Advanced quantum processing systems

Abstract

A method for performing one or more quantum operations in a quantum processor is provided, wherein the quantum processor includes a plurality of quantum dots in a semiconductor substrate, at least a subset of the quantum dots being multi-dopant quantum dots. Further, each multi-dopant quantum dot includes two or more dopant atoms, and at least one of the plurality of quantum dots confines an unpaired electron / hole. The method includes performing one or more quantum operations in the quantum processor using one or more modes of operation, including using the unpaired electron / hole spins of the quantum dots as data qubits, using the multi-dopant quantum dots as error-corrected logic qubits, using the nuclear spin of at least one of the dopant atoms of the multi-dopant quantum dots as a data qubit, or using the unpaired electron / hole spin and the nuclear spin of at least one of the dopant atoms of the multi-dopant quantum dot as a data qubit.

Description

[Technical Field]

[0001] Aspects of the present disclosure relate to advanced processing systems and methods for operating same, and more particularly to quantum processing systems that are controllable to perform quantum operations. [Background technology]

[0002] The developments described in this section are known to the inventors, but unless otherwise indicated, it should not be assumed that any of the developments described in this section are identified as prior art merely by virtue of their inclusion in this section or their being known to those skilled in the art.

[0003] Large-scale quantum processing systems are a promising technological revolution, with the potential to solve problems that are beyond the reach of classical machines. To date, several different structures, materials, and architectures have been proposed to implement quantum processing systems and create their fundamental information units (quantum bits or qubits).

[0004] One approach to fabricating qubits is to use the nuclei or electron spins of phosphorus donor atoms in, for example, silicon, allowing each phosphorus donor atom's nucleus / electron spin to act as a qubit. This fabrication technique provides near-perfect qubit state encoding due to the addressability and long coherence of the phosphorus spins. Furthermore, qubits fabricated in this manner exhibit relatively long lifetimes and benefit from a semiconductor host that allows electrical addressing and high fidelity.

[0005] However, to begin to explore the computational advantages that quantum processing systems may offer, basic quantum operations must be performed on such systems, which is not easy. Summary of the Invention [Means for solving the problem]

[0006] According to a first aspect of the present disclosure, there is provided a method for performing one or more quantum operations in 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-dopant quantum dots, each multi-dopant 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 one or more quantum operations in the quantum processor using one or more modes of operation, the modes of operation including using the spins of the unpaired electron / holes in the quantum dots as data qubits, using the multi-dopant quantum dots as error-corrected logic qubits, using the nuclear spin of at least one of the dopant atoms in the multi-dopant quantum dots as a data qubit, or using the spins of the unpaired electron / holes and the nuclear spin of at least one of the dopant atoms in the multi-dopant quantum dot as a data qubit.

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

[0008] In some embodiments, when the spins of the unpaired electron / holes of a quantum dot are used as data qubits, the nuclear spins of one or more dopant atoms in the quantum dot are used as atomic magnets.

[0009] Furthermore, when a multi-dopant quantum dot is used as an error-corrected logic qubit, the spin of the unpaired electron / hole in the multi-dopant quantum dot is used as a data qubit, and one or more nuclear spins in the multi-dopant quantum dot are 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 with neighboring quantum dots occurs via electron / hole spin shuttling between the multi-dopant quantum dot and the neighboring quantum dot, or via exchange coupling between an unpaired electron / hole in a multi-dopant quantum dot and an unpaired electron / hole in a neighboring multi-dopant quantum dot.

[0011] In some instances, the nuclear spin of the dopant atom is controlled using nuclear magnetic resonance or EDSR. In some instances, the spin of the unpaired electron / hole is controlled using electric spin resonance or EDSR.

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

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

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

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

[0016] The number of dopant atoms and / or the spatial arrangement of the dopant atoms within each quantum dot are selected to achieve a predefined hyperfine coupling range between the electron / hole spins and the respective nuclear spins within each quantum dot. Furthermore, the distance between two adjacent quantum dots is selected to achieve a predefined tunnel coupling range between the electron / hole spins coupled to the adjacent dots. In some examples, the distance between adjacent quantum dots is approximately 5-20 nanometers. Furthermore, in some examples, the predefined tunnel coupling is within the range of 1 kHz-1 THz.

[0017] Each quantum dot in the quantum processor may be less than 3 nanometers in size. Furthermore, multiple quantum dots may be arranged in one-, two-, or three-dimensional geometric patterns.

[0018] In some embodiments, the quantum processor further includes one or more sensors for measuring the final state of a qubit associated with a quantum dot of the plurality of quantum dots. In some embodiments, the quantum processor further includes one or more reservoirs near the quantum dots. The one or more reservoirs provide electrons / holes for confinement in the one or more quantum dots, and the distance between the one or more reservoirs and the one or more quantum dots is about 10-25 nanometers.

[0019] During operation of the quantum processor of the third aspect, when the unpaired electron / hole spins of the quantum dot are used as data qubits, the nuclear spins of one or more dopant atoms of the quantum dot are used for error correction or as atomic magnets; when the nuclear spins of one or more dopant atoms are used as data qubits, the unpaired electron / hole spins are used to address or measure the spins of one or more dopant atoms; or when the nuclear spins of one or more dopant atoms are used as data qubits, the unpaired electron / hole spins are used to couple the quantum dot to adjacent quantum dots.

[0020] According to a fourth aspect of the present disclosure, there is provided a method for performing multi-qubit operations, the method including providing a multi-dopant quantum dot including two or more dopant atoms and unpaired electrons / holes confined within the quantum dot, and using the spins of the unpaired electrons / holes and the nuclear spins of the two or more dopant atoms as qubits to perform the multi-qubit operations.

[0021] While the invention is susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the drawings and detailed description are not intended to limit the invention to the particular forms 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. [Brief explanation of the drawings]

[0022] [Figure 1] FIG. 1 is a schematic diagram illustrating a conventional architecture based on a single-donor qubit, where the qubit is controlled by alternating A and J gates. [Figure 2] FIG. 1 illustrates a conventional quantum processor architecture that includes three planes. [Figure 3]FIG. 1 shows an example of a flopping-mode qubit called a flip-flop qubit. [Figure 4] FIG. 10 illustrates another flopping-mode qubit architecture. [Figure 5] FIG. 1 illustrates an example of a multi-donor quantum dot according to an aspect of the present disclosure. [Figure 6] FIG. 1 is a schematic diagram showing three different multi-donor quantum dots. [Figure 7] FIG. 1 shows an example of a 1D architecture with five multi-donor quantum dots. [Figure 8A] FIG. 10 shows other examples of 1D chains with different inter-dot distances and angles. [Figure 8B] FIG. 10 shows other examples of 1D chains with different inter-dot distances and angles. [Figure 9A] FIG. 1 shows three examples of 2D architectures containing multi-donor quantum dots. [Figure 9B] FIG. 1 shows three examples of 2D architectures containing multi-donor quantum dots. [Figure 9C] FIG. 1 shows three examples of 2D architectures containing multi-donor quantum dots. [Figure 10A] FIG. 1 shows one of four examples of 3D crystal structures of multi-donor quantum dots. [Figure 10B] FIG. 1 shows one of four examples of 3D crystal structures of multi-donor quantum dots. [Figure 10C] FIG. 1 shows one of four examples of 3D crystal structures of multi-donor quantum dots. [Figure 10D] FIG. 1 shows one of four examples of 3D crystal structures of multi-donor quantum dots. [Figure 11A] FIG. 1 illustrates an example quantum processor according to aspects of the present disclosure. [Figure 11B1] 11B illustrates an example method for manufacturing the quantum processor of FIG. 11A. [Figure 11B2]11B1 shows an example of a method for manufacturing the quantum processor of FIG. 11A. FIG. [Figure 12A] FIG. 1 shows an example of a 3P quantum dot. [Figure 12B] FIG. 10 shows an example of an algorithm using a subset of control methods for use within a 3P dot. [Figure 13A] FIG. 1 shows eight ESR transitions for a 3P quantum dot. [Figure 13B] FIG. 1 shows the frequency for 3P quantum dots. [Figure 13C] FIG. 1 shows the electron-nuclear coupling for this 3P quantum dot. [Figure 14] FIG. 1 shows a schematic protocol for measuring single nuclear spins in 3P quantum dots. [Figure 15] FIG. 1 shows a schematic protocol for measuring all nuclear spins within a 3P quantum dot. [Figure 16A] FIG. 1 shows experimental state tomography of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state measured for a 3P quantum dot. [Figure 16B] FIG. 1 shows the circuit diagram used to generate a GHZ state among three nuclear spin qubits. [Figure 16C] FIG. 1 is a schematic diagram illustrating a quantum device containing donor-coupled electron spins experiencing a local hyperfine field. [Figure 17] FIG. 1 shows an example of connectivity of electron and nuclear spin qubits in 2P and 3P dots, where each dot acts as a logical qubit. [Figure 18A] FIG. 1 illustrates an existing algorithm for the correction of a single-qubit phase error in a system with three qubits. [Figure 18B] FIG. 1 illustrates an implementation of an error correction algorithm in a 2P quantum dot according to an embodiment of the present disclosure. [Figure 19]FIG. 1 illustrates the shuttling mode for a 1D chain of four quantum dots and one electron. [Figure 20] FIG. 1 illustrates the connectivity of spin qubits for exchange-coupled 2P and 3P dots. [Figure 21A] FIG. 1 shows an example of a multi-donor dot array having four quantum dots. [Figure 21B] Figure 21B shows the connectivity available in the example array of Figure 21 A. This demonstrates a natural avenue for scaling up, as these multi-donor quantum dot arrays form natural multi-qubit gates. DETAILED DESCRIPTION OF THE INVENTION

[0023] Although the quantum processors and quantum dots described herein show donor atoms and unpaired electrons, it will be recognized that these are merely examples and that the quantum processors and quantum dots of the present disclosure can be formed from donor or acceptor atoms (commonly referred to as dopant atoms) and that unpaired electrons or holes can be confined within such quantum dots without departing from the scope of the present disclosure.

[0024] Several quantum processing architectures in silicon have been disclosed. One such architecture, proposed by BE Kane in 1998, involved an array of nuclear spins located on donor atoms in silicon. Electron-mediated nuclear spin interactions could be used to perform logic operations in such devices. Furthermore, voltages applied to metal gates in semiconductor devices could control the electron-mediated nuclear spin interactions, enabling the external manipulation of nuclear spin dynamics necessary for quantum computing.

[0025] Figure 1 shows two qubits in a one-dimensional array design based on the above architecture. The array contains phosphorus donor atoms and electrons in a silicon host. The donor atoms are positioned below the silicon substrate surface, and gates are positioned above the silicon substrate surface. The A gate controls the resonant frequency of the nuclear spin qubit, and the J gate controls the electron-mediated coupling between neighboring nuclear spins.

[0026] Quantum mechanical calculations using this architecture proceed through precise control of three external parameters: (1) A gates above the donors control the strength of the hyperfine interaction, thereby controlling the resonance frequency of the nuclear spins below them; (2) J gates between the donors turn on and off the electron-mediated coupling between the nuclear spins; and (3) a globally applied AC magnetic field (B AC ) flips the nuclear spins at resonance. Each spin flips its neighbors and B AC Custom tuning of the coupling with the gates allows different actions to be performed on each spin simultaneously. Finally, measurements are performed by transferring the nuclear spin polarization to the electrons and determining the electron spin state through its effect on the electron's orbital wave function, which can be probed using capacitance measurements between adjacent gates.

[0027] While this architecture can yield high-speed one- and two-qubit logic operations using A and J gates, it poses several challenges. For example, it requires the deterministic creation of single phosphorus donor atoms at precise locations and orientations within silicon. Furthermore, the tunability of the exchange coupling (J) between qubits is limited.

[0028] According to another quantum processor architecture in silicon, quantum information may be encoded in phosphorus donor atoms arranged in a 2D square array. Figure 2 shows this architecture, which includes three planes. In the top and bottom planes, nanowires form a regular crisscross grid of control lines. In the middle plane, a 2D lattice of P donor qubits is patterned with atomic precision and tunnel-coupled to phosphorus-doped quantum dots that form islands of vertical single-electron transistor (SET) structures. The top series of nanowires act as the SET source (S) and the top gate (G A ), while a lower set of complementary control lines are the SET drain (D) and lower gate (G B), alternating as . Each qubit in this architecture is addressed by a set of upper / lower gate intersections around each cell. In any given unit cell, SET islands facilitate the loading and unloading of electron spins, controlled by bias conditions defined by the associated intersections of nearby source, drain, and gates. The bias conditions can be set to independently couple SET islands to specific neighboring donors to load / unload electrons for activation / deactivation, and the control layout allows this operation to be multiplexed across the array. Once activated, qubits can be controlled by externally applied (global) radio frequency (RF) and / or microwave (MW) fields acting on the nuclear-electron states, based on well-understood electron spin resonance (ESR) and nuclear magnetic resonance (NMR) techniques, to simultaneously perform single-qubit and two-qubit quantum gates on the activated donor qubits. Unactivated qubits are sufficiently detuned and remain unaffected by the global control. Initialization and readout of qubit nuclear spins follows a well-established protocol based on swapping quantum information from nuclear spin to electron spin together with spin-dependent electron tunneling to the SET island.

[0029] Although this architecture does not require a vertical gate, it does pose some challenges. Because this architecture is based on a single donor atom as a qubit, it also requires the deterministic creation of a single phosphorus donor atom at a precise location and orientation within silicon. Furthermore, the gate operation between two qubits in this architecture can be slow.

[0030] In certain instances, electric dipole spin resonance (EDSR) may be used to control spin qubits with local electric fields. EDSR is generally achieved by coupling the qubit's spin with the charge degree of freedom. This spin-charge coupling can be induced by spin-orbit interaction. This so-called spin-orbit coupling (SOC) is commonly present in atoms and solids, where relativistic effects cause electrons entering an electric field gradient to experience an effective magnetic field in their own reference frame. However, SOC in silicon is inherently weak.

[0031] To increase the strength of the SOC, several different mechanisms can be used, such as the use of large spin-orbit coupling materials or large gradient magnetic fields from micromagnets. Alternatively, modulating the hyperfine interaction between the electron and the surrounding nuclear spin qubits allows for electrical control of the qubits without the need for any additional control elements, such as magnetic field generators, reducing the power required to control the qubits' operations.

[0032] One such qubit processor architecture, which uses the hyperfine interaction of electrons with surrounding nuclear spins, incorporates a flopping-mode qubit based on a single electron spin that can be in two different charge states. By carefully adjusting the electric field (E), the electron can be forced into a superposition of charge between two sites (forming a charge qubit). When the Zeeman splitting of the electron spin is comparable to the charge qubit splitting, the electron's spin and charge states are hybridized. This hybridization results in a spin-charge coupling proportional to the difference in the transverse terms of the Hamiltonian at each site. Figure 3 shows one such flopping-mode qubit, called a flip-flop qubit.

[0033] In this configuration, the qubit contains one quantum dot 304 and a donor atom 306. In a flip-flop qubit, spin-charge coupling arises from the hyperfine interaction of the electron spin with the nuclear spin of a single phosphorus donor atom 306 and can be used to generate electron-nuclear spin flip-flop transitions. Flopping-mode operation of EDSR is achieved by positioning the electron in a superposition of charge states between the donor nucleus and the interface quantum dot 304 created using an electrostatic gate 308. In this charge superposition state, the hyperfine interaction changes significantly with small changes in detuning between the two sites.

[0034] 3 shows a quantum processing device 300 including a flopping-mode qubit 307. The qubit 307 is formed of one quantum dot 304 and one donor atom 306 that share a single electron and wave function. The donor atom 306 is located in a silicon substrate, and the quantum dot 304 is formed near the interface to confine the electron of the donor atom 306. A gate 308 is positioned above the quantum dot 304 (above the dielectric).

[0035] The gate electrode 308 is operable to interact with the donor atoms 306. For example, the gate 308 may be used to induce an AC electric field in the region between the interface and the donor atoms 306 to modulate the hyperfine interaction between electrons located in the quantum dot 304 and the donor nuclear spins.

[0036] When the qubit is driven electrically, the electron spin flips-flops with the donor's nuclear spin: an electric field can be used to control the quantum state of the qubit, which is associated with a pair of electron-nuclear spin eigenstates: "electron spin up, nuclear spin down" and "electron spin down, nuclear spin up."

[0037] These types of flopping mode qubits have several disadvantages: for example, the quantum processing device requires precise design and fabrication of the qubits, which is often very difficult to achieve.

[0038] Another type of flopping-mode qubit architecture is shown in Figure 4. The flopping-mode qubit 401 of Figure 4 includes two quantum dots 402A and 404B. Each quantum dot consists of a donor cluster. Qubit 401 uses hyperfine interactions with the electron-nuclear systems naturally present in the donor clusters to generate synthetic spin-orbit coupling (SOC).

[0039] The entire device 400 is epitaxial; that is, the donor clusters 402A, 402B are fabricated within the substrate and are far from the interface. Each qubit may be controlled by one or more gates (one gate 406 is shown here), allowing for full electrostatic control of the qubit 401. DC electric fields, fast electric pulses, and microwave (MW) electric fields may be applied to the two gates separately or together. One gate 406 may be tunnel-coupled to one of a pair of quantum dots (402A, 402B) to allow electron loading and unloading to the qubit 401. Using that gate 406 to drive the qubit is advantageous because of the increased electrostatic coupling of that gate 406 to the qubit 401.

[0040] Qubit readout may be performed by a separate charge sensor (not shown) or may be performed in a distributed manner using one of the one or more gates described above (eg, gate 406).

[0041] In the flopping mode, the electron-nuclear hyperfine interactions of the qubits promote an effective energy gradient oriented along the transverse direction with respect to the external magnetic field. The magnetic field along this direction is used to drive the qubits. However, even this architecture has some problems. For example, logic operations in this architecture have not been demonstrated, and each spin must be controlled individually.

[0042] Yet another quantum processing architecture uses singlet-triplet qubits. Two-electron singlet-triplet spin qubits offer the advantage of all-electric control (i.e., no micromagnets or high-frequency RF antennas are required). Furthermore, these qubits exhibit immunity to global magnetic field noise compared to their single-spin qubit counterparts. Double quantum dots in this architecture can be arranged on a silicon substrate. In particular, two quantum dots, each with one or more donors, are constructed side-by-side and arranged so that they are tunnel-coupled. A singlet-triplet qubit can then be encoded at the double quantum dot site. The reduced scale of the encoded singlet-triplet qubit enables large inter-qubit coupling, on the order of 5 GHz to 50 GHz, a regime unthinkable in previous quantum processor architectures. This increased coupling paves the way for faster two-qubit gates in fault-tolerant quantum computing architectures, implemented via electric dipole coupling (also known as "capacitive coupling") between adjacent qubits.

[0043] However, this architecture also faces certain challenges: for example, the logic operations in this architecture are unproven and require individual control of each spin.

[0044] Aspects of the present disclosure are directed to novel quantum processing architectures and quantum processors that include quantum dots formed with multiple donor atoms. Unlike previously known architectures in which qubits are formed from either electron spin or nuclear spin, the quantum processors of the present disclosure can use electron spin and / or nuclear spin of quantum dots to serve as qubits for a variety of different types of quantum operations. For example, electron spins can be used as data qubits while nuclear spins of quantum dots can be used as atomic magnets. Similarly, electron spins can be used as data qubits while nuclear spins of quantum dots can be used for error correction, allowing the dot to function as an error-corrected logic qubit. In another example, nuclear spins in a quantum dot can be used as data qubits while electron spins in the quantum dot can be used to address or measure the nuclear spin qubit. In another example, nuclear spins can be used as data qubits while electron spins in a quantum dot can be used to couple the quantum dot to an adjacent quantum dot via electron shuttling or exchange coupling. Finally, both electron spins and one or more nuclear spins can be combined and used as data qubits.

[0045] This architecture and / or device will be particularly useful in the near term in the so-called Noisy Intermediate-Scale Quantum (NISQ) era, where multi-donor quantum dots offer several benefits, but this architecture may also enable the creation of large-scale universal quantum computers using atomic qubits created with STM.

[0046] Typically, multiple quantum operations may be required to execute a given algorithm, such as initialization, several SWAP gates, several CROT gates, error correction, etc. Traditionally, multiple resources are required to perform these operations, and previously known quantum architectures typically require numerous control sequences to perform some or all of these quantum operations. The quantum processing architectures and devices of the present disclosure enable these multiple types of quantum operations to be performed relatively easily within the same quantum dot by using the quantum dot in the different modes described above. In particular, as discussed above, the quantum processing systems of the present disclosure may encode quantum information in the electron spin and / or nuclear spin of the quantum dot, thereby enabling the electron spin or any one of the nuclear spins to be used for gate operations, to perform error correction, to be used as a data qubit, etc.

[0047] Furthermore, because quantum dots can contain multiple donor atoms, the quantum processor of the present disclosure is easier to manufacture than previously known systems. In addition, each quantum dot does not necessarily have to have the same number of donor atoms. Some quantum dots may have two donor atoms, others may have three donor atoms, and still others may have four or more donor atoms. The system is also tolerant of cases where some quantum dots are unintentionally created with a single donor atom.

[0048] Additionally, the quantum processing architectures of the present disclosure are readily scalable in one, two, or three dimensions, where connectivity between adjacent dots can be achieved via electron shuttling or exchange coupling.

[0049] Furthermore, multi-donor dot structures offer unique properties by enabling multi-qubit gates within a native gate set and single-qubit gates that can be constructed using these multi-qubit gates. Qubits can be encoded in nuclear spin and / or electron spin. 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 larger numbers of qubits using exchange coupling. Native multi-qubit gates offer an essential advantage because building such gates using one-qubit and two-qubit gates is resource-intensive. The reduced number of gate operations allows for a reduction in circuit depth, as more complex quantum algorithms can be performed within the qubit coherence time.

[0050] In addition to the above, the exchange interaction between two adjacent asymmetric donor dots is more tunable than that between adjacent symmetric single-donor quantum dots. Because the precise spatial location of the nuclear spins within a quantum dot can vary, the resonance energy of each electron spin can be different for each dot, improving the addressability of the quantum dots. That is, individual quantum dots can be easily tuned and addressed using global electric or magnetic signals. Finally, the strong confinement potential induced by multi-donor quantum dots results in smaller electron wave functions, resulting in longer relaxation or coherence times.

[0051] 5 shows an example of a multi-donor quantum dot device 500 as disclosed herein. The quantum dot device 500 includes quantum dots 501 located in a semiconductor substrate 504. In this example, the semiconductor substrate 504 is 28 silicon. The silicon substrate 504 is covered by a barrier material / dielectric 505, such as silicon dioxide.

[0052] Multi-donor quantum dot 501 includes multiple dopant dots 510 embedded in a semiconductor substrate 504. In this example, quantum dot 501 includes three dopant atoms 510A, 510B, and 510C. The distance between the dopant dots is less than the Bohr radius, so that the electron wave function simultaneously covers all the dopant atoms. In one example, the distance is 3 nanometers or less.

[0053] Additionally, a gate 511 may be located on the dielectric 505 in a region above the donor clusters of donor atoms 510A, 510B, and 510C. A voltage may be applied to the gate 511 to confine one or more electrons 512 within the quantum dot 501. These electrons 512 are confined by the Coulombic potential of the donor atoms. In this example, one electron 512 is confined within the quantum dot 501. However, the 3P quantum dot shown in FIG. 5 may confine more electrons. While the gate 511 is shown as a surface gate, it will be appreciated that (in some implementations) it may be an in-plane gate fabricated in a silicon substrate in the same plane as the quantum dot 501.

[0054] Generally speaking, donor atoms 510 are placed in a silicon substrate 504 with atomic-scale precision using scanning tunneling lithography techniques. In particular, during fabrication, a lithographic patch may be defined in the semiconductor substrate. A predetermined number of donor atoms 510 may then be placed in the lithographic patch. In some examples, the donor atoms 510 may be located approximately 50 nm below the surface. In the example shown in FIG. 5, three donor atoms are placed in the lithographic patch.

[0055] As mentioned above, multi-donor quantum dot 501 may have two or more donor atoms. Figure 6 shows schematic diagrams of three different multi-donor quantum dots 501A-501C. Large circles 602 represent the wave functions of unpaired electrons 512 confined in each multi-donor quantum dot 501. Small circles represent donor atoms 608-612. For example, multi-donor quantum dot 501A has two donor atoms 608 and an unpaired electron confined in quantum dot 501A, where the electron wave function is represented by 602.

[0056] In some examples, the donor atoms may be phosphorus atoms, and a multi-donor dot having m phosphorus atoms may be denoted as an mP quantum dot, where m is an integer and m > 1. Thus, multi-donor quantum dots 501A-C may be denoted as 2P, 3P, and 4P quantum dots, respectively.

[0057] A quantum processor may be formed of a plurality of such multi-donor quantum dots 501 arranged in some kind of array or pattern. In addition to multi-donor quantum dots, such a quantum processor may also include several single-donor atomic quantum dots (which may be similar to the quantum dots described above with respect to FIG. 3).

[0058] A quantum dot architecture may include a one-dimensional (1D) array of quantum dots. FIG. 7 shows an example of an architecture 700 including a 1D array of five quantum dots, QD1-QD5. Each quantum dot may have one or more donor atoms. The donor-to-donor distance or quantum dot size (r) for any given quantum dot is less than the Bohr radius. In some examples, this donor-to-donor distance / size for a quantum dot is r≦3 nanometers. The dot-to-dot distance (d), i.e., the distance between adjacent quantum dots, may be in the range of 5-20 nanometers. It will be appreciated that the dot-to-dot distance (d) between quantum dots 501 may not be uniform and may vary within the range of 5-20 nanometers. Furthermore, the size (r) of a quantum dot may be determined by the number of donor atoms present in the quantum dot. That is, the greater the number of donor atoms in a quantum dot, the greater its size or donor-to-donor distance r, and the fewer donor atoms in a quantum dot, the smaller its size. 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.

[0059] 8A and 8B each show examples of other quantum processor architectures 810, 820 that include 1D arrays of quantum dots with different inter-dot distances and angles. 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, an odd number of quantum dots are positioned along a first linear axis, and an even number of multi-donor quantum dots are positioned along a second linear axis, where the first axis is parallel to the second axis.

[0060] Array 820 is similar to array 810, except that pairs of quantum dots are positioned along first and second linear axes.

[0061] In yet another example, quantum processors including the multi-donor quantum dots described with respect to FIG. 5 may be formed in two-dimensional (2D) or three-dimensional (3D) patterns.

[0062] Figures 9A-9C show three examples of 2D quantum processor architectures that include multiple quantum dots 501, shown as circles. Figure 9A shows an example of a 4x4 square lattice 910, which includes 16 quantum dots positioned at each intersection of the square lattice.

[0063] Figure 9B shows an example of a triangular lattice 920, which includes 18 quantum dots positioned at each intersection of the triangular lattice. Figure 9C shows an example of a hexagonal 2D lattice 930, where a quantum dot is positioned at each edge of the hexagonal lattice. Each quantum dot 501 in architectures 910-930 may have a variable number of donor atoms, where the inter-donor distance is r i ≦3 nm. Furthermore, the inter-dot distance between any two adjacent quantum dots may be within the range of 5 to 20 nm.

[0064] 10A-10D show examples of 3D quantum processor architectures including multiple quantum dots. In particular, FIG. 10A shows a cubic crystal structure 1010 exhibiting eight quantum dots, each positioned at a vertex 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 is approximately 1 / 2 of the distance between the quantum dots along each axis d. x ≠d y ≠d z It may vary along

[0065] Figure 10B shows a cubic face-centered structure 1020 containing 16 quantum dots. In this example, a quantum dot is positioned at each vertex of the cubic structure, followed by a quantum dot at the center of each face of the cube. Figure 10C shows a cubic body-centered structure 1030 containing nine quantum dots. In this example, a quantum dot is positioned at each vertex of the cubic structure, followed by one quantum dot at the center of the cube. Figure 10D shows a hexagonal face-centered structure 1040 containing 17 quantum dots. In this example, a quantum dot is positioned at each vertex of the hexagonal structure, followed by one quantum dot at each of the top and bottom faces of the hexagonal structure, and three quantum dots in the middle of the hexagonal structure.

[0066] It will be appreciated that all of the example architectures shown in Figures 7-10 are merely illustrative. The quantum dots may be arranged in any of the configurations shown or in any other 1D, 2D, or 3D geometric arrangement without departing from the scope of the present disclosure, so 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 and 20 nanometers.

[0067] Furthermore, it will be appreciated that Figures 7-10 only show the arrangement of quantum dots in a quantum processor, and do not show any control gates, reservoirs, etc. Figure 11A shows an example of a quantum processor 1100 that includes these additional elements. In particular, Figure 11A shows an array of quantum dots 1102 (including multi-donor quantum dots and zero or more single-donor quantum dots). 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 zigzag array (similar to 1D array 810) having 33 quantum dots.

[0068] It will be appreciated that the quantum dots in the array may include different numbers of donors. In this example, there is one sensor for every three quantum dots. However, it will be appreciated that in other implementations or examples, the number of quantum dots per sensor may vary. Furthermore, in some examples, a SET may be used as the sensor to read out the qubit. In other examples, other types of sensors, such as gates or single-lead charge sensors, may be used instead of a SET to read out the qubit. Electrons can be deterministically loaded and unloaded from the dot 1102 by applying a voltage to the gate 1106. In some examples, the sensor 1104 may also act as an electron reservoir to provide electrons to the quantum dot for confinement. In other examples, a separate reservoir may be provided in addition to the charge sensor.

[0069] 11A shows control gates and sensors in the same plane as the quantum dots, this need not be the case in all implementations. In other cases, one or more control gates and / or one or more sensors may be formed with respect to the surface of a semiconductor substrate, while the quantum dots may be positioned within the semiconductor substrate. In a further example, one or more control gates may be provided in the form of control lines above and below the quantum dots, as shown, for example, in FIG.

[0070] Creating a Device FIG. 11B (FIGS. 11B1-11B2) outlines the individual processing steps (steps a-k) for fabricating multi-donor quantum dots according to embodiments of the present disclosure.

[0071] First, a clean 2 × 1 surface of Si is formed by heating it to near its melting point in ultra-high vacuum (UHV). This surface has a 2 × 1 unit cell and consists of an array of σ-bonded Si dimers, with the remaining dangling bond of each Si atom forming a weak π bond with the Si atom of the other dimer containing it.

[0072] Treatment step (a) (i.e., monohydride deposition) involves exposing a clean Si 2x1 surface to atomic H to break weak Si π bonds and allow H atoms to bond with Si dangling bonds. Under controlled conditions, a monolayer of H can be formed, with one H atom bonded to each Si atom, filling the reactive dangling bonds and effectively passivating the surface. See step (a).

[0073] Next, in process step (b) (i.e., hydrogen desorption), the STM tip is used to selectively desorb H atoms from the passivated surface by application of an appropriate voltage and tunneling current to form a pattern in the H resist, see step (b).

[0074] It will be appreciated that H atoms are desorbed from the precise locations where donor atoms are to be placed. For example, when a quantum processor includes a 2D square lattice of quantum dots, H atoms are desorbed in a manner to create multiple lithographic patches in a square lattice configuration, where the distance between adjacent patches is 5-20 nanometers. Furthermore, the size of each lithographic patch created by hydrogen desorption may depend on the number of donor atoms that need to be placed within the quantum dot. In one example, when one donor atom is positioned in one lithographic patch (to form a 1P quantum dot) and two donor atoms are positioned in an adjacent lithographic patch (to form a 2P quantum dot), an STM tip may be used to desorb six hydrogen atoms at a first location to create the first patch and fifteen hydrogen atoms at a second location 5-20 nanometers away to create the second, larger patch. Similarly, when a larger number of donor atoms are placed in a patch, more hydrogen atoms may be desorbed to create a larger sized lithographic patch. In other examples, the size of the patch may be smaller or larger than those described in the above examples. Furthermore, in some examples, machine learning techniques may be used to control the number of donor atoms placed in any lithographic patch.

[0075] This process is repeated to create locations for other quantum dots, exposing areas of bare reactive Si atoms along the dimer rows, which then allow for direct adsorption of reactive species onto the Si surface.

[0076] Returning to FIG. 11B, in step (c) (i.e., PH3 dosing), phosphine (PH3) gas is introduced into the vacuum system through a controlled leak valve connected to a specially designed phosphine microdosing system. The phosphine molecules bind strongly to the exposed Si surface through holes in the hydrogen resist. See step (c). As mentioned above, at a particular donor site, the phosphine molecule may bind to any one of the exposed silicon dimers.

[0077] Subsequent heating of the STM-patterned surface for crystal growth causes dissociation of the phosphine molecules, resulting in the incorporation of P into the first layer of Si (see step (d)). Therefore, it is exposure of the STM-patterned H-passivated surface to PH that is used to generate the required donor molecules.

[0078] The hydrogen may then be desorbed in step (e), followed by overgrowing silicon on the surface at room temperature in step (f). An alternative is to grow silicon directly through the hydrogen layer, as shown in step (g).

[0079] In step (h), the surface is rapidly annealed.

[0080] Silicon is then 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 barrier, also known as a locking layer, may be grown, as shown in step (j). Finally, a conductive gate may be aligned on the surface using electron beam lithography, as shown in step (k). The gate may be aligned at a lateral distance of 300±50 nm from the embedded quantum dots using a registration marker, for example, an evaporated metal marker. Additionally, an antenna may also be aligned on the surface to generate an oscillating magnetic field B1 perpendicular to the substrate at the location of the quantum dots.

[0081] The manner in which quantum dot 500 is fabricated defines how the donor nuclei and / or electrons within the quantum dot can be used as qubits. In particular, the particular geometry and placement of donors within the lithographic patch or within the quantum dot allows for reliable control of hyperfine coupling, tunneling coupling, and tunneling rates to control quantum operations for single-qubit, two-qubit, or multi-qubit gates as described above.

[0082] The donor atoms incorporated within a given site form a collective confinement potential for coupling with electrons. The number of donors within each quantum dot and their spatial arrangement determine the confinement strength, which in turn determines the hyperfine coupling between the electron spin and each nuclear spin.

[0083] As mentioned above, by patterning lithographic openings with a separation of about 5–20 nanometers, tunnel coupling between electron spins coupling to two neighboring dots can be achieved, enabling high-fidelity two-qubit gates between electron spin qubits.

[0084] In the disclosed quantum processor, quantum information is encoded in electron spin and / or nuclear spin. Readout of the electron spin is achieved using a process called spin-to-charge conversion. In this process, a single-electron transistor (SET) charge sensor is used to determine the state of the electron spin qubit. The qubit-to-reservoir distance determines the electron tunneling rate, i.e., how quickly the electron spin can be measured. For fast and robust spin readout, the qubit-to-reservoir distance should ideally be approximately 10-25 nm.

[0085] Control Method The electron spin and / or nuclear spin qubits in the multi-donor quantum dot 501 may be controlled using five main control methods: electron spin resonance (ESR), nuclear magnetic resonance (NMR), electrically driven spin resonance (EDSR), initialization, and readout.

[0086] Figure 12A shows an example of a 3P quantum dot 1200 with three donor atoms with nuclear spins designated A, B, and C. An electron is confined in this quantum dot 1200, and its wave function is represented by an oval 1202. Figure 12B is a schematic of the control method. The four horizontal lines in this schematic represent the electron spin 1203 and the three donor spins 1204, 1206, and 1208.

[0087] The first control method 1210 is ESR, which can be used to control electron spin 1203. ESR is a direct means to drive electrons between their two spin states (up and down). In the presence of an external magnetic field B, the electron's spin energy levels are no longer degenerate.

[0088]

number

[0089] The two spin states in Equation 1 and Equation 2 above are separated by an energy difference ΔE. Thus, by applying an AC magnetic field to quantum processor 1100, electron spin 1203 can be changed from a spin-down state to a spin-up state, or vice versa. ESR occurs when the magnetic moment of an electron couples to an external magnetic field.

[0090] In particular, ESR is a transition between opposite electron spin states but the same nuclear spin configuration. For example, a 2P dot has four ESR transitions, as shown in Equation 3 below.

[0091]

number

[0092] Here, the first arrow indicates the spin state of the electron, and the double arrows indicate the spin states of each of the two nuclear spins. For a 2P quantum dot, there are four possible nuclear spin configurations:

[0093]

number

[0094] 13A and 13B are plots showing the eight ESR transitions 1300 and frequencies 1310, respectively, of the 3P quantum dot 1200. A total of 2 3 There are 8 nuclear spin configurations, for a total of 16 overall spin states. The eight nuclear spin states are designated by their relative energy levels. The bottom row of states corresponds to the eight nuclear spin states with spin-down electrons, and the top row corresponds to the eight nuclear spin states with spin-up electrons. Figure 13A also shows eight vertical ESR transitions, designated 1301-1308. ESR transitions flip only the electron spin; the nuclear spins remain unaffected. Thus, an ESR transition connects the bottom state with the top state directly above it.

[0095] For example, to excite 3P quantum dot 1200 from the spin state of (Equation 5) below to the spin state of (Equation 6), a single frequency corresponding to the ESR frequencies shown in plot 1310 may be applied to a control gate near the quantum dot. ESR frequencies 1311-1318 correspond to ESR transitions 1301-1308, respectively. The ESR frequencies are proportional to the applied magnetic field and can vary over a large range.

[0096]

number

[0097] The second control method 1215 is EDSR. EDSR may be used to control the electron and nuclear spins in a multi-donor dot. The EDSR transition is an electron-nuclear flip-flop transition that can be achieved through modulation of the hyperfine interaction between each nuclear spin 1204, 1206, 1208 and the electron spin 1203. Modulation of this hyperfine interaction may be achieved by applying an electric field that shifts the electron wave function away from the donor nucleus. Thus, EDSR is mediated by an electric field that simultaneously flips the electron spin and one of the nuclear spins in a multi-donor system. For a 3P system, there are 12 possible EDSR transitions (not shown).

[0098] Another control method for use in controlling nuclear spins in multi-donor quantum dots is to use nuclear magnetic resonance (NMR). This is shown in FIG. 12B at 1220. In particular, when the nuclear spins are individually addressable, NMR allows control over the nuclear spins 1204, 1206, and 1208. Each nuclear spin in a multi-donor quantum dot may have a different hyperfine coupling strength. In one example of a 3P dot, the hyperfine coupling strengths for the three phosphorus donors may be 6 MHz, 68 MHz, and 101 MHz, respectively. In such a case, an NMR pulse may be applied at a frequency corresponding to this transition using one or more control gates near the quantum dot 501 to flip the nuclear spin state from that of Equation 5 to that of Equation 7 below:

[0099]

number

[0100] As shown in Figure 1220, three different NMR pulses are possible in this 3P system. Three additional NMR pulses at different frequencies are also available, corresponding to electrons in the (Equation 1) state rather than the (Equation 2) state. The addressability frequencies of individual nuclear spins depend on their environment. Typically, frequencies for addressing nuclear spins are in the MHz range, while EDSR and ESR frequencies for addressing electron spins are in the GHz range.

[0101] 12B shows the electron spin initialization and measurement control, and 1240 shows the nuclear spin measurement control.

[0102] Initialization and measurement of the electron spins, shown at 1230 in FIG. 12B, can be achieved using spin-to-charge conversion processes such as Elzerman-style readout or ramped readout. Readout of the nuclear spins can be achieved by combining ESR control with electron spin readout, as shown schematically at 1240 in FIG. 12B. Readout of the nuclear spins relies on the fact that the ESR behavior on the electron spins is conditional on the state of the nuclear spins within a given multi-donor dot. An example protocol for nuclear spin readout in a 3P dot is shown in FIG. 14. In this example, a series of four ESR pulses are applied to the electron spins 1203, where the four frequencies correspond to nuclear spins that mark Q3 as being in the up state. Therefore, subsequent readout of the electron spins 1203 can be used to effectively determine the state of the nuclear spins. To read out all the nuclear spins simultaneously, the protocol shown in Figure 15 can be used, where an ESR pulse of each frequency is applied followed by a readout of the electron spins, so that the exact combination of the three nuclear spin states can be determined.

[0103] Operation Mode In the quantum processor example described above, the above-identified control mechanisms may be used to perform single-qubit, two-qubit, and multi-qubit operations on the quantum dot, where multi-qubit operations are understood to mean operations on three or more qubits. To perform these quantum operations, the quantum dot may be operated in four different modes: a) using electron spins as data qubits and nuclear spins as atomic magnets, b) using electron spins as data qubits and nuclear spins for error correction, c) using nuclear spins as data qubits, and d) using both electron spins and nuclear spins as qubits.

[0104] Using electron spin as a data qubit In this mode of operation, nuclear spins are used as atomic magnets, while electron spins are used as data qubits. The nuclear spins increase or decrease the qubit energy. The nuclear spins of the electron-hosting donor atoms affect the electron spin qubit energy splitting via hyperfine interactions A. The nuclear spins can be controlled using AC magnetic fields via nuclear magnetic resonance (NMR) or AC electric fields via electron-dot-resonance (EDSR). Thus, the nuclear spins can be initialized to a predetermined spin configuration. In particular, by controlling the orientation of the nuclear spins, an energy difference ΔEz can be controllably created between two electron spin qubits in adjacent quantum dots, affecting the operation of a two-qubit gate between the two qubits.

[0105] This electron spin qubit encoding mode enables the efficient operation of arrays of electron spin qubits with dynamically controllable splitting energies, which is beneficial for addressability and high-fidelity two-qubit gates. When performing gate operations, neighboring electron spin qubits can be exchange-coupled to perform the required gate operation.

[0106] In Figures 16A and 16B, the operation of a four-qubit quantum processor consisting of three nuclear spins (3P) and one electron spin is experimentally demonstrated.

[0107] Figure 16A shows a plot of the state tomography of a three-qubit Greenberger-Horn-Zeilinger (GHZ) state for three nuclear spins. GHZ states are entangled quantum states involving at least three particles. The height and color of each bar correspond to the amplitude and phase of each element in the computationally measured density matrix.

[0108] By comparing the measured state with the ideal three-qubit GHZ state, a fidelity of 79.7±2.0% can be determined, where the ideal GHZ for three qubits is:

[0109]

number

[0110] With a fidelity greater than 50%, this confirms that the three nuclear spin qubits are entangled. The successful creation of a GHZ state confirms that the control methods described in this disclosure can indeed be used with high fidelity to operate a multi-donor dot as a multi-qubit processor.

[0111] Figure 16B shows a circuit 1610 used to generate a three-qubit GHZ state. The four horizontal lines in this schematic represent the electron spin 1612 and three donor spins 1614, 1616, and 1618. At the start of circuit 1610, the electron spin and three nuclear spins are initialized to their spin-down states. The circuit consists of five NMR pulses and two ESR pulses. At the end of the circuit, a 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.

[0112] FIG. 16C schematically illustrates two adjacent quantum dots 1622 and 1624 in a multi-qubit quantum processing device (such as device 1100). Each quantum dot may include one or more donor atoms. In this example, the left quantum dot 1622 includes two P donor atoms 1626 and 1628, and the right quantum dot 1624 includes one P donor atom 1630. Furthermore, an electron spin qubit may be confined by the P donors in each of the left and right quantum dots 1622 and 1624. In particular, an electron may be spatially coupled to a donor atom in each quantum dot. In the example shown here, an electron may be confined by a pair of closely spaced P donors in the left donor dot 1622, and another electron may be confined by a single phosphorus donor atom in the right donor dot 1624. The ovals 1632 and 1634 around the dopant atoms indicate electron wave functions. The ovoid shape and electron confinement geometry are determined based on the number of P atoms in each donor dot: the left dopant dot contains two donor atoms, so the electron wave function 1632 is ovoid, while the right dopant dot contains one donor atom, so the electron wave function 1634 is more spherical.

[0113] For such quantum dots, the energy difference between the two quantum dots, ΔE Z is governed by the hyperfine interactions A between the electrons (ovals 1632 and 1634) and the nuclear spins (double-lined arrows 1626, 1628, and 1630) and the orientation of the nuclear spins. The hyperfine interactions A can be controlled by several parameters, particularly the number of donor atoms in each quantum dot, the arrangement of the donor atoms in the quantum dot and in the silicon crystal lattice 1636, the number of electrons in the quantum dot, and the strain and electric fields (applied / background fields) in the device.

[0114] Error Correction Quantum error correction (QEC) is an essential component for building a universal quantum computer. One type of error correction is a parity-check operation, in which bit-flip or phase-flip errors in a single qubit can be detected and corrected without measuring the encoded quantum state. A single multi-donor dot can be used as an error-corrected logic qubit, using electron spins as data qubits while using nuclear spins for stabilizer measurements and error correction schemes.

[0115] Figure 17 shows an example of connectivity between nuclear and electron spin qubits that allows error correction methods to be applied to 2P and 3P quantum dots. The top three lines in Figure 17 correspond to the spins of the 2P dot (two nuclear spins and one electron spin), and the bottom four lines correspond to the spins available in the 3P dot (one electron spin and three nuclear spins). As shown in this figure, the electron spins of 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 spin of each quantum dot can be used as an auxiliary error correction qubit. In one example, the 2P quantum dot (two nuclear spins and one electron spin) is used as the first logical qubit 1702, and the 3P quantum dot (three nuclear spins and one electron) is used as the second logical qubit 1704.

[0116] Parity check operations are typically performed before and after other quantum operations, and in some algorithms, this parity check operation may occur at regular intervals within the algorithm.

[0117] Figure 18A shows an existing algorithm for quantum error correction (QEC) of a single-qubit phase error in a system with three qubits: one data qubit and two auxiliary qubits. Each horizontal line in Figure 18A represents a qubit:

[0118]

number

[0119] This algorithm includes 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 in (Equation 8) below, and then on the second pair of qubits in (Equation 9).

[0120]

number

[0121] A √X gate is then applied to all three qubits, which rotates all three qubits on the X axis so that the error correction scheme corrects the phase error.

[0122] The next stage of QEC is the decoding stage. This stage includes an opposite rotation gate -√X and the same CNOT gate in reverse. When an error occurs in the first qubit |Ψ〉, it is detected via the other two qubits shown below (Equation 10).

[0123]

number

[0124] This detection is done by flipping the qubits conditionally to the state of |Ψ〉 via a CNOT gate.

[0125] The final stage of QEC is the restoration stage, which involves a single step in which the state of |Ψ〉 is flipped conditionally on the other two qubits, correcting any errors that may have occurred.

[0126] 18B shows the same QEC implementation in a 2P quantum dot according to an embodiment of the present disclosure. Because there is an unpaired electron and two nuclear spins in the 2P dot, there are a total of three potential qubits or spins. The electron spin is the data qubit, labeled |Ψ〉, and the two nuclear spins act as auxiliary qubits, labeled as (Equation 10), where the subscripts distinguish between the two nuclear spins.

[0127] The sequence begins with an encoding stage that includes two CNOT gates and four √X rotation gates. The CNOT gates are performed between the electron spin and each nuclear spin using NMR. Then, four electron √X rotation gates are applied using ESR. For example, a √X gate may be performed on an electron |Ψ〉 based on the following conditions: both nuclear spins in the dot are in state |1〉; one nuclear spin is in state |1〉; and neither nuclear spin in the dot is in state |1〉. Now, all four possible ESR √X gates are applied, so together they implement a single-qubit √X gate on the electron.

[0128] Next, four other √X rotation gates are applied to the two nuclear spins based on whether the electron spin is in the |1〉 or |0〉 state. These phase gates are applied using NMR, similar to the ESR pulses described above, to apply single-qubit √X gates to both nuclear spins. Each pair of NMR gates (i.e., an NMR gate applied to each nuclear spin for a different electron spin condition) performs a single-qubit gate on each nuclear spin. The reason for this repetition is that to decouple the spins, the pulses must be conditioned on all possibilities of the other spin.

[0129] Next, an opposite gate is performed using ESR and NMR as described above (-√X), followed by a CNOT gate again using ESR, and finally a conditional flip of the electronic state based on the nuclear spin state.

[0130] "In this way, if an error occurs in one of the electron or nuclear spins, it can be detected and subsequently corrected via the 2P quantum register. The entire sequence can be repeated by reinitializing the nuclear spins, increasing the coherence time and thus improving the quality of the quantum operation performed by the multi-donor quantum dot."

[0131] It will be appreciated that QEC may be performed in a similar manner in quantum dots with three or more donor atoms.

[0132] Using nuclear spins as data qubits while using electrons for readout and addressability Nuclear spins can be used as data qubits for other operations, such as data storage. In these cases, the nuclear spins can be read out via the electron spins within the quantum dot. When electrons are present in a multi-donor quantum dot, specific NMR or EDSR frequencies can be used to address individual nuclear spins, as described above, because hyperfine coupling provides addressability. Furthermore, single-qubit gates on nuclear spins can be achieved by combining EDSR and ESR techniques or by using NMR directly. Furthermore, multi-qubit gates can be performed between nuclear spin qubits within the same dot via geometric gates using hyperfine coupling, i.e., ESR.

[0133] Using nuclear spin as a data qubit and electron spin to couple neighboring dots In shuttling mode, electrons can be shuttled between adjacent quantum dots. This may be useful for coherently transferring information from one quantum dot to another. This can also be used to modify the addressability of the quantum dot. For example, when an electron is present in the dot, each nucleus can be controlled individually, but when the dot has no electrons, only all nuclei can be controlled at once. This could be used to perform global gates on many qubits by "turning off qubits" by removing electrons, or to reduce the spectral density required to control many qubits. When used to transfer data, nuclear spins may be used as data qubits because of their longer coherence time, and electron spins can be used to transfer data from one quantum dot to another.

[0134] Figure 19 shows the shuttling mode for a 1D chain of four quantum dots 1902, 1904, 1906, 1908, with 2P, 4P, 2P, 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.

[0135] By adjusting the voltages of one or more control gates near the first and second quantum dots, an electron may be moved from the first quantum dot to the second quantum dot. Then, by adjusting the gate voltages near the second and third quantum dots, an electron may be moved between the second and third quantum dots. Similarly, by adjusting the gate voltages near the third and fourth quantum dots, an electron may be moved between the third and fourth quantum dots. In this example, an electron wave function 1910 is shown at the third quantum dot after it has been moved from the second quantum dot but before it is moved to the fourth quantum dot.

[0136] It will be appreciated that although this mode is primarily operated with a single unpaired electron, it is also possible to use this mode with multiple unpaired electrons simultaneously when the number of unpaired electrons is less than the number of quantum dots.

[0137] In this mode, inter-dot coupling can be achieved by entangling nuclear spins with electrons via hyperfine interactions and then coherently transferring the electrons to different dots. The electrons effectively mediate an entanglement gate between nuclear spins located in separate dots. An entanglement gate is a gate that operates nontrivially on two or more qubits, providing an effect that cannot be achieved using single-qubit gates alone. The state of each qubit in an entanglement gate depends on the state of the other qubits in the gate. In one example, an entanglement gate can be a two-qubit CNOT gate, a two-qubit √SWAP gate, a three-qubit Toffoli gate, or the like. In this mode, entanglement can be distributed throughout the multi-donor dot quantum processor 1100 via exchange-based electron-electron gates or by moving electrons from one dot to another.

[0138] Importantly, the nuclear spins of all unoccupied donor dots share the same resonance frequency, which means that all idle qubits (i.e., quantum dots with no electron spin) have the same resonance frequency and can be actively isolated from the noisy environment in a straightforward manner via a series of NMR control pulses.

[0139] In the exchange coupling scheme, connectivity between adjacent dots can be achieved using exchange coupling controlled via gate voltages. Specifically, whereas in the previously discussed qubit shuttling mode of operation, where only one electron exists between adjacent dots and is transported back and forth, in this mode, electron spins exist in both adjacent quantum dots, and two-qubit gates, such as CROT gates, conditional phase gates, and √SWAP gates, can be implemented between them. Figure 21A shows four quantum dots 2102, 2104, 2106, and 2108 in a two-dimensional array. In this example, adjacent quantum dots, i.e., quantum dots 2102 and 2106, 2106 and 2108, 2104 and 2108, and 2102 and 2104, are exchange coupled (J) via their respective electron spins, allowing two-qubit operations to be performed between these adjacent quantum dots.

[0140] Combination Mode In this mode, a qubit can be encoded in either the electron or the nuclear spin of a quantum dot. In this scheme, the electron spin qubit is coupled to all nuclear spin qubits within a given quantum dot. In addition, all spins in two neighboring donor dots are coupled via a controllable exchange interaction.

[0141] Figure 20 shows coupled spins for 2P and 3P dots coupled via the exchange interaction J. In this example, electron Qe1 of the 2P dot is coupled to electron Qe2 of the 3P dot, which is shown by connection 2002. Electron Qe1 is also coupled to both nuclear spins of the 2P dot (2004, 2006). In addition, electron Qe2 is coupled to all three nuclear spins of the 3P dot (2008, 2010, 2012).

[0142] In this mode of operation, any of the six qubit interactions may be addressed by controlling the exchange coupling using ESR, NMR, and EDSR. This exchange interaction may be controlled by applying a voltage to one or more control gates near each quantum dot. When switched on, this exchange interaction allows a multi-qubit gate between the two electron spins and all nuclear spins to be linked to these two electrons.

[0143] Figure 21A shows an example of a multi-donor dot array with four quantum dots 2102-2108. There are four electrons in this array, one bound to each quantum dot. These electrons are labeled e1, e2, e3, and e4. The donor dots in this system may be referred to as 3P (2102), 1P (2104), 2P (2106), and 3P (2108) quantum dots. In this mode, each electron spin qubit is coupled to all nuclear spin qubits within a given donor dot. In addition, all spins in two neighboring donor dots are coupled via a controllable exchange interaction.

[0144] Figure 21B shows the connectivity available in this example array, demonstrating a natural avenue for scaling up, as these multi-donor quantum dot arrays form natural multi-qubit gates.

[0145] As used herein, the term "comprising" (and grammatical variations thereof) is used in the inclusive sense of "having" or "including" and not in the sense of "consisting only of."

[0146] Those skilled in the art will recognize that numerous 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, and the present embodiments are therefore to be considered in all respects as illustrative and not restrictive.

Claims

1. 1. A method for performing one or more quantum operations in a quantum processor, the quantum processor comprising a plurality of quantum dots in a semiconductor substrate, at least a subset of the quantum dots being multi-dopant quantum dots, each multi-dopant quantum dot comprising two or more dopant atoms, and at least one of the plurality of quantum dots confines an unpaired electron / hole, the method comprising: performing the one or more quantum operations in the quantum processor using one or more modes of operation, the modes of operation including: using the unpaired electron / hole spins of quantum dots as data qubits; using multi-dopant quantum dots as error-corrected logic qubits; using the nuclear spin of at least one of the dopant atoms of the multi-dopant 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-dopant quantum dot as a data qubit.

2. 10. The method of claim 1, wherein adjacent quantum dots in the plurality of quantum dots are positioned 5 to 20 nanometers apart.

3. 3. The method of claim 1, wherein the nuclear spins of the one or more dopant atoms in a quantum dot are used as atomic magnets when the spins of the unpaired electron / holes in the quantum dot are used as data qubits.

4. 3. The method of claim 1, wherein when the multi-donor quantum dot is used as the error-corrected logic qubit, the spins of the unpaired electron / holes of the multi-donor quantum dot are used as data qubits and the nuclear spins of the one or more dopant atoms of the multi-dopant quantum dot are used for error correction.

5. 3. The method of claim 1 or 2, wherein when at least one nuclear spin of a dopant atom is used as a data qubit, the corresponding spin of the unpaired electron / hole is used for readout, addressability, or coupling with adjacent quantum dots.

6. 6. The method of claim 5, wherein coupling with adjacent quantum dots is achieved through electron / hole spin shuttling between the multi-dopant quantum dot and an adjacent quantum dot, or through exchange coupling between an unpaired electron / hole in the multi-dopant quantum dot and a paired electron / hole in the adjacent quantum dot.

7. The method of any one of claims 1 to 6, wherein the nuclear spins of the dopant atoms are controlled using nuclear magnetic resonance or EDSR.

8. The method of any one of claims 1 to 7, wherein the spin of the unpaired electron / hole is controlled using electric spin resonance or EDSR.

9. The method of any one of claims 1 to 8, wherein the one or more quantum operations comprise at least one of a single-qubit gate operation, a two-qubit operation, or a multi-qubit operation.

10. 10. The method of claim 9, wherein when the one or more quantum operations are multi-qubit operations, the quantum operations are performed using the spins of the unpaired electron / hole and the nuclear spins of the dopant atoms in a multi-dopant quantum dot.

11. 1. A method for performing one or more quantum operations in a quantum processor, the quantum processor comprising a plurality of quantum dots in a silicon substrate, at least a subset of the quantum dots being multi-dopant quantum dots each comprising two or more dopant atoms, and at least one of the plurality of quantum dots confines an unpaired electron / hole, the method comprising: performing the one or more quantum operations in the quantum processor using one or more modes of operation, the modes of operation including: using one or more of the multi-dopant quantum dots as error-corrected logic qubits; using the nuclear spin of at least one of the dopant atoms of the multi-dopant quantum dot as a data qubit; or using the spin of the unpaired electron / hole and at least one nuclear spin of a multi-dopant quantum dot as a data qubit.

12. 1. A quantum processor, comprising: silicon substrate, a layer of dielectric material on said silicon substrate; a plurality of quantum dots fabricated in the silicon substrate, each quantum dot comprising at least one dopant atom, at least a subset of the quantum dots being multi-dopant quantum dots having two or more dopant atoms, one or more of the plurality of quantum dots confine an unpaired electron / hole; A quantum processor wherein, during operation of the quantum processor, the spins of the unpaired electrons / holes and / or the nuclear spins of the one or more dopant atoms in a quantum dot are used as data qubits.

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

14. 14. The quantum processor of claim 12 or 13, wherein the distance between two adjacent quantum dots is selected to achieve a predefined tunnel coupling range between the unpaired electron / hole spins coupled to the adjacent dots.

15. 15. The quantum processor of claim 12, wherein the distance between adjacent quantum dots is about 5 to 20 nanometers.

16. 15. The quantum processor of claim 14, wherein the predefined tunnel junction is in the range of 1 kHz to 1 THz.

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

18. 18. The quantum processor of claim 12, further comprising one or more sensors for measuring the final state of a qubit associated with a quantum dot of the plurality of quantum dots.

19. further comprising one or more reservoirs proximate the quantum dots, the one or more reservoirs providing electrons / holes for confinement in one or more of the quantum dots; 19. The quantum processor of claim 12, wherein the distance between the one or more reservoirs and the one or more quantum dots is about 10 to 25 nanometers.

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

21. During operation, when the spins of the unpaired electron / hole of a quantum dot are used as data qubits, the nuclear spins of the one or more dopant atoms of the quantum dot are used for error correction or as atomic magnets; when the nuclear spins of the one or more dopant atoms are used as data qubits, the spins of the unpaired electron / holes are used to address or measure the nuclear spins of the one or more dopant atoms; or 21. The quantum processor of claim 12, wherein when the nuclear spins of the one or more dopant atoms are used as data qubits, the spins of the unpaired electrons / holes are used to couple the quantum dot to adjacent quantum dots.

22. 1. A method for performing multi-qubit operations, the method comprising: providing a multi-dopant quantum dot comprising two or more dopant atoms and an unpaired electron / hole confined within the multi-dopant quantum dot; using the spins of the unpaired electron / hole and the nuclear spins of the two or more dopant atoms as qubits, and performing the multi-qubit operation using the qubits.

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