Quantum phononic links between solid-state qubits

Abstract

A quantum device includes: a solid-state material; a plurality of qubits on or in the solid-state material, each of the qubits comprising at least two quantum dots; and, a quantum phononic link (QPL) localized on or in the solid-state material, the QPL configured to guide phonons between a pair of qubits of the plurality of qubits to quantum-mechanically couple the pair of qubits, the pair of qubits spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits and is at least about 10 nm. The device is particularly useful for quantum computing.

Description

[0001] QUANTUM PHONONIC LINKS BETWEEN SOLID-STATE QUBITS

[0002] Cross-reference to Related

[0003] This application claims the benefit of USSN 63 / 715,548 filed November 2, 2024, the entire contents of which is herein incorporated by reference.

[0004] Field

[0005] This application relates to quantum devices, in particular to scalable quantum computing (QC) circuits and architectures based on quantum phononic links (QPL) and solid-state spin qubits.

[0006] In quantum computing architectures, in particular in surface code quantum computing architectures which contain many axillary qubits for error-correction protocols, it is important to be able to coherently couple arbitrary qubits to each other in order to establish entanglement, to perform quantum algorithms, and to transfer quantum bits of information between non-neighboring qubits. This is a very challenging roadblock in the contemporary rush for scalable quantum architectures like quantum computing, quantum internet, distributed quantum sensing, and other applications.

[0007] Currently, two-qubit operations, (i.e., two-qubit quantum gates) in semiconductor qubit devices are limited to the nearest neighbors using tunnel coupling to produce entangled states and two-qubit gates. However, it is an outstanding technological problem to couple non-neighboring qubits on the same chip at arbitrary distance between fractions of a micrometer and full size of the silicon wafer. Non-neighboring qubits are qubits that are spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits. There have been attempts to tackle this problem of connectivity between nonneighboring qubits by using an electrically generated surface conveyor belt (transporting charge carriers similar to charge-coupled device (CCD) technology but at a single electron level)

[0027] , surface acoustic waves (SAW) and superconducting (SC) microwave cavities.

[0028] These methods are more complex in fabrication and operation, e.g. require pluralities of electrodes, possess much bigger footprint, and are not scalable to large number of quits at arbitrary distances. While there have been methods suggested to address quantum fault- tolerant computers such as topological protection (Majorana Fermions and non-abelian anyons physics), these methods are not practical. Despite the above-mentioned approaches being useful for fundamental research and in certain situations connecting two distant qubits, they are not scalable to very large- scale integrated qubit-circuits aimed at a large number of qubits, up to 1 million, due to the sizes of SAW and SC cavities. For example, superconducting cavities are tens of millimeters long, which dramatically limits the scalability and suitability, e.g., when distance between qubits is just a few micrometers. Further, nano-mechanical cavities are actively explored for hybrid systems to establish quantum connections between superconducting (SC) qubits [6, 29], between SC qubits and light [30, 31], and other disparate quantum entities [6] using mechanical vibrations as the interconnection medium between otherwise non-interacting quantum entities.

[0008] There remains a need to be able to couple non-neighboring solid-state qubits in a quantum device.

[0009] Summary

[0010] A quantum device comprises: a solid-state material; a plurality of qubits on or in the solid-state material, each of the qubits comprising at least two quantum dots; and, a quantum phononic link (QPL) localized on or in the solid-state material, the QPL configured to guide phonons between a pair of qubits of the plurality of qubits to quantum-mechanically couple the pair of qubits, the pair of qubits spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits and is at least about 10 nm.

[0011] In some embodiments, a quantum device comprises: a solid-state material comprising a layered germanium-on-silicon (GoS) stack, the layered germanium-on-silicon (GoS) stack comprising: a base layer of doped or undoped Si(001); a buffer layer of intrinsic germanium (i-Ge) deposited on the base layer; a relaxed layer of relaxed graded SiGe deposited on the buffer layer; a non-piezoelectric compressively strained (cs-Ge) quantum well epilayer deposited on the relaxed layer; and, a SiGe cap deposited on the cs-Ge quantum well epilayer; a plurality of voltage-gated qubits in the solid-state material, each of the qubits comprising at least two quantum dots monolithically formed in the solid-state material; and, a localized quantum phononic link (QPL) defined by the non-piezoelectric compressively strained germanium (cs-Ge) quantum well epilayer in the solid-state material through which phonons having a wavelength are guided between a pair of qubits of the plurality of voltage-gated qubits to enable quantum-mechanical coupling of the pair of qubits, the pair of qubits spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits and is at least 10 nm, the two quantum dots in each qubit of the pair of qubits separated from each other by a quantum dot-separation distance, a half-wavelength of the phonons being a multiple of the quantum dot-separation distance.

[0012] Disclosed herein are devices, methods and systems in which non-neighboring qubits, i.e., qubits separated by a qubit-separation distance longer than a direct-tunneling distance of the qubits, are quantum-mechanically coupled through a quantum phononic link (QPL). Quantum-mechanical coupling is an effect in which two or more quantum systems (e.g., atoms, electrons, or even larger objects like tiny mechanical resonators) are bound such that a change in one of the quantum states in one of the systems will cause an instantaneous change in all the bound systems, even when the bound systems are separated. This phenomenon is particularly highlighted by quantum entanglement, where the state of one quantum system cannot be described independently of the others. In the field of quantum computing, quantum-mechanical coupling refers specifically to qubit coupling. The direct-tunneling distance of the qubits depends on one or more of the types of qubits and the nature of the material in which the qubits are formed. In some embodiments, the qubit-separation distance is at least about 10 nm. In some embodiments, the qubit-separation distance is at least about 100 nm. In some embodiments, the qubits comprise spin qubits, superconducting qubits, on-chip ion trap qubits, or the like. In some embodiments, the qubits comprise spin qubits. In some embodiments, the qubits comprise semiconductor hole spin qubits.

[0013] In some particularly preferred embodiments, a method and semiconductor structure are provided for enabling coherent coupling between spatially separated semiconductor spin qubits formed in gated double quantum dot (DQD) devices through the use of engineered quantum phononic structures, herein referred to as quantum phononic links (QPLs).

[0014] The devices comprise a solid-state material. The solid-state material may be any material, e.g., semiconductor material, that can support a qubit and that can be configured to localize phonons in order to guide the phonons between at least two qubits thereby providing a localized quantum phononic link between the at least two qubits. A phonon is a quantum of acoustic vibrations. Localizing phonons involves isolating phonon propagation in undesired directions in the solid-state material while permitting phonon propagation in a desired direction. In some embodiments, localized phonons are contained in the QPL where phonon-spin interactions in the solid-state material are increased in the desired direction so that the at least two qubits are coupled to phononic modes in the QPL. The QPL localizes phononic vibrations so that the wave functions of the qubits and the phonons overlap at 100%. In some embodiments, the phonons have energies that are larger than ambient temperature around the device. In some embodiments, the localized QPL comprises a phononic waveguide or a phononic cavity. In some embodiments, the localized QPL provides a quantum link over a distance of about 0.1 micron to about 100 millimeters.

[0015] In some embodiments, the localized QPL contains the phonons in a volume and is provided by one or more of: a physical structure of the solid-state material; an atomic lattice arrangement in the solid-state material; and, a physical property of the solid-material. In some embodiments, the localized QPL is formed integrally with the solid-state material. The physical structure of the solid-state material includes, for example, one or more of the physical forms of the solid-state material (e.g., the configuration and arrangement of walls (i.e., edge faces) of the solid form of the solid-state material), the presence of physical holes, voids or the like in the solid-state material, and the configuration and arrangement of interfaces between different layers in the solid-state material. In some embodiments, the physical structures are provided by wet or dry etching of the solid-state material. Physical structures, especially repeating physical structures, serve to channel the phonons between the at least two qubits. The atomic lattice arrangement is determined by the relative spatial positions of the atoms in the solid-state material, including the relative spatial positions of the atoms in individual layers of the solid-state material and the differences in the atomic lattice arrangements between the individual layers. The spatial arrangement of atoms provides a repeating structure that serves to channel the phonons between the at least two qubits. In some embodiments, at least a portion of the solid-state material is isotopically purified so that the nuclei of the atoms in the solid-state material have no magnetic moments. Magnetic moments reduce spin qubit coherence time and can affect phononic vibrations, therefore utilizing isotopically purified material helps improve qubit quality (essentially increase coherence time) and reduce or eliminate phononic scattering. Physical and / or electronic properties of layers in the solid-state material, especially relative physical and electronic properties of adjacent layers, can also help localize the QPL in the active layer where spin qubits are localized. Physical and electronic properties include, for example, the speed of sound through the material, the phonon spectrum, hole effective mass, effective g-factor, spin orbit interaction strength, etc.

[0016] In some embodiments, coupling of the at least two qubits to the phononic modes of the QPL is mediated through fields (e.g., strain or piezoelectric fields) of the phononic modes. In some embodiments, the phonons are localized within the QPL to enable quantum-mechanical coupling between the pair of qubits spaced-apart by the qubit separation distance via direct interactions induced by strain deformation potential produced by the phonons. In some embodiments, strain is used as a natural and inherent interaction mechanism allowing direct interaction between phonons and spin qubits mediated by spinorbit (SO) coupling. In some embodiments, the quantum phononic link arises from a lattice deformation originating from a phonon in an upper layer (e.g., a top layer) of a solid-state material stack, which induces strain across a lower layer of the solid-state material, wherein the induced strain is the medium that produces forces directly acting on spins (e.g., electron or hole spins). Bulky inter-digital transducers (IDT) commonly used in surface acoustic waves (SAW) technology are therefore not needed (though still can be used if desired), making the devices more compact and simpler than prior art devices, which are very desirable properties for large-scale quantum computing architectures towards one million qubits or more.

[0017] In some embodiments, phonon-induced strain fields directly couple to the orbital and spin degrees of freedom of holes confined in the quantum dots, exploiting the intrinsic properties of a compressively strained material, including:

[0018] Very small hole effective mass (n ) leading to large de Broglie wavelength of carriers and, therefore, enhanced qubit uniformity and reproducibility across large- scale circuits.

[0019] Strong spin-orbit coupling inherent to the valence band holes, facilitating efficient spin manipulation and coupling to phonons. Coupling to hole spin qubits is especially desirable because valence band holes have a much stronger spin-orbit interaction compared to conduction band electrons. Though phonon coupling to electron spins can be achieved as well, for example, by using a so-called micromagnet technology.

[0020] Large, and gate-tunable effective ^-factor for addressable large-scale quantum computing architectures.

[0021] High sensitivity of spin states to dynamic strain fields generated by phonons due to spatial confinement of both phonon vibrations and spin wavefunction in the same thin compressively strained quantum well layer.

[0022] The combination of phonon confinement within the compressively stained material and the strain-sensitive nature of hole spins enables efficient coherent phonon-mediated coupling between non-neighboring qubits without the need for intermediate charge or photonic states. In some embodiments, acoustic phonons (vibrations) are confined within a compressively strained quantum well epilayer to mediate direct spin-spin interactions over distances substantially exceeding that permitted by direct tunnelling mechanisms and scalable upto a full wafer size (e.g., upto about 450 mm or more), as enabled, for example, by the compressively strained quantum material platform.

[0023] In some embodiments, the solid-state material comprises a silicon-containing material. In some embodiments, the solid-state material comprises one or more of a layered germanium-on-silicon (GoS) material, and a silicon-on-insulator (Sol) material (e.g., SiO2), referred here as “material stack”. In some embodiments, the layered germanium-on-silicon (GoS) material comprises compressively strained germanium on silicon (cs-GoS). In some embodiments, the solid-state material comprises a layered structures containing germanium-on-silicon (GoS) stack. In some embodiments, the layered germanium-on- silicon (GoS) stack comprises a non-piezoelectric compressively strained germanium (cs- Ge) quantum well epilayer that provides the localized QPL. In some embodiments, the layered germanium-on-silicon (GoS) stack further comprises a germanium (Ge) or silicon (Si) cap.

[0024] In some embodiments, the layered germanium-on-silicon (GoS) stack comprises one or more of a base wafer (e.g., doped or undoped Si(001 )), a buffer layer (e.g., intrinsic germanium (i-Ge)); a relaxed buffer layer (e.g., relaxed graded SixGei-xwhere x is between 0.1 and 0.3) and a cap layer (e.g., SiGe, for example SixGei-x). In some embodiments, the layered germanium-on-silicon (GoS) stack comprises: a base wafer of doped or undoped Si(001); a buffer layer of intrinsic germanium (i-Ge) deposited on the base layer; a relaxed buffer layer of relaxed graded SixGei-xwhere x is between 0.1 and 0.3 deposited on the buffer layer; the cs-Ge quantum well epilayer deposited on the relaxed buffer layer; and, a SixGei-xcap layer deposited on the cs-Ge quantum well epilayer. In some embodiments, the layered germanium-on-silicon (GoS) stack further comprises a germanium (Ge) or silicon (Si) cap deposited on the SiGe (e.g., SixGei-x) cap layer. In some embodiments, the speed of sound in the cs-Ge quantum well epilayer being slower than in layers adjacent to the cs-Ge quantum well epilayer, is used to localize the quantum phononic link to the cs- Ge quantum well epilayer.

[0025] With specific reference to embodiments where the solid-state material comprises the layered germanium-on-silicon (GoS) stack, the cs-Ge layer, wherein the spin qubits are hosted, is embedded within relaxed SiGe barrier layers possessing substantially different phonon properties, for example, the sound velocities and phonon spectra, relative to the cs-Ge layer. It is thought that this acoustic impedance mismatch at the Ge / SiGe interfaces, in particular due to the lower speed velocity in the germanium quantum well layer compared to the SiGe cladding, results in phonon deformation distribution function to be strongly confined within the cs-Ge layer. This sound wave confinement effectively forms a very narrow phononic waveguide or cavity that supports simultaneously coherent phonon propagation predominantly in the Ge layer containing spin qubits. This is an important advantage for enhanced, more efficient interaction between QPL phonons and spin qubits. This phonon confinement mechanism contributes to the functionality of the QPL, as it ensures that acoustic phonons generated locally, e.g., by spin qubits formed in quantum dots, or externally remain confined within the active cs-Ge layer containing spin qubits, enabling efficient and selective coupling to hole spins via interactions induced by the strain deformation potential produced by phonons.

[0026] The device comprises a plurality of qubits on or in the solid-state material, each of the qubits comprising at least two quantum dots, for example 2, 3, 4 or more quantum dots per qubit. In some embodiments, at least a portion of the qubits are double quantum dots (DQDs) in which the at least two quantum dots form a tunnel-coupled double quantum dot. The quantum dots may be formed by any suitable method. In some embodiments, the quantum dots are formed integrally (e.g., monolithically) with the solid-state material or are formed by one or more dopants (e.g., phosphorous (P), boron (B), sodium (Na), copper (Cu), manganese (Mn), bismuth (Bi) and the like.) added to the solid-state material. In some embodiments, the device comprises quantum dots formed integrally with the solid-state material and comprises quantum dots formed by one or more dopants added to the solid- state material. In some embodiments, at least a portion of the qubits are gate-voltage tunable qubits. In some embodiments, the device further comprises voltage gates for forming the quantum dots integrally in the solid-state material. In some embodiments, the voltage gates comprise an electrically conductive metal or non-metal, for example gold, silver, copper, aluminum, metal alloys, conductive metal oxides like ZnO or l2O3, polysilicon and the like. Voltage gates are energized to form the quantum dots in the solid-state material. The quantum dots are voltage tunable to produce and / or absorb phonons to couple the non-neighboring qubits via the quantum phononic link. When the device is in a powered off state, the qubits are electrically detuned off from resonance with phonons, therefore the qubits do not interact with desired phonons for coupling to the nonneighboring qubits.

[0027] In some embodiments, the quantum dots in each qubit of the pair of qubits linked by the localized QPL are separated from adjacent quantum dots by a quantum dotseparation distance (d). In some embodiments, the phonons have a wavelength, and a half-wavelength of the phonons is a multiple of the quantum dot-separation distance. In some embodiments, the distance (d) between quantum dots matches the multiple periods (N) of the phonon wavelength (Aph) in accordance with d •ph.

[0028] In some embodiments, the solid-state material further comprises one or both of a piezoelectric layer and a non-piezoelectric dielectric layer to provide one or more additional phononic-enabled functionalities. In some embodiments, the one or more additional phononic-enabled functionalities comprises one or more of: localizing phonons in other regions of the solid-state material; and, transducing phonon vibrations to electric fields for coupling at least a portion of the qubits to other quantum entities including one or more of superconducting qubits, on-chip ion trap qubits, NV-centers in diamond, T-centers in silicon, rare earth ions and optical photons.

[0029] In some embodiments, the device further comprises a single phonon detector for detecting a single phonon.

[0030] In some embodiments, the device comprises a network of qubits coherently linked to each other. Thus, at least a portion of the qubits of the plurality of qubits may be coherently linked to each other by a network of the localized QPLs. A scalable, material- integrated solution is therefore provided for the coherent long-range coupling of distant (non-neighboring) qubits (e.g., spin qubits), which can be also applied to non-piezoelectric semiconductor material platforms, for example platforms based on elements in Group IV elements (for example, silicon and germanium, and various material stacks based on thereof, e.g., cs-GoS).

[0031] Phonons, in most cases, play a harmful role as a source of quantum decoherence, back-action and noise. In the present invention, phonons are turned into coherent channels to make phonons useful in certain tasks that cannot be solved by other means, i.e., to connect non-neighboring qubits and link qubits made from different material platforms. Herein is described a solution to the problem of how to couple two or more non-neighboring qubits on the same chip at an arbitrary distance (e.g., from fractions of a micrometer to the full size of a wafer in a chip), thereby substantially enhancing the qubit quantum engineering toolkit with new capabilities required for scalable quantum computing architectures, sensing and networking. Thus, the arbitrary range transfer of quantum information between nonneighboring qubits on a wafer is enabled, which is important for scalable quantum computing (QC) architectures, on-chip quantum networking, and other applications. The devices described herein are precisely tunable between quantum dot energy levels leading to fast QPL control of non-neighboring qubits via electrical pulses suitable for quantum computing algorithms, quantum information transfer, error correction and other protocols. Moreover, deliberate epitaxial design of the heterostructure used for forming the quantum phononic link (QPL) can provide device properties, which are not accessible by standard surface acoustic wave (SAW) technology, for example a frequency range from about 10 GHz up to or above 100 GHz.

[0032] Further features will be described or will become apparent in the course of the following detailed description. It should be understood that each feature described herein may be utilized in any combination with any one or more of the other described features, and that each feature does not necessarily rely on the presence of another feature except where evident to one of skill in the art.

[0033] Brief Description of the Drawings

[0034] For clearer understanding, preferred embodiments will now be described in detail by way of example, with reference to the accompanying drawings, in which:

[0035] Fig. 1 depicts a schematic cross-sectional diagram showing an example of a compressively strained germanium-on-silicon (cs-GoS) stack for fabrication of a quantum device having quantum phononic links (QPLs) and spin qubits formed in double quantum dots (DQD).

[0036] Fig. 2A depicts a schematic diagram showing a generic rectangular phononic waveguide on top of a compressively strained germanium-on-silicon (cs-GoS) stack.

[0037] Fig. 2B depicts a schematic diagram showing another generic quantum phononic structure comprising a compressively strained germanium (cs-Ge) or compressively strained germanium-on-silicon (cs-GoS) phononic cavity on top of a silicon substrate.

[0038] Fig. 2C depicts a schematic diagram showing another generic quantum phononic structure comprising a piezoelectric or non-piezoelectric phononic cavity on top of a compressively strained germanium-on-silicon (cs-GoS) stack.

[0039] Fig. 3A depicts a generic rectangular phononic cavity with a piezoelectric or nonpiezoelectric material for a top layer on top of a cs-GoS stack.

[0040] Fig. 3B depicts a generic rectangular phononic cavity without a piezoelectric or nonpiezoelectric material for a top layer. Fig. 4 depicts a schematic drawing of non-neighboring spin qubits formed in double quantum dots (DQDs) coupled through strain fields or piezoelectric effect, which induces electric fields.

[0041] Fig. 5 depicts a schematic diagram illustrating an example of a single phonon detection process (1 ,2) — (2,1) — (1 ,1).

[0042] Fig. 6 depicts a schematic diagram of how a deformation originating from a phonon in a top layer, e.g., a quantum phononic link (QPL) made of a piezoelectric or nonpiezoelectric material, (left panel) induces strain across a germanium-on-silicon (GoS) material stack (right panel), which is the responsible mechanism for direct phonon-spin interaction.

[0043] Fig. 7 depicts a schematic diagram of a quantum computing (QC) circuit fragment containing several spin qubit blocks and single phonon detectors for readout and storage of the readout result, where all circuit elements are connected by quantum phononic links (QPLs).

[0044] Fig. 8 depicts a schematic diagram of spin qubits confined in double quantum dots (DQDs) connected through a quantum phononic link (QPL).

[0045] Fig. 9A depicts an example of a schematic diagram of a phononic waveguide unit cell (top panel) with a Fine Element Method (FEM) simulation performed in COMSOL™ of a phonon spectrum of the phononic waveguide unit cell for in plane phonon propagation at a desired frequency range (bottom panel), where a = 436 nm, b = 529 nm, di = 295 nm, d2 = 320 nm and the thickness of the phononic waveguide unit cell is 220 nm.

[0046] Fig. 9B depicts a schematic diagram of an acoustic isolation shield unit cell (top) with a Fine Element Method (FEM) simulation performed in COMSOL™ of a phonon spectrum of the acoustic isolation shield unit cell for in plane phonons propagation at a desired frequency range (bottom panel) while isolating the same phonons as in Fig. 9A from propagating in undesired directions (right), where ax= 500 nm, bx= 265 nm, by= 29 5nm, ty= 50 nm, and t = 220 nm.

[0047] Fig. 10 depicts a schematic diagram of an engineered piezo-mechanical quantum phonon link (QPL) with a piezoelectric transducer for extended functionalities, e.g., for linking different kinds of qubits.

[0048] Fig. 11 depicts a Fine Element Method (FEM) simulation of an electric field distribution caused by a surface acoustic wave (SAW) in a piezoelectric material demonstrating that an electric field produced by the SAW can reach a germanium active layer positioned withing a layer of thickness t, roughly equal to the wavelength of the SAW.

[0049] Fig. 12A depicts a COMSOL™ simulation of a suspended phononic structure supported by a phononic shield, where simulated quality (Q) factor = 1.9x105and eigenfrequency = 5.84 GHz.

[0050] Fig. 12B is a top view of a quantum phonon link (QPL) section of the simulation of a suspended phononic structure shown in Fig. 12A.

[0051] Fig. 13 is a schematic diagram of a quantum network with interfaced qubits in different platforms including solid-state qubits connected via a quantum phononic link (QPL) bus with side communication links.

[0052] Fig. 14 depicts a COMSOL™ simulation of a confined phononic mode inside a compressively strained germanium-on-silicon (cs-GoS) material slab, where simulated quality (Q) factor = 3.6968x104and eigenfrequency = 33.215 GHz.

[0053] Fig. 15 depicts COMSOL™ simulations of a series of transverse horizontal confined phononic modes showing deformation field shape for the fundamental mode (N=1) and the N=2-7 higher modes.

[0054] Fig. 16A depicts a schematic diagram showing a three-dimensional representation of a quantum phononic link (QPL) coupling two hole spin qubits hosted in double quantum dots (DQDs) embedded within a compressively strained germanium (cs-Ge) quantum well (QW) sandwiched by SiGe barriers grown on a silicon (Si) substrate, which is the compressively strained germanium-on-silicon (cs-GoS) material stack.

[0055] Fig. 16B depicts a schematic diagram of a top view of Fig. 16A showing how resonant acoustic phonons with a wavelength matching twice the separation between the quantum dots (QDs) of the DQDs enable spin-phonon interaction and coherent quantum state transfer between the distant spin qubits.

[0056] Detailed Description

[0057] Fig. 1 depicts an example of a compressively strained germanium-on-silicon (cs- GoS) material stack 100 for fabrication of quantum phononic links (QPLs). The stack 100 comprises a silicon substrate layer 107 with (001) crystal orientation, the substrate being a full-size substrate compatible with CMOS silicon foundries. In Fig. 1 , the substrate was 450 mm in diameter. An intrinsic germanium (i-Ge) layer 106 is deposited on the substrate 107. A relaxed graded SiXGei-xlayer 105 where x is between 0.1 and 0.3 is deposited on the i- Ge layer 106. A germanium quantum well active layer 104 is deposited on the relaxed graded SixGei-xlayer 105. A Sii-xGexcap layer 103 is deposited on the germanium quantum well active layer 104. An optional germanium cap layer 102 is deposited on the S -xGexcap layer 103. The above layers form the cs-GoS material stack. In addition, a piezoelectric or non-piezoelectric layer 101 is deposited on top of the cs-GoS for extended functionalities. Bulk germanium in the cap layer 102 and the whole material stack including silicon in the substrate layer 107 are not piezoelectric materials. A lack of piezoelectric effect can have a useful property in the context of minimizing phonon induced noise, because the nonpiezoelectric layers reduce random electrical noise causing decoherence mechanisms due to piezoelectric interactions with phonons. In the stack 100, engineered strain potential for interaction of phonons with spin qubits is utilized to provide a quantum phononic link.

[0058] Fig. 2A depicts a generic rectangular phononic waveguide 201 on top of the GoS material stack 200. The waveguide 201 may be a piezoelectric strip used to guide a phononic mode at the interface near a Ge cap layer 202, in a design that is similar to strip loaded waveguides in photonics integrated waveguides. Alternatively, the waveguide 201 may be a non-piezoelectric material (e.g., diamond), which also can act as a phononic waveguide because a strain field is being employed for spin-phonon interactions. The waveguide 201 helps to add more functionalities and engineering tools of phononic structures and cavities with modes of propagation at the interface of the dielectric Ge cap layer 202 or with modes of propagation fully confined in a thin compressively strained germanium quantum well layer 204, as illustrated in Fig. 14 and Fig. 15. The GoS material stack 200 also comprises a SiGe cap layer 203 and a relaxed graded SiGe layer 205, similar to previously described.

[0059] Fig. 2B depicts another generic phononic structure 210 comprising a compressively strained germanium (cs-Ge) or compressively strained germanium-on-silicon (cs-GoS) phononic cavity 211 on top of a silicon substrate 212. Fig. 2C depicts yet another generic phononic structure 220 comprising a piezoelectric or non-piezoelectric phononic cavity 221 on top of a compressively strained germanium-on-silicon (cs-GoS) stack 222. In both Fig. 2B and Fig. 2C, interface phononic modes are localised near the dielectric / GoS interface in close proximity to the active germanium layer (see Fig. 11). The phononic cavities may have more complex mesoscopic structures engineered for specific frequency ranges and other quality factors (see Fig.10, Fig. 12, Fig. 14, Fig. 15, Fig. 16).

[0060] Fig. 3A depicts a generic rectangular phononic cavity 300 with a piezoelectric or a non-piezoelectric material for a top layer 301. Fig. 3B depicts a generic rectangular phononic cavity 320 without a piezoelectric or a non-piezoelectric material for a top layer. The cavity 300 comprises a silicon substrate layer 307 ((001 )p, e.g., 1 -5 ohm / cm, or semiinsulating, d = 625pm), an intrinsic germanium (i-Ge) layer 306 deposited on the substrate 307, a relaxed graded SiGe layer 305 deposited on the i-Ge layer 306, a germanium quantum well active layer 304 deposited on the relaxed graded SiGe layer 305, a SiGe spacer layer 303 deposited on the germanium quantum well active layer 304, and an optional germanium cap layer 302 deposited on the SiGe spacer layer 303. The top layer 301 is deposited on the germanium cap layer 302. Likewise, the phononic cavity 320 comprises a silicon substrate layer 313 ((001)p, e.g., 1 -5 ohm / cm, or semi-insulating, d = 625pm), an intrinsic germanium (i-Ge) layer 312 deposited on the substrate 313, a relaxed graded SiGe layer 311 deposited on the i-Ge layer 312, a germanium quantum well layer 310 deposited on the relaxed graded SiGe layer 311 , a SiGe spacer layer 309 deposited on the germanium quantum well layer 310, and an optional germanium cap layer 308 deposited on the SiGe spacer layer 309. In each of the cavities, 300, 320, the cavity confines phonons and increases phonon lifetime and interaction efficiency with spin qubits. The cavities 300, 320 increase the phonon-hole (electron) interactions in the same way as optically integrated nano cavities increase light-matter interactions for more efficient coupling with light. Here, more efficient coupling between spins and phonons is important for highly efficient transduction of quantum information via QPLs. The piezoelectric layer 301 can be used for achieving external access with other kinds of qubits, including superconducting qubits, using interdigital transducers (IDT), as shown in Fig. 8, Fig. 10 and Fig. 12.

[0061] Fig. 4 depicts a quantum device 400 made from a germanium-on-silicon (GoS) material stack, the device 400 comprising non-neighboring double quantum dots (DQDs) coupled through strain fields or piezoelectric effect, which induces electric fields and strain for extended functionalities. Spin qubits in the DQDs are quantum coupled to phononic modes of the quantum phononic link (QPL) through strain or piezoelectric field of the QPL acoustic modes. Electric mode can be used for coupling to other kinds of qubits in other material platforms. The QPL is deposited on a wafer 415 made of a different material (piezoelectric or non-piezoelectric), but strain propagates down the GoS material stack and reaches the qubits formed in the wafer by gate voltages (as shown in Fig. 11). The device 400 comprises a plurality of surface voltage gates forming the spin qubits in two distant DQDs connected by the QPL. The surface voltage gates comprise a source-drain tunnelling gate 401 of a first DQD, a left gate 402 of the first DQD, a left plunger gate 403 of the first DQD, a coupling gate 404 of the first DQD to control coupling between the quantum dots of the first DQD, a right plunger gate 405 of the first DQD, a right gate 406 of the first DQD, a source-drain tunnelling gate 409 of a second DQD, a left gate 410 of the second DQD, a left plunger gate 411 of the second DQD, a coupling gate 412 of the second DQD to control coupling between the quantum dots of the second DQD, a right plunger gate 413 of the second DQD, and a right gate 414 of the second DQD. Fig. 4 shows the expected position of the confining potential minimum 407 of a first quantum dot in the first DQD and the expected position of the confining potential minimum 408 of a second quantum dot in the first DQD. The confining potential minima in the second DQD are not shown but are similarly positioned in the second DQD. As described above, the GoS material stack comprises a germanium cap layer 416, a SiGe spacer layer 417, a compressively strained germanium quantum well active layer 418 and a relaxed graded SiGe layer 419.

[0062] Fig. 5 depicts an example of a single phonon detection process (1 ,2) ->■ (2,1) ->■

[0063] (1 .1). In Fig. 5, a first reservoir 501 of charge carriers (electrons or holes) is separated from a first quantum dot 500 (left) by a first tunnel barrier 513, and a second reservoir 506 of charge carriers (electrons or holes) is separated from a second quantum dot 520 (right) by a second tunnel barrier 510. The thick black vertical line signifies that the second tunnel barrier 510 is highly opaque to prevent tunneling between the second quantum dot 520 and the second reservoir 506 of charge carriers. The first tunnel barrier 513 is more transparent than the second tunnel barrier 510. The quantum dots 500, 520 are separated by a coupling tunnel barrier 511 to control phonon-electron interaction and single-phonon readout efficiency. An electron 504 occupying the ground state ((1 ,2) charge state of the second quantum dot 520) has an energy level 505. The charge state (1 ,2) is the ground equilibrium state of the double quantum dot (DQD). When the second quantum dot is excited, an electron 508 occupies the (2,1 ) charge state of the double quantum dot, which has a second energy level 507. In the detection process, a phonon 509 arriving from a quantum phononic link (QPL) interacts with the electron 508 occupying the second energy level 507 ((2,1) charge state) of the second quantum dot 520. An electron 512 tunnels between the second and first quantum dots 520, 500, respectively, due to absorption of one phonon and then tunnels out of the DQD through the first tunnel barrier 513 to the first reservoir 501 leaving the DQD in a metastable (latched) state for readout by a nearby charge sensor. The white filled arrows indicate the charge transfer. In the metastable state, an electron 502 occupies the ground state ((1 ,1) charge state of the first quantum dot 500 and has an energy level 503 that is the energy level of the first quantum dot tuned in latching-detection mode. The

[0064] (1.1) charge state is a long-lived metastable state, the so called "latched" state (because the second dot (right) barrier 510 is opaque and prevents tunneling from the second reservoir 506 to the second (right) quantum dot), which is used to read out the result of the single phonon absorption event, similar to single shot spin readout. Fig. 6 depicts how a deformation originating from a phonon in a top layer, e.g., a quantum phononic link (QPL) made of a piezoelectric or non-piezoelectric material, of a germanium-on-silicon (GoS) material stack (left panel) induces strain across the germanium-on-silicon (GoS) material stack (right panel). The GoS stack is essentially as described previously and comprises: atop layer (601 in left panel, 609 in right panel) made of a piezoelectric or non-piezoelectric material; a germanium cap layer (602 in left panel, 610 in right panel); a SiGe spacer layer (603 in left panel, 611 in right panel); a germanium quantum well active layer (604 in left panel, 612 in right panel); a relaxed graded SiGe layer (605 in left panel, 613 in right panel); an intrinsic germanium layer (606 in left panel, 614 in right panel); and, a silicon substrate layer (607 in left panel, 615 in right panel). A magnified view 608 of a portion of the SiGe spacer layer 603 in the left panel illustrates the regular crystal lattice structure when not deformed, while a magnified view 616 of the corresponding portion of the SiGe spacer layer 611 in the right panel illustrates how the crystal lattice structure is deformed when a phonon is generated in the top layer 609. Comparing the left panel to the right panel, it can be seen how the deformation caused by the phonon in the top layer 609 causes deformation, and therefore strain, in the layers below down to the germanium quantum well active layer 612. Strain is the means that produces forces directly acting on spins.

[0065] Fig. 7 depicts an example of a quantum computing (QC) circuit fragment containing several spin qubit blocks 702 and single phonon detectors 703 for readout and storage of the result, where all elements are connected by quantum phononic links (QPLs) 701.

[0066] Fig. 8 depicts spin qubits 801 confined in double quantum dots (DQDs) connected through a quantum phononic link (QPL) 804. A piezoelectric layer 805 is added to a slab of unreleased material stack 802 for extended functionalities (e.g., as shown in Fig. 13). A plunger gate of each spin qubit 801 is connected to respective unidirectional interdigital transducers (IDT) 803 to actuate and detect high frequency phonons 806 up to 100 GHz to be transmitted through the non-piezoelectric QPL 804. Phonons travel across the high quality QPL structure 804 (left to right in Fig. 8 as shown by the arrow) generating a small voltage in the other IDT 803 placed on the other end (right end). This extended functionality is beneficial for connecting different kinds of qubits, e.g., spin qubit can be replaced with a superconducting qubit, therefore, creating larger networks as shown in Fig. 13.

[0067] Fig. 9A depicts a phononic waveguide unit cell 901 (top panel) with a Fine Element Method (FEM) simulation 903 performed in COMSOL™ of a phonon spectrum of the phononic waveguide unit cell 901 for in plane phonon propagation at a desired frequency range (bottom panel), where a = 436 nm, b = 529 nm, di = 295 nm, d2= 320 nm and the thickness of the phononic waveguide unit cell 901 is 220 nm. Fig. 9B depicts an acoustic isolation shield unit cell 902 (top) with a Fine Element Method (FEM) simulation 904 performed in COMSOL™ of a phonon spectrum of the acoustic isolation shield unit cell 902 for in plane phonons propagation at a desired frequency range (bottom panel) while isolating the same phonons as in Fig. 9A from propagating in undesired directions (right), where ax= 500 nm, bx= 265 nm, by= 29 5nm, ty= 50 nm, and t = 220 nm.

[0068] Fig. 10 depicts an engineered piezo-mechanical quantum phonon link (QPL) with a piezoelectric interdigital transducer for extended functionalities, e.g., for linking different kinds of qubits. The design has four segments, from right to left: (i) a piezoacoustic phonon cavity 1004 made from a piezoelectric material layer on top of a germanium GoS stack, acoustic isolating shields 1001 , and an interdigital transducer (IDT) 1005; (ii) a phononic waveguide 1006 for in plane breathing mode at a frequency of 5 GHz in this example; (iii) a phononic cavity 1003 coupled to a metal plunger gate 1002 of a quantum dot of another kind of qubit, the plunger gate 1002 situated on top of unreleased material to connect the phononic cavity 1003 to the other qubit; and, (iv) a phononic mirror 1007 comprising void patterns that reflect phonons. A Fine Element Method (FEM) simulation 1008 of the deformation field at the given frequency is shown for the area around the phononic cavity 1003. The electrically actuated phonons at the piezoacoustic cavity 1004 are travelling through the phononic waveguide 1006 and confined in the phononic cavity (QPL) 1003 for an extended time period to interact with connected qubits. The phononic mirror 1007 is important for enhancing the cavity quality factor and the phonon qubit interaction efficiency.

[0069] Fig. 11 depicts a Fine Element Method (FEM) simulation of an electric field distribution in a cross-section of a piezoelectric material, the electric field distribution caused by a surface acoustic wave (SAW) in the piezoelectric material 1101 demonstrating that an electric field produced by the SAW can reach a germanium active layer positioned within a layer of thickness t, roughly equal to the wavelength of the SAW. In like manner, strain fields produced by phonons at a surface of a germanium-on-silicon (GoS) material stack can reach a germanium quantum well active layer positioned within the GoS stack.

[0070] Fig. 12A depicts a COMSOL™ simulation of a suspended phononic structure 1200 supported by a phononic shield, where simulated quality (Q) factor = 1.9x105and eigenfrequency = 5.84 GHz. Fig. 12B is a top view of a quantum phonon link (QPL) section of the simulation of a suspended phononic structure 1200 shown in Fig. 12A. A substrate and beam for the phononic structure 1200 are constructed from a non-piezoelectric material (e.g., silicon). A piezoacoustic cavity 1202 is made from a layer of piezoelectric material, e.g., aluminum nitride (AIN). Interdigital transducers 1201 are constructed from metal (e.g., aluminum (Al)). The phononic structure 1200 comprises a phononic waveguide 1203 and an acoustic isolating shield 1204.

[0071] Fig. 13 depicts a quantum network with interfaced qubits in different platforms connected via a quantum phononic link (QPL) bus 1301 with side quantum phononic links 1302 to the qubits. The qubits include: gated double quantum dots 1303 as an example of spin qubits, which can be the larger qubit blocks of Fig. 7; optomechanical cavities 1304 for linking to photon flying qubits; spintronic elements 1305 (e.g., based on nitrogenvacancy (NV) centers in diamond, T+centers in silicon, etc.); and, phononic-like nano- and microelectromechanical system (NEMS / MEMS) resonators and phononic crystal cavities for coupling to superconducting qubits, light and the like.

[0072] Fig. 14 depicts a COMSOL™ simulation 1401 of a confined transverse horizontal phononic propagation mode (Love mode) inside a compressively strained germanium-on- silicon (cs-GoS) material slab, where simulated quality (Q) factor = 3.6968x104and eigenfrequency = 33.215 GHz. The phonon mode is confined in a 20 nm thin germanium quantum well (QW) active layer cladded with silicon layers. Confinement of the phonon withing the germanium QW is possible because the speed of sound is smaller in the germanium layer than in the cladding silicon layers. This is similar to fiber optics, where light is confined in the fiber core having smaller light propagation velocity compared to the cladding.

[0073] Fig. 15 depicts COMSOL™ simulations of a series of transverse horizontal confined phononic modes showing deformation of mode shape for the fundamental mode (N=1) and the N=2-7 higher modes. A unit cell for a material stack 1501 similar to one used for fabrication of hole spin qubits is simulated in an eigenfrequency study to have physical properties of I = 500 nm, w = 100 nm, and h = 220 nm. A germanium quantum well active layer with 20 nm thickness is sandwiched between two 100 nm layers of silicon. Different images 1502, 1503, 1504, 1505, 1506, 1507, 1508 show the displacement field for each mode N=1 to N=7, respectively. The mode frequencies for the N = 1 to 7 modes are, respectively, 8.314 GHz, 17.214 GHz, 25.483 GHz, 32.545 GHz, 38.841 GHz, 44.635 GHz and 50.115 GHz. The quality factor for the modes starts at 463 for the fundamental mode (N=1) and reaches 5.4e6 for the highest mode, N=7. The quality factors are: Q1 = 463; Q2 = 8553; Q3 = 15,888; Q4 = 36,968; Q5 = 1 ,4e5; Q6 = 1 ,46e6; and, Q7 = 5.4e6. A top view 1509 of the second mode shows how the material stack is deformed for the transverse horizonal mode. A black and white scale 1510 shows the displacement in arbitrary units. Fig. 16A depicts a three-dimensional representation 1600 of a mesa 1601 of a compressively strained germanium-on-silicon (cs-GoS) material stack providing a quantum phononic link (QPL) 1602 coupling two hole spin qubits hosted in double quantum dots (DQDs) formed within the material stack. The quantum dots 1606 in each DQD are formed by surface gates 1603, as further explained in Fig. 4. The material stack comprises a compressively strained germanium (cs-Ge) quantum well (QW) sandwiched by SiGe barriers on a silicon (Si) substrate. The mesa 1601 is made by etching a wafer down below the germanium QW layer, so that the QPL is embedded “on a wafer”. Fig. 16B depicts a top view of the mesa 1601 , omitting the surface gates for clarity. Fig. 16B shows how resonant acoustic phonons 1607 with a wavelength matching twice the separation between quantum dots 1606 of the DQDs enable coherent quantum state transfer between the distant spin qubits. Thus, APhonon / 2 = d, where dis distance between quantum dots confining a generic qubit.

[0074] With reference to the Figures, in embodiments, five independent technologies are combined in one device to connect non-neighboring spin qubits in large quantum circuits towards scalable quantum computing containing 1 million qubits or more, quantum sensing and quantum on-chip networking applications (see Fig. 7, Fig. 8, Fig. 10, Fig. 13). The five technologies are as follows.

[0075] 1) cs-GoS material platform for combined phononic and quantum computing functionalities

[0076] The cs-GoS material system has specific properties due to the compressive strain and high quality of the material stack. The compressive strain comes from the fact that the lattice constant of germanium is larger than that of silicon, therefore, germanium-on-silicon (GoS) is compressively strained. The strain is controlled by controlling the value of x in the Sii-xGexcomposition, which is varied to engineer valence band properties, such as hole effective mass, effective g-factor, spin orbit interaction, and phononic properties like speed of sound. The choice of this material system is dictated by several favorably important parameters compared to silicon [1 ,2,3], some of which are (i) very small hole effective mass that can be engineered down to 0.035 m0, where m0is free electron mass, (ii) very large and gate-voltage-tunable effective g-factor, at least between 13 and 24, and (iii) the fact that hole energy band and other properties are strain-dependent.

[0077] Strain is an important feature of the material system, in particular for the phononic applications presented herein. Strain is equivalent to a tensor force acting on the holes’ motion including their spins. The strength and direction of the strain force depends on the mutual directions of spin, strain field and the lattice. [4, 7] Phonons in simple terms are the lattice vibrations, which produce deformation and strain. Therefore, phonons (acoustic waves) can directly interact with spins in cs-GoS [4] by-passing the need for piezoelectric transformation of strain produced by phonons into electric fields using interdigital transducers (IDTs), the well-known technology of the surface acoustic waves (SAW). [5], [6], [8], [9],

[0010] Thus, the present invention comprises direct interaction of phonons confined in a quantum phononic link (QPL) with hole spin qubits via strain-field induced interaction in a non-piezoelectric material mediated by spin-orbit coupling.

[0078] 2) High-quality nano-mechanical structures with engineered phononic spectra adopted for QPL technology applications

[0079] Herein, phonons (lattice vibrations) are confined in specially engineered QPL structures (Fig. 9, Fig. 10, Fig. 11 , Fig. 12, Fig. 13) as quantum quasi-particles to link nonneighboring spin qubits and / or qubit blocks (Fig. 7). Non-neighboring qubits are qubits at the distances that are larger than those required for direct tunneling coupling, e.g., d > IQ- 20 nm depending on the material system in which the qubits are housed. Quantum particles, electrons or holes, have very small probabilities to tunnel over distances larger than 10-20 nm, depending on the particle effective mass in the specific material system. Therefore, to link distant qubits via direct tunneling steps, a very large number of tunneling events through a long chain of QDs is required [13-15]. Thus, the technology of direct tunneling through a chain of QDs is very challenging and impractical. The QPL method described herein allows for the creation of new technology to overcome this challenging roadblock by means of realizing variable-length quantum phononic links (QPLs) between solid-state qubits positioned at arbitrary distances between a fraction of a micron to the wafer size, e.g., 450 mm, in current cs-GoS growth technology. This length flexibility in the QPL length is very advantageous compared to superconducting microwave (MW) cavity links, which are defined by the MW photon wavelength on the order of 10’s of millimeters

[0016] . The QPL property stems from phonons moving with the speed of sound, which is roughly 5 orders of magnitude smaller than the speed of light, therefore, sound wavelength is much shorter, i.e., 5 orders of magnitude shorter compared to photons for the same energy of quantum entities (phonons in the present case). In addition, sound waveforms can be engineered employing phononic cavities and waveguides, similar to photonic cavities [11 , 12] (see Fig. 10 to Fig. 12 and Fig. 14). Phonon modes in GoS engineered phononic cavities (i.e. QPLs) can be strongly localized in the germanium quantum well layer in which the QD potential is formed by top lateral gates, shown in Fig. 16A. Having spin qubits and phonons confined in the same germanium quantum well (QW) layer results in efficient overlapping of phonon and spin qubit wavefunctions, which is important for stronger spin-phonon interaction towards efficient quantum information exchange between the two, spins and phonons. This is a very advantageous property for reaching the strong coupling regime between phonons and spins required for efficient quantum information transfer protocols. Note, by linkage in the QPL technology is meant either (i) direct quantum-mechanical coupling between a high-quality phonon cavity and a spin qubit characterized by the so-called cooperativity number [17, 18], or (ii) transferring quantum information by propagating phononic wave packets in QPLs, in a way similar to photon flying qubits in free space or propagating in fibers

[0019] ,

[0020] (see an illustrative example in Fig. 8).

[0080] 3) Gate-voltage tunable qubits of the spin qubit g*-factor type based on properties of the cs-GoS system

[0081] Gate-voltage tunable qubits are important for scalable and addressable quantum computing architectures based on uniform and reproduceable arrays of quantum dots (QDs) which are fully defined by the material stack and the gate geometry and voltages. It is important to be able to simulate and predict properties of spin qubits before fabrication. This is absolutely not the case for silicon CMOS, and silicon MOSFET. Electrons and holes in silicon possess very large effective mass (compared to cs-GoS) that make the dimensions of Si QDs very small and unpredictable due to their 3D uneven geometry, dimension fluctuations, random strain, and surface charges because quantum dots fabricated by CMOS and MOSFET must be positioned very close to the surface or semiconductor-dielectric interface due to large electron or hole effective mass. In a quantum computing chip, each qubit must be carefully calibrated, which creates an impenetrable roadblock on the way towards large-scale 1 M qubit QC architectures. In a one million qubit QC circuit it is impossible for anyone, including an Al-enabled machine, to calibrate all qubits because of the time needed for such a calibration process. QC circuits based on cs-GoS can in principle be scaled to large arrays [1] based on very small hole effective mass and superior material quality, which allows larger diameter and flat quantum dots (e.g., in the shape of discs) whose properties are fully defined by the engineered material stack. The connection links between non-neighboring qubits and qubit blocks on one silicon substrate are provided by quantum phononic links QPLs as described herein (e.g., see Fig. 7). 4) Double Quantum Dots (DQDs) of spin and hybrid spin-charge qubits

[0082] A double quantum dot (DQD) geometry helps to activate spin-orbit functionalities, i.e., it helps to on-demand couple the orbital (spatial) motion of the localized hole to its spin degree of freedom. For spin-orbit coupling to be activated, some motion capability for the carrier, at least virtual, should be allowed. Spin-orbit (SO) coupling does not affect a still spin, i.e., if the hole is too strongly localized just in a single QD. If SO coupling is not activated, the spin stays immune to external electrical or strain excitations. SO interaction of holes is controllable by a gate voltage and can be turned on and off on demand for short periods of time because only the Rashba SO term is present in group IV semiconductors.

[0032] The heavy hole spins are also immune to the magnetic field excitations commonly used in electron paramagnetic resonance (EPR) spectroscopy, because holes are quantum particles with orbital momentum J=3 / 2 (J being the quantum orbital momentum number) and, therefore, the alternating magnetic field excitations from J=3 / 2 to J=-3 / 2 quantum states are forbidden by quantum physics laws for excitations with AJ>1 .

[0083] In the DQD configuration, the single spin localized in one of the dots attains a finite probability of tunneling to the second QD and back, in particular, under MW field (or strain field) excitation conditions. Therefore, SO interaction gets inherently activated and can be employed to manipulate hole spin qubits at large speeds reaching nanosecond ranges.

[0023] The inter-dot SO interaction can be tuned by a gate voltage that provides additional versatility, for example, allows fast switching between manipulation and “storage” regimes where the operation speed or the spin relaxation (storage) time are maximized, correspondingly.

[0084] A double quantum dot (DQD) geometry also permits hybridizing spin and charge qubits, which is useful for controlling direct spin to phonon coupling via phonon-mediated virtual transitions to the second dot levels of the same or opposite spin (Fig. 5). Phonons (acoustic waves) have wavelength, momentum and energy. The phonons cannot initiate the so-called vertical transitions when both quantum levels have exactly the same spatial position, i.e., belong to the same quantum dot. But, as is shown in reference

[0024] and schematically shown in Fig. 16B, phonons can efficiently produce interdot spin-flip transitions when the distance between QDs matches the one half or multiple periods of the phonon wavelength • Aphwhere d is the distance between QDs in the DQD device, andpfl= vs / fphis phonon wavelength (vsis speed of sound and fphis phonon frequency). The transition energy is efficiently controlled by the detuning energy A controlled by a gate voltage applied to the DQD plunger gates (see Fig. 4). Tunability is another important feature as tunability can be employed as the QPL operation switch turning the QPL links on and off for desired periods of time on demand. Pulse shaping can be utilized for efficient single phonon readout and / or emission protocols.

[0025]

[0085] 5) Single-shot latching detection

[0086] Single-shot latching detection can be used for single-shot phonon detection and storage of the read-out results in a metastable (latched) state for consequent readout by a near-by charge sensor. In the past, the latching technique has been employed for singleshot readout of charge and spin states. Herein, single-shot latching is employed for a single-shot phonon readout. It is not a trivial task to detect single phonons, as phonons are transient and produce very weak responses to be detected by classical electronics. To detect phonons, the quantum DQD sensor is tuned into the so-called latching regime.

[0026] To detect phonons by the DQD sensor, the two following conditions should be satisfied: (i) the distance between quantum dots should match the multiple periods of the phonon wavelength d = (N + and, (ii) energy of the phonon should be equal to the detuning energy between the dots in the DQD device controlled by the detuning gate voltage, A = Eph.

[0024] Due to small distances between quantum dot in DQD devices, in the range of about 100 nm, the operational frequency range of phonons can be much larger (e.g., up to 40 GHz for the first harmonic) compared to the accessible range by SAW and superconducting qubit technologies (from MHz up to a few GHz). A COMSOL™ simulation example of a cs-GoS phononic link operating at 33 GHz is shown in Fig. 14. COMSOL™ simulations of different modes are shown in Fig. 15 for a realistic cs-GoS material stack employed for fabrication of spin qubit devices. This property (the much higher frequency range) is unique and is important for reaching a single-phonon regime for various quantum applications including the QPL-enabled technology described herein.

[0087] The five elements described above are schematically depicted in Fig. 7. Examples of QPL devices are shown schematically in Fig. 4, Fig. 8, Fig. 12, and Fig. 16A. The more general schematic in Fig. 7 comprises qubit blocks, QPLs between spin-qubit blocks and single phonon sensors.

[0088] Examples of different kinds of phononic waveguides and cavities are known [6]. Phononic waveguides can be used as universal buses for signal transduction between different kinds of qubits (called disparate quantum entities in [6]), including superconducting transmon qubits, atom and ion qubits, nitrogen-vacancy (NV) or other defect centers in solids, and optical photons. Herein, a new qubit entity to be coupled by phonons is introduced, i.e., hole spin qubits in cs-GoS system employing strain and spin orbit (SO) interaction to facilitate direct interaction between spins and phonons. Phononic cavities are combined with gated quantum dots to attain coupling and quantum information transfer between non-neighboring qubits employing strain and spin-orbit enabled interaction between phonons and spins, which is an important element towards 1 M large-scale quantum computing and networking applications. In addition, as mentioned above, QPLs will allow inter-material integrations connecting disparate qubit entities opening wide prospects for using cs-GoS spin qubits with a variety of other quantum entities for a broad range of applications including quantum internet and distributed quantum computing.

[0089] The illustrated embodiments show a method of coupling spin-qubits with a quantum phononic link (QPLs) employing direct interaction of phonons in the QPL with hole spin qubits in gated quantum dots via strain-field mediated by spin-orbit interactions in a nonpiezoelectric compressively strained germanium-on-silicon (cs-GoS). Phonon cavities and links are made from a layered material stack, e.g., SiGe-Ge-SiGe, in which the embedded quantum well (QW) layer (Ge in the illustrated embodiments, but can be different) has a smaller speed of sound compared to the barriers around the germanium QW. Vibrations are fully confined in the material layer with the smaller speed of sound to facilitate interaction of phonons (vibrations) with a spin qubit confined in a double quantum dot (DQD) in the same layer, the DQD formed by plurality of surface gates (see Fig. 4 and Fig. 16). The cs-GoS material stack can have an added non-piezoelectric dielectric layer (e.g., diamond for extended phononic functionalities. Added non-piezoelectric dielectric layers possess different sound velocities compared to the cs-GoS serve to create engineered phononic waveguides and cavities confining acoustic waves near an interface proximate the germanium quantum well layer in which spin qubits are formed by the plurality of surface gates. The cs-GoS material stack may have an added piezoelectric layer (e.g., AIN, GaN, LiNbO3, or other materials) for extended phononic functionalities with involvement of interdigital and other (e.g., capacitive) transducers of phononic waves to electric fields to couple spin qubits in the quantum well layer to other disparate quantum entities, for example, superconducting qubits, on-chip ion trap qubits, other solid-state qubits like NV- centers in diamond, T-centers in silicon and other color centers, including rare earth ions, also, optical photons (flying qubits). The method includes a method of single-shot phonon readout employing latching detection, previously used only for spin and charge qubit readout. The combination of the five technologies enables coherent connection between non-neighboring spin qubits or blocks of qubits for scalable towards 1 M qubits quantum computing architectures and on-chip networking in the range between fractions of a micrometer to the full silicon wafer-size range. One or more of the embodiments described herein use coherent standing acoustic modes with adjustable wavelength and energy formed in nanobridges and phononic cavities, aka, artificial phononic crystals. Such artificial phononic systems can be engineered for a broad range of wavelengths and energies allowing quantum links (i.e., QPLs) of variable lengths. The QPLs described herein can be employed for electron qubits in CMOS and other silicon-based technology by employing micromagnets.

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[0121] The novel features will become apparent to those of skill in the art upon examination of the description. It should be understood, however, that the scope of the claims should not be limited by the embodiments but should be given the broadest interpretation consistent with the wording of the claims and the specification as a whole.

Claims

Claims:

1. A quantum device comprising: a solid-state material; a plurality of qubits on or in the solid-state material, each of the qubits comprising at least two quantum dots; and, a quantum phononic link (QPL) localized on or in the solid-state material, the QPL configured to guide phonons between a pair of qubits of the plurality of qubits to quantum- mechanically couple the pair of qubits, the pair of qubits spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits and is at least about 10 nm.

2. The device of claim 1 , wherein the qubit-separation distance is at least about 100 nm.

3. The device of claim 1 or claim 2, wherein the qubits are spin qubits.

4. The device of any one of claims 1 to 3, wherein the localized QPL comprises a phononic waveguide or a phononic cavity.

5. The device of any one of claims 1 to 4, wherein the localized QPL contains the phonons in a volume and is provided by one or more of: a physical structure of the solid- state material; and, an atomic lattice arrangement in the solid-state material.

6. The device of any one of claims 1 to 5, wherein at least a portion of the solid-state material is isotopically purified so that the nuclei of the solid-state material have no magnetic moments.

7. The device of any one of claims 1 to 6, wherein the solid-state material comprises one or more of: a layered germanium-on-silicon (GoS) material; and, a silicon-on-insulator (Sol) material.

8. The device of any one of claims 1 to 6, wherein the solid-state material comprises a layered germanium-on-silicon (GoS) stack and has a non-piezoelectric compressively strained germanium (cs-Ge) quantum well epilayer that provides the localized QPL.

9. The device of claim 8, wherein the phonons localized within the QPL enable quantum-mechanical coupling between the pair of qubits spaced-apart by the qubitseparation distance via direct interactions induced by strain deformation potential produced by the phonons.

10. The device of claim 8 or claim 9, wherein the layered germanium-on-silicon (GoS) stack comprises: a base wafer of doped or undoped Si(001); a buffer layer of intrinsic germanium (i-Ge) deposited on the base layer; a relaxed layer of relaxed graded SixGei-xwhere x is between 0.1 and 0.3 deposited on the buffer layer; the cs-Ge quantum well epilayer deposited on the relaxed layer; and, a SixGei-xcap layer deposited on the cs-Ge quantum well epilayer.

11. The device of claim 10, wherein the layered germanium-on-silicon (GoS) stack further comprises a germanium (Ge) or silicon (Si) cap deposited on the SixGei-xcap layer.

12. The device of any one of claims 8 to 11 , wherein speed of sound in the cs-Ge quantum well epilayer is slower than in layers adjacent to the cs-Ge quantum well epilayer.

13. The device of any one of claims 1 to 12, wherein the quantum dots in each qubit of the pair of qubits linked by the localized QPL are separated from adjacent quantum dots by a quantum dot-separation distance, d, the phonons have a wavelength, and a halfwavelength of the phonons is a multiple of the quantum dot-separation distance.

14. The device of any one of claims 1 to 13, wherein the quantum dots and the localized QPL are formed integrally with the solid-state material.

15. The device of any one of claims 1 to 14, wherein at least a portion of the qubits are gate-voltage tunable qubits, and the device further comprises voltage gates for forming the quantum dots integrally in the solid-state material.

16. The device of any one of claims 1 to 13, wherein the quantum dots are formed integrally with the solid-state material or are formed by one or more dopants added to the solid-state material.

17. The device of any one of claims 1 to 16, wherein at least a portion of the qubits are double quantum dots in which the at least two quantum dots are two quantum dots.

18. The device of any one of claims 1 to 17, further comprising a single phonon detector for detecting a single phonon.

19. The device of any one of claims 1 to 18, wherein the solid-state material further comprises one or both of a piezoelectric layer and a non-piezoelectric dielectric layer to provide one or more additional phononic-enabled functionalities.

20. The device of claim 19, wherein the one or more additional phononic-enabled functionalities comprises one or more of: localizing phonons in other regions of the solid- state material; and, transducing phonon vibrations to electric fields for coupling at least a portion of the qubits to other quantum entities including one or more of superconducting qubits, on-chip ion trap qubits, NV-centers in diamond, T-centers in silicon, rare earth ions and optical photons.21 . The device of any one of claims 1 to 20, wherein the localized QPL comprises a plurality of localized QPLs, and at least a portion of the qubits of the plurality of qubits are coherently linked to each other by a network of the localized QPLs.

22. A quantum device comprising: a solid-state material comprising a layered germanium-on-silicon (GoS) stack, the layered germanium-on-silicon (GoS) stack comprising: a base layer of doped or undoped Si(001); a buffer layer of intrinsic germanium (i-Ge) deposited on the base layer; a relaxed layer of relaxed graded SiGe deposited on the buffer layer; a non-piezoelectric compressively strained (cs-Ge) quantum well epilayer deposited on the relaxed layer; and, a SiGe cap deposited on the cs-Ge quantum well epilayer; a plurality of voltage-gated qubits in the solid-state material, each of the qubits comprising at least two quantum dots monolithically formed in the solid-state material; and, a localized quantum phononic link (QPL) defined by the non-piezoelectric compressively strained germanium (cs-Ge) quantum well epilayer in the solid-state material through which phonons having a wavelength are guided between a pair of qubits of the plurality of voltage-gated qubits to enable quantum-mechanical coupling of the pair of qubits, the pair of qubits spaced-apart by a qubit-separation distance that is longer than a direct-tunneling distance of the qubits and is at least 10 nm, the two quantum dots in each qubit of the pair of qubits separated from each other by a quantum dot-separation distance, a half-wavelength of the phonons being a multiple of the quantum dot-separation distance.

23. The device of claim 22, wherein the layered germanium-on-silicon (GoS) stack further comprises a germanium (Ge) or silicon (Si) cap deposited on the SiGe cap layer.

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