Quantum processing elements and quantum processing systems

Abstract

Disclosed is a quantum processing system and a method of operating the quantum processing system. The system includes a first qubit including a first unpaired electron bound to a first donor cluster pair embedded in a semiconductor substrate and a distance from a semiconductor surface, each donor cluster of the first donor cluster pair including at least one donor atom. The system also includes a second qubit including a second unpaired electron bound to a second donor cluster pair embedded in the semiconductor substrate and a distance from the semiconductor surface, each donor cluster of the second donor cluster pair including at least one donor atom. Further, a microwave resonator is positioned 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. Photons of the microwave resonator couple the first qubit and the second qubit.

Description

Technical Field

[0001] Various aspects of this disclosure relate to quantum processing systems, and in particular to semiconductor-based quantum processing systems and quantum processing elements. Background Technology

[0002] Universal quantum computing is a potentially revolutionary technology that can be applied to certain fields to solve problems that are difficult to solve when running the best known classical algorithms on state-of-the-art classical computers. Areas where universal quantum computers are known to have an advantage include optimization problems, advanced chemical simulations, and finding the prime factors of large numbers (which would render most common classical encryption protocols ineffective). For some of these applications, such as finding the prime factors of large numbers, quantum computers should be several times faster than classical computers. Quantum computing can also be used for certain machine learning applications.

[0003] One type of general-purpose quantum computer architecture uses qubits (or quantum bits) to encode the spin of electrons in a semiconductor substrate (such as silicon) via an electrostatic gate or by utilizing the natural confinement of donor atoms in a crystal lattice. Qubits implemented in silicon can utilize some of the well-established techniques used to fabricate conventional silicon transistors and integrated circuits. It is believed that a useful general-purpose quantum computer will consist of hundreds of error-corrected qubits and possess the crucial capability to perform two-qubit operations between these qubits.

[0004] Currently, semiconductor spin qubits have achieved sufficiently high performance to envision error-correcting architectures for quantum information processing. However, several challenges remain before a viable quantum computing processor can be demonstrated on a silicon chip. One such challenge relates to the placement of quantum dots / donors on the processor chip. It is well known that the exchange interaction between qubits decays exponentially with the spacing between the quantum dots / donors, meaning that the quantum dots / donors need to be placed very close and precisely, spaced tens to hundreds of nanometers apart. In such a two-dimensional qubit array, connecting the gates required for control and readout to the quantum dot / donor at the center of the array becomes extremely difficult. Furthermore, this dense arrangement of quantum dots / donors and control electronics means that the rate of heat dissipation is incompatible with the low temperatures required for qubit coherence.

[0005] One way to overcome these problems is to include multiple qubits or nodes in a quantum computing processor, where each node comprises a finite number of quantum dots / donors and their associated circuitry. These nodes can be connected to each other, thereby reducing the overall density while still enabling quantum computing. For this purpose, the outer edge qubits of one node need to be coupled to the corresponding outer edge qubits of another node. The main techniques for cross-node coupling of edge qubits are via superconducting microwave resonators and spin-photon coupling techniques.

[0006] However, direct spin-photon coupling between electron spin and microwave photons is inherently challenging because the magnetic dipole interaction between electron spin and microwave photons is very small, around 100 Hz. Instead, coupling between photons and spin can be enhanced by achieving so-called spin-orbit coupling between spin and the charge degree of freedom of the qubit, which is electrically coupled to the photon. However, to date, while miniature or nanomagnetic structures have been fabricated on chips to achieve spin-orbit coupling, this is a complex manufacturing process that faces new challenges when scaling up to hundreds of qubits.

[0007] The developments described in this section are known to the inventors. However, unless otherwise stated, no development described in this section should be considered prior art simply because it is included in this section, nor should it be considered well known to those skilled in the art. Summary of the Invention

[0008] According to a first aspect of this disclosure, a quantum processing system is provided, comprising: a first qubit including a first unpaired electron bound to a first donor cluster pair embedded in a semiconductor substrate at a distance from the semiconductor surface, each donor cluster in the first donor cluster pair including at least one donor atom; a second qubit including a second unpaired electron bound to a second donor cluster pair embedded in a semiconductor substrate at a distance from the semiconductor surface, each donor cluster in the second donor cluster pair including at least one donor atom; and 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; wherein photons of the microwave resonator couple the first qubit and the second qubit.

[0009] In one implementation, the donor clusters in the first donor cluster pair and the second donor cluster pair are separate, such that the tunneling frequency of the 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 conductive leads fabricated within a semiconductor substrate and close to each of the first and second qubits. The first and second conductive leads may be a phosphorus delta layer. Furthermore, the first and second 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 can be connected to a first vertical through-hole on the surface of the semiconductor substrate, and the second end of the microwave resonator can be connected to a second vertical through-hole 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 in the same plane within a semiconductor substrate and approximately 50 nanometers below the surface of the semiconductor substrate. The first and second conductive leads may be fabricated at a distance of approximately 20 nanometers from the first and second qubits, respectively.

[0013] In some implementations, the microwave resonator is made of a thin, high-energy, high-inductance superconducting material. In one embodiment, 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 includes multiple qubits, with the first qubit being part of the first node and the second qubit being part of the second node. In this case, the distance between the first and second qubits is approximately 1 millimeter to about 20 millimeters. Furthermore, the distance between donor cluster pairs within each qubit may be approximately 15-20 nanometers.

[0015] In another embodiment, the distance between the first and second qubits is 10 micrometers to about 20 millimeters, and the distance between donor cluster pairs in each qubit is about 10-20 nanometers.

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

[0017] In some embodiments, the quantum processing system further includes an additional gate (e.g., located at approximately 40-100 nanometers from the first and second qubits) situated in a semiconductor substrate and close to each of the first and second qubits. The additional gate may be configured to generate a DC electric field gradient to electrically induce spin-orbit coupling in the first and second qubits.

[0018] In another aspect of this disclosure, a method for operating the quantum processing device of the first aspect is provided, the method comprising the steps of: applying a static magnetic field to the quantum processing system to separate spin states associated with first and second unpaired electrons of first and second qubits and atomic nuclei of first and second donor atom clusters, respectively; applying a local electric field to each of the first and second qubits to cause the corresponding first and second qubits to be dispersively coupled to a microwave resonator; maintaining the first and second qubits in the dispersive coupling with the microwave resonator for a predetermined time period; and applying a local electric field to the first and second qubits after the predetermined time period to cause the first and second qubits to decouple from the dispersive coupling with the microwave resonator.

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

[0020] As used herein, unless the context otherwise requires, the term “comprise” and its variations, such as “comprising,” “comprises,” and “comprised,” are not intended to exclude other additives, ingredients, wholes, or steps.

[0021] Further aspects of the invention, and embodiments thereof, described in the preceding paragraphs, will become apparent from the following description, given by way of example and with reference to the accompanying drawings. Attached Figure Description

[0022] The features and advantages of the present invention will be apparent from the following description of its embodiments, which are illustrated by way of example only, with reference to the accompanying drawings, wherein:

[0023] Figure 1A This is a schematic diagram of an example quantum bit device.

[0024] Figure 1B This is a schematic diagram of another quantum bit device.

[0025] Figure 2 This is a schematic diagram of an apparatus according to certain embodiments of the present disclosure.

[0026] Figure 3 This is a schematic diagram of an example quantum processing unit according to certain embodiments of the present disclosure.

[0027] Figure 4 This is a side view of a microwave resonator and its qubits, which are terminated by phosphorus delta-layer leads under the silicon surface.

[0028] Figure 5 The operating point of a 1P-1P qubit coupled to a resonator in gate space is shown.

[0029] Figure 6A This is an example device layout that uses hyperfine interaction (HF) to achieve spin-orbit coupling.

[0030] Figure 6B This is an example device layout that uses both HF and the "electro-induced spin orbit (EISO) mechanism".

[0031] Figure 6C This is another example device layout based on aspects of this disclosure.

[0032] Figure 7 It is a graph of the system's energy levels as a function of detuning.

[0033] Figure 8 It is a zero-detuned system energy level diagram of symmetric and asymmetric hyperfine interactions.

[0034] Figure 9 It is a graph of spin-photon coupling as a function of an external magnetic field.

[0035] Figure 10 It is a graph of tunneling energy as a function of donor spacing.

[0036] Figure 11 It is a graph of voltage and electric field from a single photon in resonator mode as a function of distance from the delta layer lead.

[0037] Figure 12 This is a flowchart of an example method for coupling two qubits via a resonator cavity according to certain embodiments of this disclosure. Detailed Implementation

[0038] Because the magnetic dipole interaction between electron spin and microwave photons is very small, the electrical coupling between electron spin and microwave photons is more ideal. Electrical coupling can be generated and enhanced by inducing spin-charge hybridization, through external spin-orbit mechanisms (programmed by implementing an external magnetic field), or through internal spin-orbit mechanisms.

[0039] Over the past few years, many different types of quantum processing devices have been introduced that can be electrically coupled to superconducting microwave resonators. These types of quantum processing devices consist of a pair of quantum dots / addresses and are based on a single electron spin that can be in two different charge states. By carefully tuning the detuning ( Electrons can superimpose charges between two quantum dots / addresses (forming charge qubits). If the Zeeman splitting of an electron is equivalent to the splitting of a charge qubit, then spin-orbit coupling will hybridize the electron's spin and charge states.

[0040] Figure 1A and Figure 1B Two types of previously known quantum processing elements are demonstrated, which can be coupled to a superconducting cavity to enable long-distance qubit coupling.

[0041] Figure 1A The quantum processing element or device 100 shown includes a semiconductor substrate 102 and a dielectric 104. In this embodiment, the semiconductor substrate 102 is... 28 silicon( 28The semiconductor substrate 102 and the dielectric 104 are silicon dioxide (SiO2). An interface 105 is formed between the semiconductor substrate 102 and the dielectric 104, which in this embodiment is a Si / SiO2 interface. A quantum bit 106 is formed in the semiconductor substrate 102. The quantum bit 106 comprises two quantum dots 107 and 108 sharing an electron. Electron confinement of the electron in the two quantum dots is achieved by a gate 109 positioned on the dielectric 104. This type of quantum bit is called a dual-quantum-dot (DQD) quantum bit.

[0042] Furthermore, the micromagnet 110 is fabricated on the chip, specifically on the dielectric 104 together with the gate 109. The micromagnet 110 generates a local magnetic field gradient, whose longitudinal and transverse components differ at the two quantum dot addresses. The device 100 is coupled to a resonator (not shown). When the resonator field excites an electron from its orbital bonding state to an anti-bonding state, the electron experiences effective spin-orbit coupling (SOC) as it passes through this magnetic field gradient, thereby achieving spin rotation driven by the electric field of the resonator.

[0043] Figure 1B Another embodiment of a known qubit device 120 for coupling with a superconducting cavity is shown. In this arrangement, the qubit 121 comprises a quantum dot 122 and a donor atom 124. Specifically, Figure 1B The qubit device 120 shown includes a semiconductor substrate 102 and a dielectric 104. In this embodiment, the semiconductor substrate is... 28 silicon( 28 The semiconductor substrate 102 and the dielectric 104 are silicon dioxide (SiO2). An interface 105 is formed between the semiconductor substrate 102 and the dielectric 104, which in this embodiment is a Si / SiO2 interface. Quantum dots 122 are formed near the interface 105, while donor atoms 124 are located within the substrate 102. A gate 128 is located above the quantum dots 122 (on the dielectric 104).

[0044] Gate 128 is operable to interact with donor atom 124. For example, gate 128 can be used to induce an AC electric field in the region between interface 105 and donor atom 124 to modulate the hyperfine interaction between electrons (confined in quantum dot 122) and the nucleus of donor atom 124. When the qubit 121 is electrically driven, the electron spin flips with the spin of the donor atom nucleus. That is, the electric field can be used to control the quantum state of qubit 121 associated with a pair of electron-nuclear spin eigenstates, "electron spin up, nucleus spin down" and "electron spin down, nucleus spin up". This type of qubit 121 is called a flipped qubit.

[0045] In the DQD qubit 106, spin-orbit coupling is orchestrated by a micromagnet 110. Furthermore, in this case, the tip of the resonator is located at the silicon surface. Additionally, 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 micromagnet 110 to orchestrate the desired high local spatial field gradient.

[0046] Although Figure 1B The qubit 121 in the device does not require a micromagnet and utilizes hyperfine interaction at a single donor address, but it still includes a quantum dot 122 formed by a gate 128 near the interface 105. Therefore, the device 120 requires precise planning, fabrication, and control, which is challenging to implement.

[0047] To overcome one or more of the aforementioned problems, various aspects of this disclosure provide a novel quantum processing element / qubit that allows for efficient spin-cavity coupling, thereby enabling long-distance qubit entanglement. The qubit design eliminates the need for any on-chip magnets, distinguishing it from device 100. Furthermore, the qubit can be manipulated using the electric field of a single photon from a superconducting microwave resonator.

[0048] Figure 2 An example quantum bit 200 disclosed herein is shown. The quantum bit 200 is located in a semiconductor substrate 202 having a surface 204. In this embodiment, the semiconductor substrate is... 28 silicon.

[0049] The qubit 200 includes a pair of tunnel-coupled donor atom clusters 206, 208 and a single electron 209 bound to this pair of donor atom clusters 206, 208. In some embodiments, the donor atom clusters 206, 208 are placed in a silicon substrate 202 with atomic-level precision using scanning tunneling lithography. Furthermore, in some embodiments, the donor atoms 206, 208 may be located approximately 50 nanometers below the surface 204.

[0050] The qubit 200 can be coupled to a resonator (not shown), which in some embodiments may be a high-impedance, coplanar, superconducting microwave resonator positioned on a silicon surface 204. The resonator is coupled to the qubit 200 via one or more triangular layer leads positioned tens of nanometers away from one of the donors. Donor atom clusters 206 and 208 are separated such that the single electron tunneling frequency is close to the resonant frequency of the resonator. In one embodiment, the donor atom clusters 206 and 208 may be spaced approximately 15-20 nanometers apart. In another embodiment, they may be spaced approximately 10-20 nanometers apart.

[0051] Quantum 200 generates intrinsic spin-orbit coupling (SOC) using hyperfine interactions between the electron-nuclear system from the donor system. Specifically, in qubit 200, spin-charge hybridization arises from the hyperfine interaction between bound electron 209 and the nuclear spins of donor atom clusters 206 and 208. The hyperfine interaction utilizes half the spin of the donor atom nucleus. The interaction strength between electron 209 and the nuclear spin is denoted as A at the donor addresses on the left and right, respectively. L and A R The electron spin state and the nuclear spin state 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—hyperfine interaction maintains the total spin of the entire qubit 200. Spin qubit operation is achieved under the drive of the resonator electric field without the need to fabricate local micromagnets (as required by device 100).

[0052] In some embodiments, each donor atom cluster 206, 208 may have a single donor atom, which may be a phosphorus (P) atom, 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.

[0053] A constant external magnetic field is applied to separate the energy levels of the electron and donor spins. The strength of the magnetic field is chosen such that the electron spin energy segmentation is close to the resonant frequency of the coplanar microwave resonator. For the typical coplanar microwave frequency range of 4–12 GHz, the magnetic field strength is 0.14–0.43 Tesla.

[0054] Furthermore, conductive leads (not shown) are defined near the nP-mP qubit 200 using scanning tunneling lithography. These leads are located in the same crystal plane as the qubit, approximately 50 nanometers below the silicon surface. In some embodiments, these leads may be a phosphorus delta layer connected to a metal deposited on the silicon surface 204 via vertical vias. The leads closest to the donor atom clusters 206 and 208 are connected to one end of the resonator on the silicon surface.

[0055] The resonator can be made of thin (e.g., a few nanometers) high-dynamic-conductivity superconducting materials. In one embodiment, it is designed as a λ / 2 resonator such that the anti-node of the electric field is located at donor atoms 206, 208, maximally coupled to their charge dipoles. This lead can also serve as a storage device, loading a single electron onto a qubit at a timescale much slower than the resonant frequency.

[0056] The 200 qubits described in this paper can be used to transmit quantum information between qubits with lengths differing by several millimeters on the same silicon chip. Because the quantized electromagnetic field modes of the resonator mediate the quantum information transmission between the qubits, it can be implemented at low power (single microwave photon level), and the resonator can mediate dual-qubit gates. This solves the two major obstacles to scaling up mentioned earlier—quantum information can be transmitted between smaller qubit arrays to provide space for control gates in these smaller arrays, while also alleviating the energy density problem in cryogenic environments.

[0057] A quantum processing unit (or QPU) for semiconductor quantum dots can include multiple qubit arrays or nodes. Figure 3 This is a schematic diagram of an example QPU 300 according to certain embodiments of this disclosure. Figure 3 As shown, the example QPU 300 includes two qubit nodes 302—nodes 302A and 302B. It will be understood that, although... Figure 3 Two nodes are shown, but in actual implementations, a QPU can have more nodes, and the number of nodes utilized by a given QPU can depend on the specific application, the number of qubits in each node, and the computational requirements of the QPU.

[0058] Each node 302 includes a plurality of qubits 303 arranged in a two-dimensional array. The number of qubits 303 located in each node 302 depends on a number of factors, such as the distance between the qubits, the number of control lines and / or gates that can be accommodated on the node to handle each qubit in node 302, and the heat dissipated by the control circuitry. In some embodiments, the node 302 is small enough that a control gate 304 located on the chip surface or within the silicon substrate can handle each individual qubit 303, and the distance between the qubits is close enough for exchange interactions (i.e., a length scale on the order of 10 nanometers). Figure 3 In the embodiment shown, each node 302 includes 8 qubits 303.

[0059] Nodes 302 can be spaced a few millimeters apart on the same silicon chip / substrate 202. Furthermore, each node can be connected to the others via one or more resonators. In one embodiment, a resonator 306 is connected between a pair of nodes; specifically, the resonator 306 is coupled to one qubit in each of the pair of nodes 302. In the example QPU 300, qubit 303A in node 302A is coupled to qubit 303B in node 302B via resonator 306. Since resonator 306 can mediate two-qubit gate operation, quantum information can be transferred between the qubit nodes via resonator 306, allowing connectivity crucial for implementing useful quantum algorithms on the QPU.

[0060] exist Figure 3 In this context, the qubits (i.e., qubits 303A and qubits 303B) coupled to the resonator 306 on each node 302 are arranged according to... Figure 2 The qubits shown are fabricated—that is, qubits 303A and 303B are dual-donor atom cluster qubits 200. Other qubits on node 302 can also be dual-donor atom qubits 200, but this is not mandatory. In some embodiments, qubits not coupled to resonator 306 can be any other type of qubit, such as simple donor qubits or gate-controlled qubits, without departing from the scope of this embodiment. Furthermore, qubits 303 on each node 302 can be coupled to their nearest neighbor via exchange coupling.

[0061] Figure 4 This is a schematic diagram of one end of a resonator (e.g., resonator 306, particularly a λ / 2 microwave resonator). Resonator 306 is located on the surface of silicon substrate 202. In some embodiments, resonator 306 is made of a thin, high-impedance superconducting film. One end of resonator 306 contacts a vertical metal via 402, which connects resonator 306 to a lead 404 within silicon substrate 202. In some embodiments, lead 404 may be a delta-layer lead. Furthermore, lead 404 may be positioned approximately 50 nanometers below the silicon surface and in the same plane as qubit 200. This allows the electroreflection node to be close to the dual-donor atom qubit 200. The distance between lead 404 and qubit 200 is denoted as ΔL, the distance between the donor atoms is denoted as Δx, and the depth of qubit 200 from the surface of semiconductor surface 204 is denoted as Δh.

[0062] In the case that the dual-donor atomic qubit 200 is a 1P-1P system, the 1P-1P qubit strongly coupled to the quantization resonator mode operates at the (1,0)-(0,1) transition point in the gate space. Figure 5This is a graph showing the operating points of the 1P-1P qubits 200 coupled to the resonator 306 in the gate space. Specifically, along the x-axis, the graph plots the resonator voltage V. res Along the y-axis, the graph plots the gate voltage V. g (1,0) represents the electron occupancy number on the left donor cluster 206, and (0,1) represents the electron occupancy number on the right donor cluster 208. The resonator lever arm, or the coupling to the 1P-1P charge dipole, should be strong enough that the electric field ε0 of a single microwave resonator photon drives electron occupancy across this transition.

[0063] Figure 6A This is a top view of an example device 600 that uses the hyperfine interaction (HF) between electrons and atomic nuclei to achieve spin-orbit coupling. Specifically, Figure 6A A top view of a single quantum bit 200 coupled to a resonator 306 is shown, along with the circuitry required for the operation of the quantum bit 200. As shown in FIG. 6, the device 600 includes a gate 602 positioned close to the quantum bit to control the operation of the quantum bit 200. The gate 602 may include metal contacts on a semiconductor surface 204 connected via metal leads or vias to delta-layer leads (fabricated on the same plane as the quantum bit 200).

[0064] In addition to gate 602, the device may include charge sensing device 604. In some embodiments, the charge sensing device may be a single-electron transistor (SET) located close to qubit 200 and in the same plane as the qubit. In other embodiments, gate 602 or resonator 306 may serve as charge sensing device 604. In this case, an additional charge sensor may not be required.

[0065] Another approach to achieving electron spin-photon coupling is through electrically induced spin-orbit interactions. Previous studies have shown that spin-orbit coupling, which directly couples external electric and magnetic fields in the presence of an electric field at the donor cluster, is superior to Rashba spin-orbit coupling and spin orbitals from the host silicon crystal. If the electric fields from the surrounding gates differ between the two donors, the electron spin orbitals can generate an effective inhomogeneous field, thereby rotating their spins.

[0066] Figure 6B This is a top view of an example device 650 that operates 200 qubits using this electro-spin orbital (EISO) mechanism and a hyperfine mechanism. Figure 6A Same, Figure 6B A top view of a single qubit 200 coupled to resonator 306 is shown, along with the circuitry required for the operation of qubit 200 and electrically induced spin-orbit coupling. Figure 6BAs shown, device 650 includes a gate 602 positioned close to qubit 200 to control the operation of qubit 200. Device 650 also includes two additional EISO gates 652A, 652B. In some embodiments, gates 602, 652A, 652B may be located within silicon substrate 202, coplanar with qubit 200. In other examples, one or more of gates 602, 652A, 652B may be positioned on semiconductor surface 204. In this case, the gates may be connected to qubit 200 via metal wires or vias. The lateral EISO gates 652A, 652B can generate strong DC electric field gradients, which can lead to effects similar to hyperfine interactions.

[0067] Hyperfine-mediated spin-photon coupling depends on the initial nuclear state of the donor; therefore, devices operating solely based on hyperfine interactions must be initialized with the correct nuclear state before they can be operated. On the other hand, EISO interactions allow spin-photon coupling independent of the initial nuclear state; therefore, if an EISO gate is used in the device, it is not necessary to initialize the nuclear state of the donor atoms in these devices before they can be operated.

[0068] Figure 6C This is a top view of device 660, another example of spin-orbit coupling achieved through the hyperfine interaction (HF) between electrons and atomic nuclei. Specifically, Figure 6C A top view of a single qubit 200 coupled to resonator 306 is shown, along with the circuitry required for the qubit 200 to operate. The left and right points of the qubit can be positioned approximately 10-20 nanometers apart to ensure that the tunneling coupling is close to the resonant frequency of resonator 306. Figure 6C As shown, device 660 includes a storage gate 662 positioned to the left of qubit 200. The storage gate 662 is placed 15-30 nanometers away from qubit 200 and electrically connected to a resonator, such as resonator 306 (not shown in this figure), via a metal via (not shown). The short distance between the storage gate 662 and qubit 200 is chosen for this gate to act as an electron storage for qubit 200 and to maximize the resonant voltage induced on the qubit by resonator 306.

[0069] The device 660 may further include another gate 664 positioned close to the qubit to control the operation of the qubit 200. The gate 664 may include a metal contact on the semiconductor surface 204 that is connected via a metal wire or via a through-hole to a delta layer lead (fabricated on the same plane as the qubit 200).

[0070] In addition to gate 664, device 660 may include charge sensing device 666. In some embodiments, charge sensing device 666 may be a single-electron transistor (SET) positioned 30-100 nanometers away from qubit 200 and in the same plane as qubit 200. SET 604 is asymmetrically positioned relative to the two donor clusters of qubit 200 to result in different lever arm parameters and to distinguish which cluster is being probed when tracking the SET response. In other embodiments, gates 662, 664, or resonator 306 may serve as charge sensing device 666. In this case, an additional charge sensor may not be required.

[0071] Figure 7 It describes the mismatch between the various P donors ( The system energy level E is a function of the system energy level E, as shown in Figure 700. At zero detuning, electron 209 is formed by tunneling energy 2t. c Segmentation of bonds | and inverse key | Track. Here. ,in and These represent the locations of electrons on the left and right donor clusters 206 and 208, respectively. and Each of the stages is further divided in terms of energy due to the applied external magnetic field B, where the spin Zeman division between the electron spin ↓ and ↑ states is determined by... It is represented as h, where h is Planck's constant. It is the electron spin-gyromagnetic ratio. At non-zero detuning, the electron density is transferred to the donor with lower potential energy—in the extreme case of ultra-large detuning, the electron occupies only one donor site.

[0072] Due to nuclear Zeman interactions and hyperfine interactions (such as...) Figure 8 (as shown) Figure 7 Each of the energy levels depicted is further divided into four states. The qubit subspace is in bonding... Within a state manifold, it is specified that antibonding occurs. Orbital proximity plays a mediating role, enabling charge-spin coupling. Figure 7 It is symmetrical (A) L = A R ) and asymmetric (A L >A R A schematic diagram of the zero-detuned system energy level E of hyperfine interactions. Figure 8 Solid arrows in the diagram represent transitions mediated by hyperfine interactions, while dashed arrows indicate transitions prohibited by hyperfine interactions but driven by electro-spin-orbit interactions or EISO interactions.

[0073] Figure 8 The eigenstates shown are determined by the Hamiltonian operator of the entire system. ) Confirmed. Based on this, where D defines the electron as either a donor on the left or right side. or Positioning on, I L and I R Indicates the left and right nuclear spins (with polarization) or S defines electron spin. or The Hamiltonian operator is:

[0074] H = H 0+ H HF + H EISO (1)

[0075] in

[0076] (2)

[0077] τ is the Pauli matrix in the left / right donor basis, and S = and I= It consists of electron and donor spin operators, among which This is the Pauli matrix in the electron (donor) spin fundamental theory. The electron and nuclear spin gyromagnetic ratios in silicon are respectively... = 27.97 GHz / T and = -17.23 MHz / T.

[0078] H HF It is the Hamiltonian operator that describes the hyperfine interaction that mixes the spatial and spin degrees of freedom of electrons. It can be represented as:

[0079] H HF = hA L I L ·S + hA R I R ·S (3)

[0080] Where A L (A RThe denoted represents the hyperfine constant of the left (right) donor. The bulk silicon value of the hyperfine constant is approximately A. L = A R =117 MHz. The electron-nuclear spin product can be expressed as I·S = I z S z + 1 / 2 (I + S - + I - S + The dependence of hyperfine interactions on electron positioning (on the left or right donor) introduces charge-spin hybridization. This is because, due to hyperfine coupling, the eigenstates of the Hamiltonian operator H0 acquire a mixture of different spin and orbital states.

[0081] Hyperfine interactions are inherent and therefore always present in 1P-1P systems, while electro-induced spin-orbit interactions H EISO It can be turned on or off as needed. When we apply an electric field E perpendicular to the external magnetic field B in the donor region, EISO is generated (e.g., using...). Figure 6B (EISO gate shown).

[0082] For B polarized in the z-direction and E polarized in the y-direction, H EISO Take the following form:

[0083] (4)

[0084] The first matrix is ​​located in { , In the basics, and It is the Pauli x-matrix in the electron spin fundamentals. H EISO It does not affect nuclear spin, therefore it is considered an identity in the nuclear spin fundamental subspace. For a single donor in silicon, the coefficient (C) is estimated to be approximately 6 × 10⁻⁶. -14 em / T. and These correspond to the electric fields at the donor sites on the left and right sides, respectively. and The difference between them is a necessary condition for the generation of charge-spin hybridization.

[0085] exist Figure 8 The diagram shows the lowest eight eigenstates of the Hamiltonian operator H, used for symmetry (A L = A R ) and asymmetric (A L >A R or equivalent to Hyperfine interactions of <0. Symbol Describe the majority of each eigenstate. It should be noted that, due to hyperfine interactions, those eigenstates also include small but non-zero mixtures of different ground states.

[0086] The interaction between the system and cavity photons can be described by Hamiltonian operators:

[0087]

[0088] Among them, a (a † () is the annihilation (creation) operator for microwave resonator modes. It is assumed that the cavity field is composed of amplitude... 0 and frequency f r The description, and having a non-zero polarization component along the x-axis, then the charge coupling rate g c It can be defined as g c ≡ . Figure 8 The solid and dashed vertical arrows in the diagram represent all Hs of the spinning electron spin. c Driven transitions—provided the resonant frequency f r This matches the energy division between appropriate state pairs. The solid arrows indicate the situation without any electrically induced spin-orbit (i.e., even in H...). EISO This can be achieved when H = 0, and only through hyperfine interactions mediated by transitions. The dashed arrows indicate transitions accessible once EISO is enabled, where H... EISO ≠ 0 and ≠ .

[0089] The energy division between the states ⇑⇑↓ and ⇓⇓↓ is approximately (A L +A R ) / 4-2hγ P B, for a P donor in silicon, gives a value on the order of 100 MHz. The energy division between the ⇑⇓↓ and ⇓⇑↓ states depends on the hyperfine interaction asymmetry, approximately (A L -A R ) / 4. However, even in A L = A R At that time, due to ⇑⇑↓ and The (⇑⇓+⇓⇑)↑ state is mixed through hyperfine interactions, and the partition between the zero-spin states (nuclear singlet and triplet states) is not zero. This partition decreases with increasing magnetic field, and for B at approximately 0.2 T, the partition is on the order of 0.1 MHz.

[0090] exist Figure 8Each of the transitions described can be an effective point for qubit operation, where the qubit itself is defined by the initial and final eigenstates corresponding to a particular transition. A common feature of each such qubit subspace is the rotation of the electron spin. For hyperfine-mediated transitions, the electron spin rotation is accompanied by nuclear spin flipping (similar to flipped bits), while for EISO-mediated transitions, the nuclear spin configuration remains unchanged.

[0091] To select a specific operating point for a qubit, the required nuclear spin configuration needs to be initialized, which can be achieved using nuclear polarization methods such as nuclear magnetic resonance (NMR) or dynamic nuclear polarization.

[0092] For a given cavity frequency f r The qubits are brought into resonance by adjusting the external magnetic field B, thereby modulating the qubit energy split. For a standard resonator frequency bandwidth of 4–12 GHz, a magnetic field in the range of 0.14–0.43 T is required. Since spin-photon coupling depends on a mixture of different spin and orbital states leading to the H0 eigenstate, maximizing charge-spin hybridization is necessary, which depends on antibonding. The distance between the manifold and the qubit subspace.

[0093] Reference Figure 9 State 1 and State 6 (i.e., Figure 8 The cavity-spin coupling g between the leftmost transition in the middle) s / g c It is shown as for a given value 2t c / h = 7.64 GHz, a function of magnetic field B. Coupling is assessed by evaluating the relationship between eigenstates 1 and 6. To calculate: .

[0094] At B ≈ 0.272T, g s The sudden increase is due to manifold and The state degenerates together. Operating very close to this point is undesirable because it increases decoherence. However, setting the tunneling energy to be not equal to but related to f... r Quite, allowing g s >0.01g c The static significant value. The tunneling frequency in a 1P-1P system can be controlled by adjusting the donor spacing. Refer to the diagram showing the donor spacing. The tunneling rate 2t, a function of x c / h Figure 10 —This was obtained through simulations using rigorous atomic bonding. Based on this data, the optimal 1P-1P spacing is in the range of 15-20 nanometers for a cavity bandwidth of 4-12 GHz.

[0095] In contrast, for EISO-mediated transitions, and At approximately GHz Spin-photon coupling requires an electric field difference of approximately 12 MV / m between donors 206 and 208. This electric field difference can be distributed between the two donors, for example... = 6 MV / m and = -6 MV / m. For example... Figure 6B As shown, the different electric fields at the two donor addresses can be generated using an additional EISO gate.

[0096] Due to charge-photon coupling and the system dipole moment d c The amplitude of the electric field generated by a photon in the cavity The parameters are proportional to 0, therefore these two parameters need to be maximized. Since the electron wavefunction is highly localized within the donor region, the dipole moment can be well approximated as half the donor spacing, d. c ≈ eΔx / 2. As mentioned earlier, Δx (i.e., the distance between donor clusters 206 and 208 of qubit 200) is limited by the corresponding tunneling value, optimally using a value in the range of 15-20 nanometers. The cavity electric field ε0 can be adjusted... L value (see) Figure 4 This is maximized through appropriate donor placement relative to the phosphorus δ-layer leads.

[0097] Figure 11 This shows the electromotive force V and electric field from a single photon in resonator mode as a function of x (i.e., the distance to the Δ layer lead 502). The chart. In x ~ 10-20 nanometers and It is still possible to achieve L>20 nm (ensuring that the tunneling frequency from the lead to the nearest donor is slower than any other timescale in the system). Donor detuning of V ~ 0.5µV and g on the order of 100 MHz c = e V / 2h. Therefore, within a device of 200, g / g on the order of 1 MHz can be achieved. sc ~1-10% spin-cavity coupling. A notable feature of the proposed design is the contact between the two ends of the λ / 2 microwave resonator 306 and the phosphorus delta layer leads buried in the qubit layer. This allows the dual donors to be positioned in a high-electric-field region, significantly enhancing the system's charge-photon coupling.

[0098] Although the system specifications must be adjusted accordingly, the proposed device 200 can still be extended to other donor cluster systems. For systems with the same number of donors in each donor cluster, the cluster separation and the number of electrons need to be modified. For example, if each donor cluster includes 2 phosphorus donor atoms, a 2P-2P qubit can include 3 electrons. Similarly, if each donor cluster includes 3 phosphorus donor atoms, a 3P-3P qubit can include 5 electrons. Alternatively, for asymmetric systems (i.e., systems with different numbers of donor atoms in donor clusters, such as 1P-2P, 2P-3P, etc.), additional detuning is required to achieve anti-crossover of bonding-antibonding states. In both cases, the possible transitions and qubit subspaces must be refined.

[0099] Figure 12 Demonstrates the use of coupling two qubits via a resonator (e.g.) Figure 3 Example method 1200 (for qubits A and B). For example, this method describes an "iSWAP" interaction between qubits A and B via a resonator.

[0100] Method 1200 begins with step 1202, in which a magnetic field is applied to quantum bits A and B. In some embodiments, the magnetic field is a static homogenous field. The strength of the external magnetic field is such that Zeman splitting causes the quantum bit energy splitting to approach the resonator frequency. In one embodiment, the external magnetic field may be set to 0.2 T.

[0101] In step 1204, the dual-donor structure comprising qubit A and qubit B loads electrons from their respective storage devices. The number of electrons loaded in each cluster depends on the dual-donor cluster system used. If an IP-IP system is used, a single electron is loaded into qubit A and / or qubit B. Alternatively, in any other nP-mP system, more than one electron can be loaded. Electron loading can be performed using one or more gates (e.g., in...). Figure 6A or Figure 6B This is achieved using gate 602 (as shown), to apply local detuning so that in the gate space (e.g., Figure 5 The electron navigates to the appropriate electron-occupied region in the (1,0)-(0,1) transition space. By waiting in the appropriate region in the gate space, it can be ensured that the loaded electron has relaxed to its spin-down ground state.

[0102] In step 1206, the electron spin of qubit B is flipped. In one embodiment, a calibrated single-qubit gate is used, for example, by oscillating magnetic or electric fields (electron spin resonance or electric dipole spin resonance) to flip the electron spin to a spin-up state.

[0103] Next, in step 1208, qubits A and B are detuned to known energies relative to the resonator frequency, respectively. The detuning of qubit A relative to the resonator frequency may be the same as or different from the detuning of qubit B relative to the resonator frequency. In this "dispersion" mechanism, and Here, These are the energies of qubits A and B, respectively, taking into account their Zeman energies (assuming they are equal) and their respective detuning energies (which can be equal, but do not necessarily have to be). Furthermore, the energy of the microwave photon in the resonator is... ,and and These are the coupling rates of qubits A and B to the cavity, respectively.

[0104] In step 1210, the fixed detuning of qubits A and B relative to the resonator frequency is maintained for a certain period of time. .in and These represent the energy detuning of qubits A and B relative to the resonator, respectively. In this characteristic time... Within the system, the free evolution of the coupled system realizes the "iSWAP" gate between qubit A and qubit B.

[0105] In step 1212, after a period of time Afterward, both qubits should be severely detuned from the resonator frequency to end the gate interaction.

[0106] Finally, if needed, the states of qubits A and B can be measured independently to verify whether an iSWAP gate actually occurs between the two qubits. In some implementations, this readout can be achieved using conventional techniques, such as using two single-electron transistors fabricated on a chip and located close to qubits A and B.

[0107] It is understood that although method 1200 is described with reference to iSWAP gate operation, method 1200 can be implemented with slight modifications to perform other types of operations between qubits A and B without departing from the scope of this disclosure.

[0108] The methods and quantum processor architectures described in this paper utilize quantum mechanics for computation. For example, these processors can be used in a range of applications, providing enhanced computational performance, including: information encryption and decryption, advanced chemical simulation, optimization, machine learning, pattern recognition, anomaly detection, financial analysis, and verification.

[0109] Those skilled in the art will understand that many changes and / or modifications can be made to the invention shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. Therefore, the embodiments of the invention should be considered illustrative rather than restrictive in all respects.

Claims

1. A quantum processing system, comprising: A first quantum bit includes a first unpaired electron coupled to a first donor cluster pair embedded in a semiconductor substrate and spaced at a distance from the semiconductor surface, each donor cluster in the first donor cluster pair including at least one donor atom; The second qubit includes a second unpaired electron coupled to a second donor cluster pair embedded in a semiconductor substrate and spaced at a distance from the semiconductor surface, each donor cluster in the second donor cluster pair including at least one donor atom; as well as A microwave resonator located between a first qubit and a 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; The microwave resonator photons couple the first and second qubits.

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

3. The quantum processing system according to any one of claims 1-2, further comprising first and second conductive leads fabricated within a semiconductor substrate and adjacent to each of the first and second qubits.

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

5. The quantum processing system of claim 4, wherein the first and second conductive leads are respectively connected to the surface of the semiconductor substrate via first and second vertical through-holes.

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

7. The quantum processing system of claim 3, wherein the first and second qubits and the first and second conductive leads are fabricated in a semiconductor substrate and in the same plane about 50 nanometers below the surface of the semiconductor substrate.

8. The quantum processing system according to claim 3, wherein the first and second conductive leads are respectively fabricated at a distance of about 20 nanometers from the first and second qubits.

9. The quantum processing system according to any one of claims 1-2, wherein the microwave resonator is made of a thin, high-energy, inductive superconducting material.

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

11. The quantum processing system according to any one of claims 1-2, further comprising a first node and a second node, wherein each node comprises a plurality of qubits, wherein the first qubit is part of the first node and the second qubit is part of the second node.

12. The quantum processing system according to any one of claims 1-2, 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 1-2, wherein the distance between donor cluster pairs is 10-20 nanometers.

14. The quantum processing system according to any one of claims 1-2, wherein each of the first and second donor clusters comprises a single donor atom.

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

16. The quantum processing system according to any one of claims 1-2, wherein an additional gate is located in a semiconductor substrate and close to each of the first and second qubits, wherein the additional gate is configured to generate a DC electric field gradient to electrically induce spin-orbit coupling in the first and second qubits.

17. The quantum processing system according to any one of claims 1-2, wherein a continuous external magnetic field is applied to the quantum processing system to separate the spin states associated with the unpaired electrons and nuclei of the donor atom cluster.

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

19. A method of operating a quantum processing device according to any one of the preceding claims, the method comprising the steps of: A static magnetic field is applied 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 atom clusters of the first and second qubits, respectively. A local electric field is applied to each of the first and second qubits, causing the corresponding first and second qubits to undergo dispersive coupling with the microwave resonator; The dispersive coupling of the first and second qubits with the microwave resonator is maintained for a predetermined time period. After the predetermined time period, a local electric field is applied to the first and second qubits to decouple them from the dispersion coupling of the microwave resonator.

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

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