Advanced quantum processing system

Abstract

A method for performing one or more quantum operations on a quantum processor is provided. Wherein the quantum processor comprises a plurality of quantum dots in a semiconductor substrate, at least a subset of the quantum dots being multi-dopant dose quantum dots. Further, each multi-dopant quantum dot includes two or more dopant atoms, and at least one of the plurality of quantum dots restricts unpaired electrons / holes. The method includes performing the one or more quantum operations on the quantum processor using one or more modes of operation, the one or more modes of operation including: using spins of the unpaired electrons / holes of quantum dots as data qubits; using the multi-doping dose quantum dots as error correction logic quantum bits; using at least one nucleus spin of dopant atoms of the multi-dopant quantum dots as a data quantum bit; or using the spins of the non-paired electrons / holes and at least one nuclear spin of dopant atoms of multi-dopant quantum dots as data quantum bits.

Description

Technical Field

[0001] Embodiments of the present disclosure relate to advanced processing systems and methods of operating the same, and more particularly to quantum processing systems that can be controlled to perform quantum operations. Background Art

[0002] The developments described in this section are known to the inventors. However, unless otherwise indicated, none of the developments described in this section should be assumed to be prior art solely because they are included in this section or those developments are known to those skilled in the art.

[0003] Large-scale quantum processing systems are expected to bring about a technological revolution and are expected to solve problems that classical machines cannot solve. To date, several different structures, materials, and architectures have been proposed to implement quantum processing systems and fabricate their basic information units (qubits or quantum bits).

[0004] For example, one way to fabricate qubits is to use the nuclear spin or electron spin of phosphorus donor atoms in silicon, such that the nuclear / electron spin of each phosphorus donor atom serves as a qubit. Due to the addressability and long coherence of phosphorus spins, this fabrication technique provides near-ideal qubit state encoding. Additionally, qubits fabricated in this manner have demonstrated lifetimes on the order of seconds and benefit from the ability to achieve electrical addressing and high fidelity in a semiconductor host.

[0005] However, to begin to see the computational advantages that quantum processing systems can provide, it is necessary to perform basic quantum operations on such quantum processing systems - which is not easy. Summary of the Invention

[0006] According to a first aspect of the present disclosure, there is provided a method for performing one or more quantum operations on a quantum processor, the quantum processor including a plurality of quantum dots in a semiconductor substrate, at least a subset of the quantum dots being multi-doped quantum dots, each multi-doped quantum dot including two or more dopant atoms, and at least one of the plurality of quantum dots confining an unpaired electron / hole, the method including: performing the one or more quantum operations on the quantum processor using one or more operating modes, the one or more operating modes including: using the spin of the unpaired electron / hole of the quantum dot as a data qubit; using the multi-doped quantum dot as an error correction logic qubit; using the nuclear spin of at least one of the dopant atoms of the multi-doped quantum dot as a data qubit; or using the spin of the unpaired electron / hole and the nuclear spin of at least one of the dopant atoms of the multi-doped quantum dot as a data qubit.

[0007] Adjacent quantum dots among the plurality of quantum dots may be positioned approximately 5 nanometers to 20 nanometers apart.

[0008] In some embodiments, when the spin of the unpaired electron / hole of the quantum dot is used as a data qubit, the nuclear spin of the one or more dopant atoms in the quantum dot serves as an atomic magnet.

[0009] Additionally, when the multi-doped quantum dot is used as the error correction logic qubit, the spin of the unpaired electron / hole of the multi-doped quantum dot serves as a data qubit, and the nuclear spin of the one or more nuclei of the multi-doped quantum dot is used for error correction. Similarly, when the nuclear spin of at least one dopant atom is used as a data qubit, the corresponding spin of the unpaired electron / hole is used for readout, addressability, or coupling of the data qubit to adjacent quantum dots.

[0010] In some instances, coupling to adjacent quantum dots is performed via electron / hole spin shuttling between the multi-doped quantum dot and the adjacent quantum dot or via exchange coupling between the unpaired electron / hole of the multi-doped quantum dot and the unpaired electron / hole of the adjacent multi-doped quantum dot.

[0011] In some instances, nuclear magnetic resonance or EDSR is used to control the nuclear spin of the dopant atoms. In some instances, electron spin resonance or EDSR is used to control the spin of the unpaired electron / hole.

[0012] In some embodiments, the one or more quantum operations include at least one of single-qubit operations, two-qubit operations, or multi-qubit operations.

[0013] In some embodiments, when the one or more quantum operations are multi-qubit operations, the quantum operations are performed using the spin of the unpaired electron / hole and the nuclear spin of the dopant atoms in the multi-doped quantum dot.

[0014] According to a second aspect of the present disclosure, there is provided a method for performing one or more quantum operations on a quantum processor, the quantum processor including a plurality of quantum dots in a silicon substrate, at least one subset of the quantum dots being multi-doped quantum dots, each of the multi-doped quantum dots including two or more dopant atoms, and at least one of the plurality of quantum dots confining an unpaired electron / hole, the method including: performing the one or more quantum operations on the quantum processor using one or more operating modes, the one or more operating modes including at least one of: using one or more of the multi-doped quantum dots as error correction logic qubits; using the nuclear spin of at least one of the dopant atoms of the multi-doped quantum dot as a data qubit; or using the spin of the unpaired electron / hole and the nuclear spin of at least one of the multi-doped quantum dots as a data qubit.

[0015] According to a third aspect of the present disclosure, a quantum processor is provided, the quantum processor comprising: a silicon substrate; a dielectric material layer on the silicon substrate; a plurality of quantum dots fabricated in the silicon substrate, each quantum dot comprising at least one dopant atom, at least one subset of the quantum dots being multi-doped quantum dots, and one or more of the quantum dots confining unpaired electrons / holes; wherein, during operation of the quantum processor, the spins of the unpaired electrons / holes and / or the nuclear spins of one or more of the dopant atoms in the quantum dots are used as data qubits.

[0016] The number of dopant atoms within each quantum dot and / or the spatial configuration of the dopant atoms are selected to achieve a predefined hyperfine coupling range between each of the nuclear spins within each quantum dot and the spin of the electron / hole. Additionally, the distance between two adjacent quantum dots is selected to achieve a predefined tunneling coupling range between the spins of the electrons / holes bound to the adjacent quantum dots. In some instances, the distance between adjacent quantum dots is about 5 nanometers to 20 nanometers. Additionally, in some instances, the predefined tunneling coupling is in the range of 1 kHz to 1 THz.

[0017] The size of each quantum dot in the quantum processor may be less than 3 nanometers. Additionally, the plurality of quantum dots may be arranged in a one-dimensional geometric pattern, a two-dimensional geometric pattern, or a three-dimensional geometric pattern.

[0018] In some instances, the quantum processor further comprises: one or more sensors for measuring the final state of the qubits associated with the quantum dots among the plurality of quantum dots. In some instances, the quantum processor further comprises: one or more reservoirs located near the quantum dots. The one or more reservoirs provide electrons / holes for confinement in one or more of the quantum dots, and the distance between the one or more reservoirs and the one or more quantum dots is about between 10 nanometers and 25 nanometers.

[0019] During operation of the quantum processor of the third aspect: when the spin of the unpaired electron / hole of the quantum dot is used as a data qubit, the nuclear spin of the one or more dopant atoms of the quantum dot is used for error correction or as an atomic magnet; when the nuclear spin of the one or more dopant atoms is used as a data qubit, the spin of the unpaired electron / hole is used to address or measure the spin of the one or more dopant atoms; or when the nuclear spin of the one or more dopant atoms is used as a data qubit, the spin of the unpaired electron / hole is used to couple the quantum dot to an adjacent quantum dot.

[0020] According to a fourth aspect of the present disclosure, a method for performing multi-qubit operations is provided. The method includes: providing a multi-doped quantum dot including two or more dopant atoms and an unpaired electron / hole confined in the quantum dot; and using the spin of the unpaired electron / hole and the nuclear spins of the two or more dopant atoms as qubits and using the qubits to perform the multi-qubit operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] While the invention is susceptible to various modifications and alternative forms, specific embodiments are shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the drawings and detailed description are not intended to limit the invention to the particular form disclosed. The intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

[0022] Figure 1 is a schematic diagram illustrating a conventional architecture based on single-donor qubits, where the qubits are controlled using alternating A gates and J gates.

[0023] Figure 2 shows a conventional quantum processor architecture including three planes.

[0024] Figure 3 illustrates an example flip-mode qubit called a trigger qubit.

[0025] Figure 4 shows another flip-mode qubit architecture.

[0026] Figure 5 shows an example multi-donor quantum dot according to an aspect of the present disclosure.

[0027] Figure 6 is a schematic diagram showing three different multi-donor quantum dots.

[0028] Figure 7 shows an example of a 1D architecture having five multi-donor quantum dots.

[0029] Figure 8 shows other examples of 1D architectures with varying inter - dot distances and angles.

[0030] Figure 9 shows three examples of 2D architectures containing multiple donor quantum dots.

[0031] Figure 10 shows four examples of 3D crystal structures of multiple donor quantum dots.

[0032] Figure 11A Illustrate an example quantum processor according to aspects of the present disclosure.

[0033] Figure 11B Illustrate an example method for manufacturing Figure 11A a quantum processor.

[0034] Figure 12A Show an example 3P quantum dot.

[0035] Figure 12B Show an example algorithm using a subset of control methods used within a 3P dot.

[0036] Figure 13A and Figure 13B Show eight ESR transitions and frequencies for a 3P quantum dot, respectively, and Figure 13C Illustrate the electron - nuclear coupling for this 3P quantum dot.

[0037] Figure 14 Show a schematic protocol for measuring the single nuclear spin within a 3P quantum dot.

[0038] Figure 15 Show a schematic protocol for measuring all nuclear spins within a 3P quantum dot.

[0039] Figure 16A Show the experimental state tomography of a three - qubit Greenberger - Horne - Zeilinger (GHZ) state measured on a 3P quantum dot.

[0040] Figure 16B Show a circuit diagram for generating a GHZ state between three nuclear spin qubits.

[0041] Figure 16C Is a schematic diagram of a quantum device including a donor - bound electron spin experiencing a local hyperfine field.

[0042] Figure 17 Show the example connectivity of electron - spin qubits and nuclear - spin qubits in 2P and 3P dots, where each dot operates as a logical qubit.

[0043] Figure 18AShows an existing algorithm for correcting single qubit phase errors in a system with three qubits.

[0044] Figure 18B Shows an implementation of an error correction algorithm according to aspects of the present disclosure in 2P quantum dots.

[0045] Figure 19 Illustrates the shuttle mode for a 1D chain of four quantum dots and one electron.

[0046] Figure 20 Shows the connectivity of spin qubits for exchange-coupled 2P and 3P dots.

[0047] Figure 21A Shows an example multi-donor dot array with four quantum dots.

[0048] Figure 21B Illustrates Figure 21A the connectivity available in an example array. This demonstrates a natural means for scaling up these multi-donor quantum dot arrays to form natural multi-qubit gates. Detailed Description

[0049] Although the quantum processors and quantum dots described herein refer to donor atoms and unpaired electrons, it should be understood that these are merely examples, and without departing from the scope of the present disclosure, the quantum processors and quantum dots of the present disclosure can be formed from donor atoms or acceptor atoms (commonly referred to as dopant atoms) and unpaired electrons or holes can be confined in such quantum dots.

[0050] To date, several quantum processing architectures in silicon have been disclosed. One such architecture was proposed by B.E. Kane in 1998, which includes an array of nuclear spins located on donor atoms in silicon. Logic operations can be performed on such devices using electron-mediated nuclear spin interactions. Additionally, the electron-mediated nuclear spin interactions are controlled by voltages applied to metal gates in the semiconductor device, enabling external manipulation of the nuclear spin dynamics required for quantum computing.

[0051] Figure 1 Illustrates two qubits in a one-dimensional array design based on the above architecture. The array includes phosphorus donor atoms and electrons in a silicon host. The donor atoms are located below the surface of the silicon substrate, and the gates are located above the surface of the silicon substrate. The A gate controls the resonance frequency of the nuclear spin qubits, and the J gate controls the electron-mediated coupling between adjacent nuclear spins.

[0052] Quantum mechanical calculations using this architecture are performed by precise control of the following three external parameters: (1) The A gate above the donor controls the strength of the hyperfine interaction and thus the resonance frequency of the nuclear spins below the gate; (2) The J gate between donors turns on and off the electron-mediated coupling between nuclear spins; (3) A globally applied AC magnetic field (B AC ) flips the nuclear spins at resonance. Custom-tuning the coupling of each spin to its neighbors and B AC enables different operations to be performed simultaneously on each of the spins. Finally, measurements are performed by transferring the nuclear spin polarization to the electrons and determining the electron spin state by the effect of the nuclear spin polarization on the orbital wave function of the electrons, which can be probed using capacitance measurements between adjacent gates.

[0053] Although this architecture enables fast single-qubit and two-qubit logic operations using the A and J gates, it presents several challenges. For example, this architecture requires the deterministic fabrication of single phosphorus donor atoms at precise positions and orientations in silicon. Additionally, there is limited tunability of the exchange coupling (J) between qubits.

[0054] According to another quantum processor architecture in silicon, quantum information can be encoded on phosphorus donor atoms arranged in a 2D square array. Figure 2 This architecture, which includes three planes, is shown. In the upper and lower planes, nanowires form a regular cross-grid of control lines. In the middle plane, a 2D lattice of P donor qubits is patterned with atomic precision and tunnel-coupled to a phosphorus-doped quantum dot that forms the island of a vertical single-electron transistor (SET) structure. The upper series of nanowires alternates as the SET source (S) and upper gate (G A ) while the lower complementary series of control lines serves as the SET drain (D) and lower gate (G B)Alternation. Each qubit in this architecture is addressed by a set of top / bottom gate crossings around each cell. In any given unit cell, the SET island facilitates electron spin loading and unloading, controlled by the bias conditions defined by the associated crossings of the proximal source, drain, and gates. The bias conditions can be set to independently couple the SET island to a specific neighboring donor to load / unload electrons for activation / deactivation, and the control layout allows this operation to be multiplexed across the array. Once a qubit is activated, it can be controlled by externally applied (global) radio frequency (RF) and / or microwave (MW) fields acting on the nucleus-electron state, based on well-understood electron spin resonance (ESR) and nuclear magnetic resonance (NMR) techniques, to perform single-qubit and two-qubit quantum gates simultaneously on the activated donor qubits. Unactivated qubits are sufficiently detuned and remain unaffected by global control. Initialization and readout of the qubit nuclear spin follow well-established protocols based on transferring quantum information from the nuclear spin to the electron spin and spin-dependent electron tunneling to the SET island.

[0055] Although this architecture does not require vertical gates, it presents several challenges. Since this architecture is based on single donor atoms as qubits, it also requires the deterministic fabrication of single phosphorus donor atoms at precise positions and orientations in silicon. Additionally, gate operations between two qubits in this architecture can be slow.

[0056] In some instances, electric dipole spin resonance (EDSR) can be utilized to control spin qubits with a local electric field. EDSR is typically achieved by coupling the spin of the qubit to the charge degree of freedom. This spin-charge coupling can be caused by spin-orbit interactions. This so-called spin-orbit coupling (SOC) is generally present in atoms and solids - due to relativistic effects, electrons moving in an electric field gradient experience an effective magnetic field in their reference frame. However, in the case of silicon, SOC is inherently weak.

[0057] To increase the strength of SOC, several different mechanisms can be used, such as using materials with large spin-orbit coupling or large gradient magnetic fields from micromagnets. Alternatively, the hyperfine interaction between the electron and the surrounding nuclear spin qubits can be modulated to electrically control the qubits without the need for any additional control elements (such as magnetic field generators, etc.), and the operation of controlling the qubits requires less power.

[0058] One such qubit processor architecture that utilizes the hyperfine interaction between an electron and the spins of surrounding atomic nuclei is a qubit processor architecture incorporating flip-mode qubits, which are based on the spin of a single electron that can be in two different charge states. By carefully tuning the electric field (E), the electron can be placed in a charge superposition between two sites (thereby forming a charge qubit). If the electron spin Zeeman splitting is comparable to the charge qubit splitting, the spin state and charge state of the electron become mixed. This mixing results in a spin-charge coupling proportional to the difference in the transverse terms of the Hamiltonian at each site. Figure 3 An example of such a flip-mode qubit is referred to as a trigger qubit.

[0059] In this arrangement, the qubit includes a quantum dot 304 and a donor atom 306. In a trigger qubit, the spin-charge coupling results from the hyperfine interaction between the electron spin and the nuclear spin of a single phosphorus donor atom 306, which can be used to generate an electron-nuclear spin trigger transition. The flip-mode operation EDSR is performed by positioning the electron in a superposition of charge states between the donor nucleus and an interface quantum dot 304 created using an electrostatic gate 308. In this charge superposition state, the hyperfine interaction changes significantly due to small changes in the detuning between the two sites.

[0060] Specifically, Figure 3 A quantum processing device 300 including a flip-mode qubit 307 is shown. The qubit 307 is formed by a quantum dot 304 and a donor atom 306 that share a single electron and wave function. The donor atom 306 is located within a silicon substrate, and the quantum dot 304 is formed near the interface to confine the electron of the donor atom 306. The gate 308 is positioned above the quantum dot 304 (on a dielectric).

[0061] The gate electrode 308 is operable to interact with the donor atom 306. For example, the gate 308 can be used to induce an AC electric field in the region between the interface and the donor atom 306 to modulate the hyperfine interaction between the electron located at the quantum dot 304 and the donor nuclear spin.

[0062] When the qubit is electrically driven, the electron spin flips along with the nuclear spin of the donor. That is, the electric field can be used to control the quantum state of the qubit associated with the electron-nuclear spin eigenstate pairs (i.e., 'electron spin up, nuclear spin down' and 'electron spin down, nuclear spin up').

[0063] These types of flip-mode qubits have some disadvantages. For example, this quantum processing device requires precise design and fabrication of the qubits - which is often difficult to achieve.

[0064] Another type of flip-mode qubit architecture is inFigure 4 is shown in Figure 4 The flip-mode qubit 401 in Figure 4 includes two quantum dots 402A and 404B. Each quantum dot is composed of donor clusters. The qubit 401 uses the hyperfine interaction from the electron-nuclear system naturally existing in the donor system to generate synthetic spin-orbit coupling (SOC).

[0065] The entire device 400 is epitaxial - that is, the donor clusters 402A, 402B are fabricated within the substrate and away from the interface. Each qubit can be controlled by one or more gates (one gate 406 is shown here), and the one or more gates allow full electrostatic control of the qubit 401. DC electric fields, fast electrical pulses, and microwave (MW) electric fields can be applied to these two gates individually or jointly. One of the gates 406 can be tunnel-coupled to one of the quantum dots (402A, 402B) in the pair to allow electron loading and unloading on the qubit 401. Due to the increased electrostatic coupling of the gate 406 to the qubit 401, it is advantageous to use the gate 406 to drive the qubit.

[0066] Qubit readout can be performed using a separate charge sensor (not shown) or dispersively using one of the one or more previously mentioned gates (e.g., gate 406).

[0067] In the flip mode, the electron-nuclear hyperfine interaction of the qubit promotes an effective energy gradient oriented along the transverse direction relative to the external magnetic field (the magnetic field along this direction is used to drive the qubit). However, even in this architecture, there are still some problems - for example, logical operations have not been demonstrated in this architecture, and each spin requires individual control.

[0068] Another quantum processing architecture utilizes singlet-triplet qubits. The two-electron singlet-triplet spin qubits offer the advantage of full electrical control (i.e., no micro magnets or high-frequency RF antennas are required). Additionally, when compared with the single-spin qubit counterparts of these qubits, these qubits exhibit immunity to global magnetic field noise. The double quantum dots of this architecture can be disposed on a silicon substrate. Specifically, two quantum dots (each having one or more donors) are constructed side by side and tuned such that the two quantum dots are tunnel-coupled. Then, the singlet-triplet qubits can be encoded in the double quantum dot sites. The smaller-scale encoded singlet-triplet qubits are capable of achieving: large inter-qubit couplings in the order of 5 GHz - 50 GHz; a system not considered in previous quantum processor architectures. Such larger couplings open up a path to implementing faster two-qubit gates in a fault-tolerant quantum computing architecture, which are performed via the electric dipole coupling (also known as 'capacitive coupling') between adjacent qubits.

[0069] However, this architecture also faces certain challenges. For example, logical operations have not been demonstrated in this architecture, and each spin requires individual control.

[0070] ***

[0071] Aspects of the present disclosure relate to a novel quantum processing architecture and quantum processor including quantum dots formed by a plurality of donor atoms. Different from previously known architectures in which qubits are formed by electron spins or nuclear spins, in the presently disclosed quantum processor, the electron spins and / or nuclear spins of the quantum dots can be used to act as qubits for various different types of quantum operations. For example, the electron spins can be used as data qubits, while the nuclear spins of the quantum dots are used as atomic magnets. Similarly, the electron spins can be used as data qubits, while the nuclear spins of the quantum dots are used for error correction, such that the dots can be used as error correction logical qubits. In another example, the nuclear spins in the quantum dots can be used as data qubits, while the electron spins in the quantum dots are used for addressing or measuring the nuclear spin qubits. In another example, the nuclear spins can be used as data qubits, while the electron spins in the quantum dots are used to couple the quantum dot to an adjacent quantum dot via electron shuttling or exchange coupling. Finally, both the electron spins and one or more nuclear spins can be combined and used as data qubits.

[0072] This architecture and / or device is particularly beneficial in the near term in the so-called noisy intermediate-scale quantum (NISQ) era, where multi-donor quantum dots offer several advantages. However, this architecture will also allow for the use of atom qubits fabricated using STM to produce large-scale universal quantum computers.

[0073] Generally, to execute a given algorithm, multiple quantum operations may be required, such as initialization, several SWAP gates, several CROT gates, error correction, etc. Conventionally, multiple resources are required to perform these operations, and heretofore, known quantum architectures typically require a large number of control sequences to perform some or all of these quantum operations. The presently disclosed quantum processing architecture and device are capable of achieving the relatively easy execution of these multiple types of quantum operations within the same quantum dot by using the quantum dots in the different modes described above. Specifically, as previously mentioned, the presently disclosed quantum processing system can encode quantum information in the electron spins and / or nuclear spins of the quantum dots, thereby allowing either of the nuclear spins or the electron spins to be used for gate operations, performing error correction, acting as data qubits, etc.

[0074] In addition, since the quantum dots can include multiple donor atoms, the presently disclosed quantum processors are easier to fabricate compared to previously known systems. Further, the individual quantum dots do not necessarily have to have the same number of donor atoms. Some quantum dots can have two donor atoms, some can have three donor atoms, and some can have four or more donor atoms. The system can also tolerate some quantum dots being inadvertently fabricated with a single donor atom.

[0075] The presently disclosed quantum processing architecture can also be easily scaled in one, two, or three dimensions, where the connectivity between adjacent dots can be achieved via electron shuttling or exchange coupling.

[0076] In addition, the multi-donor dot structure provides unique properties as it enables multi-qubit gates within a native gate set, as well as single-qubit gates that can be constructed using these multi-qubit gates. The qubits can be encoded in nuclear spins and / or electron spins. Each multi-donor dot can be understood as a register of nuclear spin qubits coupled to a single unpaired electron spin via hyperfine interactions. Additionally, multi-qubit gates can be extended to a larger number of qubits using exchange coupling. The native multi-qubit gates offer inherent advantages as constructing such multi-qubit gates using single-qubit and two-qubit gates is resource-intensive. A reduced number of gate operations can allow for a reduced circuit depth as more complex quantum algorithms can be executed within the qubit coherence time.

[0077] In addition to the above, the exchange interaction between quantum dots is more tunable between two adjacent asymmetric donor dots compared to adjacent symmetric single-donor quantum dots, and since the exact spatial position of the nuclear spins in the quantum dots can vary, the resonance energy of each electron spin can be different from dot to dot, which improves the addressability of the quantum dots. That is, it is easy to tune and address individual quantum dots using global electrical or magnetic signals. Finally, the strong confinement potential generated by the multi-donor quantum dots results in smaller electron wave functions and thus longer relaxation or coherence times.

[0078] Figure 5 An exemplary multi-donor quantum dot device 500 as disclosed herein is illustrated. Quantum dot device 500 includes a quantum dot 501 located in a semiconductor substrate 504. In this example, the semiconductor substrate 504 is 28 silicon. There is a blocking material / dielectric 505 (such as silicon dioxide) on top of the silicon substrate 504.

[0079] The multi-donor quantum dot 501 includes a plurality of dopant dots 510 embedded in a semiconductor substrate 504. In this example, the quantum dot 501 includes three dopant atoms 510A, 510B, and 510C. The distance between the dopant dots is below the Bohr radius such that the electron wave functions cover all the dopant atoms simultaneously. In one example, the distance is less than or equal to 3 nanometers.

[0080] Additionally, the gate 511 can be located on the dielectric 505 in a region above the donor cluster of the donor atoms 510A, 510B, and 510C. A voltage can be applied to the gate 511 to confine one or more electrons 512 in the quantum dot 501. These electrons 512 are confined by the Coulomb potential of the donor atoms. In this example, one electron 512 is confined in the quantum dot 501. However, Figure 5 the 3P quantum dot shown can confine more electrons. It should be understood that although the gate 511 is shown as a surface gate, the gate (in some embodiments) can be a planar gate fabricated within the silicon substrate and in the same plane as the quantum dot 501.

[0081] Generally, the donor atoms 510 are placed in the silicon substrate 504 with atomic precision using scanning tunneling lithography. Specifically, during fabrication, a lithographic patch can be defined in the semiconductor substrate. Then, a predetermined number of donor atoms 510 can be placed in the lithographic patch. In some examples, the donor atoms 510 can be located approximately 50 nm below the surface. In Figure 5 the example shown, three donor atoms are placed in the lithographic patch.

[0082] As described above, the multi-donor quantum dot 501 can have two or more donor atoms. Figure 6 A schematic diagram showing three different multi-donor quantum dots 501A - 501C. The large circles 602 represent the wave functions of the unpaired electrons 512 confined to each multi-donor quantum dot 501. The small circles represent the donor atoms 608 - 612. For example, in the multi-donor quantum dot 501A, there are two donor atoms 608 and an unpaired electron confined to the quantum dot 501A, where the electron wave function is represented by 602.

[0083] In some examples, the donor atoms can be phosphorus atoms, and a multi-donor dot with m phosphorus atoms can be labeled as an mP quantum dot, where m is an integer and m ≥ 1. Thus, the multi-donor quantum dots 501A - C can be labeled as 2P quantum dot, 3P quantum dot, and 4P quantum dot, respectively.

[0084] A quantum processor can be formed by a plurality of such multi-donor quantum dots 501 arranged in an array or pattern. In addition to the multi-donor quantum dots, such a quantum processor can also include some single-donor atom quantum dots (which can be the same as those described above with respect to Figure 3The quantum dots described above).

[0085] The quantum dot architecture may include a one-dimensional (1D) array of quantum dots. Figure 7 An example architecture 700 showing a 1D array including five quantum dots QD1 - QD5 is shown. Each quantum dot may have one or more donor atoms. The inter-donor distance or the size (r) of any given quantum dot is less than the Bohr radius. In some examples, this inter-donor distance / size of the quantum dot is r ≤ 3 nanometers. The inter-dot distance (d) - the distance between adjacent quantum dots - may be in the range of 5 nanometers to 20 nanometers. It should be understood that the inter-dot distance (d) between the quantum dots 501 may not be uniform but may vary in the range of 5 nanometers to 20 nanometers. Additionally, the size (r) of the quantum dot may be determined by the number of donor atoms present in the quantum dot - the more donor atoms in the quantum dot, the larger the size or inter-donor distance r of the quantum dot, and the fewer donor atoms in the quantum dot, the smaller the size of the quantum dot. For example, the size of a 1P quantum dot may be about 0.7 nanometers, the size of a 2P quantum dot may be about 1 nanometer, and the size of a 3P quantum dot may be about 1.5 nanometers.

[0086] Figure 8A and Figure 8B Examples of other quantum processor architectures 810, 820 each showing a 1D array of quantum dots with varying inter-dot distances and angles are shown. The quantum dots are shown as circles positioned along the 1D array. For example, array 810 has a staggered geometry where the quantum dots are not aligned along a single axis. Instead, the odd-numbered quantum dots are positioned along a first line axis, and the even-numbered multi-donor quantum dots are positioned along a second line axis, where the first axis is parallel to the second axis.

[0087] Array 820 is similar to array 800, but in this case, the quantum dot pairs are positioned along the first line axis and the second line axis.

[0088] In other examples, a quantum processor including the multi-donor quantum dots described above may be formed by a two-dimensional (2D) pattern or a three-dimensional (3D) pattern. Figure 5 Examples of three 2D quantum processor architectures showing a plurality of quantum dots 501 shown as circles are shown.

[0089] Figures 9A to 9C An example 4×4 square lattice 910 showing 16 quantum dots positioned at each of the intersections of a square lattice is shown. Figure 9A

[0090] Figure 9B ​Illustrates an example triangular lattice 920 including 18 quantum dots located at each of the intersections of a triangular lattice. Figure 9C Illustrates an example hexagonal 2D lattice 930 in which quantum dots are located on each edge of the hexagonal lattice. Each quantum dot 501 in architectures 910 - 930 may have a variable number of donor atoms, where the donor - to - donor distance is ri ≤ 3 nanometers. Additionally, the inter - dot distance between any two adjacent quantum dots may be in the range of 5 nm - 20 nm.

[0091] Figures 10A to 10D Depicts an example 3D quantum processor architecture including a plurality of quantum dots. Specifically, Figure 10A Illustrates a cubic crystal structure 1010 that shows 8 quantum dots, each located at the vertices of the cubic structure 1010. In this case, the distance between the quantum dots may be substantially uniform. In some examples, the crystal may be a simple orthorhombic crystal structure, where the nearest - neighbor distance may vary along each of the axes, d x ≠d y ≠d z .

[0092] Figure 10B Illustrates a face - centered cubic structure 1020 including 16 points. In this example, quantum dots are located at each vertex of the cubic structure, and then quantum dots are located at the centers of each face of the cube. Figure 10C Illustrates a body - centered cubic structure 1030 including 9 quantum dots. In this example, quantum dots are located at each vertex of the cubic structure, and then one quantum dot is located at the center of the cube. Figure 10D Illustrates a face - centered hexagonal structure 1040 including 17 quantum dots. In this example, quantum dots are located at each vertex of the hexagonal structure, and then one quantum dot is located at each of the top and bottom faces of the hexagonal structure, and three quantum dots are located in the middle of the hexagonal structure.

[0093] It should be understood that Figures 7 to 1 All of the example architectures depicted in 0 are merely exemplary. Quantum dots can be arranged in any one of the depicted configurations or any other 1D, 2D, or 3D geometric arrangement without departing from the scope of the present disclosure as long as each quantum dot maintains a maximum size less than the Bohr radius and the distance between adjacent quantum dots in any arrangement is between 5 nanometers and 20 nanometers.

[0094] Additionally, it should be understood that Figures 7 to 1 0 depicts only the arrangement of quantum dots in a quantum processor and does not depict any control gates, reservoirs, etc. Figure 11A Illustrates an example quantum processor 1100 including these additional elements. Specifically, Figure 11ADepict an array of quantum dots 1102 (including multi-donor quantum dots and zero or more single-donor quantum dots). The processor 1100 further includes a plurality of sensors 1104 and a plurality of control gates 1106. In this example, the quantum dot array is a 1D staggered array with 33 quantum dots (similar to the 1D array 810).

[0095] It should be understood that the quantum dots in the array can contain different numbers of donors. In this example, there is a ratio of one sensor to three quantum dots. However, it should be understood that in other embodiments or examples, the number of quantum dots per sensor can vary. Additionally, in some examples, the SET can be used as a sensor for reading out qubits. In other examples, other types of sensors (such as gate sensors or single-lead charge sensors) can be used instead of the SET to read out qubits. Electrons can be deterministically loaded and unloaded onto the dots 1102 by applying a voltage to the gate 1106. In some examples, the sensor 1104 can also act as an electron reservoir for providing electrons to the quantum dots for confinement. In other examples, an independent reservoir can be provided in addition to the charge sensor.

[0096] Although Figure 11A the depicted quantum processor shows control gates and sensors coplanar with the quantum dots, this is not the case in all embodiments. In other cases, one or more of the control gates and / or one or more of the sensors can be formed near the surface of the semiconductor substrate, while the quantum dots can be located within the semiconductor substrate. In additional examples, one or more of the control gates can be arranged in the form of control lines above and below the quantum dots, for example, as Figure 2 depicted.

[0097] Device fabrication

[0098] Figure 11B Outline the individual processing steps (steps a - k) for fabricating multi-donor quantum dots according to aspects of the present disclosure.

[0099] First, a clean Si 2×1 surface is formed in ultra-high-vacuum (UHV) by heating to near the melting point. This surface has a 2×1 unit cell and consists of rows of σ-bonded Si dimers, where the remaining dangling bonds on each Si atom form weak π-bonds with the other Si atom of the dimer they are part of.

[0100] Processing step (a), i.e., monohydride deposition, involves exposing the clean Si 2x1 surface to atomic H to break the weak Siπ-bonds, thereby allowing the H atoms to bond to the Si dangling bonds. Under controlled conditions, a monolayer of H can be formed with one H atom bonded to each Si atom, thus satisfying the reactive dangling bonds and effectively passivating the surface; see step (a).

[0101] Next, at process step (b) (i.e., hydrogen desorption), the STM tip is used to selectively desorb H atoms from the passivated surface by applying an appropriate voltage and tunneling current, thereby forming a pattern in the H resist; see step (b).

[0102] It should be understood that the H atoms desorb from the exact locations where the donor atoms are to be placed. For example, if the quantum processor includes a 2D square lattice of quantum dots, the H atoms are desorbed in such a way that multiple lithographic patches are created in the formation of the square lattice, where the distance between adjacent patches is between 5 nanometers and 20 nanometers. Additionally, the size of each of the lithographic patches created by hydrogen desorption can depend on the number of donor atoms required to be placed in the quantum dots. In one example, if 1 donor atom is to be positioned in one of the lithographic patches (to form a 1P quantum dot), and 2 donor atoms are to be positioned in adjacent lithographic patches (to form a 2P quantum dot), the STM tip can be used to desorb 6 hydrogen atoms in a first location to create a first patch, and 15 hydrogen atoms in a second location separated by 5 nanometers to 20 nanometers to create a second larger patch. Similarly, if a larger number of donor atoms are to be placed in a patch, more hydrogen atoms can be desorbed to create a larger-sized lithographic patch. In other examples, the size of the patch can be smaller or larger than that described in the above examples. Additionally, in some examples, machine learning techniques can be utilized to control the number of donor atoms placed in any lithographic patch.

[0103] This process is repeated to generate positions for other quantum dots. In this way, regions of exposed reactive Si atoms are exposed along the dimer rows, thereby allowing reactive species to subsequently adsorb directly to the Si surface.

[0104] Returning to Figure 11B , at step (c) (i.e., PH3 dosing), phosphine (PH3) gas is introduced into the vacuum system via a controlled leak valve connected to a specially designed phosphine micro-dosing system. The phosphine molecules bond firmly to the exposed Si surface through the pores in the H resist; see step (c). As previously noted, at specific donor sites, the phosphine molecules can bond to any of the exposed silicon dimers.

[0105] Subsequently, the STM-patterned surface is heated for crystal growth causing dissociation of the phosphine molecules and resulting in P binding to the first layer of Si; see step (d). Thus, the STM-patterned H-passivated surface is exposed to PH3, which is used to generate the desired donor molecules.

[0106] Then, hydrogen can be desorbed (at step (e)), followed by 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).

[0107] At step (h), rapid annealing of the surface is performed.

[0108] Then, silicon is grown on the surface at an elevated temperature, as shown in step (i). In one example, approximately 50 ± 10 nm of epitaxial silicon is grown at a temperature of 250 °C. In some cases, a blocking portion, also referred to as a locking layer, can be grown as shown in step (j). Finally, an electrically conductive gate can be aligned on the surface using electron beam lithography, as shown in step (k). Using registration markers (such as evaporated metal markers), the gate can be aligned at a lateral distance of 300 ± 50 nm from the buried quantum dots. Additionally, an antenna can also be aligned on the surface to generate an oscillating magnetic field B1 orthogonal to the substrate at the location of the quantum dots.

[0109] The manner in which the quantum dot 500 is fabricated determines the manner in which the donor atomic nuclei and / or electrons within the quantum dot can be used as qubits. Specifically, the specific geometry and placement of the donors within the lithographic patch or within the quantum dot enable reliable control of the hyperfine coupling, tunneling coupling, and tunneling rate to control the quantum operations of the single qubit gate, two-qubit gate, or multi-qubit gate as described above.

[0110] The donor atoms incorporated within a given site form a collective confinement potential for binding electrons. The number of donors and the spatial configuration of the donors within each quantum dot determine the confinement strength. The confinement strength in turn determines the hyperfine coupling between each of the nuclear spins and the electron spin.

[0111] As described above, the lithographic openings can be patterned at intervals of approximately 5 nanometers to 20 nanometers such that the tunneling coupling between the electron spins bound to two neighboring sites allows for high-fidelity two-qubit gates to be achieved between the electron spin qubits.

[0112] In the presently disclosed quantum processor, quantum information is encoded within the electron spin and / or nuclear spin. For electron spin, a process called spin-to-charge conversion is used to achieve readout. In this process, a single electron transistor (SET) charge sensor is used to determine the state of the electron spin qubit. The qubit-reservoir distance determines the electron tunneling rate - that is, how quickly the electron spin can be measured. To achieve fast and robust spin readout, the qubit-reservoir distance should ideally be approximately 10 nm to 25 nm.

[0113] Control method

[0114] The electron spin qubits and / or nuclear spin qubits in the multi-donor quantum dot 501 can be controlled using five main control methods: electron spin resonance (ESR), nuclear magnetic resonance (NMR), electrically driven spin resonance (EDSR), initialization, and readout.

[0115] Figure 12A An example 3P quantum dot 1200 with three donor atoms having nuclear spins labeled A, B, and C is shown. The electron is confined to the quantum dot 1200 and the wave function of the electron is represented by the ovoid 1202. Figure 12B Is a schematic diagram of the control method. The four vertical lines in the schematic diagram represent the electron spin 1203 and the three donor spins 1204, 1206, 1208.

[0116] The first control method 1210 is ESR. This can be used to control the electron spin 1203. ESR is a direct method of driving the electron between two spin states (up and down) of the electron. In the presence of an external magnetic field B0, the spin energy levels of the electron are no longer degenerate. The two spin states |↑>, |↓> are separated by an energy difference ΔE. Thus, by applying an AC magnetic field to the quantum processor 1100, the electron spin 1203 can be changed from the spin-down state to the spin-up state, or vice versa. ESR occurs because the magnetic moment of the electron couples to the external magnetic field.

[0117] Specifically, ESR is a transition between opposite electron spin states but the same nuclear spin configuration. For example, in a 2P dot, there are four ESR transitions: where the first arrow indicates the spin state of the electron, and the double arrows indicate the spin state of each of the two nuclear spins. For a 2P quantum dot, there are four possible nuclear spin configurations:

[0118] Figure 13A and Figure 13B Are plots showing the eight ESR transitions 1300 and frequencies 1310 of the 3P quantum dot 1200, respectively. For the 3P quantum dot 1200, there are a total of 2 3 = 8 nuclear spin configurations, and a total of 16 spin states. The 8 nuclear spin states are shown by the relative energy levels. The states in the bottom row correspond to the 8 nuclear spin states with spin-down electrons, and the top row corresponds to the 8 nuclear spin states with spin-up electrons. There are also Figure 13AAs shown, eight vertical ESR transitions indicated by 1301 - 1308. The ESR transition only flips the electron spin and does not affect the nuclear spin. Therefore, the ESR transition connects the bottom state to the top state directly above the bottom state.

[0119] For example, to excite the 3P quantum dot 1200 from the spin state to the spin state a single frequency corresponding to the ESR frequency shown in plot 1310 can be applied to a control gate near the quantum dot. The ESR frequencies 1311 - 1318 correspond to the ESR transitions 1301 - 1308 respectively. The ESR frequency is proportional to the applied magnetic field and can be varied over a wide range.

[0120] The second control method 1215 is EDSR. EDSR can be used to control the electron spin and nuclear spin in a multi - donor dot. The EDSR transition is an electron - nuclear trigger transition that can be performed by modulating the hyperfine interaction between each nuclear spin 1204, 1206, 1208 and the electron spin 1203. This modulation of the hyperfine interaction can be achieved by applying an electric field that shifts the electron wave function away from the donor nucleus. Therefore, EDSR is mediated by an electric field that simultaneously flips one of the nuclear spins and the electron spin in a multi - donor system. For a 3P system, there are twelve possible EDSR transitions (not shown).

[0121] Another control method for controlling the nuclear spin in a multi - donor quantum dot is to use nuclear magnetic resonance (NMR). This is shown as 1220 in Figure 12B Specifically, if the nuclear spins can be individually addressed, NMR allows control of the nuclear spins 1204, 1206, 1208. Each nuclear spin in a multi - donor quantum dot can have a different hyperfine coupling strength. In one example of a 3P dot, the hyperfine coupling strengths for three phosphorus donors can be 6 MHz, 68 MHz, and 101 MHz respectively. In this case, to flip the nucleus from the spin state to the state one or more of the control gates near the quantum dot 501 can be used to apply an NMR pulse at the frequency corresponding to this transition.

[0122] As shown at 1220, three different NMR pulses are possible in this 3P system. Three additional NMR pulses are also available at different frequencies, corresponding to the electron being in the |↑> state rather than the |↓> state. The frequency at which an individual nuclear spin can be addressed depends on the environment of that nuclear spin. Typically, the frequencies used to address nuclear spins are in the MHz range, while the EDSR frequencies and ESR frequencies used to address electron spins are in the GHz range.

[0123] Electron spin initialization and measurement control are depicted at 1230 in Figure 12B and nuclear spin measurement control is depicted as 1240 in Figure 12B .

[0124] In Figure 12B the initialization and measurement of the electron spin depicted at 1230 can be achieved using a spin-to-charge conversion process (such as Elzerman readout or ramp readout). The readout of the nuclear spin can be achieved by combining ESR control with electron spin readout, as schematically shown at 1240 in Figure 12B . The readout of the nuclear spin depends on the fact that the ESR operation on the electron spin depends on the state of the nuclear spin within a given multi-donor dot. An example protocol for nuclear spin readout in a 3P dot is shown in Figure 14 . In this example, a series of four ESR pulses are applied to the electron spin 1203, where the four frequencies correspond to the nuclear spin in the up state labeled Q3. Thus, using the subsequent readout of the electron spin 1203, the state of the nuclear spin can be effectively determined. To read out all nuclear spins simultaneously, the protocol shown in Figure 15 can be used, where ESR pulses at each frequency are applied, followed by a readout of the electron spin, such that the exact combination of the three nuclear spin states can be determined.

[0125] Operating mode

[0126] The control mechanisms identified above can be used in the example quantum processor described above to perform single-qubit operations, two-qubit operations, and multi-qubit operations on the quantum dots. Where multi-qubit operations are understood to be operations on three or more qubits. To perform such quantum operations, the quantum dots can operate in four different modes - a) using the electron spin as a data qubit and the nuclear spin as an atomic magnet; b) using the electron spin as a data qubit and the nuclear spin for error correction; c) using the nuclear spin as a data qubit; and d) using both the electron spin and the nuclear spin as qubits.

[0127] Using electron spin as a data qubit

[0128] In this operating mode, the nuclear spin is used as an atomic magnet, while the electron spin is used as a data qubit. The nuclear spin increases or decreases the qubit energy. The nuclear spin of the electron donor atom affects the energy splitting of the electron spin qubit via the hyperfine interaction A. The nuclear spin can be controlled via NMR using an AC magnetic field or via EDSR using an AC electric field. Thus, the nuclear spin can be initialized to a predetermined spin configuration. Specifically, controlling the orientation of the nuclear spin controllably generates an energy difference ΔE between two electron spin qubits on adjacent quantum dots, Z , thereby affecting the two-qubit gate operation between the two qubits.

[0129] The electron spin qubit encoding mode allows for the efficient operation of an array of electron spin qubits, whose splitting energy can be dynamically controlled. This is beneficial for addressability and high-fidelity two-qubit gates. When performing a gate operation, adjacent electron spin qubits can be exchange-coupled to perform the desired gate operation.

[0130] The operation of a four-qubit quantum processor consisting of three nuclear spins (3P) and one electron spin is experimentally demonstrated in Figure 16A and Figure 16B .

[0131] Figure 16A is a plot for state tomography of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state for three nuclear spins. The GHZ state is an entangled quantum state involving at least three particles. The height and color of each bar correspond to the amplitude and phase of each element in the density matrix measured in the computational basis, respectively.

[0132] By comparing the measured state with the ideal three-qubit GHZ state, the fidelity can be determined to be 79.7 ± 2.0%. The ideal GHZ for three qubits is:

[0133]

[0134] This confirms that the three nuclear spin qubits are entangled because the fidelity is greater than 50%. The successful generation of the GHZ state confirms that the control method described within this disclosure can be used in practice with high fidelity to operate multi-donor dots as multi-qubit processors.

[0135] Figure 16BIt is the circuit 1650 for generating the three-qubit GHZ state. The four vertical lines in the schematic diagram represent the electron spin 1652 and the three donor spins 1654, 1656, 1658. At the beginning of the circuit 1650, the electron spin and the three nuclear spins are initialized to the spin-down state. This circuit consists of five NMR pulses and two ESR pulses. At the end of this circuit, state tomography (Tomog. operation) is performed by independently measuring the x, y, and z projections of each nuclear spin to reconstruct the GHz density matrix.

[0136] Figure 16C Two adjacent quantum dots 1622 and 1624 within a multi-qubit quantum processing device (such as device 1100) are schematically shown. Each quantum dot may include one or more donor atoms. In this example, the left quantum dot 1622 includes two P donor atoms 1626, 1628, and the right quantum dot 1624 includes one P donor atom 1630. Additionally, the electron spin qubits may be respectively confined by the P donors in the left quantum dot 1622 and the right quantum dot 1624. Specifically, the electrons can be spatially bound to the donor atoms in each quantum dot. In the example shown here, one electron can be confined by the closely placed pair of P donors in the left donor dot 1622, and another electron can be confined by the single phosphorus donor atom in the right donor dot 1624. The ovoids 1632 and 1634 around the dopant atoms show the electron wave functions. The shape of the ovoids and the electron confinement are determined based on the number of P atoms in each donor dot. Since the left dopant dot includes two donor atoms, the electron wave function 1632 has an elliptical shape, while the right dopant dot includes one donor atom, and the electron wave function 1634 is more spherical in shape.

[0137] For such quantum dots, the energy difference ΔE between the two quantum dots Z is dominated by the hyperfine interaction A between the electrons (ovoids 1632 and 1634) and the nuclear spins (double-headed arrows 1626, 1628, and 1630) and the orientation of the nuclear spins. The hyperfine interaction A can be controlled by several parameters, specifically the number of donor atoms in each of the quantum dots, the arrangement of the donor atoms within the quantum dots and within the silicon crystal lattice 1636, the number of electrons in the quantum dots, and the strain and electric fields (applied / background fields) in the device.

[0138] Error correction

[0139] Quantum error correction (QEC) is an integrated component for building a universal quantum computer. One type of error correction is the parity operation, where single qubit flip or phase flip errors can be detected and corrected without measuring the encoded quantum state. A single multi-donor dot can be used as an error correction logical qubit that uses electron spin as the data qubit while using nuclear spin for stabilizer measurements and error correction schemes.

[0140] Figure 17 Shows an example connectivity between nuclear spin qubits and electron spin qubits that allows error correction methods to be applied to 2P quantum dots and 3P quantum dots. Figure 17 The top three lines in correspond to the spins of the 2P dot (2 nuclear spins and 1 electron spin), and the bottom four lines correspond to the available spins in the 3P dot (1 electron spin and 3 nuclear spins). As shown in this figure, the electron spins of the two quantum dots can be used as data qubits and are exchange-coupled to each other to perform two-gate operations (e.g., 1706 and 1708), while the nuclear spins in each of the quantum dots can be used as auxiliary error correction qubits. In one example, the 2P quantum dot (2 nuclear spins and 1 electron spin) is used as the first logical qubit 1702, and the 3P quantum dot (3 nuclear spins and 1 electron) is used as the second logical qubit 1704.

[0141] Parity operations are typically performed before and after other quantum operations. In some algorithms, this parity operation can be performed at regular intervals within the algorithm.

[0142] Figure 18A Shows an existing algorithm for quantum error correction (QEC) of single qubit phase errors in a system with three qubits (one data qubit and two auxiliary qubits). Figure 18A Each horizontal line in represents a qubit, i.e., |Ψ>, This algorithm consists of three stages: encoding, decoding, and recovery. The encoding stage includes two CNOT gates and a rotation gate. The CNOT gates are performed on the first pair of qubits |Ψ>, and then on the second pair of qubits |Ψ>, Then, the √X gate is applied to all three qubits. This gate performs a rotation about the X axis on all three qubits, such that the error correction scheme corrects the phase error.

[0143] The next stage of QEC is the decoding stage. This stage includes the inverse rotation gates -√X and the same CNOT gates in reverse. If an error occurs in the first qubit |Ψ>, the error is detected via the other two qubits. This is done by conditionally flipping the qubit according to the state of |Ψ> via the CNOT gate.

[0144] The last stage of QEC is the recovery stage. This stage includes a step where the state of |Ψ> is conditionally flipped according to the other two qubits, and if an error occurs, the error is corrected.

[0145] Figure 18B An implementation of the same QEC in a 2P quantum dot according to aspects of the present disclosure is shown. In a 2P dot, there are unpaired electrons and two nuclear spins - so there are a total of three potential qubits or spins. The electron spin is the data qubit and is labeled |Ψ>, and the two nuclear spins act as ancillary qubits and are labeled where the subscripts distinguish the two nuclear spins.

[0146] The sequence starts with an encoding stage that includes two CNOT gates and four √X rotation gates. The CNOT gates are performed between each of the nuclear spins and the electron spin using NMR. Then, four electron √X rotation gates are applied using ESR. For example, the √X gate can be performed on the electron |Ψ> based on the condition that both nuclear spins in the dot are in the state |1>; one of the nuclear spins is in the state |1>; neither of the nuclear spins in the dot is in the state |1>. Here, all four possible ESR √X gates have been applied, jointly implementing a single-qubit √X gate on the electron.

[0147] Next, four more √X rotation gates are applied to the two nuclear spins based on the condition that the electron spin is in the |1> state or the |0> state. These phase gates are applied using NMR similar to the ESR pulses described above, and a single-qubit √X gate is applied on the two nuclear spins. Each pair of NMR gates (i.e., applied to each nuclear spin due to different electron spin conditions) performs a single-qubit gate on the respective nuclear spin. The reason for the repetition is that the pulses must be conditional on all possibilities of the other spins in order to decouple that spin.

[0148] Next, the inverse gates (-√X) are performed using ESR and NMR as described above. The CNOT gates are applied again after using ESR, and later a conditional flip of the electron state is performed based on the state of the nuclear spins.

[0149] In this way, if an error occurs in either the nuclear spin or the electron spin, the error can be detected via the 2P quantum register and subsequently corrected. This entire sequence can be repeated by re-initializing the nuclear spin, thereby extending the coherence time and thus the quality of the quantum operations performed using the multi-donor quantum dot.

[0150] It should be understood that QEC can be performed on quantum dots having three or more donor atoms in a similar manner.

[0151] Using nuclear spin as a data qubit while using electrons for readout and addressability

[0152] The nuclear spin can be used as a data qubit for other operations such as storing data. In these cases, the nuclear spin can be read via the electron spin in the quantum dot. When an electron is present at the multi-donor quantum dot, individual nuclear spins can be addressed using specific NMR or EDSR frequencies because the hyperfine coupling provides the addressability as described above. Additionally, single qubit gates on the nuclear spin can be achieved by combining the EDSR and ESR techniques or directly using NMR. Additionally, multi-qubit gates can be performed between nuclear spin qubits within the same dot via the hyperfine coupling (geometric gates using ESR).

[0153] Using nuclear spin as a data qubit and using electron spin for coupling adjacent points

[0154] In the shuttle mode, electrons can shuttle between adjacent quantum dots. This can be useful for coherently transferring information from one quantum dot to another. It can also be used to change the addressability of the quantum dot. For example, if an electron resides on the dot, each of the nuclei can be individually controlled, while if the dot does not have an electron, only the nuclei can be controlled simultaneously. This can be used to perform global gates on many qubits or to reduce the spectral density required to control many qubits by "turning off the qubits" by removing the electrons. When used to transfer data, the nuclear spin can be used as a data qubit because the nuclear spin has a longer coherence time, and the electron spin can be used to transfer data from one quantum dot to another.

[0155] Figure 19 Illustrates the shuttle mode of a 1D chain of four quantum dots 1902, 1904, 1906, 1908 having 2P configurations, 4P configurations, 2P configurations, and 3P configurations respectively. In this example, one electron is confined to the first 2P dot and no other electrons are confined to the other quantum dots.

[0156] Electrons can shuttle from a first point to a second point by tuning the voltage of one or more control gates near these quantum dots. Then, electrons can shuttle between the second quantum dot and the third quantum dot by tuning the gate voltages near the second and third quantum dots. Similarly, electrons can shuttle between the third quantum dot and the fourth quantum dot by tuning the gate voltages near the third and fourth quantum dots. In this example, the electron wave function 1910 after the electrons shuttle from the second quantum dot and before the electrons shuttle to the fourth quantum dot is shown on the third quantum dot.

[0157] It should be understood that although this mode mainly operates on a single unpaired electron, this mode can be utilized for multiple unpaired electrons simultaneously, where the number of unpaired electrons is less than the number of quantum dots.

[0158] In this mode, the inter-dot coupling can be achieved by entangling the nuclear spins with the electrons via the hyperfine interaction and then coherently moving the electrons to different points. In fact, the electrons mediate entanglement gates between the nuclear spins located in separate dots. An entanglement gate is a gate that acts non-trivially on two or more qubits, as this effect cannot be achieved using only single-qubit gates. The state of each qubit in the entanglement gate depends on the states of the other qubits in the gate. In one example, the entanglement gate can be a two-qubit CNOT gate, a two-qubit gate, a three-qubit Toffoli gate, etc. In this mode, entanglement can be distributed throughout the multi-donor dot quantum processor 1100 via an exchange-based electron-electron gate or by shuttling electrons from one point to another.

[0159] Importantly, the nuclear spins of all unoccupied donor dots share the same resonance frequency. This means that all idle qubits (i.e., quantum dots without an electron spin) have the same resonance frequency and can be actively decoupled from the noisy environment in a straightforward manner via a series of NMR control pulses.

[0160] In the exchange coupling scheme, the connectivity between adjacent dots can be achieved using exchange coupling controlled by the gate voltage. Specifically, in this mode, both adjacent quantum dots will have an electron spin present and two-qubit gates (such as a CROT gate, a conditional phase gate), and the gates can be performed between adjacent quantum dots, different from the qubit shuttle operation mode discussed previously where there is only a single electron shuttling back and forth between adjacent points. Figure 21AFour quantum dots 2102, 2104, 2106, and 2108 in the two-dimensional array are marked. In this example, adjacent quantum dots (i.e., quantum dots 2102 and 2106, 2106 and 2108, 2104 and 2108, and 2102 and 2104) are coupled by the respective electron spin exchanges (J) of the adjacent quantum dots, such that two-qubit operations can be performed between the adjacent quantum dots.

[0161] Combined mode

[0162] In this mode, qubits can be encoded in either the nuclear spins or electrons of the quantum dots. In this scheme, the electron spin qubits are coupled to all the nuclear spin qubits within a given quantum dot. Additionally, all the spins at two neighboring donor dots are coupled by a controllable exchange interaction.

[0163] Figure 20 Coupled spins via the exchange interaction J for 2P and 3P dots are shown. In this example, the electron Qe1 from the 2P dot and the electron Qe2 from the 3P dot are coupled—as illustrated by the connection 2002. The electron Qe1 is also coupled to two nuclear spins (2004, 2006) in the 2P dot. And the electron Qe2 is coupled to all three nuclear spins (2008, 2010, 2012) in the 3P dot.

[0164] In this operating mode, any one of the six qubit interactions can be addressed using ESR, NMR, EDSR, and by controlling the exchange coupling. This exchange interaction can be controlled by applying a voltage to one or more control gates near the respective quantum dots. When turned on, the exchange interaction enables multi-qubit gates between two electron spins and all the nuclear spins to be linked to these two electrons.

[0165] Figure 21A An example multi-donor dot array with four quantum dots 2102 - 2108 is shown. In this array, there are four electrons, each bound to each of the quantum dots. The electrons are labeled e1, e2, e3, e4. The donor dots in this system can be labeled as 3P(2102) quantum dot, 1P(2104) quantum dot, 2P(2106) quantum dot, and 3P(2108) quantum dot. In this mode, each electron spin qubit is coupled to all the nuclear spin qubits within a given donor dot. Additionally, all the spins at two neighboring donor dots are coupled by a controllable exchange interaction.

[0166] Figure 21BShows the connectivity available in this example array. This demonstrates a natural way to scale up these multi-donor quantum dot arrays to form a natural multi-qubit gate. This demonstrates a natural way to scale up because these multi-donor quantum dot arrays form a natural multi-qubit gate.

[0167] ***

[0168] As used herein, the term 'comprising' (and its grammatical variants) is used in an inclusive sense of 'having' or 'including' and not in the sense of 'consisting only of'.

[0169] Those skilled in the art will appreciate that many variations 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. Accordingly, the embodiments of the invention are to be considered in all respects as illustrative and not restrictive.

Claims

1. A method for performing one or more quantum operations on a quantum processor, the quantum processor including a plurality of quantum dots in a semiconductor substrate, at least one subset of the quantum dots being multi-doped quantum dots, each multi-doped quantum dot including two or more dopant atoms, and at least one of the plurality of quantum dots confining an unpaired electron / hole, the method including: Performing the one or more quantum operations on the quantum processor using one or more operation modes, the one or more operation modes including: Using the spin of the unpaired electron / hole of the quantum dot as a data qubit; Using the multi-doped quantum dot as an error correction logical qubit; Using the nuclear spin of at least one of the dopant atoms of the multi-doped quantum dot as a data qubit; or Using the spin of the unpaired electron / hole and the nuclear spin of at least one of the dopant atoms of the multi-doped quantum dot as a data qubit.

2. The method according to claim 1, wherein Adjacent quantum dots among the plurality of quantum dots are positioned to be separated by 5 nanometers to 20 nanometers.

3. The method according to any one of claims 1 to 2, wherein When the spin of the unpaired electron / hole of the quantum dot is used as a data qubit, the nuclear spin of the one or more dopant atoms in the quantum dot is used as an atomic magnet.

4. The method according to any one of claims 1 to 2, wherein When the multi-donor quantum dot is used as the error correction logical qubit, the spin of the unpaired electron / hole of the multi-donor quantum dot is used as a data qubit, and the nuclear spin of the one or more dopant atoms of the multi-doped quantum dot is used for error correction.

5. The method according to any one of claims 1 to 2, wherein, When the nuclear spin of at least one of the dopant atoms is used as a data qubit, the spin of the corresponding unpaired electron / hole is used for readout, addressability, or coupling to an adjacent quantum dot.

6. The method according to claim 5, wherein Coupling to an adjacent quantum dot is performed via an electron / hole spin shuttle between the multi-doped quantum dot and the adjacent quantum dot or via an exchange coupling between the unpaired electron / hole of the multi-doped quantum dot and the paired electron / hole of the adjacent quantum dot.

7. The method according to any one of the preceding claims, wherein, Using nuclear magnetic resonance or EDSR to control the nuclear spin of the dopant atoms.

8. The method according to any one of the preceding claims, wherein, Using electron spin resonance or EDSR to control the spin of the unpaired electron / hole.

9. The method according to any one of the preceding claims, wherein, The one or more quantum operations include at least one of a single qubit gate operation, a two-qubit operation, or a multi-qubit operation.

10. The method according to claim 9, wherein, When the one or more quantum operations are multi-qubit operations, the quantum operations are performed using the spin of the unpaired electron / hole and the nuclear spin of the dopant atoms in the multi-doped quantum dot.

11. A method for performing one or more quantum operations on a quantum processor, the quantum processor including a plurality of quantum dots in a silicon substrate, at least one subset of the quantum dots being multi-doped quantum dots, each of the multi-doped quantum dots including two or more dopant atoms, and at least one of the plurality of quantum dots confining an unpaired electron / hole, the method including: Performing the one or more quantum operations on the quantum processor using one or more operation modes, the one or more operation modes including at least one of the following: Use one or more of the multi-doped dose quantum dots as error correction logic qubits; Use the nuclear spin of at least one dopant atom in the multi-doped dose quantum dot as a data qubit; Or Use the spin of the unpaired electron / hole and the nuclear spin of at least one of the multi-doped dose quantum dots as data qubits.

12. A quantum processor, comprising: A silicon substrate, A dielectric material layer on the silicon substrate; A plurality of quantum dots fabricated in the silicon substrate, each quantum dot including at least one dopant atom, at least one subset of the quantum dots being multi-doped dose quantum dots having two or more dopant atoms, and one or more of the plurality of quantum dots confining unpaired electrons / holes; Wherein, during operation of the quantum processor, the spin of the unpaired electrons / holes and / or the nuclear spin of the one or more dopant atoms in the quantum dots is used as a data qubit.

13. The quantum processor according to claim 12, wherein, The number of dopant atoms within each quantum dot and / or the spatial configuration of the dopant atoms are selected to achieve a predefined hyperfine coupling range between each of the nuclear spins within each quantum dot and the spin of the unpaired electrons / holes.

14. The quantum processor according to any one of claims 12 to 13, wherein, The distance between two adjacent quantum dots is selected to achieve a predefined tunneling coupling range between the spins of the unpaired electrons / holes bound to the adjacent quantum dots.

15. The quantum processor according to any one of claims 12 to 14, wherein, The distance between adjacent quantum dots is approximately 5 nanometers - 20 nanometers.

16. The quantum processor according to claim 14, wherein, The predefined tunneling coupling is in the range of 1 kHz - 1 THz.

17. The quantum processor according to any one of claims 12 to 16, wherein, The size of each quantum dot is less than 3 nanometers.

18. The quantum processor according to any one of claims 12 to 17, further comprising: One or more sensors for measuring the final state of the qubits associated with the quantum dots in the plurality of quantum dots.

19. The quantum processor according to any one of claims 12 to 18, further comprising: One or more reservoirs located near the quantum dots, the one or more reservoirs providing electrons / holes for confinement in one or more of the quantum dots; Wherein the distance between the one or more reservoirs and the one or more quantum dots is approximately between 10 nanometers - 25 nanometers.

20. The quantum processor according to any one of claims 12 to 19, wherein, The plurality of quantum dots are arranged in a one-dimensional geometric pattern, a two-dimensional geometric pattern, or a three-dimensional geometric pattern.

21. The quantum processor according to any one of claims 12 to 20, wherein, During operation: When the spin of the unpaired electrons / holes in the quantum dot is used as a data qubit, the nuclear spin of the one or more dopant atoms in the quantum dot is used for error correction or as an atomic magnet; When the nuclear spin of the one or more dopant atoms is used as a data qubit, then the spin of the unpaired electrons / holes is used to address or measure the nuclear spin of the one or more dopant atoms; Or When the nuclear spin of the one or more dopant atoms is used as a data qubit, then the spin of the unpaired electrons / holes is used to couple the quantum dot to an adjacent quantum dot.

22. A method for performing multi-qubit operations, the method comprising: Provided are multi-doped dose quantum dots including two or more dopant atoms and unpaired electrons / holes confined in the multi-doped dose quantum dots; Using the spins of the unpaired electrons / holes and the nuclear spins of the two or more dopant atoms as qubits and using the qubits to perform the multi-qubit operation.

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