploded view 1120 of a silicon quantum computing structure. The structure 1120 is broken down into three different silicon planes. The structure is made of isotopically purified silicon 28 ( 28 The structure is formed in a Si (Si) substrate (e.g. using the process described with reference to FIG. 9 ). In particular, multiple donor atoms 1104 are embedded in the silicon lattice along the

[110] direction. One possible technique for making this structure is to start with a pure silicon wafer and use the lithography capabilities of a scanning tunneling microscope and silicon epitaxy to make the structure on each plane. In operation, the entire device is cooled to the mK state and operated in a magnetic field of about B=2T with externally applied (global) RF and MW control.

[0113] Two groups of control lines extend across the architecture. The control lines are arranged on a plane above the plane including the donor atoms, and the control lines are arranged on a plane below the plane including the donor atoms. The control lines are arranged vertically relative to each other in a cross-shaped configuration. In some embodiments, the control lines may intersect at an angle different from 90 °. The control lines in the two planes do not physically intersect, but they define the intersection point where they pass through two vertically aligned parts of the lattice. Around some of these intersections, control elements provided in the form of heavily doped silicon islands 1110 are formed. Each island forms a single electron transistor (SET) having corresponding control members arranged above and below the island. A pair of these control members serves as the source and drain of the transistor, and another pair serves as the transistor gate.

[0114] In structure 1120, the control wires on the bottom plane are divided into two staggered groups 1022 and 1024. Control wire 1122 serves as the drain of the SET, and control wire 1124 serves as the gate of the SET 1112. A similar configuration is shown for the control wires on the top planes 1126 and 1128, which serve as the source and gate of the SET, respectively. Each SET 1112 interacts with one or more donor atoms 1104 through a corresponding control island 1110. In the embodiment described, each island 1110 is configured to interact with four donor atoms 1104 to form a single unit of the architecture. By applying electrical signals to the control wires 1126-1124, the SET 1112 can be controlled to load or unload electrons on each donor atom 1104 in the architecture, or to control the spin orientation of the electrons or nuclei of one or more donor atoms. In addition, the configuration of the donor atoms 1104 and the control wires allows for loading or unloading electrons on multiple donor atoms arranged simultaneously in a predetermined pattern. For example, electrons may be charged to a plurality of donor atoms disposed on a quadrilateral pattern.

[0115] Reference now Fig. 11B , shows another view 1130 of the donor atom 1104 in a qubit memory state with corresponding control lines and control islands. In this "memory" state, the hyperfine interaction is naturally exactly zero since there are no electrons. The energy diagram 1150 shows the energy levels associated with ESR / NMR control. The four energy levels have four allowed transitions, two RF NMR transitions, and two microwave ESR transitions. Each of these transitions can be individually targeted to perform single qubit rotations and electron-nuclear spin interactions.

[0116] By selectively loading electrons on specific donor atoms, quantum gate operations can be selectively and simultaneously performed on this quantum processor architecture.

[0117] Electrons are loaded onto a given donor site by pulsing the corresponding gate, which immediately imparts a non-zero hyperfine interaction between the donor's nuclear and electron spins after the electron is loaded. This shifts the resonant frequency of a given donor's nuclear spin. Thus, a given group of qubits can be independently resonated with the global RF / MW field to affect a desired single qubit gate. This is a highly uniform digital change in the hyperfine values ​​and is controlled by the donor-island tunneling process, which can be engineered with atomic precision and characterized during the system build phase.

[0118] In the memory state, the qubit nuclear spins are far away from resonance and are not affected by the global control field.

[0119] Two-qubit gates between nearest neighbor nuclear spin qubits are also controlled by electron loading / unloading operations. In the absence of bound electrons, the interactions between nuclear spins at these separations are negligible. However, when electrons are loaded onto neighboring atoms, the spin-spin dipole interaction increases (gμ) in addition to any exchange coupling felt by the electrons. B / g n μ n ) 2 ≈3×10 6 The interaction between qubits is effectively digitally converted by a factor of . In the presence of a global control field, the two-qubit logic gate can be decomposed into a series of well-defined single-qubit and two-qubit interactions. Therefore, all gates, initializations, and readouts are ultimately controlled by the unit cell gate group and can be implemented with a high degree of parallelism.

[0120] U.S. Patent Publication US20160125311, “Apparatus and method for quantum processing” describes a quantum processor implemented with semiconductor materials and a method of operating the quantum processor to perform error-corrected quantum computing, and its entire contents are incorporated herein.

[0121] It should be understood that the architecture described in the above embodiments allows for better coupling control via exchange interactions. Having limited variation in exchange interaction values ​​for multiple qubits in a silicon substrate allows for more efficient control of the qubits and provides a more feasible path toward error-corrected quantum computing architectures based on donors in silicon.

[0122] As used herein, the term "comprising" (and its grammatical variations) is used in the inclusive sense of "having" or "including," rather than in the sense of "consisting only of."

[0123] Those skilled in the art will appreciate that many changes and / or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. Therefore, the embodiments of the present invention are considered in all aspects to be illustrative and not restrictive.

Claims

1. A quantum processing system comprising: a plurality of donor atoms positioned in a silicon crystalline substrate, each donor atom being positioned at a donor site; a plurality of conductive control electrodes arranged around the donor atoms to operate the donor atoms as qubits; Wherein, at least two pairs of nearest adjacent donor atoms among the plurality of donor atoms are arranged along the [110] direction of the silicon crystal substrate and are configured to operate as quantum bits.

2. The quantum processing system according to claim 1, in, Each pair of nearest neighbor donor atoms has an exchange coupling value of , and Wherein, the maximum change of the exchange coupling value between the donor atom pairs is less than a predetermined factor.

3. The quantum processing system according to claim 2, wherein: The predetermined factor is 10.

4. The quantum processing system according to any one of claims 1 to 3, wherein: The silicon crystal substrate includes a plurality of donor sites arranged along the [110] direction, each site including a plurality of positions, and wherein a first donor atom is located at a first position among the plurality of positions at a first donor site, and a second donor atom is located at a second position among the plurality of positions at a second donor site, and wherein the first position is different from the second position.

5. The quantum processing system according to claim 4, wherein: The donor sites include six locations.

6. The quantum processing system according to claim 1, wherein: The distance between donor atoms in a pair of donor atoms is at least 10 nm.

7. The quantum processing system according to claim 1, wherein: The distance between donor atoms in a pair of donor atoms is between 10 nm and 25 nm.

8. The quantum processing system according to claim 4, wherein: When the first donor atom is located at any of the plurality of positions at the first donor site and the second donor atom is located at any of the plurality of positions at the second donor site, two-dimensional protection is provided to the exchange coupling J against valley interference.

9. The quantum processing system of claim 1, further comprising a plurality of control gates arranged around the donor atoms to create a detuned field to increase the exchange coupling values ​​between at least 90% of the donor atom pairs to a specific exchange coupling value.

10. A quantum processing system comprising: a plurality of donor atoms positioned at donor sites in a silicon crystalline substrate; a plurality of conductive control electrodes arranged around the donor atoms to operate the donor atoms as qubits; Wherein, at least one pair of nearest adjacent donor atoms is arranged in one of a plurality of mutually inequivalent donor-donor positions along the [110] direction of the silicon crystal substrate, wherein each inequivalent donor-donor position is associated with a normalized exchange coupling value, and the variation of the normalized exchange coupling value with respect to all the plurality of inequivalent donor-donor positions is less than a predetermined factor.

11. The quantum processing system according to claim 10, wherein: The plurality of non-equivalent donor-donor positions includes 10 positions.

12. A quantum processing system according to any one of claims 10 or 11, wherein: When the at least one pair of nearest neighbor donor atoms is arranged in any one of the plurality of inequivalent donor-donor positions, a two-dimensional protection is provided to the exchange coupling J against valley interference.

13. The quantum processing system according to claim 10, wherein: The predetermined factor is 10.

14. The quantum processing system according to claim 10, wherein: The distance between donor atoms in a pair of donor atoms is at least 10 nm.

15. The quantum processing system according to claim 10, wherein: The distance between donor atoms in a pair of donor atoms is between 10 nm and 25 nm.

16. The quantum processing system of claim 10, further comprising a plurality of control gates arranged around the plurality of donor atoms to create a detuned field to increase the exchange coupling value between at least 90% of the donor atom pairs to a specific exchange coupling value.

17. A quantum processing system comprising: a plurality of qubits created by positioning donor atoms along a [110] direction in a silicon crystal substrate such that the difference in magnitude of exchange coupling between pairs of donor atoms is less than a predetermined factor; as well as A plurality of control gates are arranged around the donor atoms to create a detuned field to increase the exchange coupling value between at least 90% of the donor atom pairs to a specific exchange coupling value.

18. The quantum processing system of claim 17, wherein: A pair of control gates of the plurality of control gates are arranged to control a pair of qubits to create a detuned electric field.

19. The quantum processing system of claim 18, wherein: The pair of quantum bits are at least 10 nm apart.

20. A quantum processing system according to any one of claims 17 to 19, wherein: The predetermined factor is 10.

21. The quantum processing system of claim 17, further comprising a plurality of conductive control electrodes arranged around the donor atoms to operate the donor atoms as qubits.

22. A structure for use in a quantum processing system, the structure comprising: A silicon crystal substrate, the silicon crystal substrate comprising a plurality of donor atom sites arranged along a [110] direction of the silicon crystal substrate, each donor atom site comprising a plurality of possible positions for positioning a donor atom; a plurality of donor atoms, each donor atom positioned in a corresponding donor atom site of the plurality of donor atom sites in any one of the plurality of possible positions; wherein the donor atoms closest to each other in the [110] direction interact with each other, and each pair of nearest neighboring donor atoms has an exchange coupling value of Wherein, the maximum variation of the exchange coupling values ​​between multiple pairs of nearest neighboring donor atoms is less than a predetermined factor.

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