Storage and transmission of quantum information

Abstract

Methods and apparatus for storing and conducting quantum information provide luminescent centers in silicon that are controllably coupled to undergo quantum interaction with a first quantum bit, such as a superconducting quantum bit. For example, the luminescent centers can be T centers or a collection of T centers. The same or different quantum information can be stored in one or more of the unpaired electron or hole spins and / or three nuclear spins of the T centers. The stored quantum information can later be returned to the first quantum bit or transferred to a visible photon state.

Description

[0001] Cross-reference of related applications

[0002] This application claims priority to U.S. Application No. 63 / 057796, filed July 28, 2020, entitled Storage and Transmission of Quantum Information, which is hereby incorporated herein by reference for all purposes. For U.S. purposes, this application claims the benefit of U.S. Application No. 63 / 057796, filed July 28, 2020, entitled Storage and Transmission of Quantum Information, pursuant to 35 U.S. SC § 119. Technical Field

[0003] This invention relates to the storage and manipulation of quantum information. Some embodiments provide methods and apparatus for transmitting quantum information between qubits having quantum states separated by different energies. For example, one application of this invention is transmitting quantum information from qubits having energy levels separated according to microwave wavelengths to visible photons. Another application of this invention is storing quantum information. Yet another application is forming quantum entanglement between multiple qubits. Background Technology

[0004] Quantum computing has the potential to revolutionize computer science. In quantum computing, the states of quantum systems are used to represent data. For example, the spin direction of a particle (such as an electron) relative to a magnetic field can represent a binary value of 1 or 0, depending on whether the spin is oriented parallel to the magnetic field (downspin) or antiparallel to the magnetic field (upspin). One advantage of quantum computing is that quantum systems can exist in a superposition of states. For example, in a sense, a quantum system can simultaneously have both upspin and downspin. Another advantage of quantum computing stems from the fact that the states of different quantum systems can be entangled.

[0005] One difficulty in building quantum computers is that after setting a quantum system to a desired state and simultaneously manipulating it to attempt to place it in that desired state, the quantum system can become decoherent due to its interaction with its environment. This causes the quantum system to no longer be in the desired state. Some quantum systems experience decoherence for extremely short periods of time (e.g., about one nanosecond). The effect of decoherence on a particular quantum system can be reduced by keeping the quantum system at an extremely cold temperature (e.g., mK).

[0006] Further technological advancements are still needed to drive progress in quantum computing.

[0007] definition

[0008] A "quantum system" is a system that has two or more states and can exist in a superposition of two or more states. For example, quantum systems can include particles (such as electrons, protons, neutrons, atomic nuclei, atoms, and groups of atoms), pseudoparticles (such as phonons, excitons, and magnetons), photons, and so on.

[0009] A “quantum interaction” refers to the interaction between quantum states of two or more qubits. Examples of quantum interactions include state transfer interactions and quantum entanglement operations.

[0010] "Quantum coherence" refers to the degree to which the relationship between the phases of different quantum states in a quantum system (such as a qubit) is preserved.

[0011] "Quantum decoherence" is the change in the quantum state of a quantum system caused by the interaction between the quantum system and its environment.

[0012] When applied to two or more quantum systems, "entanglement" means that the quantum state of one of the entangled quantum systems cannot be described independently of the state of the other (the entangled quantum system).

[0013] "Emitting center" refers to a quantum system having an excited state that decays to a lower energy state by emitting a visible photon via a transition dipole moment of at least 0.1 Debye. In a preferred embodiment, the emitting center, while in the excited state, will undergo a transition of 50 μs or less and emit a visible photon with a relatively high probability (e.g., 1% or greater).

[0014] "Visible photon" refers to a photon that emits electromagnetic radiation with a wavelength between the far-infrared and ultraviolet rays. Examples of visible photons include those with wavelengths ranging from 15 μm to 10 nm. Examples of visible photons include those with wavelengths ranging from 2 μm to 380 nm.

[0015] A "qubit" refers to a quantum system in which a superposition of states that can represent data exists. An example of a qubit is the quantum spin of a particle that can be oriented either parallel to a magnetic field ("downspin") or antiparallel to a magnetic field ("upspin"). For instance, an upspin state can be associated with logic "1" and a downspin state can be associated with logic "0".

[0016] "Quantum measurement" refers to the process of determining values ​​for measurable quantities of a quantum system. An example of quantum measurement is the process of determining whether a quantum particle's spin is up or down. When a quantum system is in a superposition of quantum states and the measurable quantities have different values ​​for each of these states, the result of a quantum measurement is that the quantum system will be in one of the quantum states corresponding to the value determined immediately after the quantum measurement.

[0017] When applied to quantum particles or other quantum systems, "superposition" refers to the simultaneous existence of a quantum system in two or more separate quantum states. For example, a quantum particle with non-zero spin in a magnetic field can be in two different spin states simultaneously. Summary of the Invention

[0018] The present invention has various aspects. These include, but are not limited to:

[0019] • Systems and methods for extending the coherence time of qubits in quantum computers;

[0020] Systems and methods for providing data to qubits in a quantum computer and reading data from qubits in a quantum computer;

[0021] • Systems and methods for using visible photons to interact with qubits in which states are separated by sub-light energy;

[0022] Systems and methods for quantum computing;

[0023] Systems and methods for entanglement of microwaves and visible photons;

[0024] These aspects can be applied individually or in any combination.

[0025] One aspect of the present invention provides a method for storing quantum information. The method includes providing a first qubit in a first quantum state encoding first quantum information. The first qubit has an energy ΔE corresponding to a microwave frequency. SQ Separated first and second quantized energy levels. In some embodiments, the first qubit includes a superconducting qubit. The method includes coupling the first qubit to a first luminescent center in silicon via a microwave photonic state, such that the quantum states of the first qubit and the first luminescent center undergo quantum interactions, wherein the quantum state of the first luminescent center encodes the first quantum information.

[0026] Some embodiments include decoupling the first qubit from the first luminescent center.

[0027] Some embodiments include coupling the first qubit to the first luminescent center for a time substantially equal to n half-cycles of the two-qubit Rabi frequency of the first qubit and the first luminescent center, where n is an odd integer.

[0028] In some embodiments, the first luminescent center has an energy ΔE LC1 Separating the first and second quantized energy levels, and coupling the first qubit to the first luminescent center includes adjusting the energy ΔE. LC1 and the energy ΔE SQ One or both of them make ΔE LC1 With ΔE SQ They are basically equal.

[0029] Some embodiments include adjusting the energy ΔE by applying an electric field to the first luminescent center. LC1 Some embodiments include adjusting the energy ΔE by applying an RF drive signal to the first luminescent center. LC1 Some embodiments include adjusting the energy ΔE by applying strain to the silicon in which the first light-emitting center is located. LC1 In some embodiments, the first luminescent center is in a magnetic field, and the method includes adjusting the energy ΔE by changing the strength of the magnetic field at the luminescent center. LC1 .

[0030] In some embodiments, the first luminescent center has an energy difference ΔE LC2 A third energy level separated from the first energy level, and the method includes coupling the quantum state of the first luminescent center to a state corresponding to ΔE. LC2 The photon state in the first resonator at the resonant frequency of the first resonator encodes the first quantum state. In some embodiments, the photon state in the first resonator is a visible photon state. In some embodiments, the photon state in the first resonator corresponds to a light wavelength in the range of about 1 μm to about 5 μm.

[0031] Some embodiments include delivering a photon of the photon state to a second resonator and coupling the second resonator to a second luminescent center, such that the quantum state of the second luminescent center encodes the first quantum information.

[0032] In some embodiments, the photon state in the first resonator is entangled with another photon state in the second resonator, and the method includes coupling the second resonator to a second luminescent center such that the quantum state of the second luminescent center encodes the first quantum information.

[0033] Some embodiments include encoding the first quantum information in the quantum state of the second matter qubit by coupling the second luminescent center to the second matter qubit via another microwave photon state, wherein the quantum states of the second matter qubit and the second luminescent center participate in quantum interactions, such that the quantum state of the second matter qubit encodes the first quantum information. Some embodiments include decoupling the second matter qubit from the second luminescent center. Some embodiments include entanglement of the photon state with three or more luminescent centers. Some embodiments include returning the first quantum information to the first qubit by coupling the first luminescent center to the first qubit via another microwave photon state, such that the quantum states of the first qubit and the first luminescent center participate in quantum state transfer interactions, such that the quantum state of the first qubit encodes the first quantum information.

[0034] In some embodiments, the first light-emitting center includes a crystal defect in the silicon crystal. In some embodiments, the first light-emitting center includes a set of light-emitting centers, wherein each of the light-emitting centers in the set includes a crystal defect in the silicon crystal.

[0035] In some embodiments, the crystal defect includes a T-center. In some embodiments, the crystal defect has an unpaired ground-state spin and includes an I-center, an M-center, an Al1-center, a Ga1-center, a nitrogen-carbon center, or a silicon damage center.

[0036] In some embodiments, the crystal defect includes at least one of an electron having an electron spin and a hole having a hole spin, and the first and second quantized energy levels of the first luminescent center respectively include the downspin state and the upspin state of the electron or the hole. In some embodiments, the crystal defect includes at least one nuclear spin, and the method further includes encoding the quantum state of the electron or the hole with the quantum state of the nuclear spin, such that the nuclear spin encodes the first quantum information.

[0037] In some embodiments, the crystal defect includes at least one unpaired electron or hole spin and at least one nuclear spin, and the method further includes encoding the first quantum information as a joint quantum state of the at least one unpaired electron or hole spin and the at least one nuclear spin. In some embodiments, encoding the first quantum information as a joint quantum state of the unpaired electron or hole spin and the nuclear spin includes inducing a crossover transition. In some embodiments, the crossover transition includes an electron dipole spin resonance (EDSR) transition. Some embodiments include recovering the first quantum information by setting the unpaired electron or hole spin to have an initialized quantum state and inducing a spin transition of the unpaired electron or hole spin and / or the nuclear spin.

[0038] In some embodiments, the crystal defect comprises multiple nuclear spins, and the method includes:

[0039] The first quantum information is encoded using the first of the nuclear spins;

[0040] This causes the first qubit to encode the second quantum information;

[0041] The first qubit is coupled to the first luminescent center through the second microwave photon state, such that the quantum states of the first qubit and the electrons or holes of the first luminescent center undergo quantum interaction and the quantum states of the electrons or holes of the first luminescent center encode the second quantum information.

[0042] Decouple the first qubit from the first luminescent center; and

[0043] The quantum state of the electron or hole is encoded by the quantum state of the second of the nuclear spins, such that the second of the nuclear spins encodes the second quantum information.

[0044] Some embodiments include forming a bound exciton by illuminating the crystal defect center with a light pulse before coupling the first qubit to the first luminescent center. Some embodiments include encoding the first quantum information in the spin state of the hole. In some embodiments, the luminescent center comprises an impurity atom in a silicon crystal.

[0045] In some embodiments, the impurity atom includes a dual donor atom. In some embodiments, the dual donor is a selenium, tellurium, or sulfur atom.

[0046] In some embodiments, at least 95% of the silicon atoms in the silicon crystal are silicon-28.

[0047] In some embodiments, the first qubit is in a first freezer and the second material qubit is in a second freezer, and the first and second resonators are connected via an optical path passing outside the first and second freezers. In some embodiments, at least a portion of the optical path outside the first and second freezers is greater than ΔE. SQ / k B The temperature, where k B It is the Boltzmann constant. In some embodiments, the optical path includes an optical fiber. In some embodiments, ΔE SQ It is 1.3 meV or less.

[0048] In some embodiments, the first qubit is a superconducting qubit. In some embodiments, the first qubit includes a quantum dot or an ion trap.

[0049] Another aspect of the present invention provides a method for transmitting the quantum states of a superconducting qubit to visible photons. The method includes: coupling a superconducting qubit having two quantum states with corresponding energy levels separated by an energy ΔE1 to a light-emitting center in silicon, the light-emitting center having first and second quantum states with corresponding energy levels separated by an energy close to ΔE1, and third and fourth quantum states having corresponding energy levels separated by energies ΔE2 and ΔE3, respectively, from the energy levels corresponding to the first and second states; and subsequently coupling the light-emitting center to an optical structure that supports photon modes having frequencies corresponding to the energies ΔE2 and / or ΔE3.

[0050] In some embodiments, ΔE2≠ΔE3.

[0051] In some embodiments, coupling the superconducting qubit to the luminescent center is performed by a resonator having a microwave resonant frequency corresponding to the energy ΔE1.

[0052] Some embodiments include maintaining the coupling between the superconducting qubit and the luminescent center for an odd number of cycles equal to the Rabi frequency of the two qubits of the coupled superconducting qubit and the luminescent center, and then decoupling the superconducting qubit from the luminescent center.

[0053] In some embodiments, the optical structure is an optical resonator.

[0054] Some embodiments include detecting photons in the optical structure.

[0055] Another aspect of the present invention provides a method for transmitting the quantum state of a superconducting qubit to a visible photon. The method includes entanglement of the quantum state of the superconducting qubit with the quantum state of a luminescent center via microwave photons; and subsequently entanglement of the quantum state of the luminescent center with a visible photon state.

[0056] Some embodiments include manipulating the quantum state of the luminescent center before entanglement of the quantum state of the luminescent center with the visible photon state.

[0057] Another aspect of the present invention provides a method for storing first quantum information. The method includes: coupling a qubit having a first quantum state to an electron spin or hole spin in a T-center of silicon to transfer the first quantum state to the quantum state of the electron spin or hole spin; and decoupling the electron spin or hole spin from the qubit.

[0058] Some embodiments include a quantum interaction between the quantum state that subsequently causes the electron spin or hole spin and the quantum state of the first nuclear spin among the plurality of nuclear spins at the T center, such that some or all of the first quantum information is encoded with the first nuclear spin.

[0059] Some embodiments include setting the qubit to have a second quantum state; and

[0060] The qubit is coupled to the electron spin or hole spin in the center of the T to transfer the second quantum state to the electron spin or hole spin.

[0061] Some embodiments include decoupling the electron spin or hole spin from the qubit; and

[0062] The quantum state of the electron spin or hole spin is then transferred to the quantum state of the second nuclear spin among the plurality of nuclear spins at the center of T.

[0063] Another aspect of the present invention provides a device for storing quantum information. The device includes: a first qubit having an energy ΔE corresponding to a microwave frequency. SQ Separated first and second quantized energy levels; luminescent centers in silicon, which have energy ΔE LC1 Separated first and second quantized energy levels; and a component for coupling the first qubit to the luminescent center via microwave photons.

[0064] In some embodiments, the first quantum bit is a superconducting quantum bit.

[0065] In some embodiments, the first quantum bit is a quantum dot or an ion trap.

[0066] In some embodiments, the component for coupling includes a microwave resonator.

[0067] In some embodiments, the coupling component includes elements for adjusting the energy ΔE. LC1 and the energy ΔE SQ One or both of them make ΔE LC1 With ΔE SQ Components that are essentially the same.

[0068] Some embodiments include a means for coupling the first qubit to the light-emitting center for a time substantially equal to n half-cycles of the two-qubit Rabi frequency of the first qubit and the light-emitting center, where n is an odd integer.

[0069] In some embodiments, the light-emitting center includes a T-center.

[0070] In some embodiments, the luminescent center includes a T-center set.

[0071] Some embodiments include components for selectively coupling unpaired electrons of the T-center to the nuclear spin of the T-center.

[0072] In some embodiments, the light-emitting center is in a silicon substrate and the first qubit is supported on the silicon substrate.

[0073] Another aspect of the present invention provides a device for transmitting the quantum states of a superconducting qubit to visible photons. The device includes: a superconducting qubit having two quantum states with corresponding energy levels separated by an energy ΔE1; a light-emitting center in silicon having first and second quantum states with corresponding energy levels separated by an energy close to ΔE1, and third and fourth quantum states having corresponding energy levels separated by energies ΔE2 and ΔE3, respectively, from the energy levels corresponding to the first and second quantum states; a component for coupling the superconducting qubit to the light-emitting center; and a component for coupling the light-emitting center to an optical structure supporting photon modes having frequencies corresponding to the energies ΔE2 and / or ΔE3.

[0074] Another aspect of the present invention provides a method for forming quantum entanglement among a plurality of spaced-apart qubits. Each of the qubits has an energy ΔE corresponding to a microwave frequency. SQSeparated first and second quantized energy levels. The method includes: coupling each of the qubits to a corresponding luminescent center in silicon via microwave photonic states, the luminescent center having at least first, second, and third quantized energy levels, wherein the first and second energy levels are separated by an energy difference corresponding to the energy of the microwave photonic states and the first and third energy levels are separated by an energy difference corresponding to the energy of visible photons; and coupling each of the luminescent centers to the others in the corresponding luminescent centers via an optical structure supporting one or more visible photonic states having energies corresponding to quantum transitions of the luminescent center between the first and third energy levels.

[0075] Another aspect of the present invention provides a method for quantum computing. The method includes: storing quantum information as qubit states in a defect in a silicon crystal, wherein the defect comprises a plurality of impurity atoms, the plurality of impurity atoms collectively comprising at least one unpaired electron having a corresponding electronic spin state and a plurality of nuclear spins each having a corresponding nuclear spin state; and setting one of the spin states to represent the qubit information and using the plurality of nuclear spins to perform quantum error correction or error detection on the qubit information.

[0076] Some embodiments include using the plurality of nuclear spins for majority-determined local error correction.

[0077] Some embodiments include using the plurality of nuclear spins as an aid for encoding the qubit information in logical qubits.

[0078] In some embodiments, the defect includes a T-center, an I-center, or an M-center.

[0079] In some embodiments, the defect includes a T-center.

[0080] In some embodiments, the energy levels of the transitions between different nuclear spin states of the nuclear spin are different for different nuclear spins.

[0081] Another aspect of the present invention provides a method for purifying quantum entanglement. The method includes: providing first and second defects in a silicon crystal, wherein each of the first and second defects includes an operational qubit comprising an electron or hole spin and at least one memory qubit comprising a nuclear spin; and entangled the quantum states of the operational qubits of the first and second defects; and transferring the entanglement to the at least one memory qubit of each of the first and second defects via state transfer.

[0082] Some embodiments include repeating the following steps: entangle the quantum states of the operational qubits of the first and second defects; and transferring the entanglement to at least one memory qubit of each of the first and second defects via state transfer.

[0083] In some embodiments, the defect includes a T-center, an I-center, or an M-center. In some embodiments, the defect includes a T-center.

[0084] Another aspect of the present invention provides a method for storing quantum information in a defect in a silicon crystal. The method includes: setting a quantum state of the electron or hole spin of the defect to encode first quantum information and initializing a first nuclear spin of the defect to a first initial nuclear spin state; and illuminating the defect with a first photon having a first wavelength matching the energy of a first spin transition involving the electron or hole spin and the first nuclear spin.

[0085] Some embodiments include setting the quantum state of the electron or hole spin of the defect to encode second quantum information and initializing the second nuclear spin of the defect to a second initial nuclear spin state; and illuminating the defect with a second photon having a second wavelength that matches the energy of a second spin transition involving the electron or hole spin and the second nuclear spin.

[0086] In some embodiments, the first transition is a cross transition.

[0087] In some embodiments, the first photon is provided in the form of a coherent pi pulse.

[0088] In some embodiments, the defect includes a T-center, an I-center, or an M-center.

[0089] In some embodiments, the defect includes a T-center.

[0090] Other aspects and exemplary embodiments are illustrated in the accompanying drawings and / or described in the following description.

[0091] It should be emphasized that the present invention relates to all combinations of the above features, even if these are described in different technical solutions. Attached Figure Description

[0092] The accompanying drawings illustrate non-limiting examples and embodiments of the present invention.

[0093] Figure 1 The schematic diagram illustrates a system comprising short-lived qubits and a device for extending the lifetime of short-lived qubits.

[0094] Figure 1AThe schematic diagram illustrates the energy of the quantum states of short-lived and long-lived qubits and the interaction between photons and short-lived and long-lived qubits.

[0095] Figure 2 It is a diagram illustrating the evolution of the probability density of two coupled quantum systems.

[0096] Figure 3 This is a flowchart illustrating an example method for preserving the quantum state of short-lived qubits.

[0097] Figure 4 It is a schematic diagram illustrating the construction of an example system containing both short-lived and long-lived qubits.

[0098] Figure 5 It is a schematic diagram showing the qubits of both microwaves and visible photons that are arranged to couple quantum information to an external system.

[0099] Figure 6 It is an example energy level diagram of quantum states that can be coupled to both microwave and visible photons in qubits.

[0100] Figure 6A This is a schematic diagram illustrating long-lived qubits that are positioned to couple to microwave photons through interaction with electric or magnetic fields.

[0101] Figure 6B This is a schematic diagram illustrating the energy levels of a quantum system that can contain bound excitons in which the spin state of holes can act as long-lived qubits.

[0102] Figure 7A and 7B These are schematic diagrams illustrating the cross-sectional and planar views of a system in which qubits are arranged to couple to visible photons.

[0103] Figure 8 This is a schematic diagram illustrating a system in which qubits in multiple cryocells can be coupled by visible photons.

[0104] Figure 9 This demonstrates the structure of T-centers in silicon. Detailed Implementation

[0105] Specific details are set forth throughout the following description to provide a more thorough understanding of the invention. However, the invention may be practiced without these details. In other instances, well-known elements have not been shown or described in detail to avoid unnecessarily obscuring the invention. Therefore, the specification and drawings should be regarded as illustrative rather than limiting.

[0106] One aspect of the present invention provides a device for extending the lifetime of qubits. For example, the qubit may include a superconducting qubit. A disadvantage of superconducting qubits is their undesirably short lifetime (typically having a coherence time of around 100 μs or less). This hinders the ability to process quantum information using superconducting qubits.

[0107] Figure 1 The schematic diagram illustrates a system 10 containing short-lived qubits 12. For example, the short-lived qubits 12 may include superconducting qubits, such as transons or other charge- or flux-based superconducting qubits.

[0108] System 10 utilizes the fact that qubits provided in a silicon crystal can have lifetimes several orders of magnitude longer than short-lived qubits (e.g., superconducting qubits). System 10 comprises a body 14 made of silicon. Preferably, but optionally, body 14 comprises a purified isotope of silicon (“silicon 28”) having an atomic weight of 28. For example, body 14 may be part of a substrate on which short-lived qubits 12 are formed. Body 14 contains at least one long-lived qubit 16.

[0109] For example, the long-lived qubit 16 may include unpaired spins (e.g., electron spin, nuclear spin, or hole spin in an exciton) or several excitons. For example, excitons may be formed by illuminating the luminescent center with light radiation having a frequency corresponding to the energy of the exciton.

[0110] The long-lived qubit 16 can be provided by one or more particles or quasi-particles in the luminescent center. In some embodiments, the luminescent center is provided by a crystal defect in the body 14, such as a color center with unpaired ground-state spin (e.g., a T center, I center, or M center, Al1 center, Ga1 center, or nitrogen-carbon center, or a spin-active silicon radiation-damaged center or a silicon color center with unpaired ground-state spin). When the luminescent center is a crystal defect, the particle or quasi-particle can be, for example, an electron, hole, atomic nucleus, or exciton of the luminescent center. Some types of crystal defects provide multiple particles or quasi-particles that can be used individually or in groups to provide the long-lived qubit. For example, a T center has at least three nuclear spins, electron spins, the possibility of hole spins in bound excitons, and the number of excitons, all of which can be used as the long-lived qubit 16.

[0111] In some cases, crystal defects may contain one or more impurity atoms. In some embodiments, the luminescent center is provided by the impurity atom, in which case the long-lived qubit 16 may be provided by one or both of the electron spin and nuclear spin of the impurity atom.

[0112] In some embodiments, the long-lived qubit 16 includes unpaired spins provided by atoms of impurities (e.g., selenium, sulfur, or tellurium in a silicon crystal).

[0113] System 10 also includes a controllable coupling 18. The coupling between short-lived qubit 12 and long-lived qubit 16 via coupling 18 can be controlled to selectively allow the short-lived qubit 12 and long-lived qubit 16 to interact with each other.

[0114] Coupling 18 is configured to allow sufficiently strong coupling between short-lived qubit 12 and long-lived qubit 16 to facilitate state transfer or entanglement between them. For example, the coupling may include a resonator designed to accommodate photons having energies corresponding to quantum transitions of the short-lived qubit 12 and the long-lived qubit 16.

[0115] One measure of the coupling strength between short-lived qubit 12 and long-lived qubit 16 is the two-qubit Rabi frequency, described elsewhere in this paper. The two-qubit Rabi frequency increases as the coupling between the two qubits strengthens. To facilitate efficient quantum interaction between short-lived qubit 12 and long-lived qubit 16, the period of the Rabi frequency should be greater than the coherence time of both short-lived qubit 12 and long-lived qubit 16. For example, “cooperation” can be defined as follows:

[0116]

[0117] Where C represents synergy, f R It is the rabi frequency, R SL R is the decoherence rate of short-lived qubits (i.e., the reciprocal of the decoherence time), and R LL It is the decoherence rate of the long-lived qubit. In some embodiments, when coupling 18 couples the short-lived qubit 12 to the long-lived qubit 16, the coupling strength is given by the cooperability value C≥1.

[0118] In some embodiments, C>1 is achieved at a two-qubit Rabi frequency of less than 50 kHz. For example, with a short-lived qubit 12 having a coherence time of 1 μs (typical for some superconducting qubits) and a long-lived qubit 16 having a coherence time of 1 ms (typical for electron spin in T-centers), C>1 can be achieved at a two-qubit Rabi frequency of 30 kHz or greater. As another example, with a short-lived qubit 12 having a coherence time of 1 μs and a long-lived qubit having a coherence time of about 1 s (typical for nuclear spin in T-centers in silicon), a two-qubit Rabi frequency of 1 kHz or greater is sufficient to achieve C>1.

[0119] The Rabi frequency can be increased by increasing the coupling strength between the short-lived qubit 12 and the long-lived qubit 16. For example, this can be achieved through one or more of the following:

[0120] • To more closely match the transition energies of short-lived qubit 12 with those of long-lived qubit 16;

[0121] • To make the short-lived qubit 12 and the long-lived qubit 16 physically closer to each other;

[0122] • To more closely match the resonant frequency of coupling 18 (e.g., a resonator) with the transition energies of short-lived qubit 12 and long-lived qubit 16.

[0123] • Provides a geometry in which short-lived qubit 12 and long-lived qubit 16 can each be coupled to an antinode of an electromagnetic mode that couples short-lived qubit 12 and long-lived qubit 16.

[0124] Short-lived qubits can represent qubit values ​​in various ways, for example, the construction of superconducting qubits that store quantum information by phase, charge, or flux is all known.

[0125] In some embodiments, coupling 18 includes a resonator arranged such that the maximum value of the electromagnetic field associated with the short-lived qubit 12 is coupled to the resonator. For example, if the short-lived qubit 12 is a superconducting flux qubit, the resonator may be inductively coupled to the magnetic field antinode of the superconducting flux qubit. As another example, if the short-lived qubit 12 is a superconducting charge qubit or a superconducting phase qubit, the resonator may be capacitively coupled to the electric field antinode of the short-lived qubit 12.

[0126] The resonator of coupling 18 can be arranged such that the maximum electromagnetic field of the photonic mode supported by the resonator is located at or near the location of the long-lived qubit 16.

[0127] In some embodiments, coupling 18 is provided by the direct interaction of the electromagnetic field of short-lived qubit 12 with that of long-lived qubit 16. In these embodiments, coupling 18 is provided by a relative physical arrangement of short-lived qubit 12 relative to long-lived qubit 16, which allows them to be coupled for quantum interactions, as described herein. Long-lived qubit 16 may be located at or near a point where the electromagnetic field associated with short-lived qubit 12 has a maximum value. For example, in the case where short-lived qubit 12 comprises a superconducting flux qubit containing a flux loop, long-lived qubit 16 (e.g., a T-center) may be located within the flux loop where it can be directly coupled to the magnetic field generated by the flux loop. In the case where short-lived qubit 12 is a charge or phase qubit, long-lived qubit 16 may be located at or near the maximum electric field value of the electric field generated by short-lived qubit 12. In some embodiments, the long-lived qubit 16 is located at a position where the electromagnetic field of the short-lived qubit 12 interacting with the long-lived qubit 16 has an intensity no more than 3 dB or 2 dB lower than the intensity of the electromagnetic field at the position where the electromagnetic field has the maximum intensity.

[0128] In some embodiments, the energy difference between the quantum states of each of the short-lived qubit 12 and the long-lived qubit 16 corresponds to a photon frequency in the radio frequency (RF) or microwave region. For example, in some embodiments, the photon frequency is in the range of about 1 MHz to 100 GHz. In some embodiments, the photon frequency is in the range of 1 GHz to 100 GHz. In some embodiments, the photon frequency is in the range of 3 GHz to 8 GHz.

[0129] The relationship between energy and photon frequency is given by the following:

[0130] E = hυ

[0131] Where E is the energy difference, h is Planck's constant, and υ is the photon frequency. The photon frequency is related to the photon wavelength by the following equation:

[0132] υ=c / λ

[0133] Where c is the speed of light and λ is the wavelength of the photon.

[0134] System 10 may include operations that cause the energy difference ΔE between quantum states in short-lived qubits 12 to... S The energy difference ΔE between the quantum states in long-lived qubit 16 and the quantum state is... L Equal or nearly equal institutions. Those skilled in the art will understand that even ΔE S With ΔE LA slight difference exists, and short-lived qubit 12 and long-lived qubit 16 can still participate in quantum interactions (e.g., state transfer or quantum entanglement operations). For convenience, in this disclosure, when two energies are stated as "equal" (e.g., in ΔE...),... S =ΔE L When referring to two energies as equal or matched (e.g., the resonant frequency of a resonator and the frequency of a photon), for the intended purpose (e.g., to excite a photon mode in a resonator), this means that the two energies are exactly equal or sufficiently close to equal.

[0135] Need to make ΔE S With ΔE L How well the quantum states approach or become equal to achieve the desired quantum interaction depends on several factors, such as the coupling strength between the short-lived qubit 12 and the long-lived qubit 16, and the linewidth of the quantized transitions of the short-lived qubit 12 and the long-lived qubit 16. In some embodiments, the energy difference ΔE between the quantum states in the short-lived qubit 12 is... S The energy difference ΔE between the quantum states in long-lived qubit 16 and the quantum state is... L They are equal within 1%, 1 / 2%, or one ten-thousandth.

[0136] In some embodiments, ΔE S With ΔE L They are not equal unless one or both are controlled to achieve ΔE. S =ΔE L For example, this mechanism can adjust ΔE by applying a magnetic field, electric field, or RF control field to the short-lived qubit 12 and / or the long-lived qubit 16 and / or by applying strain to the substrate in which the long-lived qubit 16 is located. S and ΔE L One or both of them.

[0137] System 10 optionally also includes a mechanism for adjusting the coupling between the short-lived qubit 12 and the long-lived qubit 16. For example, this mechanism may include an adjustable resonator that can be adjusted to match or mismatch with a value equal to ΔE. S and ΔE L The resonant frequency of the energy of the photon.

[0138] When ΔE S ≠ΔE L When the coupling between short-lived qubit 12 and long-lived qubit 16 is deactivated in some other way, the quantum states of short-lived qubit 12 and long-lived qubit 16 can evolve substantially independently of each other.

[0139] When ΔE S =ΔE L Furthermore, when the coupling between short-lived qubit 12 and long-lived qubit 16 is sufficient, the quantum states of short-lived qubit 12 and long-lived qubit 16 can be entangled via microwave photons. This diagram illustrates this. Figure 1A middle.

[0140] Figure 1A The diagram schematically illustrates states 12H and 12L of short-lived qubit 12 and states 16H and 16L of long-lived qubit 16. Short-lived qubit 12 can emit photon 19 and transition from state 12H to state 12L. Short-lived qubit 12 can absorb photon 19 and transition from state 12L to state 12H. Long-lived qubit 16 can emit photon 19 and transition from state 16H to state 16L. Long-lived qubit 16 can absorb photon 19 and transition from state 16L to state 16H.

[0141] Since qubits 12 and 16 are quantum systems, in the absence of quantum measurement, a larger system comprising qubits 12, 16, and photon 19 may contain a superposition of states in which either or both of qubits 12 and 16 have emitted photon 19 and states in which either or both of qubits 12 and 16 have absorbed photon 19. The states of qubits 12 and 16 are entangled with each other and with the state of photon 19, the quantum states of the qubits being coupled through the photon.

[0142] The coherent coupling between short-lived qubit 12 and long-lived qubit 16 can be selectively enabled, for example, by adjusting one or more of the following to entangle the quantum states of short-lived qubit 12 and long-lived qubit 16 and / or transfer the quantum state of short-lived qubit 12 to long-lived qubit 16 and / or transfer the quantum state of long-lived qubit 16 to short-lived qubit 12:

[0143] ·ΔE S ;

[0144] ·ΔE L ;and

[0145] • Coupling between qubits 12 and 16.

[0146] In some embodiments, the coupling between the short-lived qubit 12 and the long-lived qubit 16 is facilitated by a resonator 20 having a resonant frequency corresponding to the frequency of microwave photons 19 emitted / absorbed during quantum state transitions between the short-lived qubit 12 and the long-lived qubit 16. For example, the resonator 20 may comprise a piece of superconducting material in a circuit designed to have a resonant frequency corresponding to the photon 19. For example, the resonator 20 may comprise a coplanar waveguide resonator or an LC resonator.

[0147] Resonator 20 can be positioned sufficiently close to each of qubits 12 and 16 to provide a sufficient level of coupling between qubits 12, 16 and each of photons 19 in resonator 20. The capacitive or inductive coupling between superconducting qubit 12 and resonator 20 can have a relatively long range, such that the spacing between qubit 12 and resonator 20 can be, for example, ≥ several micrometers. As another example, the coupling between the quantum dot used as qubit 12 and resonator 20 typically has a much shorter range, such that resonator 20 is optimally located closer to the quantum dot than about 1 μm or closer than 100 nm. The coupling between resonator 20 and long-lived qubit 16 can have a range of several micrometers, in which case resonator 20 can be located within several micrometers of long-lived qubit 16.

[0148] A mechanism can be provided for adjusting the energy gap between the quantum states of a qubit. The properties and construction of the mechanism will depend on the properties of the quantum system on which the qubit is based. For example:

[0149] • In cases where qubits are provided by electron spin, hole spin, or nuclear spin in a magnetic field, the energy difference between the up-spin and down-spin states can be adjusted by changing the magnetic field strength at the position of the electron or atomic nucleus.

[0150] When the qubit is a superconducting qubit, the energy difference between states can be adjusted by modifying the quantized magnetic flux of the superconducting circuit implementing the superconducting qubit. For example, this can be done by changing the capacitance or inductance of the superconducting circuit.

[0151] • When qubits are provided by atoms or defects in a crystal lattice, the energy levels of the qubits can be changed by applying strain to the crystal lattice.

[0152] When qubits are provided by electron spin, hole spin, or nuclear spin in a magnetic field, the energy levels of the qubits can be adjusted by applying an RF driving field. For example, the frequency of the RF driving field can be set within a range such that the photon energy of the RF driving field is at least approximately equal to (e.g., within about 1%, 1 / 2%, or one ten-thousandth) the energy difference between the energy levels of the qubits. The energy levels of the qubits can be changed by adjusting the frequency and / or amplitude of the RF driving field.

[0153] In cases where qubits are provided by electron spin, hole spin, or nuclear spin in a magnetic field, the energy level of the qubit can be adjusted by applying an electric field at the location of the qubit. In some embodiments, the electric field is oriented parallel to the magnetic field.

[0154] When short-lived qubit 12 and long-lived qubit 16 are coupled via coupler 18 as described above, energy can be transferred back and forth between them via photons 19. This probability of energy transfer causes an oscillation in the probability density function, which indicates the probability of finding the short-lived qubit 12 in a particular quantum state (e.g., 12H or 12L). This oscillation occurs at a so-called two-qubit Rabi frequency, dependent on the coupling between the short-lived qubit 12 and the long-lived qubit 16.

[0155] The Rabi frequency can be determined in advance. The Rabi frequency of two qubits can be measured during the calibration procedure. For example, the calibration procedure may include: initializing the long-lived qubit 16 and the short-lived qubit 12 to a known quantum state, connecting the coupling for a certain time 'tau', disconnecting the coupling, and then independently measuring both qubits 12 and 16. By repeating this measurement sequence for different values ​​of tau, the following can be obtained: Figure 2 The graph shown herein allows for the easy determination of the Rabi frequency. The Rabi frequency determined through a calibration process can be stored in a data storage device for future use. For example, the data storage device may include a memory location accessible via control circuitry connected to control the coupling between the long-lived qubit 16 and the short-lived qubit 12 using any of the mechanisms described herein.

[0156] Figure 2 It is a graph showing the probability density of short-lived qubit 12 being in the higher energy level of two non-degenerate binary quantum states (curve 22A) and the probability of long-lived qubit 16 being in the higher energy level of two non-degenerate binary quantum states (curve 22B).

[0157] exist Figure 2At time 0, short-lived qubit 12 is in its higher-energy quantum state and long-lived qubit 16 is in its lower-energy quantum state. This can be achieved by performing quantum measurements at time 0 or by manipulating the states of qubits 12 and 16. At time 0, system 10 is configured to couple the states of short-lived qubit 12 and long-lived qubit 16.

[0158] The probability density represented by curve 22A cycles with a period T. At time T / 2, the long-lived qubit 16 has a high probability of being in its higher energy state, and the short-lived qubit 12 has a low probability of being in its lower energy quantum state. Essentially, the quantum state of the short-lived qubit 12 has been transferred to the long-lived qubit 16, and vice versa.

[0159] Figure 2 The principle illustrated in the diagram also applies to other quantum states of short-lived qubit 12 and long-lived qubit 16, as well as their superposition.

[0160] As described above, the state of short-lived qubit 12 (which may be a superconducting qubit) can be transferred to long-lived qubit 16 (e.g., which may be a spin qubit), stored in long-lived qubit 16 for a period of time longer than the lifetime of short-lived qubit 12, and then returned to short-lived qubit 12 for further processing.

[0161] Figure 3 The diagram illustrates a method 30 for extending the lifetime of a quantum state of a short-lived qubit 12. In block 32A, the short-lived qubit 12 is placed in a desired quantum state. The quantum state may be a superposition of a higher-energy state and a lower-energy state. For example, block 32A may include performing quantum computation in a quantum computer, where the short-lived qubit is part of the quantum computer.

[0162] In block 32B, a short-lived qubit is coupled to a long-lived qubit 16, for example, via coupler 18 as described above. For instance, block 32B may include adjusting the energy difference ΔE between the higher and lower energy quantum states of the long-lived qubit 16. L And / or adjust the energy difference ΔE between the higher and lower energy quantum states of short-lived qubit 12. S To achieve ΔE S =ΔE L .

[0163] In block 32C, the coupling between short-lived qubit 12 and long-lived qubit 16 is maintained for a time τ equal to an odd number N (N = 1, 3, 5, ...) half-cycles T / 2 (e.g., half a cycle) of the Rabi period, and then the coupling is interrupted (e.g., by adjusting ΔE). S and ΔE LOne or both of them make ΔE S ≠ΔE L And / or by changing the resonant frequency of resonator 20 to interrupt coupling). The time τ is significantly shorter than the decoherence time of the short-lived qubit 12.

[0164] The time τ for maintaining the coupling between short-lived qubit 12 and long-lived qubit 6 can be controlled by a timer that uses a stored value determined in the calibration step, equal to or derived from the two-qubit Rabi frequency of a specific pair of short-lived qubit 12 and long-lived qubit 16, to set the time for maintaining the coupling.

[0165] At the end of box 32C, the desired quantum state of short-lived qubit 12 has been transferred to long-lived qubit 16.

[0166] In block 32D, a time period has elapsed. This time period may be longer than the decoherence time of the short-lived qubit 12. The time period may be shorter than the decoherence time of the long-lived qubit 16. In some embodiments, the time period may be longer than 10 μs, 100 μs, 1 s, or 1 minute.

[0167] In block 32E, the short-lived qubit 12 is coupled to the long-lived qubit 16 again, for example, via coupler 18 as described above. For instance, block 32E can operate in the same manner as described herein for block 32B.

[0168] In block 32F, the coupling between short-lived qubit 12 and long-lived qubit 16 is maintained for an odd number (N = 1, 3, 5, ...) half-cycles T / 2 of the Dalabi period and then the coupling is broken. For example, block 32F can be performed as described above for block 32C.

[0169] At the end of box 32F, short-lived qubit 12 has been restored to the desired quantum state.

[0170] Figure 4 This diagram illustrates a possible simplified physical structure of a system 40 that provides short-lived qubits 12 and long-lived qubits 16 that can be selectively coupled and decoupled to perform method 30 or other similar methods. System 40 includes a silicon substrate 42. Substrate 42 is preferably purified silicon 28 (i.e., silicon with more than 92.23% silicon 28). In one embodiment, the material of substrate 42 is at least 96%, 99%, 99.5%, or 99.9% (by atomic number) silicon 28.

[0171] The light-emitting center 43 in the substrate 42 can provide long-lived qubits 16. For example, the light-emitting center may include a light-emitting center selected from the following: defects, such as T centers, I centers or M centers, or nitrogen-carbon centers, or Al1 or Ga1 centers, or radiation-damaged centers with unpaired ground-state spin; or impurities, such as atoms of selenium or tellurium or sulfur or other dual donor impurities.

[0172] A superconducting structure 44 supported on substrate 42 can provide short-lived qubits 12. Structure 44 may include a patterned layer of a metal that is superconducting at low temperatures and has been deposited on substrate 42. For example, the layer may include a superconducting circuit containing a Josephson junction. An electrically insulating layer 45 may be present between the superconducting structure 44 and the bulk of substrate 42 in which the light-emitting center 43 is located.

[0173] A portion 44A of the superconducting structure 44 provides a coupler (which performs the function described above for coupler 18), said portion being designed to provide resonance at a frequency corresponding to an energy, allowing the energy difference ΔE to be... S and ΔE L Both are equal to the energy. For example, portion 44A may include a superconducting material tab in a circuit having a resonant frequency in the microwave range. Portion 44A may be physically superimposed on the luminescent center 43.

[0174] The luminescent center 43 should be sufficiently spaced from the portion 44A to couple to the electric or magnetic field components of the photons in the portion 44A. For coupling to the electric field, the luminescent center 43 should have a non-negligible capacitance to the portion 44A. In some embodiments, the luminescent center 43 is spaced from the portion 44A by a distance of approximately 1 μm or less, or approximately 100 nm or less. Preferably, the portion 44A is aligned with the crystal axis relative to the substrate 42, such that the electric or magnetic field of the photon mode in the portion 44A is well coupled to the luminescent center 43. In some embodiments, the magnetic field of the photon mode is not parallel (e.g., orthogonal) to the external magnetic field applied to the luminescent center 43.

[0175] Figure 4 An adjustable magnet 46 is also shown, operable to alter the magnitude of the magnetic field at the location of the luminescent center 43 (and thus change the energy difference between the upper and lower spin states of the spin (e.g., the electron spin used to provide the long-lived qubit 16)). A control circuit 46A is connected to control the adjustable magnet 46 (e.g., to turn the coupling between the long-lived qubit 16 and the short-lived qubit 12 on and off). One or more permanent magnets 46B near the luminescent center 43 can enhance the magnetic field from the adjustable magnet 46. The magnets 46B may be deposited on, in, or near the substrate 42.

[0176] It is generally beneficial to minimize the transverse component of the magnetic field generated by magnets 46 and 46B that is perpendicular to the plane of the superconducting structure 44. This is because the critical magnetic field of a thin-film superconductor (i.e., the magnetic field strength above which the superconductor no longer conducts superconductivity) is generally much lower for the transverse (vertical) magnetic field than for the field in which the field lines are parallel to the superconducting structure 44.

[0177] Figure 4 Also shown is a coil 47 that can be driven by an RF signal source 47A to manipulate the quantum state of the long-lived qubit 16 via a resonant effect (e.g., electron spin resonance – “ESR”) known to those skilled in the art. The RF signal source can be controlled to generate radiation pulses (e.g., pi pulses or pi / 2 pulses) that, when delivered, manipulate the quantum state of the long-lived qubit 16.

[0178] Figure 4 A suitable light source 48 is also shown, arranged to illuminate the location of the long-lived qubit 16. For example, the light source 48 may emit light with a wavelength corresponding to an optical transition of the long-lived qubit 16 (e.g., exciton formation). For example, the long-lived qubit 16 may include excitons in crystal defects (e.g., T-centers). The light source 48 may be operated to form excitons by emitting light pulses of appropriate wavelengths. Quantum information may then be stored in the excitons, for example, as the spin state of the excitons. For example, the light source 48 may include a laser. The laser may be tunable to emit light with wavelengths corresponding to different optical transitions of the long-lived qubit 16.

[0179] The substrate 42 is housed within a cryostat 49 capable of achieving a low temperature that enables the structure 44 to become superconducting. In some embodiments, the operating temperature of the structure 44 may be extremely low (e.g., several mK or several Kelvin).

[0180] In addition to storing quantum information or as an alternative to storing quantum information, the system described herein can also be used as a path for transmitting quantum information to or from a quantum information processing system in which the short-lived qubit 12 is part, and / or as a mechanism for generating visible photons representing the quantum state of the short-lived qubit 12.

[0181] Figure 5 The schematic diagram illustrates a device 50 of an example embodiment in which a long-lived qubit 16 is connected to an external system 54 via a quantum communication path 52.

[0182] For example, quantum information path 52 may carry quantum information in the form of visible photons. For example, quantum information path 52 may include a waveguide 53 capable of carrying photons that carry quantum information. In some advantageous embodiments, the visible photons have wavelengths in the range of about 1.3 μm to about 1.7 μm or about 1 μm to about 3 μm.

[0183] Quantum information path 52 can be coupled to long-lived qubit 16 via optical resonator 55 located close to long-lived qubit 16. To facilitate coupling of long-lived qubit 16 to visible photons in optical resonator 55, long-lived qubit 16 should have available quantum states with energy levels separated by an energy difference corresponding to the energy of the visible photon. In this case, long-lived qubit 16 can undergo permitted transitions in which it emits or absorbs visible photons.

[0184] In some cases, photons emitted or absorbed in different permissible transitions of the long-lived qubit 16 may have different polarizations. In these cases, the polarization of the emitted photon can encode the quantum state of the long-lived qubit 16 from which the photon was emitted. In some cases, the long-lived qubit 16 becomes entangled with a photon having a specific polarization state, and therefore, quantum information represented by the spin state of the qubit 16 can be accessed via the polarization state of the entangled photon.

[0185] Figure 6 A simplified example structure of the energy levels of a long-lived qubit 16 is shown. For example, levels 16H and 16L can correspond to unpaired spin-up and spin-down states (e.g., of electrons or holes), such that levels 16H and 16L can be the result of hyperfine splitting caused by the interaction between the nuclear spin and electron spin at the location of the long-lived qubit 16. The energy difference between levels 16H and 16L can correspond to the energy of a photon at a microwave wavelength.

[0186] The long-lived qubit 16 also possesses states 17H and 17L, which correspond to unpaired spin-up and spin-down states (e.g., electrons or holes), respectively. States 17H and 17L can be associated with states 16H and 16L via orbital transitions or exciton transitions, respectively. The energy difference between states 17H and 16H, or between states 17L and 16L, corresponds to the energy of a photon at a light wavelength.

[0187] like Figure 6 As shown, the energy difference ΔE1 between states 16H and 17H is different from the energy difference ΔE2 between states 16L and 17L. In some embodiments, the difference between ΔE1 and ΔE2 corresponds to a frequency difference of at least about 1 MHz (i.e., about 6.6 × 10⁻⁶). -28 J). This creates opportunities for visible photons, depending on whether the unpaired spin is up- or down-spin, which may or may not interact with the long-lived qubit 16.

[0188] For example, when a visible photon 66 with a wavelength corresponding to an energy equal to ΔE1 is provided, the long-lived qubit 16 can absorb one of the photons 66 and transition from state 16H to state 17H. The long-lived qubit 16 can then transition from state 17H ​​to state 16H and emit a photon 66 with the same energy ΔE1.

[0189] However, since the long-lived qubit 16 is a quantum system, it does not necessarily need to be in a definite quantum state. Instead, the long-lived qubit can be in a superposition of states. Furthermore, the long-lived qubit 16 and the visible photon 66 can coexist in a superposition of states in which the long-lived qubit 16 has already interacted with or has not yet interacted with the photon. In general, the quantum states of the quantum system consisting of the long-lived qubit 16 and the visible photon 66 encompass a wide variety of possible interactions between them. Therefore, the quantum states of the long-lived qubit 16 and the visible photon 66 can be entangled.

[0190] As seen, for example Figure 6 The energy structures illustrated herein can be used to couple long-lived qubits 16 to other quantum objects via either microwave photons or visible photons. This property can be used to store quantum information from a selected source among multiple sources in the long-lived qubits 16 and / or to transfer quantum information from the long-lived qubits 16 to one or more selected destinations. This property can also be used to convert quantum information from microwave photons to visible photons and / or from visible photons to microwave photons via the long-lived qubits 16.

[0191] Long-lived qubit 16 can be coupled to microwave photons and / or short-lived qubit 12 via various mechanisms. These include:

[0192] • Coupling via electric field; and

[0193] • Coupled via magnetic field;

[0194] Some embodiments have physical configurations that optimize one or more of these coupling mechanisms.

[0195] In some embodiments, the coupling facilitates electronic dipole spin resonance (“EDSR”) interactions.

[0196] The long-lived qubit 16 can be coupled to the electric field component of the microwave photon. To optimize the electric coupling, the microwave photon can exist as a standing wave mode in the resonator, wherein the standing wave mode has one or more antinodes with maximum electric field strength. The long-lived qubit 16 can be located very close to the antinode with maximum electric field strength (e.g., within a few micrometers of the antinode).

[0197] According to Figure 6A In the illustrated example embodiment of the device 60, microwave photons may be present in a metallic resonator structure 61 on a silicon layer 63. An electrically insulating layer 62 (e.g., a silicon dioxide layer) separates the resonator structure 61 from the layer 63. The microwave photons in the resonator structure 61 have a standing wave mode in which the electric field strength is maximized at the antinode 64. Long-lived qubits 16-1 are located in or on the silicon substrate 63 near node 64.

[0198] The electric field interaction has a sufficiently long range that, in some embodiments, the long-lived qubit is coupled to the electric field of a photon not in the resonant cavity (e.g., a photon in the optical waveguide close to the long-lived qubit 16).

[0199] The long-lived qubit 16 can be coupled to the magnetic field component of microwave photons. To optimize electromagnetic coupling, the microwave photons can exist as standing-wave modes in the resonator, wherein the standing-wave modes have one or more antinodes with maximum magnetic field strength and / or one or more antinodes with maximum electric field strength. For example, the long-lived qubit 16 can be located very close to the antinodes with maximum magnetic field strength (e.g., within a few micrometers). Figure 6A Long-lived qubits 16-2 are shown located in or on a silicon substrate 63, close to an antinode 65, where the magnetic field strength of the standing wave mode is maximized.

[0200] In some embodiments, resonator structure 61 includes a coplanar waveguide (“CPW”) resonator. The CPW resonator may include a coplanar waveguide having signal pins segmented into short pillars capacitively coupled to a signal feed line. The CPW resonator may support standing wave resonance at frequencies depending on the length of the short pillars. Antinodes of the electric field are located at the ends of the short pillars.

[0201] In some embodiments, the resonator structure 61 has a quality factor (“Q factor”). The Q factor is the ratio of the center frequency of the resonator to the bandwidth of the resonator. In some embodiments, the resonator structure 61 has a quality factor of at least 10. 5 Or at least 10 6 The Q factor.

[0202] symbol Indicates a quantum state, where the electron (or hole) represented by the first arrow is down-spin and the nucleon represented by the second arrow is up-spin.

[0203] Spin transitions can occur in systems in which bound excitons can form. Quantum number 0 indicates an unbound exciton, and quantum number 1 indicates the presence of a bound exciton. In the notation indicating the quantum state of a system that can contain exciton states, electron (or hole) spin states, and nuclear spin states, the exciton quantum number may be followed by the electron (hole) spin, and the electron (hole) spin may be followed by the nuclear spin. For example, the notation... The indicator quantum state contains a bound exciton, where the hole is downspin and the nucleus is upspin. Figure 6B Use this symbol in the right-hand column.

[0204] exist Figure 6B In the system illustrated in the diagram, after absorbing energy ΔE A Photons can form bound excitons. At the T center, ΔE A This corresponds to a photon wavelength of approximately 1326 nm. Bound excitons can be formed by guiding light of this wavelength to the center of T. When bound excitons are present, Figure 6B The higher energy levels 67A, 67B, 67C, and 67D shown on the right are available. When no bound excitons are present, only the lower energy levels 66A, 66B, 66C, and 66D are available. It is possible for the T-center to be in a superposition of states containing bound excitons and another state without bound excitons.

[0205] Figure 6B Transitions between any of the energy levels on the right-hand side are possible. These transitions can be classified as follows:

[0206] • Transitions that flip electron or hole spins but not nuclear spins (e.g., electron paramagnetic resonance (EPR) transitions). Transitions 69C1, 69C2, 69D1, and 69D2 are examples of transitions in which only electron or hole spins are flipped;

[0207] • Transitions that flip nuclear spin but not electron spin (e.g., nuclear magnetic resonance (NMR) transitions). Transitions 69C3, 69C4, 69D3, and 69D4 are examples of transitions that only flip nuclear spin;

[0208] • Cross transitions in which both electron or hole spin and nuclear spin are flipped. (e.g., the EDSR transition). Transitions 69C5, 69C6, 69D5, and 69D6 are examples of cross transitions.

[0209] Transitions between states containing bound excitons and states not containing bound excitons are also possible (e.g., transitions from one of states 66A, 66B, 66C, 66D to one of states 67A, 67B, 67C, 67D).

[0210] In quantum systems containing multiple nuclear spins (e.g., T-centers), the energy levels of transitions are generally different for different nuclear spins. A specific available nuclear spin can be selected to quantum interact with another qubit via a chosen transition described above by coupling the nuclear spin to the other qubit as described herein, such that transitions between the quantum states of the other qubit involve an energy difference matching the energy difference of the selected transition.

[0211] In a quantum system with unpaired electrons and supporting bound exciton states (e.g., a T-center), quantum information can be stored in the unpaired electrons or in the holes of the bound excitons. As described below, the energy difference for transitions involving holes differs from the energy difference for transitions involving electrons. Quantum interaction between a selected electron or hole spin and another qubit can be achieved by coupling the system containing the electron or hole to the other qubit, as described herein, such that transitions between the quantum states of the other qubit involve energy differences matching the energy difference of the selected transitions of the electron or hole.

[0212] The transitions 69C1, 69C2, 69C3, 69C4, 69C5, 69C6, 69D1, 69D2, 69D3, 69D4, 69D5, and 69D6 can be used to encode quantum information using electron or hole spin, nuclear spin, or a combination of both or more of these. These transitions correspond to energies ΔE, respectively. C1 ΔE C2 ΔE C3 ΔE C4 ΔE C5 ΔE C6 ΔE D1 ΔE D2 ΔE D3 ΔE D4 ΔE D5 and ΔE D6 With respect to center T, these energies correspond to ΔE. C5 ΔE C6 ΔE D5 and ΔE D6 With frequencies ranging from approximately 1 MHz to 100 MHz and targeting ΔE C1 ΔE C2 ΔE C3 ΔE C4 ΔE D1 ΔE D2 ΔE D3 and ΔE D4 Photons with frequencies ranging from approximately 1 GHz to approximately 100 GHz.

[0213] In some embodiments, the nuclear spin and electron or hole spin at the T center are initialized to a known quantum state. For example, the spin can be set to the desired state by optically pumping the spin to the desired energy level and / or by applying a pulse to flip the spin (“pi pulse”). For example, the initial state may be... Subsequently, the center of T is coupled to a point that may contain energy ΔE. C1 The waveguide for photons. The coupling can be achieved by controlling the wavelength of the photons and controlling ΔE. C1 And / or control of the coupling mechanisms described elsewhere in this document to achieve this.

[0214] Photons can lead to a state The transition occurs. Photons can exist in a superposition of states (e.g., presence and absence). As a result, a system of nuclear spin and electron or hole spin can ultimately be in a state that encodes quantum information based on photon states. and A specific superposition. If a photon is coupled to the luminescent center via a cross-transition, then upon absorption or emission of the photon, both the nuclear spin and the electron or hole spin immediately flip. These transitions can therefore be used to generate states. and A specific superposition. As part of the entangled state, the nuclear spin, when considered alone, is in the state of... and Spin mixing.

[0215] Another example utilizes driven transitions to store quantum states in the nuclear spin at the center of T or in other crystal defects containing both nuclear spin and electron or hole spin. In this example, the electron or hole spin is initially in a specific quantum state (e.g., spin up, spin down, or a superposition of spin up and spin down). For instance, the quantum state of the electron or hole spin can be set by causing quantum state transfer between a short-lived qubit and the electron or hole spin, as described elsewhere herein.

[0216] If desired, the available nuclear spins can be initialized to a known state, such as downspin or upspin. The T-center can then be illuminated by photons from an external source (e.g., a laser) having a wavelength matching the energy of the spin transitions involving the nuclear spins. In some cases, the transitions are cross-transitions involving both electrons and holes. In the T-center or other crystal defects where multiple nuclear spins exist, the energy of the photons illuminating the T-center can be used to select which of the nuclear spins undergoes a quantum interaction with the electron or hole spin. Photons can be provided in the form of coherent pi pulses. Using transitions triggered by pi pulses is an efficient way to store electron or hole spin states using nuclear spins.

[0217] In EDSR, transitions occur where both electron spin and nuclear spin flip. (In terms of state...) The initial EDSR transition will generate a state. EDSR transitions advantageously couple strongly to an electric field. Some embodiments utilize EDSR transitions to transfer the quantum state of an electron spin to a nuclear spin state and / or to transfer the quantum state of a nuclear spin to an electron or hole spin state and / or to entangle the quantum states of electron or hole spins with those of the nuclear spin. In some such embodiments, the nuclear spin and the electron or hole spin are located at the T-center.

[0218] This invention describes and explains various ways of using electron spin by coupling the quantum state of electron spin with the quantum state of nuclear spin. Generally, in the presence of a bound exciton containing a hole spin, the hole spin can be coupled to the nuclear spin in the same manner described herein, except that the energy level of the hole spin in the bound exciton will typically be different from the energy level of the electron spin.

[0219] The primary reason for the difference in energy levels between electron and hole spins is that, depending on the environment of the hole, the g-factor of the hole can differ from that of the electron by as much as a factor of at least two (e.g., when the g-factor of the electron is 2, the g-factor of the hole can range from about 1 to 4, depending on the environment). Energy levels typically expand and contract roughly linearly with respect to the g-factor. The same mechanism described herein for changing ΔE to flip the spin of the electron can also be applied to changing ΔE to flip the spin of the hole.

[0220] As another example, energy ΔE can be used. C5 Photons to use jumps arrive By controlling the wavelength of the photon and controlling ΔE C5 And / or control the coupling mechanisms described elsewhere in this document to achieve coupling.

[0221] Figure 7A and 7B A schematic diagram illustrates a system 70 in which long-lived qubits 16 are arranged to couple to visible photons 66. System 70 has... Figure 4 The system 40 shares common components. (See Figure 7 for examples.) Figure 4 The same references in the text mention these elements.

[0222] In system 70, long-lived qubits 16 are provided by a light-emitting center 43 located in or very close to the optical resonator 72. The optical resonator 72 is designed to have energies corresponding to ΔE1 or ΔE2 (see [link to system 70]). Figure 6 The resonant frequency of the photon. Advantageously, the long-lived qubit 16 can be located at the mode maximum of the intrinsic optical electric field of the optical resonator.

[0223] The optical resonator 72 can have any suitable structure. Various designs of optical resonators are known. The system 70 can incorporate any optical resonator suitable for integration with the substrate 42 containing the light-emitting center 43. Figure 7A In this embodiment, optical resonator 72 includes a ring resonator. For example, resonator 72 can be fabricated as described in Tait et al. arXiv:2001.05100, which is hereby incorporated herein by reference for all purposes. For example, a micro-ring resonator can be fabricated on a silicon-on-insulator (SOI) platform comprising a thin (e.g., ~200 nm to 500 nm thick) silicon layer (ideally, silicon-28). The silicon-28 layer can be formed on a thicker (e.g., ~3 μm thick) silicon oxide layer on a host silicon wafer (which may have a natural isotopic concentration of silicon). In some embodiments, photons at or very close to the resonant frequency of resonator 72 have a whispering-gallery mode.

[0224] The optical resonator 72 is optically coupled to the optical waveguide 74, whereby visible photons 66 can be introduced into or transported from the resonator 72 to other locations.

[0225] The long-lived qubit 16 has a position and orientation selected to allow sufficient coupling between the photon 66 and the long-lived qubit 16. For example, in some embodiments, the long-lived qubit 16 is located on an axis corresponding to the center of the micro-ring resonator and extending perpendicular to the plane of the micro-ring resonator. In some embodiments, the long-lived qubit 16 has a depth of 500 nm or less from the material interface. In some embodiments, the long-lived qubit 16 has a depth approximately halfway through the silicon-on-insulator (SiI) device layer.

[0226] The coupling between the long-lifetime qubit 16 and the photon 66 in the optical resonator 72 can be adjusted by controlling ΔE1 or ΔE2 and / or the resonant frequency of the optical resonator 72 so that the optical frequency of the optical resonator 72 is closely matched with one of ΔE1 and ΔE2.

[0227] For example, ΔE1 and ΔE2 can be adjusted by changing the intensity of the electromagnetic field at the location of the long-lived qubit 16. In the illustrated embodiment, this is achieved by controlling the power supply 75 to apply a potential difference between portion 44A and electrical conductor 75A.

[0228] For example, the resonant frequency of resonator 72 can be adjusted by the following operation:

[0229] • For example, by manipulating a microelectromechanical system (MEMS), the optical properties of the boundary of the resonator 72 can be changed;

[0230] • Change the structural properties, for example, by introducing a gas attached to the boundary of the resonator 72 and altering its interaction with the photon 66;

[0231] • The resonator 72 is strained by applying force to the substrate 42 or to the resonator 72 itself.

[0232] • Change the driving strength and / or the coupling of the long-lifetime qubit 16 to the resonator 72 to take advantage of the nonlinear effects in the resonator 72.

[0233] • Apply an electromagnetic field to the resonator 72.

[0234] • Change the temperature of resonator 72.

[0235] In some embodiments, the resonant frequency of the optical resonator 72 encompasses a frequency range including ΔE1 or ΔE2.

[0236] System 70 employs a quantum transition having an energy difference corresponding to a frequency used for coupling to visible photons 66 within the optical range. For example, this transition may include an orbital transition or a transition that forms an exciton. The transition affects the quantum states (e.g., electron spin, hole spin, nuclear spin, spin combination, excitons) of the quantum system in which quantum information is stored. The transition can cause the quantum state of the long-lived qubit 16 to become entangled with the photon state in the optical resonator 72.

[0237] In some embodiments, the long-lived qubit 16 comprises a plurality of quantum particles that can individually or collectively store quantum information. For example, the long-lived qubit 16 may include both electron or hole spins and at least one nuclear spin. The nuclear spin may have a longer coherence time than the electron or hole spin. Storing the quantum state of the superconducting qubit 12 as the quantum state of the nuclear spin may be desirable.

[0238] In some embodiments, quantum state transfer is used to cause the state of the superconducting qubit to be transferred to the quantum state of the nuclear spin. An example of doing this is to transfer the quantum state of the superconducting qubit 12 to the quantum state of the electron or hole spin, as described above, and then transfer the quantum state of the electron or hole to the quantum state of the nuclear spin.

[0239] Quantum interactions can be induced using methods similar to the state transfer process described above, such as state transfer or entanglement between long-lived spin qubits and short-lived superconducting qubits. For example, both the spin qubit and the superconducting qubit can be prepared to enter appropriate eigenstates. Then, they can be coherently interacted using the methods described above, thereby producing a state transfer or entanglement similar to... Figure 2The two qubits exhibit Rabi oscillations are shown in the diagram. If this interaction ceases after an odd number of half-Rabi cycles, then state transfer is achieved. Alternatively, if the interaction ceases after (N / 2 + 1 / 4) Rabi cycles, where N is an integer, then an entangled state is generated between the two qubits.

[0240] The quantum state of superconducting qubit 12 can be transmitted over long distances to visible photons using electron spin or hole spin qubits. For example, the electron spin of a long-lived qubit can be entangled with an incident photon by initializing an electron to an up-spin state and allowing it to interact with one of two photons in an entangled pair. This interaction transmits the entanglement to the electron spin, thus forming a spin-photon entangled state. The electron spin can then be entangled with superconducting qubit 12 using a method similar to that described above. After this entanglement is established, joint measurements can be performed on superconducting qubit 12 and the electron spin qubit in a Bell state (entanglement) basis. The results of those measurements can be applied to select an operation to be performed on a second photon from the original entangled pair to “feed forward” the state of superconducting qubit 12 to the photon qubit. For example, the measurement results can be supplied to classical control electronics that can look up the feedforward operation in a lookup table and then control circuitry to implement the feedforward operation. The photonic qubit can then transmit the quantum information to a distant electron spin qubit, which in turn can transmit the state to a distant superconducting qubit.

[0241] The entanglement of the long-lived qubit 16 with the visible photon 66 facilitates the coupling of the long-lived qubit 16 to an external system. Visible photons possess energy significantly higher than the thermal energy at room temperature (approximately 26 meV - kJ / kWh). B T is given, where k B (Where T is the Boltzmann constant and is the temperature in Kelvin). For example, the energy of a near-infrared visible photon with a wavelength of 1 μm is approximately 1.2 eV. In this example, the visible photon has more than 40 times the energy of room temperature heat. Therefore, visible photons 66 can be transported outside a cryostat where long-lived qubits 16 are located without being excessively affected by thermal noise. Long-distance transport of photons 66 is possible using suitable optical fibers or other known photon transport mechanisms.

[0242] This mechanism can be used to form entanglement between a long-lived qubit 16 and one, two, or more other qubits that may be located away from qubit 16. In some embodiments, the other qubits with which the long-lived qubit 16 is caused to become entangled are other long-lived qubits 16 described herein. The long-lived qubit 16 can be identical. For example, the entangled long-lived qubit 16 can be a T-center.

[0243] In the above description, the long-lived qubit 16 has been described as being provided by a single luminescent center (e.g., an impurity atom or crystal defect). This is possible, but not required. In any embodiment, the long-lived qubit may be provided by multiple identical or nearly identical luminescent centers. Some advantages of this are better coupling to photons and the need for less precise placement of individual luminescent centers. A collection of long-lived qubits 16 can be effectively represented as a single, strongly coupled long-lived qubit 16.

[0244] As an example of the effective use of a long-lived qubit set as a single long-lived qubit, in some embodiments, a plurality of long-lived qubits 16 are located in or closely adjacent to an optical resonator 72. For example, the plurality of long-lived qubits 16 may include a T-center. For example, the plurality of long-lived qubits 16 may be located within the ring of an optical ring resonator at the mode maximum of the photon's optical electric field at the resonant frequency of the ring resonator.

[0245] In some embodiments, long-lived qubits are composed of 1 to about 10 5 The number of luminescent centers ranges from approximately 1 to 2000 or from approximately 40 to 1000. The coupling of photons to a set of N identical long-lived qubits often varies. The number N increases. However, the larger the number N, the more difficult it becomes to make the long-lived qubits behave identically or nearly identically. If the long-lived qubits behave differently, then the coherence time of the ensemble can be reduced. For larger values ​​of N, a larger number of spaced-apart long-lived qubits can have a wider environmental range and can be exposed to the field at locations with different intensities of the field of the photons they are coupled to, compared to a smaller number of long-lived qubits. Therefore, N can be chosen to be large enough to obtain the desired coupling strength of the photons (microwave or visible photons) while still having a sufficiently long coherence time for the given application.

[0246] In cases where it is desirable to use a set of luminescent centers for long-lived qubits, it is advantageous to make the luminescent centers identical to each other and to place them such that the strength of the magnetic or electric field through which the luminescent centers couple to photons is similar for all luminescent centers contained in the long-lived qubit 16.

[0247] A defect center (e.g., a T-center) may have any of several orientations relative to the lattice in which it is located. For example, a T-center may have any of 12 orientations. In some embodiments, defect centers with multiple different orientations are included in a set that provides long-lived qubits. In some embodiments, defect centers with certain selected orientations are excluded from the set that provides long-lived qubits. For example, this can be done by selectively shifting the energy levels of defect centers with selected orientations so that these defect centers cannot couple to photons that can be coupled to by defect centers included in the set. The energy levels can be shifted for the selected orientation of the defect centers, for example, by straining the lattice along the selected orientation.

[0248] Figure 8 The schematic diagram illustrates an example architecture of a quantum computer system 80 consisting of multiple modules 82 (illustrating modules 82-1, 82-2 to 82-N). According to any embodiment described herein, each module 82 includes a freezer 82A that cools a quantum computing subsystem 82B comprising one or more short-lived qubits 12, each coupled to a corresponding long-lived qubit 16. Modules 82 may include other environmental control systems, such as high-vacuum systems, electromagnetic radiation shielding, and vibration isolation, as needed. The short-lived qubits 12 may be part of a quantum information processing system 13, which includes other qubits, devices for manipulating the quantum states of the qubits, information for coupling the qubits in different ways, etc. In the illustrated example, the long-lived qubit 16 is coupled to the short-lived qubit 12 via a microwave resonator 20.

[0249] The photon carrier 84 extends between a long-lived qubit 16 in one module 82-1 and a long-lived qubit in another module 82-2. For example, the photon carrier 84 may include optical fibers, optical waveguides, optical systems consisting of optical elements (e.g., mirrors, lenses, refractive elements, etc.) that guide photons 56 through free space. The photon carrier 84 provides a path through which photons 56 can travel near a long-lived qubit 16, exit a freezer 82A containing the first long-lived qubit 16, travel to a freezer 82A containing a second long-lived qubit 16, enter the freezer containing the second long-lived qubit 16, and interact with the second long-lived qubit 16. This mechanism allows the quantum states of the first and second long-lived qubits 16 to become entangled. The photon carrier 84 may optionally be connected to carry photon states to multiple destinations that co-load multiple remote qubits, such that the long-lived qubit 16 can be simultaneously entangled with multiple remote qubits through the visible photon states in the photon carrier 84.

[0250] In some embodiments, any module 82 may include two or more long-lived qubits 16 coupled to one or more other modules 82. In these embodiments, a single photon may entangle two, three, four or more long-lived qubits 16, some or all of which may be in different modules 82.

[0251] The general architecture of system 80 is advantageous because it allows the qubits of the quantum computer (e.g., short-lived qubits 12) to be distributed among multiple cryovials 82A. This is beneficial because making cryovials large enough to house large quantum computers while simultaneously cooling the components of the quantum computer to the necessary cryogenic temperatures presents extreme difficulties and operational challenges. Furthermore, the possibility of having photon carriers 84 of extended length in system 80 can be used to widely distribute modules 82. For example, system 80 can be used to securely distribute quantum information among widely distributed modules 82.

[0252] In the embodiments discussed above, it has been found that the T center can be advantageously used as a long-lived qubit 16. Figure 9 The diagram illustrates the structure of the T-center 90. The T-center is where a silicon atom in the silicon crystal has been replaced by two carbon atoms 91A and 91B, and a hydrogen atom 92 bonded to carbon atom 91B. Carbon atom 91A possesses one unpaired electron. The spin state of the unpaired electron of carbon atom 91A can be used as a long-lived qubit 16.

[0253] The T-center can also be loaded with bound excitons. Several bound excitons (e.g., 0 or 1) can be used as long-lived qubits 16. The spin state of holes in the bound excitons can also be used as long-lived qubits 16 or as intermediate states for encoding quantum information with nuclear spin.

[0254] Bound excitons can be formed and destroyed so that they exist only when needed. Excitons can be used to receive quantum information from external sources (e.g., visible or microwave photons) and transmit said quantum information to spin manifolds (e.g., nuclear spin) with extremely long coherence times containing quantum information. The wavefunction of holes in bound excitons has a relatively large spatial range, which facilitates the coupling of hole spin to photons, as described elsewhere herein.

[0255] The T-center possesses the following properties that make it particularly suitable for use as a long-lived qubit 16:

[0256] • The T-center exhibits long spin coherence times (>2.1 ms electron spin and >1 s nuclear spin);

[0257] • The T-center has a narrow optical linewidth (<30MHz);

[0258] • The T-center can couple to O-band photons (containing a wavelength of approximately 1326 nm);

[0259] • The T-center can provide multiple (e.g., 4) accessible spin manifolds;

[0260] • The T center is weakly but controllably coupled to the lattice strain;

[0261] • The center of T is weakly but controllably coupled to the electric field;

[0262] The T-center can support excitons that can be used to store quantum information (e.g., in hole spin).

[0263] T-centers can be formed in a silicon substrate by irradiating it with high-energy carbon and high-energy hydrogen. This irradiation is followed by high-temperature annealing to achieve T-center formation. In some embodiments, T-centers are formed at desired locations by applying a hard mask to the silicon substrate and irradiating the desired locations within the silicon substrate through the apertures in the hard mask.

[0264] As mentioned above, the T-center has several accessible spin manifolds. These include:

[0265] • An unpaired electron spin;

[0266] • A spin exciton hole (if an exciton is present);

[0267] • A hydrogen nucleus spin; and

[0268] • Two carbon nuclei with spins.

[0269] Quantum information may be stored in the quantum state of any of these spins.

[0270] Quantum information can be stored in any of the nuclear spin manifolds. This can be accomplished through various methods. These methods can be applied to store the same or different quantum information in each of two or more of the nuclear spin manifolds. In some embodiments, quantum information from microwaves or visible photons is encoded in the quantum state of the electron or hole spin state, as described elsewhere herein. Subsequently, the quantum information is encoded in the spin state of one of the nuclear spins. In some embodiments, quantum information from microwaves or visible photons is encoded simultaneously in the spin states of the electron or hole spin and one or more nuclear spins.

[0271] Generally, in a quantum system containing electron or hole spins and multiple different nuclear spins (the T-center is an example of such a system), various spin transitions can be selected by the frequency of the photons involved in the interaction. For each pair of electron or hole spins and nuclear spins, a set of energy levels is available. For example, these energy levels can be identified as:

[0272] · Energy = 0;

[0273] · Energy = NMR1;

[0274] · Energy = EPR1; and

[0275] · Energy = NMR2 + EPR1;

[0276] In this diagram, a single arrow represents an electron or hole spin, and a double arrow represents a nuclear spin. These energy levels are typically different for different nuclear spins, allowing for the selection of individual nuclear spins for these transitions. Transitions between these energy levels can be combined with orbital transitions and / or the formation or destruction of bound excitons. Depending on which nuclear spins are involved, these combinations will also typically correspond to different energies.

[0277] This can be achieved, for example, by simultaneously applying an RF frequency modulation selected to stimulate an electronic reversal transition (e.g., by applying...). Connected to The system optically cycles through the downspin electron state while selectively initializing individual nuclear spins to have the desired spin state (e.g., upspin) by simultaneously modulating the frequency of the system with a frequency corresponding to the energy EPR2. The excited state |1↓> can be relaxed by a mechanism that flips the nuclear spin or electron spin, and the electron will eventually accumulate the probability of being flipped. However, if the nuclear spin is upspin when the electron flips to the upspin state, then the EPR1 RF frequency modulation will drive the electron back to the downspin state. If the resulting state has a downspin electron, it will be rapidly re-excited by the light field. Similarly, if the system relaxes to... The EPR2 field then returns the electron to its downspin state, at which point it is rapidly re-excited. Only The state will not be rapidly re-excited, therefore the system is initialized to that state. In the presence of multiple nuclear spins, the energy EPR2 will be different for each nuclear spin. It is possible to select which of the multiple nuclear spins to initialize by applying an RF frequency modulation, the RF frequency modulation corresponding to the value of EPR2 used for the selected nuclear spin.

[0278] Another way to initialize the nuclear spin to the desired state is to measure the nuclear spin, and if the nuclear spin is not already in the desired spin state, then apply a pi pulse to bring the nuclear spin to the desired spin state.

[0279] As an example application of the techniques described herein, a superconducting quantum bit can be stored in a specific state. For instance, this can be accomplished by performing quantum computation in a quantum computer in which the superconducting quantum bit is part. The quantum state of the superconducting quantum bit can then be stored by the electron spin at the center of T and subsequently transferred to the longer-lived hydrogen spin at the center of T. This process can be repeated for each of the carbon spins at the center of T. This process can store up to three states of the superconducting quantum bit, optionally operating the stored states as spins, and subsequently retrieving any of the three states to the superconducting quantum bit as needed. Alternatively, any of the three states can be transferred to a visible photon and transported anywhere.

[0280] In some embodiments, multiple nuclear spins in the T-center or other crystal defects are applied to quantum error correction. For example, the techniques described herein can be applied to majority local error correction using multiple nuclear spins. According to any of the examples described herein, the state of the qubit of interest can be stored on a single nuclear spin. Two or more other nuclear spins can then be used as aids for encoding the state of interest in logical qubits for error correction or error detection. Error correction can be operated, for example, as described in Quantum error correction in a solid-state hybrid spin register (Nature 506, 204-207 (2014)) by Waldherr et al., which is hereby incorporated herein by reference.

[0281] In some embodiments, long-lived qubits 16 (e.g., T-centers) are used for entanglement purification. In these embodiments, electron or hole spins can be used as operational qubits and nuclear spins can be used as memory qubits. For example, it is desirable to consider a scenario where entanglement is formed between quantum states at two or more nodes that may be far apart from each other. Each node may contain long-lived qubits 16 including electron or hole spins and at least one nuclear spin. Entanglement can be established between operational qubits (e.g., using visible photons, as described herein). The resulting entanglement can then be transferred to memory qubits via state transfer, as described herein. The operational qubits are then entangled again, but this time, the entanglement is mapped to each memory qubit at each node via conditional operations. By repeating this process and by performing appropriate measurements, memory qubits at different nodes can be entangled with extremely high purity. The entanglement can then be mapped back to the operational qubits, if necessary. Reference to the description of the basic principles of quantum purification using the long-lived qubit 16 described herein is Kalb et al., Science 356, 928-932 (2017), which is hereby incorporated herein by reference.

[0282] In some of the examples given above, the short-lived qubits are superconducting qubits. The present invention can also be applied to cases where the short-lived qubits are another type of qubit (e.g., quantum dots or ion traps). In cases where the short-lived qubits are provided by quantum dots, the quantum dots can be positioned relative to other structures described herein (e.g., resonators, optical structures, long-lived qubits, silicon substrates in which long-lived qubits are located, etc.). In cases where the short-lived qubits include ions trapped by a magnetic field (i.e., ion trap qubits), the magnetic field can be configured to trap ions on the surface of the device containing the long-lived qubits and / or the long-lived qubits near the resonator, such that the ion trap qubits can be coupled to the long-lived qubits, as described herein.

[0283] The methods and systems described in this paper can be applied to any quantum information processing system. For example, a short-lived qubit 12 can be part of any currently known or future quantum information processing system.

[0284] Systems incorporating the techniques described herein may also include non-quantum computer systems configured to control a set of qubits to perform quantum computation by performing functions such as:

[0285] • Set the state of the qubit,

[0286] • Manipulating the state of qubits

[0287] • This causes the quantum states of different qubits to become entangled with each other, and / or

[0288] • Perform quantum measurements.

[0289] This non-quantum computer system can be configured to perform the above functions in order to implement commands in a programming language suitable for quantum computing. The non-quantum computer system can be implemented using: specially designed hardware, configurable hardware, a programmable data processor configured by the deployment of software (optionally including "firmware") that can be executed on the data processor, a dedicated computer or data processor specially programmed, configured, or constructed to perform one or more steps of the methods explained in detail herein, and / or a combination of both or more of these. Examples of specially designed hardware are: logic circuits, application-specific integrated circuits ("ASICs"), large-scale integrated circuits ("LSIs"), very large-scale integrated circuits ("VLSIs"), etc. Examples of configurable hardware are: one or more programmable logic devices, such as programmable array logic ("PALs"), programmable logic arrays ("PLAs"), and field-programmable gate arrays ("FPGAs"). Examples of programmable data processors are: microprocessors, digital signal processors ("DSPs"), embedded processors, graphics processors, math coprocessors, general-purpose computers, server computers, cloud computers, host computers, computer workstations, etc. For example, one or more data processors in the control circuitry of the device can implement the methods described herein by executing software instructions in a processor-accessible program memory.

[0290] Non-quantum computer systems can be centralized or distributed. In the case of distributed processing, information containing software and / or data can be maintained centrally or distributedly. This information can be exchanged between different functional units via communication networks (such as local area networks (LANs), wide area networks (WANs), or the Internet), wired or wireless data links, electromagnetic signals, or other data communication channels.

[0291] Those skilled in the art to which this disclosure pertains will understand that the techniques described above have many aspects and applications. These include, but are not limited to:

[0292] A. An apparatus and method for operating to transfer quantum information from a first qubit to one or more third qubits using a second qubit provided by a quantum system having a first pair of quantum states with a first energy difference corresponding to a microwave frequency and a second pair of quantum states with a second energy difference corresponding to a light frequency. The method causes a quantum interaction to occur between the first and second qubits mediated by microwave photon states at the microwave frequency, thereby entanglement of the first and second qubits and / or transfer of all or part of the quantum state of the first qubit to the second qubit. The method then causes a quantum interaction to occur between the second qubit and one or more third qubits mediated by visible photon states at the light frequency, thereby entanglement of the second and third qubits and / or transfer of the quantum state of the second qubit to the third qubit. For example, the first qubit may be provided by a superconducting circuit, a quantum dot, or an ion trap; in some embodiments, the second qubit is provided by a defect center (e.g., a T-center) in silicon. For example, the first pair of quantum states may include: the spin-up and spin-down states of unpaired electrons at the T center, the spin-up and spin-down states of the nuclear spin at the T center, and the spin states of a multi-particle spin system separated by spin-flip transitions (e.g., the spin states of unpaired electron spins and nuclear spins). For example, the second pair of quantum states may include states separated by orbital transitions or exciton-forming transitions, wherein the transitions have different energies in two cases: when the second qubit is in one of the quantum states of the first pair, and when the second qubit is in the other of the quantum states of the first pair. In some embodiments, the first, second, and third qubits are part of a quantum computer.

[0293] B. An apparatus and method for storing quantum information in a defect center in silicon. In some embodiments, the defect center is a T-center. In some embodiments, quantum information is received from a first qubit, stored in the defect center, and subsequently returned to the first qubit. In some embodiments, the quantum information is stored in the defect center for a time longer than the coherence time of the first qubit. In some embodiments, the first qubit comprises a superconducting circuit, a quantum dot, or an ion trap. In some embodiments, the quantum information is transferred from the defect center to a third qubit. In some embodiments, the quantum information is manipulated while it is stored in the defect center.

[0294] C. An apparatus and method for storing quantum information in a T-center in silicon. In some embodiments, quantum information is stored in the spin states of unpaired electrons in the T-center. In some embodiments, quantum information is stored in the spin states of nuclear spins in the T-center. In some such embodiments, quantum information is transferred directly from a first qubit to the nuclear spin. In some embodiments, quantum information is transferred from a first qubit to the spin states of unpaired electrons in the T-center and subsequently from the unpaired electron spin states to the nuclear spin states. In some embodiments, the T-center is used to simultaneously store two, three, or four sets of quantum information in two, three, or four of the four spin states of the T-center (three nuclear spins and one unpaired electron spin). In some embodiments, the same quantum information is stored in two, three, or four of the spin states of the T-center. In some embodiments, the same quantum information is stored in three or more spin states of the T-center and quantum error correction is performed using two or more of the said spin states.

[0295] D. An apparatus and method for storing quantum information using a set of identical crystal defects on atoms in silicon. In some embodiments, the crystal defect is a T-center.

[0296] E. Apparatus and methods for quantum computing in a quantum computer system having multiple qubits distributed in multiple physically separated controlled environments. For example, the controlled environments may include ultra-low temperature and / or high vacuum environments. The techniques described herein can be used to transfer quantum information between qubits in different individual controlled environments.

[0297] F. An apparatus and method for entanglement of physically separated qubits or for transmitting quantum interactions therebetween, the qubits storing quantum information in quantum states separated by energies of 1.3 meV or less. The method involves transmitting some or all of the quantum information from the first qubit to a visible photon by coupling a first qubit to a second qubit via microwave photons and then coupling the second qubit to a visible photon. In some embodiments, the second qubit is a light-emitting center in silicon. For example, the second qubit may include impurity atoms, defect centers (e.g., T-centers), or a collection of atoms or defect centers.

[0298] Explanation of terms

[0299] Unless the context clearly requires otherwise, this applies throughout the description and claims:

[0300] • Terms like “comprise” and “comprising” should be understood in a sense of inclusion, in contrast to their exclusive or exhaustive meanings; that is, in the sense of “including but not limited to”.

[0301] • “Connection”, “coupling” or any variation thereof means any direct or indirect connection or coupling between two or more elements; the coupling or connection between elements may be physical, logical or a combination thereof;

[0302] • When used to describe this specification, the words “in this document,” “above,” “below,” and similar introductory terms refer to this specification as a whole and do not refer to any particular part of this specification.

[0303] • When referring to a list of two or more items, “or” encompasses all of the following interpretations of the word: either one of the items in the list, all the items in the list, and any combination of the items in the list;

[0304] • The singular forms “(a)”, “(an)”, and “the” also include the meaning of any appropriate plural form.

[0305] The directional terms used in this specification and any of the appended claims, such as “vertical,” “lateral,” “horizontal,” “up,” “down,” “forward,” “backward,” “inward,” “outward,” “left,” “right,” “front,” “back,” “top,” “bottom,” “below,” “above,” “under,” etc. (where applicable), depend on the specific orientation of the device described and illustrated. Various alternative orientations may be adopted for the objects described herein. Therefore, these directional terms are not strictly defined and should not be interpreted narrowly.

[0306] In the context of the above references to components (e.g., software modules, processors, assemblies, devices, circuits, etc.), unless otherwise indicated, references to said components (including references to “components”) shall be interpreted as including any component that performs the function of the described component (i.e., functionally equivalent) as an equivalent of said component, including components that perform the function of the illustrated exemplary embodiments of the invention but are not structurally equivalent to the disclosed structure.

[0307] In the context of methods comprising sequences of steps and / or actions described herein, alternative instances may perform the steps and / or actions in a different order. Some processes or blocks may be deleted, moved, added, subdivided, combined, and / or modified and / or adopted in sub-combinations to provide alternative embodiments. Furthermore, each step or action may be implemented in various different ways. And, although steps or actions are sometimes presented as being performed sequentially, these steps or actions may alternatively be performed in parallel, or may be performed at different times.

[0308] For illustrative purposes, specific examples of systems, methods, and devices have been described herein. These are merely examples. The techniques provided herein are applicable to systems other than those described above. Many changes, modifications, additions, omissions, and arrangements are possible in the practice of this invention. This invention includes variations of the described embodiments that will be apparent to those skilled in the art, including variations obtained by: replacing features, elements, and / or actions with equivalent features, elements, and / or actions; mixing and matching features, elements, and / or actions from different embodiments; combining features, elements, and / or actions from the embodiments described herein with features, elements, and / or actions from other technologies; and / or omitting combined features, elements, and / or actions from the described embodiments.

[0309] Various features are described herein as existing in "some embodiments". Such features are not mandatory and may not be present in all embodiments. Embodiments of the invention may include zero, any one, or any combination of two or more of such features. This is limited to the degree to which some of such features are incompatible with others of such features, in a sense that it would be impossible for someone skilled in the art to construct a practical embodiment combining these incompatible features. Therefore, the description of "some embodiments" having feature A and "some embodiments" having feature B should be interpreted as an explicit instruction to the inventors to also consider embodiments combining features A and B (unless otherwise stated in the description or features A and B are fundamentally incompatible).

[0310] Therefore, the appended claims and the described technical solutions are intended to be interpreted as encompassing all such modifications, arrangements, additions, omissions, and sub-combinations that can be reasonably inferred. The scope of the claims should not be limited to the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with this description as a whole.

Claims

1. A method for storing quantum information, the method comprising: A first qubit is provided in a first quantum state that encodes first quantum information, the first qubit having an energy ΔE corresponding to a microwave frequency. SQ The first and second quantized energy levels are separated. The first qubit is coupled to a first light-emitting center in silicon via microwave photonic states, causing the quantum states of the first qubit and the first light-emitting center to undergo quantum interactions, wherein the quantum state of the first light-emitting center encodes the first quantum information. The first luminescent center has an energy ΔE LC1 Separating the first quantized energy level and the second quantized energy level, and coupling the first qubit to the first luminescent center includes adjusting the energy ΔE. LC1 and the energy ΔE SQ One or both of them make ΔE LC1 With ΔE SQ They are basically equal.

2. The method according to claim 1, further comprising decoupling the first qubit from the first luminescent center.

3. The method of claim 2, comprising coupling the first qubit to the first light-emitting center for n half-cycles of time substantially equal to the two-qubit Rabi frequency of the first qubit and the first light-emitting center, wherein n is an odd integer.

4. The method of claim 1, further comprising adjusting the energy ΔE by applying an electric field to the first luminescent center. LC1 .

5. The method of claim 1, further comprising adjusting the energy ΔE by applying an RF driving signal to the first light-emitting center. LC1 .

6. The method of claim 1, further comprising adjusting the energy ΔE by applying strain to the silicon in which the first light-emitting center is located. LC1 .

7. The method of claim 1, wherein the first luminescent center is in a magnetic field, and the method includes adjusting the energy ΔE by changing the strength of the magnetic field at the luminescent center. LC1 .

8. The method according to any one of claims 1 to 3, wherein the first luminescent center has an energy difference ΔE LC2 A third quantized energy level separated from the first quantized energy level, and the method includes coupling the quantum state of the first luminescent center to a state corresponding to ΔE. LC2 The photon state in the first resonator at the resonant frequency of the first resonator encodes the first quantum state.

9. The method of claim 8, wherein the photon state in the first resonator is a visible photon state.

10. The method of claim 9, wherein the photon state in the first resonator corresponds to a light wavelength in the range of 1 µm to 5 µm.

11. The method of claim 9, further comprising delivering a photon of the photon state to a second resonator and coupling the second resonator to a second luminescent center, such that the quantum state of the second luminescent center encodes the first quantum information.

12. The method of claim 9, wherein the photon state in the first resonator is entangled with another photon state in the second resonator, and the method includes coupling the second resonator to a second luminescent center such that the quantum state of the second luminescent center encodes the first quantum information.

13. The method of claim 11, further comprising encoding the first quantum information in the quantum state of the second material qubit by coupling the second luminescent center to the second material qubit via another microwave photonic state, wherein the quantum states of the second material qubit and the second luminescent center participate in quantum interactions such that the quantum state of the second material qubit encodes the first quantum information.

14. The method of claim 13, further comprising decoupling the second material qubit from the second luminescent center.

15. The method of claim 13, further comprising entangled the photon state with three or more luminescent centers.

16. The method of claim 2 or 3, further comprising returning the first quantum information to the first qubit by coupling the first luminescent center to the first qubit via another microwave photonic state, such that the quantum states of the first qubit and the first luminescent center participate in quantum state transfer interaction, such that the quantum state of the first qubit encodes the first quantum information.

17. The method according to any one of claims 1 to 3, wherein the first light-emitting center comprises a crystal defect in the silicon crystal.

18. The method according to any one of claims 1 to 3, wherein the first light-emitting center comprises a set of light-emitting centers, wherein each of the light-emitting centers in the set comprises a crystal defect in the silicon crystal.

19. The method of claim 17, wherein the crystal defect includes a T-center.

20. The method of claim 17, wherein the crystal defect has an unpaired ground-state spin and includes an I center, an M center, an Al1 center, a Ga1 center, a nitrogen-carbon center, or a silicon damage center.

21. The method of claim 17, wherein the crystal defect includes at least one of an electron having an electron spin and a hole having a hole spin, and the first quantized energy level and the second quantized energy level of the first luminescent center respectively include the downspin state and the upspin state of the electron or the hole.

22. The method of claim 21, wherein the crystal defect comprises at least one nuclear spin, and the method further comprises encoding the quantum state of the electron or the hole in the quantum state of the nuclear spin, such that the nuclear spin encodes the first quantum information.

23. The method of claim 17, wherein the crystal defect comprises at least one unpaired electron or hole spin and at least one nuclear spin, and the method further comprises encoding the first quantum information as a joint quantum state of the at least one unpaired electron or hole spin and the at least one nuclear spin.

24. The method of claim 23, wherein encoding the first quantum information with the joint quantum state of the unpaired electron or hole spin and the nuclear spin includes inducing a crossover transition.

25. The method of claim 24, wherein the crossover transition comprises an electronic dipole spin resonance (EDSR) transition.

26. The method of claim 23, further comprising recovering the first quantum information by setting the unpaired electron or hole spin to have an initialized quantum state and causing a spin transition of the unpaired electron or hole spin and / or the nuclear spin.

27. The method of claim 19, wherein the crystal defect comprises a plurality of nuclear spins, and the method comprises: The first quantum information is encoded using the first of the nuclear spins; This causes the first qubit to encode the second quantum information; The first qubit is coupled to the first luminescent center through the second microwave photon state, such that the quantum states of the first qubit and the electrons or holes of the first luminescent center undergo quantum interaction and the quantum states of the electrons or holes of the first luminescent center encode the second quantum information. Decouple the first qubit from the first luminescent center; and The quantum state of the electron or hole is encoded by the quantum state of the second of the nuclear spins, such that the second of the nuclear spins encodes the second quantum information.

28. The method of claim 17, further comprising forming a bound exciton by illuminating the crystal defect center with a light pulse prior to coupling the first qubit to the first luminescent center.

29. The method of claim 21, further comprising encoding the first quantum information in the spin state of the hole.

30. The method according to any one of claims 1 to 3, wherein the light-emitting center comprises impurity atoms in the silicon crystal.

31. The method of claim 30, wherein the impurity atom comprises a dual donor atom.

32. The method of claim 31, wherein the dual donor is a selenium, tellurium, or sulfur atom.

33. The method of claim 17, wherein at least 95% of the silicon atoms in the silicon crystal are silicon-28.

34. The method of claim 13, wherein the first qubit is in a first freezer and the second material qubit is in a second freezer, and the first and second resonators are connected by an optical path passing outside the first and second freezers.

35. The method of claim 34, wherein at least a portion of the optical path outside the first and second freezers is greater than ΔE. SQ / k B The temperature, where k B It is the Boltzmann constant.

36. The method of claim 34, wherein the optical path comprises an optical fiber.

37. The method according to any one of claims 1 to 3, wherein ΔE SQ It is 1.3 meV or less.

38. The method according to any one of claims 1 to 3, wherein the first quantum bit is a superconducting quantum bit.

39. The method according to any one of claims 1 to 3, wherein the first quantum bit comprises a quantum dot or an ion trap.

40. A device for storing quantum information, the device comprising: The first qubit has an energy ΔE corresponding to the microwave frequency. SQ The first and second quantized energy levels are separated. The light-emitting centers in silicon have an energy ΔE LC1 The first and second quantized energy levels are separated. and A component for coupling the first qubit to the luminescent center via microwave photons. The component used for coupling includes a component for adjusting the energy ΔE. LC1 and the energy ΔE SQ One or both of them make ΔE LC1 With ΔE SQ Components that are essentially the same.

41. The device of claim 40, wherein the first quantum bit is a superconducting quantum bit.

42. The device of claim 40, wherein the first quantum bit is a quantum dot or an ion trap.

43. The device according to any one of claims 40 to 42, wherein the component for coupling comprises a microwave resonator.

44. The device according to any one of claims 40 to 42, comprising means for coupling the first qubit to the light-emitting center for a time substantially equal to n half-cycles of the two-qubit Rabi frequency of the first qubit and the light-emitting center, wherein n is an odd integer.

45. The device according to any one of claims 40 to 42, wherein the light-emitting center includes a T-center.

46. ​​The device according to any one of claims 40 to 42, wherein the light-emitting center comprises a T-center set.

47. The device of claim 45, further comprising means for selectively coupling unpaired electrons of the T-center to the nuclear spin of the T-center.

48. The device according to any one of claims 40 to 42, wherein the light-emitting center is in a silicon substrate and the first qubit is supported on the silicon substrate.

Images