Quantum processing elements and quantum processing systems

Abstract

A quantum processing system and a method of operating the same are disclosed. The system includes a first qubit including a first unpaired electron coupled to a first pair of donor clusters embedded in a semiconductor substrate at a distance from the semiconductor surface, each donor cluster in the first pair of donor clusters including at least one donor atom. The system further includes a second qubit including a second unpaired electron coupled to a second pair of donor clusters embedded in the semiconductor substrate at a distance from the semiconductor surface, each donor cluster in the second pair of donor clusters including at least one donor atom. In addition, a microwave resonator is located between the first and second qubits, a first end of the microwave resonator is coupled to the first qubit and a second end of the microwave resonator is coupled to the second qubit. Photons of the microwave resonator couple the first and second qubits.

Description

Technical Field

[0001] Aspects of the present disclosure relate to quantum processing systems, and more particularly to semiconductor-based quantum processing systems and quantum processing elements.

Background Art

[0002] Universal quantum computing can be a revolutionary technology applicable to specific fields in order to solve problems that are difficult to solve when executing the best-known classical algorithms currently known in state-of-the-art classical computers. Examples of fields where universal quantum computers are known to offer advantages include classes of optimization problems, advanced chemical simulations, and finding large numbers of prime factors, which would defeat the most common classical encryption protocols. For some of these applications, such as finding large numbers of prime factors, quantum computers should be exponentially faster than their classical counterparts. Quantum computing can also be useful for certain machine learning applications.

[0003] One such universal quantum computer architecture uses qubits (or qubits) encoded in the spins of electrons localized within a semiconductor substrate (such as silicon), where this localization is done electrostatically by gates or using the natural confinement of donor atoms hosted in the crystal lattice. Qubits implemented in silicon can utilize some of the mature technologies used to fabricate conventional silicon transistors and integrated circuits. A useful universal quantum computer is thought to include hundreds of error-corrected qubits and have the important ability to implement two-qubit operations between some of these qubits.

[0004] While semiconductor spin qubits have now reached a sufficiently high figure of performance to evoke error-corrected architectures for quantum information processing, several unresolved challenges remain before we can demonstrate a viable quantum computing processor within silicon. One such challenge concerns the placement of quantum dots / donors on a processor chip. It is known that the exchange interaction between qubits decreases exponentially with increasing separation of quantum dots / donors, meaning that quantum dots / donors must be placed close together and precisely, tens to hundreds of nanometers apart. In such two-dimensional qubit arrays, it is extremely difficult to incorporate the gates necessary for control and readout into the quantum dots / donors at the center of the array. Furthermore, the rate of heat dissipation resulting from such high-density quantum dots / donors and control electronics is currently not suitable for the cryogenic temperatures required for qubit coherence.

[0005] One option to overcome these problems is to include multiple qubits or nodes in the quantum computing processor, with each node containing a limited number of quantum dots / donors and their associated circuits. These nodes may be connected to each other to reduce the overall density while still enabling the execution of quantum computations. To do this, it would be necessary to couple the outer edge qubits of one node to the corresponding outer edge qubits of another node. The main techniques for coupling edge qubits between nodes are via superconducting microwave resonators and spin-photon coupling.

[0006] However, direct spin-photon coupling between electron spins and microwave photons is inherently difficult due to the small magnetic dipole interaction on the order of 100 Hz between electron spins and microwave photons. Instead, so-called spin-orbit coupling can be achieved between the spin and the charge degree of freedom of the qubit, thereby facilitating photon-spin coupling by electrically coupling the qubit's charge degree of freedom with the photon. However, while micro-magnets or nano-magnets have been fabricated on chips to achieve spin-orbit coupling, this is a complex manufacturing process, presenting new challenges when scaling up to hundreds of qubits.

[0007] The developments described in this section are publicly known to the inventors. However, unless otherwise indicated, no development described in this section should be considered prior art simply because it is included in this section, nor should it be considered publicly known to a person skilled in the art. [Overview of the project] [Means for solving the problem]

[0008] According to a first aspect of the present disclosure, a quantum processing system is provided, which includes: a first qubit comprising a first unpaired electron coupled to a first pair of donor clusters embedded in a semiconductor substrate at a distance from the semiconductor surface, wherein each donor cluster in the first pair of donor clusters comprises at least one donor atom; a second qubit comprising a second unpaired electron coupled to a second pair of donor clusters embedded in a semiconductor substrate at a distance from the semiconductor surface, wherein each donor cluster in the second pair of donor clusters comprises at least one donor atom; and a microwave resonator located between the first and second qubits, wherein a first end of the microwave resonator is coupled to the first qubit and a second end of the microwave resonator is coupled to the second qubit; and photons of the microwave resonator couple the first and second qubits.

[0009] In one embodiment, the donor clusters in the first pair of donor clusters and the second pair of donor clusters are separated such that the tunneling frequency of unpaired electrons is close to the resonant frequency of the microwave resonator.

[0010] In some embodiments, the quantum processing system further includes first and second electrically conductive leads fabricated in proximity to each of the first and second qubits in a semiconductor substrate. The first and second electrically conductive leads may be phosphorus delta layers. In addition, the first and second electrically conductive leads may be connected to the surface of the semiconductor substrate via first and second vertical vias, respectively.

[0011] Furthermore, the first end of the microwave resonator may be connected to a first vertical via on the surface of the semiconductor substrate, and the second end of the microwave resonator may be connected to a second vertical via on the surface of the semiconductor substrate.

[0012] In some embodiments, the first and second qubits and the first and second conductive leads are fabricated on the same plane within the semiconductor substrate, approximately 50 nm below the surface of the semiconductor substrate. The first and second conductive leads may be fabricated approximately 20 nanometers from the first and second qubits, respectively.

[0013] In some embodiments, the microwave resonator is made of a thin, high-kinetic-inductance superconducting material. In one example, the microwave resonator is a λ / 2 resonator.

[0014] In some embodiments, the quantum processing system includes a first node and a second node. Each node contains multiple qubits, where the first qubit is part of the first node and the second qubit is part of the second node. In such cases, the distance between the first qubit and the second qubit is from 1 millimeter to about 20 millimeters. Furthermore, the distance between pairs of donor clusters within each qubit may be about 15 to 20 nanometers.

[0015] In another example, the distance between the first qubit and the second qubit is 10 micrometers to about 20 millimeters, and the distance between pairs of donor clusters within each qubit is about 10 to 20 nanometers.

[0016] In one embodiment, each of the first and second donor clusters includes a single donor atom, which may be a phosphorus atom.

[0017] In some examples, the quantum processing system further includes additional gates located in close proximity to each of the first and second qubits in the semiconductor substrate (e.g., located about 40–100 nm from the first and second qubits). These additional gates may be configured to generate a DC electric field gradient for electrically inducing spin-orbit coupling in the first and second qubits.

[0018] In another aspect of the present disclosure, a method for operating a quantum processing device of a first aspect is provided, the method comprising: applying a static magnetic field to the quantum processing system to separate the spin states associated with the first and second unpaired electrons and nuclei of the first and second donor atomic clusters of the first and second qubits, respectively; applying a local electric field to each of the first and second qubits to bring about dispersive coupling between the corresponding first and second qubits and a microwave resonator; maintaining the dispersive coupling between the first and second qubits and the microwave resonator for a predetermined period of time; and applying a local electric field to the first and second qubits after the predetermined period to eliminate the dispersive coupling between the first and second qubits and the microwave resonator.

[0019] In some examples, the amplitude of the static magnetic field is set such that the frequencies of the first and second qubits are within a threshold range of the microwave resonator frequency.

[0020] Unless the context requires otherwise, the term “comprise” as used herein, and its variations such as “comprising,” “comprises,” and “comprised,” are not intended to exclude further additions, components, integers, or steps.

[0021] Further aspects of the present invention, and further embodiments of the aspects described in the preceding paragraphs, will become apparent from the following description, which is given as an example with reference to the accompanying drawings.

[0022] The features and advantages of the present invention will become apparent from the following description of embodiments of the invention as merely examples with reference to the accompanying drawings. [Brief explanation of the drawing]

[0023] [Figure 1A] This is a schematic diagram showing an example of a qubit device. [Figure 1B] This is a schematic diagram showing another example of a qubit device. [Figure 2] This is a schematic diagram illustrating a device according to several embodiments of the present disclosure. [Figure 3] This is a schematic diagram illustrating examples of quantum processing units according to several embodiments of the present disclosure. [Figure 4] This is a schematic side view showing a microwave resonator terminated in the phosphorus δ layer lead beneath the Si surface, and a qubit. [Figure 5] This figure shows the operating point in gate space for a 1P-1P qubit coupled to a resonator. [Figure 6A] This figure shows an example of a device layout for using hyperfine interaction (HF) for spin-orbit coupling. [Figure 6B] This figure shows an example of a device layout for using both HF and electrically-induced spin orbit (EISO) mechanisms. [Figure 6C] This figure shows another example of a device layout according to an aspect of this disclosure. [Figure 7] This figure shows a graph of the system energy level as a function of detuning. [Figure 8] This figure shows the scheme of system energy levels for zero detuning for symmetric and asymmetric hyperfine interactions. [Figure 9] This figure shows a graph of the spin-photon coupling as a function of the external magnetic field. [Figure 10] This figure shows a graph of the tunneling energy as a function of donor separation. [Figure 11] This figure shows graphs of the voltage and electric field from a single photon in the resonator mode as a function of distance from the delta layer lead. [Figure 12] This figure shows a flowchart illustrating an example of a method for coupling two qubits through a resonator cavity, according to some embodiments of the present disclosure. [Modes for carrying out the invention]

[0024] Because the magnetic dipole interaction between electron spins and microwave photons is small, electrical coupling between electron spins and microwave photons is preferred. Electrical coupling can be generated and promoted by inducing spin-charge hybridization through either an exogenous spin-orbit mechanism (operated through the implementation of an external magnetic field) or an intrinsic spin-orbit mechanism.

[0025] Over the past few years, several different types of quantum processing elements have been introduced that can be electrically coupled to superconducting microwave resonators. These types of quantum processing elements contain a pair of quantum dots / sites and are based on a single electron spin that can be in two different charge states. By carefully tuning the detuning (ε), the electron can be placed into a superposition of charges between the two quantum dots / sites (forming a charge qubit). When electron Zeeman splitting is comparable to charge qubit splitting, the spin and charge states of the electron can be hybridized by spin-orbit coupling.

[0026] Figures 1A and 1B show two previously known types of quantum processing elements that can be coupled to superconducting cavities to enable long-range qubit coupling.

[0027] The quantum processing element or device 100 shown in Figure 1A includes a semiconductor substrate 102 and a dielectric 104. In this example, the semiconductor substrate 102 is 28 silicon( 28The semiconductor substrate 102 is Si, and the dielectric 104 is silicon dioxide (SiO2). The semiconductor substrate 102 and the dielectric 104 form an interface 105, which in this example is a Si / SiO2 interface. A qubit 106 is formed within the semiconductor substrate 102. The qubit 106 contains two quantum dots 107 and 108 that share a single electron. Electronic confinement of the electron in the two quantum dots is achieved by a gate 109 positioned on the dielectric 104. This type of qubit is called a double quantum dot (DQD) qubit.

[0028] In addition, the micromagnet 110 is fabricated on-chip, specifically on the dielectric 104 together with the gate 109. The local magnetic field gradient generated by the micromagnet 110 has different longitudinal and transverse components at the two quantum dot sites. Device 100 is coupled to a resonator (not shown). When the field of the resonator excites electrons from their orbital coupled state to an anticoupled state, the electrons undergo effective spin-orbit coupling (SOC) as they move across this magnetic field gradient, thus achieving spin rotation driven by the electric field of the resonator.

[0029] Figure 1B shows another example of a known qubit device 120 for coupling with a superconducting cavity. In this arrangement, the qubit 121 includes one quantum dot 122 and a donor atom 124. In particular, the qubit device 120 shown in Figure 1B includes a semiconductor substrate 102 and a dielectric 104. In this example, the semiconductor substrate is 28 silicon( 28 The semiconductor substrate 102 is Si, and the dielectric 104 is silicon dioxide (SiO2). The semiconductor substrate 102 and the dielectric 104 form an interface 105, which in this example is a Si / SiO2 interface. A quantum dot 122 is formed near the interface 105, while the donor atom 124 is located within the substrate 102. The gate 128 is positioned above the quantum dot 122 (above the dielectric 104).

[0030] The gate electrode 128 is operable to interact with the donor atom 124. For example, gate 128 may be used to modulate the hyperfine interaction between the electron (confined within the quantum dot 122) and the nucleus of the donor atom 124 by inducing an AC electric field in the region between the interface 105 and the donor atom 124. When the qubit 121 is electrically driven, the electron spin flips and flops along with the donor's nuclear spin. That is, the electric field can be used to control the quantum state of the qubit 121 associated with a pair of electron-nucleus spin eigenstates, namely "electron spin up, nuclear spin down" and "electron spin down, nuclear spin up". This type of qubit 121 is called a flip-flop qubit.

[0031] In the DQD qubit 106, spin-orbit coupling is manipulated by a micro-magnet 110. Furthermore, in this case, the tip of the resonator is on the silicon surface. In addition, the DQD qubit 106 requires an additional confinement gate to form the qubit. Finally, the DQD qubit 106 requires the precise design and fabrication of the micro-magnet 110 to manipulate the desired highly localized spatial field gradient.

[0032] The qubit 121 in Figure 1B does not require a micromagnet and utilizes hyperfine interactions at a single donor site; however, the qubit 121 still includes quantum dots 122 formed by gates 128 near interface 105. Therefore, device 120 requires precise manipulation, fabrication, and control, which can be difficult to realize.

[0033] To overcome one or more of these problems, aspects of the present disclosure provide a novel quantum processing element / qubit that enables a wide range of qubit entanglement by allowing efficient spin-cavity coupling. This qubit design does not require any on-chip magnets, which distinguishes it from device 100. Furthermore, the qubit can be manipulated by an electric field from a single photon of a superconducting microwave resonator.

[0034] Figure 2 shows an example of a qubit 200 disclosed herein. The qubit 200 is located in a semiconductor substrate 202 having a surface 204. In this example, the semiconductor substrate is 28 It is silicon.

[0035] The qubit 200 includes a pair of tunnel-coupled donor atom clusters 206, 208 and a single electron 209 coupled to the pair of donor atom clusters 206, 208. In certain embodiments, the donor atom clusters 206, 208 are positioned within the silicon substrate 202 with atomic-scale precision using scanning tunneling lithography techniques. Furthermore, in some examples, the donor atoms 206, 208 may be located about 50 nm below the surface 204.

[0036] The qubit 200 may be coupled to a resonator (not shown), in some examples the resonator may be a high-impedance coplanar superconducting microwave resonator positioned on the silicon surface 204. The resonator is coupled to the qubit 200 by one or more delta layer leads positioned several tens of nanometers away from one of the donors. The donor clusters 206 and 208 are separated such that their single-electron tunneling frequencies are close to the resonant frequencies of the resonator. In one example the donor atomic clusters 206 and 208 may be about 15-20 nm apart from each other. In another example the donor atomic clusters 206 and 208 may be about 10-20 nm apart.

[0037] Qubit 200 generates intrinsic spin-orbit coupling (SOC) using the hyperfine interaction between the electron-nucleus system in the donor system. In particular, in Qubit 200, spin-charge hybridization occurs through the hyperfine interaction between the coupled electron 209 and the nuclear spins of donor atomic clusters 206 and 208. The hyperfine interaction uses the half-spin of the donor nucleus. The interaction strength between electron 209 and the nuclear spin is A at the left and right donor sites, respectively. L and A RThis is shown. The electron and nuclear spin states are entangled, and the resonator field can drive a transition to an excited state, in which the electron spin and one of the nuclear spins have a flipped orientation. The hyperfine interaction preserves the total spin of the entire qubit 200. Spin qubit operation driven by the resonator's electric field is achieved without requiring the fabrication of local micromagnets (as required by device 100).

[0038] In certain embodiments, each donor cluster 206, 208 may have a single donor atom, and the donor atom may be a phosphorus (P) atom, thereby making the qubit 200 a 1P-1P system. In other embodiments, the qubit 200 may be an nP-mP system, and the donor atom clusters 206, 208 may have any other number of phosphorus donor atoms.

[0039] A constant external magnetic field is applied to split the energy levels of the electron and donor spins. The strength of the magnetic field is selected so that the electron spin energy splitting is close to the resonant frequency of the coplanar microwave resonator. For a typical coplanar microwave frequency range of 4–12 GHz, the magnetic field strength would be 0.14–0.43 Tesla.

[0040] In addition, electrically conductive leads (not shown) are defined near the nP-mP qubit 200 by scanning tunneling lithography in the same crystal plane as the qubit, approximately 50 nm below the silicon surface. In some embodiments, these leads may be phosphorus δ layers, and they are connected by vertical vias to a metal deposited on the silicon surface 204. The leads closest to donor atomic clusters 206 and 208 are connected to one end of the resonator at the silicon surface.

[0041] The resonator may be made of a thin (e.g., a few nanometers) high-kinetic-inductance superconducting material. In one example, the resonator is designed to be a λ / 2 resonator so that the electric field wave antinodes are located at donor atoms 206, 208, maximizing coupling to their charge dipole. This lead may also act as a reservoir from which a single electron can be loaded into the qubit at a time scale considerably slower than the resonant frequency.

[0042] The qubit 200 described herein can be used to transfer quantum information between qubits separated by a length scale of up to several millimeters on the same silicon chip. Because the quantized electromagnetic field modes of the resonator intervene in the quantum information transfer between qubits, this transfer can be achieved with low power (at the level of a single microwave photon), and the resonator can intervene in a 2-qubit gate. This addresses two of the main obstacles to the aforementioned scaling up: namely, quantum information can be transferred between smaller qubit arrays, thus providing space for control gates in these smaller arrays, and this mitigates energy density concerns in cryogenic environments.

[0043] A quantum processing unit (i.e., a QPU) for semiconductor quantum dots may include multiple arrays or nodes of qubits. Figure 3 is a schematic diagram of an example QPU300 according to some embodiments of the present disclosure. As seen in Figure 3, the example QPU300 includes two qubit nodes 302, i.e., nodes 302A and 302B. Although Figure 3 shows two nodes, it will be recognized that a QPU may have many more nodes in a real implementation, and the number of nodes used for a given QPU may depend on the particular application, the number of qubits located at each node, and the computational requirements of the QPU.

[0044] Each node 302 contains multiple qubits 303 arranged in a two-dimensional array. The number of qubits 303 located in each node 302 depends on several factors, such as the distance between qubits, the number of control lines and / or gates that can be accommodated in the node to address each qubit within the node 302, and the heat dissipated by the control circuit. In some examples, the node 302 is made small enough so that control gates 304 located on the chip surface or within the silicon substrate can address each individual qubit 303, and the qubits are close enough (i.e., on a length scale of 10 nm) to exchange interactions. In the example shown in Figure 3, each node 302 contains eight qubits 303.

[0045] Nodes 302 can be separated by several millimeters on the same silicon chip / substrate 202. Furthermore, nodes can be connected to each other by one or more resonators. In one implementation, a resonator 306 is connected between a pair of nodes, and in particular, the resonator 306 is coupled to one qubit in each of the pair of nodes 302. In the example of QPU300, qubit 303A of node 302A is coupled to qubit 303B of node 302B via resonator 306. Since resonator 306 can intervene in 2-qubit gate operation, quantum information can be transferred between qubit nodes via resonator 306, enabling connectivity that is important for realizing quantum algorithms useful in QPUs.

[0046] In Figure 3, the qubits coupled to the resonator 306 at each node 302 (i.e., qubits 303A and 303B) are manufactured as the qubits shown in Figure 2. That is, qubits 303A and 303B are double donor cluster qubits 200. Other qubits at node 302 may also be double donor atom qubits 200, but this is not required. In some examples, qubits not coupled to the resonator 306 may be any other type of qubit, such as simple donor qubits or gate control qubits, without departing from the scope of this embodiment. Furthermore, qubit 303 at each node 302 may be coupled to its nearest neighbor qubit via exchange coupling.

[0047] Figure 4 is a schematic diagram of one end of a resonator, such as a resonator 306, particularly a λ / 2 microwave resonator. The resonator 306 is located on the surface of a silicon substrate 202. In some examples, the resonator 306 is fabricated from a thin, high-impedance superconducting film. One end of the resonator 306 contacts a vertical metal via 402, which connects the resonator 306 to a lead 404 in the silicon substrate 202. In some examples, the lead 404 may be a delta-layer lead. Furthermore, the lead 404 may be positioned on the same plane as the qubit 200, approximately 50 nm below the silicon surface. This brings the electric wave antinode closer to the double donor atom qubit 200. The distance between the lead 404 and the qubit 200 is denoted as ΔL, the distance between the donor atoms is denoted as Δx, and the depth of the qubit 200 from the surface of the semiconductor surface 204 is denoted as Δh.

[0048] When the double donor atom qubit 200 is a 1P-1P system, the gate space operating point for a 1P-1P qubit strongly coupled to the quantized resonator mode is at the (1,0)-(0,1) transition. Figure 5 shows the gate space operating point for a 1P-1P qubit 200 coupled to resonator 306. In particular, this figure shows the resonator voltage V along the x-axis. resis plotted, and this figure plots the gate voltage V along the y-axis g is plotted. (1,0) indicates the electron occupancy in the left donor cluster 206, and (0,1) indicates the electron occupancy in the right donor cluster 208. The coupling to the resonator lever arm or 1P-1P charge dipole should be strong enough so that the electric field ε0 of a single microwave resonator photon drives the electron occupancy across this transition.

[0049] FIG. 6A is a top view of an example of a device 600 that uses the hyperfine interaction (HF) between electrons and nuclei for spin-orbit coupling. In particular, FIG. 6A shows a top view of a single qubit 200 coupled to a resonator 306 and the circuitry necessary for the qubit 200 to function. As shown in FIG. 6, the device 600 includes a gate 602 positioned near the qubit to control the operation of the qubit 200. The gate 602 may include a metal contact on the semiconductor surface 204, and this metal contact is connected via a metal lead or via to a δ-layer lead (fabricated on the same plane as the qubit 200).

[0050] In addition to the gate 602, the device may include a charge sensing device 604. In some embodiments, this charge sensing device may be a single electron transistor (SET) positioned on the same plane as the qubit near the qubit 200. In other embodiments, the gate 602 or the resonator 306 may serve the role of the charge sensing device 604. In such cases, an additional charge sensor may not be necessary.

[0051] Another way to achieve electron-spin-photon coupling is through electrically induced spin-orbit interaction. Previous studies have shown that when an electric field is present in the donor cluster, spin-orbit coupling that directly couples external electric and magnetic fields can prevail over Rashva spin-orbit coupling and spin orbits due to bulk Si crystals. When the electric fields from the surrounding gates differ between the two donors, the electron spin orbits create an effective heterogeneous field, which can therefore rotate their own spins.

[0052] Figure 6B is a top view of an example device 650 that uses such electrically induced spin-orbit (EISO) mechanisms in conjunction with hyperfine mechanisms to operate a qubit 200. Similar to Figure 6A, Figure 6B shows a top view of a single qubit 200 coupled to a resonator 306 and the circuitry necessary for the qubit 200 to function and electrically induce spin-orbit coupling. As shown in Figure 6B, device 650 includes a gate 602 positioned near the qubit 200 to control its operation. Device 650 also includes two additional EISO gates 652A and 652B. In some examples, gates 602, 652A, and 652B may be located on the same plane as the qubit 200 in the silicon substrate 202. In other examples, one or more of gates 602, 652A, and 652B may be located on the semiconductor surface 204. In these cases, the gates may be connected to the qubit 200 via metal leads or vias. The side EISO gates 652A and 652B can produce a strong DC electric field gradient, potentially resulting in effects similar to hyperfine interaction.

[0053] Because hyperfine interaction-dependent spin-photon coupling depends on the initial nuclear state of the donor, devices that operate simply on hyperfine interactions would need to be initialized with the correct nuclear state before they can operate. On the other hand, EISO interactions enable spin-photon coupling independent of the initial nuclear state, so when EISO gates are used in a device, it would not be necessary to initialize the nuclear state of its donor atom before such a device can operate.

[0054] Figure 6C is a top view of another example of device 660 that uses electron-nucleus hyperfine interaction (HF) for spin-orbit coupling. In particular, Figure 6C shows a top view of a single qubit 200 coupled to a resonator 306 and the circuitry required for the qubit 200 to function. The left and right dots of the qubit may be positioned about 10-20 nanometers apart to ensure tunnel coupling close to the resonant frequency of the resonator 306. As shown in Figure 6C, device 660 includes a reservoir gate 662 positioned to the left of the qubit 200. The reservoir gate 662 is positioned 15-30 nanometers away from the qubit 200 and is electrically connected to a resonator, such as the resonator 306 (not shown in this figure), via a metallic via (not shown). This short distance between the reservoir gate 662 and the qubit 200 is chosen so that the gate acts as an electron reservoir for the qubit 200 and to maximize the resonant voltage induced by the resonator 306 in the qubit.

[0055] Device 660 may further include another gate 664 positioned close to the qubit 200 to control the operation of the qubit 200. The gate 664 may include a metal contact on the semiconductor surface 204, which is connected to a δ-layer lead (fabricated on the same plane as the qubit 200) via a metal lead or via.

[0056] In addition to gate 664, device 660 may include a charge sensing device 666. In some embodiments, this charge sensing device 666 may be a single-electron transistor (SET) positioned 30 to 100 nanometers away from qubit 200 and on the same plane as qubit 200. The SET 604 is positioned asymmetrically with respect to two donor clusters of qubit 200, resulting in different lever-arm parameters, which allows for distinction of which cluster was explored when tracking the SET response. In other embodiments, gates 662, 664, or resonator 306 may serve as the charge sensing device 666. In such cases, an additional charge sensor may not be required.

[0057] Figure 7 is a graph 700 showing the system energy level E as a function of detuning (ε) between P donors. In zero detuning, electron 209 has a tunneling energy of 2t c This forms bond |-> and antibond |+> orbitals that are split by this.

[0058]

number

[0059] Here, |L〉 and |R〉 indicate the localization of electrons in the left and right donor clusters 206 and 208, respectively. The |-〉 and |+〉 levels, respectively, are determined by the applied external magnetic field B, which is hγ e The energy is further split by the spin Zeeman splitting of the electron spin ↓ and ↑ states shown in B. Here, h is Planck's constant, and γ e is the electron-spin-gyromagnetic ratio. In non-zero detuning, electron density is shifted to donors with lower potential energy. In the extreme case of very large detuning, electrons occupy only one donor site.

[0060] Each of the energy levels shown in Figure 7 further splits into four states by nuclear Zeeman interactions and hyperfine interactions (shown in Figure 8). The qubit subspace is defined within the coupled |-> state variety, while the proximity of the antibonding |+> orbitals acts as an intermediary, enabling charge-spin coupling. Figure 7 shows the symmetry (A L =A R ) and asymmetric (A L >A R This is a schematic diagram of the system energy level E with respect to zero detuning for the hyperfine interaction. In Figure 8, solid arrows indicate transitions mediated by the hyperfine interaction, while dashed arrows indicate transitions that are forbidden by the hyperfine interaction but driven by electrically induced spin-orbit interaction or EISO interaction.

[0061] The eigenstates shown in Figure 8 are determined by the total Hamiltonian H. |DI L I R Based on S, D defines electron localization |L〉 or |R〉 in the left or right donor, and I L and I R This is the left and right nuclear spin (polarization).

[0062]

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[0063] When it shows that (having) and S defines electron spin (|↑〉 or |↓〉, the Hamiltonian is as follows: H = H0 + H HF +H EISO (1) Here H0 = -t c τ x +ετ z +hγ e B·S+Σ j=L,R hγ e B·I j (2)

[0064] τ is a Pauli matrix based on left / right donors, on the other hand

[0065]

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[0066] σ are the electron and donor spin operators, where σ e (σ P ) is the Pauli matrix based on electron (donor) spin. The electron and nuclear spin gyromagnetism ratios in Si are γ, respectively. e =27.97GHz / T and γ P = -17.23MHz / T.

[0067] H HF This is the Hamiltonian that describes the hyperfine interaction that mixes the spatial and spin degrees of freedom of electrons. It can be expressed as follows:

[0068]

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[0069] Here A L (A R ) represents the hyperfine constant of the left (right) donor. The Si bulk value of the hyperfine constant is approximately A L =A R = 117 MHz. The electron-nucleus spin product is I·S = I z S z +1 / 2(I + S - +I - S + This can be expressed as follows: Charge-spin hybridization is introduced by the dependence of the hyperfine interaction on electron localization (in the left or right donor). This is because, due to the hyperfine coupling, the eigenstates of the Hamiltonian H0 acquire a mixture of different spin and orbital states.

[0070] The hyperfine interaction is intrinsic and therefore always present in 1P-1P systems, whereas the electrically induced spin-orbit interaction H EISOIt can be switched on and off as needed. EISO occurs when an electric field E perpendicular to the external magnetic field B is applied within the donor region (for example, using the EISO gate shown in Figure 6B). H for B and E in the z-direction and y-direction, polarized in z. EISO It takes the following form:

[0071]

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[0072] Here, the first matrix is ​​based on {|L〉,|R〉},

[0073]

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[0074] This is the Pauli x matrix based on electron spin. EISO Since this does not affect nuclear spin, this is considered an identity in a subspace based on nuclear spin. The coefficient (C) is approximately 6 × 10 for a single donor in silicon. -14 It is estimated to be em / T.

[0075]

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[0076] These correspond to the electric fields at the left and right donor sites, respectively. To generate charge-spin hybridization,

[0077]

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[0078] A difference is necessary.

[0079] In Figure 8, symmetry (A L =A R ) and asymmetric (A L >AR Alternatively, the eight lowest eigenstates of the Hamiltonian H for ε<0) hyperfine interactions are shown.

[0080]

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[0081] The signs {↑,↓} and {|-〉,|+〉} describe the main part of each eigenstate. Note that these eigenstates also include some small non-zero mixtures of different foundational states due to the hyperfine interaction.

[0082] The system interaction with cavity photons can be described by the following Hamiltonian.

[0083]

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[0084] Here

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[0085] This is the annihilation (generation) operator for microwave resonator modes. The cavity field has amplitude ε0 and frequency f r Assuming that it is described by and has a non-zero polarization component along the x-axis, the charge coupling rate g c teeth

[0086]

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[0087] It can be defined as follows. The solid and dashed vertical arrows in Figure 8 represent the resonator frequency f r When this is adapted to the energy splitting between appropriate pairs of states, all H that rotate the electron spin c The drive transition is shown. The solid arrow indicates a transition without any electrically induced spin trajectory (i.e., H EISOThis shows transitions mediated solely by hyperfine interactions, which are possible even when EISO = 0. The dashed arrows indicate that EISO is H EISO ≠0 and

[0088]

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[0089] This indicates the transitions that become accessible when switched on.

[0090]

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[0091] Energy splitting between states is approximately (A L +A R ) / 4-2hγ P B is the value, which gives a value on the order of 100 MHz for the P donor in silicon.

[0092]

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[0093] The energy splitting between states depends on the asymmetry of the hyperfine interaction, which is approximately (A L -A R ) / 4. However, even if A L =A R Even so, the splitting between the zero-nucleus and spin states (singlet and triplet states of the nucleus) is due to the hyperfine interaction.

[0094]

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[0095] The mixing of states results in a non-zero state. This splitting decreases with increasing magnetic field, reaching an order of 0.1 MHz for approximately 0.2 T of B.

[0096] Each of the transitions shown in Figure 8 may be an effective point for qubit operation, and the qubit itself is defined by the initial and final eigenstates corresponding to a particular transition. A common feature of each of these qubit subspaces is the rotation of electron spin. Electron spin rotation for hyperfine intervening transitions is accompanied by nuclear spin flips (similar to flip-flop qubits), whereas the nuclear spin configuration for EISO intervening transitions is conserved.

[0097] To select a specific qubit point of action, it is necessary to initialize the desired nuclear spin configuration, which can be achieved, for example, by nuclear polarization methods such as nuclear magnetic resonance (NMR) or dynamic nuclear polarization.

[0098] By adjusting the external magnetic field B, the qubit energy splitting can be controlled, and a given cavity frequency f r The qubit resonates with respect to the magnetic field. A magnetic field in the range of 0.14–0.43 T is required for a typical resonator frequency bandwidth of 4–12 GHz. Since spin-photon coupling depends on the mixing of different spin and orbital states for the H0 eigenstates, it is desirable to maximize charge-spin hybridization, which depends on how close the anticoupling |+〉 manifold is to the qubit subspace.

[0099] Referring to Figure 9, the cavity-spin coupling g between states 1 and 6 (i.e., the leftmost transition in Figure 8) s / g c However, the given value is 2t c The relationship is expressed as a function of the magnetic field B for / h = 7.64 GHz. The coupling is between eigenstates 1 and 6. c It is calculated by evaluating [the following].

[0100]

number

[0101] g at ​​B≈0.272T sThe rapid increase in is due to the degeneracy of the |-↑〉 manifold by the |+↓〉 state. Operating very close to that point is undesirable for increasing decoherence. However, the tunneling energy f r By setting it to be not equal but equivalent, a significant value of g still remains. s >0.01g c This can be obtained. By adjusting the donor separation, the tunneling rate in the 1P-1P system can be controlled. Referring to Figure 10, the tunneling rate 2t as a function of the donor separation Δx, calculated by atomic strong coupling simulations, can be obtained. c The / h value is shown. According to that data, the optimal 1P-1P separation for a cavity bandwidth of 4-12 GHz is in the range of 15-20 nm.

[0102] For comparison, B = 0.2T and 2t c Approximately g at h=7.64GHz s = 0.01g c For the EISO-mediated transition that yields spin-photon coupling, an electric field difference of approximately 12 MV / m would need to be applied between donors 206 and 208. The electric field difference can be distributed between both donors as shown in the following example.

[0103]

number

[0104] The different electric fields at the two donor sites can be generated by an additional EISO gate, as shown in Figure 6B.

[0105] The charge-photon coupling is a system dipole moment d c And since it is proportional to the amplitude ε0 of the electric field due to one photon in the cavity, it is desirable to maximize both parameters. Because the electron wave function is strongly localized within the donor region, the dipole moment can be well approximated by half of the donor separation. d c≈ eΔx / 2. As mentioned above, Δx (i.e., the distance between donor clusters 206 and 208 of qubit 200) is limited by the corresponding tunneling value and optimally takes a value in the range of 15-20 nm. The cavity electric field ε0 can be maximized by adjusting the ΔL value (see Figure 4) and by appropriate donor arrangement for the phosphorus delta layer leads.

[0106] Figure 11 is Chart 1100 showing the potential V and electric field (ε0) due to a single photon in the resonator mode as a function of x (i.e., distance from the δ layer lead 502). ΔV and g are approximately 0.5 μV on the order of 100 MHz, with Δx and ΔL > 20 nm (to ensure the tunneling frequency from the lead to the nearest donor is slower than any other time scale in the system). c Donade tuning of =eΔV / 2h can still be achieved. Therefore, within device 200, approximately 1-10% g s / g c The spin-cavity coupling allows for frequencies on the order of 1 MHz. A unique feature of the proposed design is the contact of the ends of the λ / 2 microwave resonator 306 with phosphorus delta layer leads embedded in the qubit layer. This allows the dual donor to be positioned in the high-electric-field region, significantly promoting charge-photon coupling in the system.

[0107] The proposed device 200 can be extended to other donor cluster systems, but the system specifications must be adjusted accordingly. For systems with the same number of donors in each cluster, both cluster separation and electron count must be changed. For example, when each donor cluster contains two Lindonner atoms, this 2P-2P qubit may contain three electrons. Similarly, when each donor cluster contains three Lindonner atoms, this 3P-3P qubit may contain five electrons. Alternatively, for asymmetric systems (i.e., systems with different numbers of donor atoms in donor clusters, e.g., 1P-2P, 2P-3P, etc.), additional detuning is required to make the system anti-cross-bound and anti-bonded. In either case, the possible transitions and qubit subspaces must be refined.

[0108] Figure 12 shows an example of Method 1200 for coupling two qubits, such as qubit A and qubit B in Figure 3, via a resonator. For example, this method describes the "iSWAP" interaction between qubit A and qubit B via a resonator.

[0109] Method 1200 begins in step 1202, where a magnetic field is applied to qubits A and B. In some embodiments, the magnetic field is a static and homogeneous field. The strength of the external magnetic field is set such that Zeeman splitting results in qubit energy splitting close to the resonator frequency. In one example, the external magnetic field may be set to 0.2T.

[0110] In step 1204, electrons are loaded from their respective reservoirs into a double donor structure containing qubits A and B. The number of electrons loaded into each cluster depends on the double donor cluster system used. When an IP-IP system is used, a single electron is loaded into qubit A and / or qubit B. Alternatively, for any other nP-mP system, two or more electrons may be loaded. Electron loading can be achieved by applying local detuning using one or more gates (e.g., gate 602 shown in Figure 6A or Figure 6B) to advance to a suitable electron-occupied region in gate space (e.g., the (1,0)-(0,1) transition space in Figure 5). By waiting in a suitable region of gate space, it is ensured that the loaded electrons relax and enter their spin-down ground state.

[0111] In step 1206, the electron spin of qubit B is flipped. In one embodiment, the electron spin is flipped to a spin-up state using a calibrated 1-qubit gate, for example, through an oscillating magnetic or electric field (electron spin resonance or electric dipole spin resonance).

[0112] Next, in step 1208, known energy detuning with respect to the resonator frequency is applied to qubit A and qubit B individually. The detuning of qubit A with respect to the resonator frequency may or may not be the same as the detuning of qubit B with respect to the resonator frequency. In this "dispersive" region, E A ,E B <hf0、および

[0113]

number

[0114] Here E A , Bis the energy of qubits A and B, considering the Zeeman energy (assumed equal) of qubits A and B respectively, and the energy due to individual detuning (which may be equal but need not be). Further, here the energy of the microwave photons in the resonator is hf0, and g A and g B are the coupling rates of qubits A and B to the cavity respectively.

[0115] In step 1210, the fixed detuning of qubits A and B with respect to the resonator frequency is maintained for the next time.

[0116]

Equation

[0117] Here, Δ A and Δ B represent the energy detuning of qubits A and B from the resonator respectively. At this characteristic time τ, the freely occurring coupled system results in an "iSWAP" gate between qubits A and B.

[0118] In step 1212, after time τ, both qubits should be detuned far from the resonator frequency to end the gate interaction.

[0119] Finally, if desired, the states of qubits A and B can be measured independently to verify that an iSWAP gate has actually occurred between the two qubits. In certain embodiments, this readout can be achieved by conventional techniques such as using two single-electron transistors fabricated on-chip near qubits A and B.

[0120] Although Method 1200 has been described with reference to the iSWAP gate operation, it will be recognized that Method 1200 can be implemented with minor modifications to perform other types of operations between qubits A and B without departing from the scope of this disclosure.

[0121] The methods and quantum processor architectures described herein employ quantum mechanics to perform computations. These processors may be used in a variety of applications, for example, to provide improved computational performance, including, in particular, encryption and decryption of information, progressive chemical simulation, optimization, machine learning, pattern recognition, anomaly detection, financial analysis, and verification.

[0122] Those skilled in the art will recognize that numerous changes and / or modifications may be made to the invention as shown in particular embodiments without departing from the spirit or scope of the invention as broadly described. Therefore, these embodiments should be considered in all respects illustrative and not limiting.

Claims

1. A quantum processing system, A first qubit comprising a first unpaired electron coupled to a first pair of donor clusters embedded in a semiconductor substrate at a distance from the semiconductor surface, wherein each donor cluster in the first pair of donor clusters comprises at least one donor atom, A second qubit comprising a second unpaired electron coupled to a second pair of donor clusters embedded in the semiconductor substrate at a distance from the semiconductor surface, wherein each donor cluster in the second pair of donor clusters comprises at least one donor atom, A microwave resonator located between the first qubit and the second qubit, wherein a first end of the microwave resonator is coupled to the first qubit and a second end of the microwave resonator is coupled to the second qubit, A quantum processing system in which photons from the microwave resonator couple the first qubit and the second qubit.

2. The quantum processing system according to claim 1, wherein the donor clusters in the first pair of the donor clusters and the second pair of the donor clusters are separated such that the tunneling frequency of the unpaired electrons is close to the resonant frequency of the microwave resonator.

3. The quantum processing system according to claim 1 or 2, further comprising a first electrically conductive lead and a second electrically conductive lead manufactured in the semiconductor substrate in proximity to each of the first qubit and the second qubit.

4. The quantum processing system according to claim 3, wherein the first electrically conductive lead and the second electrically conductive lead are phosphorus δ layers.

5. The quantum processing system according to claim 4, wherein the first electrically conductive lead and the second electrically conductive lead are connected to the surface of the semiconductor substrate via a first vertical via and a second vertical via, respectively.

6. The quantum processing system according to claim 5, wherein the first end of the microwave resonator is connected to the first vertical via on the surface of the semiconductor substrate, and the second end of the microwave resonator is connected to the second vertical via on the surface of the semiconductor substrate.

7. The quantum processing system according to claim 3, wherein the first qubit and the second qubit, and the first electrically conductive lead and the second electrically conductive lead are manufactured on the same plane within the semiconductor substrate, approximately 50 nm below the surface of the semiconductor substrate.

8. The quantum processing system according to claim 3, wherein the first electrically conductive lead and the second electrically conductive lead are manufactured approximately 20 nanometers from the first qubit and the second qubit, respectively.

9. The quantum processing system according to any one of claims 1 to 8, wherein the microwave resonator is made of a thin, high-kinetic-inductance superconducting material.

10. The quantum processing system according to any one of claims 1 to 9, wherein the microwave resonator is a λ / 2 resonator.

11. A quantum processing system according to any one of claims 1 to 10, further comprising a first node and a second node, each node comprising a plurality of qubits, wherein the first qubits are part of the first node and the second qubits are part of the second node.

12. The quantum processing system according to any one of claims 1 to 11, wherein the distance between the first qubit and the second qubit is from 100 micrometers to about 20 millimeters.

13. The quantum processing system according to any one of claims 1 to 12, wherein the distance between pairs of donor clusters is about 10 to 20 nanometers.

14. The quantum processing system according to any one of claims 1 to 13, wherein each of the first donor cluster and the second donor cluster includes a single donor atom.

15. The quantum processing system according to claim 14, wherein the donor atom is phosphorus.

16. A quantum processing system according to any one of claims 1 to 15, wherein an additional gate is located in the semiconductor substrate adjacent to each of the first qubit and the second qubit, and the additional gate is configured to generate a DC electric field gradient for electrically inducing spin-orbit coupling in the first qubit and the second qubit.

17. The quantum processing system according to any one of claims 1 to 16, wherein a continuous external magnetic field is applied to the quantum processing system in order to separate the spin states associated with the unpaired electrons and nuclei of the donor atom cluster.

18. The quantum processing system according to claim 17, wherein the strength of the magnetic field is between 0.14 and 0.43 Tesla.

19. A method for operating a quantum processing device according to any one of claims 1 to 18, wherein the method is A step of applying a static magnetic field to the quantum processing system to separate the spin states associated with the first unpaired electrons and the second unpaired electrons and nuclei of the first and second donor atom clusters of the first and second qubits, respectively. A step of applying a local electric field to each of the first and second qubits to bring about dispersive coupling between the corresponding first and second qubits and the microwave resonator, A step of maintaining the dispersive coupling between the first qubit and the second qubit and the microwave resonator for a predetermined period of time. A method comprising the step of applying a local electric field to the first qubit and the second qubit after the predetermined period of time to eliminate the dispersive coupling between the first qubit and the second qubit and the microwave resonator.

20. The method according to claim 19, wherein the amplitude of the static magnetic field is such that the frequencies of the first qubit and the second qubit are within a threshold range of the frequency of the resonator.

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