Quantum information storage and transformation

Abstract

A method and apparatus for storing and converting quantum information provides a luminescent center in silicon that is controllably coupled to undergo quantum interaction with a first qubit, such as a superconducting qubit. The luminescent center can be, for example, a T-center or a collection of T-centers. The same or different quantum information can be stored in the unpaired electron or hole spin and / or one or more of the three nuclear spins of the T-center. The stored quantum information can later be returned to the first qubit or transferred to an optical photon state.

Description

[Technical Field]

[0001] The present technology relates to the storage and manipulation of quantum information. Some embodiments provide methods and apparatus for converting quantum information between qubits having quantum states separated by different energies. For example, one application of the present technology is to convert quantum information from qubits with energy level separations comparable to microwave wavelengths to optical photons. Another application of the present technology is to store quantum information. Another application of the present invention is to generate quantum entanglement between multiple qubits.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Application No. 63 / 057796, filed July 28, 2020, entitled "Quantum Information Storage and Transformation," which is incorporated herein by reference for all purposes. In the United States, this application claims the benefit under 35 U.S.C. § 119 of U.S. Application No. 63 / 057796, filed July 28, 2020, entitled "Quantum Information Storage and Transformation." [Background technology]

[0003] Quantum computing has the potential to revolutionize computer science. In quantum computing, the state of a quantum system is used to represent data. For example, the orientation of the spin of a particle such as an electron with respect to a magnetic field can represent a binary value of 1 or 0 depending on whether the spin is oriented parallel (spin down) or antiparallel (spin up) to the magnetic field. One advantage of quantum computing is that a quantum system can be in a superposition of states. For example, in some sense a quantum system can be spin up and spin down simultaneously. Another advantage of quantum computing comes from the ability to entangle the states of different quantum systems.

[0004] One difficulty in building a quantum computer is that after a quantum system has been set to a particular desired state, and also during attempts to manipulate the quantum system to achieve the desired state, the quantum system can lose coherence by interacting with its environment. This causes the quantum system to no longer be in the desired state. Some quantum systems undergo decoherence over very short times (e.g., on the order of nanoseconds). The effects of decoherence on certain quantum systems can be mitigated by keeping the quantum system at very low temperatures (e.g., mK).

[0005] There remains a need for technological advances that will accelerate progress in quantum computing.

[0006] definition A "quantum system" is a system that has two or more states and can exist in a superposition of two or more states. Quantum systems can include particles such as electrons, protons, neutrons, nuclei, atoms, groups of atoms, quasi-particles (e.g., phonons, excitons, magnetons), photons, etc.

[0007] "Quantum interaction" includes interactions between the quantum states of two or more qubits. Examples of quantum interactions include state transfer interactions and quantum entanglement operations.

[0008] "Quantum coherence" refers to the degree to which the phase relationship between different quantum states of a quantum system, such as a qubit, is preserved.

[0009] "Quantum decoherence" is a change in the quantum state of a quantum system resulting from the interaction of the quantum system with its environment.

[0010] "Entanglement," when applied to two or more quantum systems, means that the quantum state of any one of the entangled quantum systems cannot be described independently of the states of the others of the entangled quantum systems.

[0011] "Luminescent center" means a quantum system having an excited state that can decay to a lower energy state with the emission of an optical photon via a transition having a transition dipole moment of at least 0.1 Debye. In preferred embodiments, the luminescent center, when in the excited state, undergoes a transition in 50 microseconds or less and emits an optical photon with a relatively high probability (e.g., 1% or greater).

[0012] "Optical photon" means a photon of electromagnetic radiation having a wavelength between far infrared and ultraviolet. Photons having wavelengths in the range of 15 μm to 10 nm are examples of optical photons. Photons having wavelengths in the range of 2 μm to 380 nm are examples of optical photons.

[0013] "Qubit" means a quantum system that can exist in a superposition of states that can represent data. One example of a qubit is the quantum spin of a particle, which can be oriented parallel ("spin down") or antiparallel ("spin up") to a magnetic field. The spin-up state can be associated, for example, with a logical value of "1," and the spin-down state can be associated with a logical value of "0."

[0014] "Quantum measurement" means the process of determining a value for a measurable quantity of a quantum system. An example of a quantum measurement is the process of determining whether the spin of a quantum particle is spin up or spin down. If a quantum system is a superposition of quantum states, and the measurable quantity has different values ​​for each quantum state, the result of a quantum measurement is that the quantum system enters one of the quantum states corresponding to the value determined immediately after the quantum measurement.

[0015] "Superposition," as applied to quantum particles or other quantum systems, means that the quantum system exists in two or more distinct quantum states simultaneously. 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 [Means for solving the problem]

[0016] The present technology has various aspects, including but not limited to: Systems and methods for extending the coherence time of qubits in a quantum computer; Systems and methods for providing data to and reading data from qubits in a quantum computer; Systems and methods for using optical photons to interact with qubits whose states are separated by sub-optical energies; Systems and methods for quantum computing, Systems and methods for entangling microwave and optical photons Includes: These aspects can be used individually or in any combination.

[0017] One aspect of the present invention provides a method for storing quantum information, the method including providing a first qubit in a first quantum state that encodes first quantum information, the first qubit storing energy ΔE corresponding to a microwave frequency. SQ In some embodiments, the first qubit comprises a superconducting qubit. The method includes coupling the first qubit to a first luminescent center in silicon by a microwave photon state such that quantum states of the first qubit and the first luminescent center undergo a quantum interaction, and the quantum state of the first luminescent center encodes the first quantum information.

[0018] Some embodiments include decoupling the first qubit from the first luminescent center.

[0019] Some embodiments include coupling the first quantum bit to the first luminescent center for a time substantially equal to n half periods of the Rabi frequency of the two quantum bits of the first quantum bit and the first luminescent center, where n is an odd number.

[0020] In some embodiments, the first luminescent center has an energy ΔE LC1and coupling the first qubit to the first luminescent center produces an energy ΔE LC1 and energy ΔE SQ Adjust one or both of the above to obtain the energy ΔE LC1 and energy ΔE SQ are substantially equal.

[0021] Some embodiments may generate an electric field at the first luminescent center to generate an energy ΔE LC1 Some embodiments include adjusting the energy ΔE by applying an RF drive signal to the first luminous center. LC1 Some embodiments involve adjusting the energy ΔE by applying strain to the silicon where the first luminescence 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 varying the strength of the magnetic field at the luminescent center. LC1 This includes adjusting the

[0022] In some embodiments, the first luminescent center has an energy difference ΔE LC2 and a third energy level separated from the first energy level by ΔE LC2 coupling the quantum state of the first luminescent center to a photon state in a first resonator having a resonant frequency corresponding to λ / 2, λ / 3, λ / 4, λ / 5, λ / 6, λ / 7, λ / 8, λ / 9, λ / 10, λ / 11, λ / 22, λ / 33, λ / 44, λ / 55, λ / 56, λ / 67, λ / 70, λ / 82, λ / 90, λ / 12, λ / 14, λ / 20, λ / 22, λ / 35, λ / 46, λ / 57, λ / 16, λ / 20, λ / 38, λ / 25, λ / 39, λ / 40, λ / 59, λ / 59, λ / 26, λ / 27, λ / 39, λ / 40, λ / 28, λ / 39, λ / 45, λ / 58, λ / 29, λ / 39, λ / 40, λ / 29, λ / 10, λ / 20, λ / 25, λ / 39, λ / 26, λ / 39, λ / 27, λ / 39, λ / 40, λ / 28, λ / 29, λ / 39, λ / 29, λ / 39, λ / 40, λ / 26, λ / 27, λ / 39, λ / 28, λ / 39, λ / 40, λ / 29, λ / 39, λ / 29, λ / 39, λ / 40, λ / 29, λ / 26, λ / 39, λ / 28, λ / 39, λ / 29, λ / 39, λ / 40, λ / 29, λ /

[0023] Some embodiments include delivering photons 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.

[0024] In some embodiments, a photon state in the first resonator is entangled with another photon state in a 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.

[0025] Some embodiments include encoding the first quantum information into the quantum state of the second matter qubit by coupling a second luminescent center to the second matter qubit by another microwave photon state, where the quantum states of the second matter qubit and the second luminescent center quantum interact 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 transferring the first quantum information back to the first qubit by coupling the first luminescent center to the first qubit by another microwave photon state such that the quantum states of the first qubit and the first luminescent center quantum state transfer interaction such that the quantum state of the first qubit encodes the first quantum information.

[0026] In some embodiments, the first luminescent center comprises a crystalline defect in the silicon crystal. In some embodiments, the first luminescent center comprises a collection of luminescent centers, each of which comprises a crystalline defect in the silicon crystal.

[0027] In some embodiments, the crystalline defect comprises a T center. In some embodiments, the crystalline defect has an unpaired ground state spin and comprises an I center, an M center, an Al center, a Ga center, a nitrogen carbon center, or a silicon damage center.

[0028] In some embodiments, the crystalline defect comprises 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 luminescence center comprise a spin-down state and a spin-up state of the electron or hole, respectively. In some embodiments, the crystalline defect comprises at least one nuclear spin, and the method further comprises encoding the quantum state of the electron or hole into the quantum state of the nuclear spin, such that the nuclear spin encodes the first quantum information.

[0029] In some embodiments, the crystalline 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 in a coupled 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 in the coupled 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.

[0030] In some embodiments, the crystalline defects comprise a plurality of nuclear spins, and the method comprises: encoding first quantum information onto a first one of the nuclear spins; encoding second quantum information into the first qubit; coupling the first qubit to the first luminescent center by a second microwave photon state such that the first qubit and the electron or hole quantum states of the first luminescent center undergo a quantum interaction, and the electron or hole quantum state of the first luminescent center encodes second quantum information; decoupling the first quantum bit from the first luminescent center; encoding the quantum state of the electron or hole into the quantum state of a second one of the nuclear spins, such that the second one of the nuclear spins encodes second quantum information; Includes:

[0031] Some embodiments include generating a bound exciton by irradiating a crystal defect center with a light pulse prior to coupling the first quantum bit to the first luminescence center. Some embodiments include encoding the first quantum information into the spin state of the hole. In some embodiments, the luminescence center comprises an impurity atom in a silicon crystal.

[0032] In some embodiments, the impurity atom comprises a double donor atom, hi some embodiments, the double donor is a selenium atom, a tellurium atom, or a sulfur atom.

[0033] In some embodiments, at least 95% of the silicon atoms in the silicon crystal are silicon-28.

[0034] In some embodiments, the first qubit is in a first cooling device, the second matter qubit is in a second cooling device, and the first and second resonators are connected by an optical path that passes outside the first and second cooling devices. In some embodiments, at least a portion of the optical path that is outside the first and second cooling devices has a ΔE SQ / k B At temperatures higher than k B is Boltzmann's constant. In some embodiments, the optical path comprises an optical fiber. In some embodiments, ΔE SQ is less than 1.3 meV.

[0035] In some embodiments, the first qubit is a superconducting qubit. In some embodiments, the first qubit comprises a quantum dot or an ion trap.

[0036] Another aspect of the invention provides a method for transferring the quantum state of a superconducting qubit to optical photons, the method including coupling a superconducting qubit having two quantum states with corresponding energy levels separated by an energy ΔE1 to a luminescent 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 with corresponding energy levels separated by energies ΔE2 and ΔE3 from the energy levels corresponding to the first and second states, respectively, and subsequently coupling the luminescent center to an optical structure supporting a photon mode having a frequency corresponding to energies ΔE2 and / or ΔE3.

[0037] In some embodiments, ΔE2≠ΔE3.

[0038] 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 ΔE 1 .

[0039] Some embodiments include maintaining the coupling between the superconducting qubit and the luminescent center for a time equal to an odd number of periods of the Rabi frequency of the two coupled qubits, the superconducting qubit and the luminescent center, and subsequently decoupling the superconducting qubit and the luminescent center.

[0040] In some embodiments, the optical structure is an optical resonator.

[0041] Some embodiments include detecting photons in an optical structure.

[0042] Another aspect of the invention provides a method for transferring the quantum state of a superconducting qubit to an optical photon, the method comprising entangling the quantum state of the superconducting qubit with the quantum state of a luminescent center by microwave photons, and subsequently entangling the quantum state of the luminescent center with an optical photon state.

[0043] Some embodiments involve converting the quantum state of the luminescent center into an optical photon.situation This involves manipulating the quantum state of the luminescent center before entangling it with the

[0044] Another aspect of the invention provides a method for storing first quantum information, the method including coupling a qubit having a first quantum state with an electron spin or a hole spin of a T-center in silicon to transfer the first quantum state to a quantum state of the electron spin or the hole spin, and decoupling the electron spin or the hole spin from the qubit.

[0045] Some embodiments include subsequently inducing a quantum interaction between the quantum state of the electron spin or hole spin and the quantum state of a first nuclear spin of the plurality of nuclear spins at the T-center, such that some or all of the first quantum information is encoded in the first nuclear spin.

[0046] Some embodiments include setting the qubit to have a second quantum state and coupling the qubit to an electron spin or a hole spin of the T-center to transfer the second quantum state to the electron spin or the hole spin.

[0047] Some embodiments include decoupling the electron spin or hole spin from the qubit and subsequently transferring the quantum state of the electron spin or hole spin to the quantum state of a second nuclear spin of the plurality of nuclear spins at the T-center.

[0048] Another aspect of the present invention provides a device for storing quantum information, the device having an energy ΔE corresponding to a microwave frequency. SQ a first qubit having first and second quantized energy levels separated by an energy ΔE LC1 a light-emitting center in silicon having first and second quantized energy levels separated by a microwave photon; and means for coupling the first quantum bit to the light-emitting center by a microwave photon.

[0049] In some embodiments, the first qubit is a superconducting qubit.

[0050] In some embodiments, the first qubit is a quantum dot or an ion trap.

[0051] In some embodiments, the means for coupling includes a microwave resonator.

[0052] In some embodiments, the means for coupling comprises an energy ΔE LC1 and energy ΔE SQ Adjust one or both of the above to achieve ΔE LC1 and ΔE SQ are substantially equal.

[0053] Some embodiments include means for coupling the first quantum bit to the luminescent center for a time substantially equal to n half periods of the Rabi frequency of the two quantum bits, the first quantum bit and the luminescent center, where n is an odd number.

[0054] In some embodiments, the luminescent center comprises a T center.

[0055] In some embodiments, the luminescent center comprises a collection of T centers.

[0056] Some embodiments include means for selectively coupling the unpaired electron of the T center to the nuclear spin of the T center.

[0057] In some embodiments, the luminescent center is in a silicon substrate and the first qubit is supported on the silicon substrate.

[0058] Another aspect of the invention provides an apparatus for transferring the quantum state of a superconducting qubit to optical photons, the apparatus including: a superconducting qubit having two quantum states with corresponding energy levels separated by an energy ΔE1; a luminescent 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 with corresponding energy levels separated by energies ΔE2 and ΔE3 from the energy levels corresponding to the first and second quantum states, respectively; means for coupling the superconducting qubit to the luminescent center; and means for coupling the luminescent center to an optical structure supporting a photon mode having a frequency corresponding to energies ΔE2 and / or ΔE3.

[0059] Another aspect of the invention provides a method for generating quantum entanglement between a plurality of spaced apart qubits, each of which receives an energy ΔE corresponding to a microwave frequency. SQ The method includes coupling each of the qubits to a corresponding luminescent center in silicon by a microwave photon state, the luminescent centers having at least first, second, and third quantized energy levels, the first and second quantized energy levels separated by an energy difference corresponding to the energy of the microwave photon state, and the first and third quantized energy levels separated by an energy difference corresponding to the energy of the optical photon, and the method includes coupling each of the luminescent centers to another of the corresponding luminescent centers by an optical structure supporting one or more optical photon states having energies corresponding to quantum transitions between the first and third energy levels of the luminescent centers.

[0060] Another aspect of the invention provides a method for quantum computing, the method including storing quantum information as qubit states in defects in a silicon crystal, the defects including a plurality of impurity atoms collectively including at least one unpaired electron having a corresponding electronic spin state and a plurality of nuclear spins, each having a corresponding nuclear spin state, the method including setting one of the spin states to represent qubit information and using the plurality of nuclear spins for quantum error correction or error detection of the qubit information.

[0061] Some embodiments include using multiple nuclear spins for majority vote local error correction.

[0062] Some embodiments involve using multiple nuclear spins as ancillaries to encode qubit information into logical qubits.

[0063] In some embodiments, the defect comprises a T center, an I center, or an M center.

[0064] In some embodiments, the defect comprises a T center.

[0065] In some embodiments, the energy levels of the transitions between the different nuclear spin states are different for the different nuclear spins.

[0066] Another aspect of the invention provides a method for quantum entanglement purification, the method including providing first and second defects in a silicon crystal, the first and second defects each including an operation qubit including an electron or hole spin and at least one memory qubit including nuclear spin, the method including entangling quantum states of the operation 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 by state transfer.

[0067] Some embodiments include repeating the steps of entangling the quantum states of the first and second defective operation qubits and transferring the entanglement to at least one memory qubit for each of the first and second defects via state transfer.

[0068] In some embodiments, the defect comprises a T center, an I center, or an M center. In some embodiments, the defect comprises a T center.

[0069] Another aspect of the invention provides a method for storing quantum information in defects in a silicon crystal, the method including setting a quantum state of an 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 irradiating the defect with first photons having a first wavelength that matches the energy of a first spin transition involving the electron or hole spin and the first nuclear spin.

[0070] Some embodiments include setting a quantum state of the electron or hole spin of the defect to encode second quantum information, initializing a second nuclear spin of the defect to a second initial nuclear spin state, and irradiating the defect with second photons having a second wavelength that matches the energy of a second spin transition involving the electron or hole spin and the second nuclear spin.

[0071] In some embodiments, the first transition is a crossover transition.

[0072] In some embodiments, the first photon is provided in the form of a coherent π pulse.

[0073] In some embodiments, the defect comprises a T center, an I center, or an M center.

[0074] In some embodiments, the defect comprises a T center.

[0075] Further aspects and example embodiments are illustrated in the accompanying drawings and / or described in the following description.

[0076] It is emphasized that the invention relates to all combinations of the above features, even if they are recited in different claims. [Brief explanation of the drawings]

[0077] The accompanying drawings illustrate non-limiting exemplary embodiments of the present invention.

[0078] [Figure 1] 1 illustrates a schematic diagram of a system including a short-lived qubit and an apparatus for extending the lifetime of the short-lived qubit.

[0079] [Figure 1A] 1 shows a schematic representation of the energies of quantum states of short-lived and long-lived qubits and the interaction of photons with short-lived and long-lived qubits.

[0080] [Figure 2] 1 is a graph showing the change in probability density of two coupled quantum systems.

[0081] [Figure 3] 1 is a flowchart illustrating an exemplary method for preserving the quantum state of a short-lived qubit.

[0082] [Figure 4] FIG. 1 is a schematic diagram illustrating the configuration of an exemplary system including short-lived and long-lived qubits.

[0083] [Figure 5] FIG. 1 is a schematic diagram showing a qubit coupling to both microwaves and optical photons arranged to couple quantum information to an external system.

[0084] [Figure 6] FIG. 1 is an exemplary energy level diagram of quantum states within a qubit that can couple to both microwaves and optical photons.

[0085] [Figure 6A] FIG. 1 is a schematic diagram showing a long-lived qubit arranged to couple to microwave photons through the interaction of an electric or magnetic field.

[0086] [Figure 6B] FIG. 1 is a schematic diagram illustrating the energy levels of a quantum system in which the hole spin state can contain a bound exciton that can function as a long-lived qubit.

[0087] [Figure 7] 7A and 7B are cross-sectional and plan views, respectively, that show schematic diagrams of a system in which qubits are arranged to couple to optical photons.

[0088] [Figure 8] FIG. 1 is a schematic diagram illustrating a system in which qubits in multiple refrigerators can be coupled by optical photons.

[0089] [Figure 9] The structure of the T center in silicon is shown. DETAILED DESCRIPTION OF THE INVENTION

[0090] Throughout the following description, specific details are set forth 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 in an illustrative rather than a restrictive sense.

[0091] One aspect of the present invention provides an apparatus for extending the lifetime of a qubit. The qubit may include, for example, a superconducting qubit. One drawback of superconducting qubits is that they have an undesirably short lifetime (typically having a coherence time on the order of 100 microseconds or less). This hinders the ability to process quantum information using superconducting qubits.

[0092] 1 illustrates a schematic diagram of a system 10 that includes a short-lived qubit 12. The short-lived qubit 12 may include a superconducting qubit, such as a transmon or other charge-based or flux-based superconducting qubit.

[0093] System 10 takes advantage of the fact that qubits built into silicon crystals can have lifetimes orders of magnitude longer than short-lived qubits, such as superconducting qubits. System 10 includes a body 14 made of silicon. Optionally, but preferably, body 14 includes a purified isotope of silicon having an atomic weight of 28 (“silicon-28”). Body 14 may, for example, be part of a substrate on which short-lived qubits 12 are formed. Body 14 includes at least one long-lived qubit 16.

[0094] Long-lived qubit 16 can include, for example, an unpaired spin (e.g., electron spin, nuclear spin, exciton hole spin) or several excitons, which can be generated, for example, by irradiating the luminescent center with optical radiation having a frequency corresponding to the energy of the exciton.

[0095] The long-lived qubit 16 can be provided by one or more particles or quasiparticles in the luminescence center. In some embodiments, the luminescence center is provided by a crystalline defect in the body 14, such as a color center with an unpaired ground state spin (e.g., a T center, an I center, or an M center, an Al center or a Ga center, a nitrogen carbon center, a spin-active silicon radiation damage center, or a silicon color center with an unpaired ground state spin). When the luminescence center is a crystalline defect, the particle or quasiparticle can be, for example, an electron, a hole, a nucleus, or an exciton of the luminescence center. Some types of crystalline defects provide multiple particles or quasiparticles that can be used individually or in groups to provide a long-lived qubit. For example, a T center has at least three possibilities for nuclear spin, electron spin, hole spin in a bound exciton, and exciton number, all of which can be used as a long-lived qubit 16.

[0096] In some cases, the crystal defects may include one or more impurity atoms. In some embodiments, the luminescence center is provided by an 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.

[0097] In some embodiments, long-lived qubit 16 comprises an unpaired spin provided by atoms of impurities such as selenium or sulfur or tellurium in a silicon crystal.

[0098] System 10 also includes a controllable coupling 18. Coupling of short-lived qubit 12 and long-lived qubit 16 by coupling 18 12 and long-lived qubits 16 can be controlled to selectively allow them to interact with each other.

[0099] Coupling 18 is configured to allow a sufficiently strong coupling between short-lived qubit 12 and long-lived qubit 16 to facilitate state transfer or entanglement between short-lived qubit 12 and long-lived qubit 16. Coupling may include, for example, a resonator designed to accommodate photons having energies corresponding to quantum transitions of short-lived qubit 12 and long-lived qubit 16.

[0100] One measure of the coupling strength between a short-lived qubit 12 and a long-lived qubit 16 is the Rabi frequency of the two qubits, as described elsewhere herein. The Rabi frequency of the two qubits increases as the coupling between the two qubits becomes stronger. To promote efficient quantum interaction between the short-lived qubit 12 and the long-lived qubit 16, the period of the Rabi frequency should be greater than the coherence time of the short-lived qubit 12 and the long-lived qubit 16. For example, "cooperativity" can be defined as follows:

number

[0101] In some embodiments, C>1 is achieved at a two-qubit Rabi frequency of less than 50 kHz. For example, if short-lived qubit 12 has a coherence time of 1 microsecond (typical for some superconducting qubits) and long-lived qubit 16 has a coherence time of 1 millisecond (typical for T-center electron spins), C>1 can be achieved at a two-qubit Rabi frequency of 30 kHz or greater. As another example, if short-lived qubit 12 has a coherence time of 1 microsecond and long-lived qubit has a coherence time on the order of 1 second (typical for T-center nuclear spins in silicon), a two-qubit Rabi frequency of 1 kHz or greater is sufficient to achieve C>1.

[0102] The Rabi frequency can be increased by increasing the strength of the coupling between the short-lived qubit 12 and the long-lived qubit 16. This can be done, for example, by - To more closely match the transition energies of the short-lived qubit 12 and the long-lived qubit 16, Bringing the short-lived qubit 12 and the long-lived qubit 16 closer physically; Matching the resonant frequency of the coupling 18 (e.g., resonator) more closely to the transition energies of the short-lived qubits 12 and the long-lived qubits 16; providing a geometric arrangement that allows the short-lived qubit 12 and the long-lived qubit 16 to be coupled to antinodes of the electromagnetic mode that couples the short-lived qubit 12 and the long-lived qubit 16, respectively; This can be achieved by one or more of the following:

[0103] Short-lived qubits 12 can represent qubit values ​​in a variety of ways; for example, superconducting qubit configurations in which quantum information is stored by phase, charge, or magnetic flux are all known.

[0104] In some embodiments, coupling 18 includes a resonator positioned such that a maximum in the electromagnetic field associated with short-lived qubit 12 couples to the resonator. For example, if short-lived qubit 12 is a superconducting flux qubit, the resonator may be inductively coupled to an antinode of the magnetic field of the superconducting flux qubit. As another example, if short-lived qubit 12 is a superconducting charge qubit or a superconducting phase qubit, the resonator may be capacitively coupled to an antinode of the electric field of short-lived qubit 12.

[0105] The resonator of coupling 18 may be positioned so that the electromagnetic field maximum of the photonic mode that the resonator supports is located at or near long-lived qubit 16 .

[0106] In some embodiments, coupling 18 is provided by direct interaction of the electromagnetic field of short-lived qubit 12 with long-lived qubit 16. In such embodiments, coupling 18 is provided by the relative physical placement of short-lived qubit 12 with respect to long-lived qubit 16, allowing them to couple for quantum interaction as described herein. Long-lived qubit 16 may be positioned at or near a point where the electromagnetic field associated with short-lived qubit 12 has a maximum. For example, if short-lived qubit 12 comprises a superconducting flux qubit that includes a magnetic flux loop, long-lived qubit 16 (e.g., T-center) may be positioned inside the flux loop such that it can couple directly to the magnetic field generated by the flux loop. If short-lived qubit 12 is a charge or phase qubit, long-lived qubit 16 may be positioned at or near an electric field maximum 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 with which it interacts has an intensity that is 3 dB or 2 dB or more lower than the intensity of the electromagnetic field at the position where the electromagnetic field has its maximum intensity.

[0107] In some embodiments, the energy difference between the respective quantum states of short-lived qubit 12 and long-lived qubit 16 corresponds to a photon frequency in the radio frequency (RF) or microwave range. 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.

[0108] The relationship between energy and photon frequency is given by the following relationship: E=hυ Here, 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 as follows: υ=c / λ where c is the speed of light and λ is the photon wavelength.

[0109] System 10 is configured to measure the energy difference ΔE between the quantum states of short-lived qubits 12. S and the energy difference ΔE between the quantum states of the long-lived qubit 16 L Those skilled in the art will appreciate that the present invention may include mechanisms that operate to make ΔE equal or approximately equal. S and ΔE L It will be appreciated that even if there is a small difference between the short-lived qubit 12 and the long-lived qubit 16, the short-lived qubit 12 and the long-lived qubit 16 can still engage in quantum interactions (e.g., state transfer or entanglement operations). For convenience, this disclosure describes the two energies as "equal" (e.g., ΔE S = ΔE L When two energies are said to be equal or coincident (e.g., the resonant frequency of a resonator and the frequency of a photon), it means that the two frequencies are exactly equal or coincident for the desired purpose (e.g., excitation of a photon mode in the resonator).

[0110] How strictly ΔE is required to achieve the desired quantum interaction? S and ΔE L Whether or not the energy differences ΔE between the quantum states of short-lived qubits 12 and long-lived qubits 16 need to be equal depends on factors such as the strength of the coupling between short-lived qubits 12 and long-lived qubits 16 and the linewidths of the quantized transitions of short-lived qubits 12 and long-lived qubits 16. In some embodiments, the energy differences ΔE between the quantum states of short-lived qubits 12 may be different. S and the energy difference ΔE between the quantum states of the long-lived qubit 16 L are equalized to within 1% or 1 / 2% or 1 part in 10,000.

[0111] In some embodiments, ΔE S and ΔE L One or both of them are ΔE S = ΔE L Such mechanisms can be implemented, for example, by applying a magnetic, electric, or RF control field to short-lived qubit 12 and / or long-lived qubit 16, and / or by applying strain to the substrate on which long-lived qubit 16 is disposed, to achieve ΔE S and ΔE L One or both of these can be adjusted.

[0112] System 10 also optionally includes a mechanism for adjusting the coupling between short-lived qubit 12 and long-lived qubit 16. This mechanism may, for example, adjust ΔE S and ΔE L The optical fiber may include a tunable resonator having a resonant frequency that can be tuned to either match or not match the frequency of photons having energy equal to .gt.

[0113] ΔE S ≠ΔE L and / or if the coupling between short-lived qubit 12 and long-lived qubit 16 is otherwise nullified, the quantum states of short-lived qubit 12 and long-lived qubit 16 can change essentially independently of each other.

[0114] ΔE S = ΔEL and there is sufficient coupling between short-lived qubit 12 and long-lived qubit 16, then the quantum states of short-lived qubit 12 and long-lived qubit 16 can be entangled by microwave photons. This is shown in Figure 1A.

[0115] FIG. 1A 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 a photon 19 and transition from state 12H to 12L. Short-lived qubit 12 can absorb a photon 19 and transition from state 12L to 12H. Long-lived qubit 16 can emit a photon 19 and transition from state 16H to 16L. Long-lived qubit 16 can absorb a photon 19 and transition from state 16L to 16H.

[0116] Because qubits 12 and 16 are quantum systems, in the absence of quantum measurements, the larger system including qubit 12, qubit 16, and photon 19 can exist in a superposition of states that may include a state in which either or both qubits 12 and 16 have emitted photon 19 and a state in which either or both 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 to which their quantum states are coupled.

[0117] Coherent coupling of short-lived qubit 12 and long-lived qubit 16 may be used, for example, to entangle the quantum states of short-lived qubit 12 and long-lived qubit 16, and / or to transfer the quantum state of short-lived qubit 12 to long-lived qubit 16 and / or to transfer the quantum state of long-lived qubit 16 to short-lived qubit 12. ΔE S , ΔE L , 12 and 16 qubit coupling can be selectively enabled by adjusting one or more of:

[0118] In some embodiments, coupling between short-lived qubits 12 and long-lived qubits 16 is facilitated by a resonator 20 having a resonant frequency corresponding to the frequency of microwave photons 19 emitted / absorbed when short-lived qubits 12 and long-lived qubits 16 transition between quantum states. Resonator 20 may include, for example, a patch of superconducting material in a circuit designed to have a resonant frequency corresponding to photons 19. Resonator 20 may include, for example, a coplanar waveguide resonator or an LC resonator.

[0119] The resonator 20 may be positioned sufficiently close to each of the qubits 12 and 16 to provide a sufficient level of coupling between each of the qubits 12, 16 and the photon 19 within the resonator 20. The capacitive or inductive coupling between the superconducting qubit 12 and the resonator 20 may have a relatively long range, such that the spacing between such qubit 12 and the resonator 20 may be several microns or more. As another example, the coupling between a quantum dot used as the qubit 12 and the resonator 20 typically has a much shorter range, such that the resonator 20 is positioned closer than about 1 micron or closer than 100 nm to the quantum dot. The coupling between the resonator 20 and the long-lived qubit 16 may have a range of several microns, in which case the resonator 20 may be positioned within a few microns of the long-lived qubit 16.

[0120] A mechanism may be provided for tuning the energy gap between the quantum states of the qubit. The nature and configuration of the mechanism depends on the nature of the quantum system on which the qubit is based. For example, If the qubit is provided by electron spin or hole spin or nuclear spin in a magnetic field, the energy difference between the spin-up and spin-down states can be tuned by changing the strength of the magnetic field at the location of the electron or nucleus. If the qubit is a superconducting qubit, the energy difference between the states can be adjusted by adjusting the quantized magnetic flux through the superconducting circuit that implements the qubit, for example by changing the capacitance or inductance of the superconducting circuit. If the qubits are provided by atoms or defects in a crystal lattice, the energy levels of the qubits can be altered by applying strain to the crystal lattice. When a qubit is provided by electron spin, hole spin, or nuclear spin in a magnetic field, the energy level of the qubit can be tuned by applying an RF drive field to the qubit. The frequency of the RF drive field can be set, for example, so that the energy of a photon in the RF drive field is at least approximately equal to the energy difference between the energy levels of the qubit (e.g., within about 1%, 1 / 2%, or 1 part in 10,000). The energy level of the qubit can be changed by adjusting the frequency of the RF drive field and / or the amplitude of the RF drive field. When a qubit is provided by electron spin, hole spin, or nuclear spin in a magnetic field, the energy level of the qubit can be tuned by applying an electric field to the location of the qubit. In some embodiments, the electric field is oriented parallel to the magnetic field.

[0121] When the short-lived qubit 12 and the long-lived qubit 16 are coupled by coupler 18 as described above, photons 19 can be used to transfer energy back and forth between the short-lived qubit 12 and the long-lived qubit 16. The possibility of such energy transfer results in oscillations in the probability density function (PDF) that indicates the probability of finding the short-lived qubit 12 in a particular quantum state (e.g., 12H or 12L). These oscillations occur at the so-called two-qubit Rabi frequency, which is determined by the coupling between the short-lived qubit 12 and the long-lived qubit 16.

[0122] The Rabi frequencies can be determined in advance. The Rabi frequencies of the two qubits can be measured during a calibration step. The calibration step can include, for example, initializing the long-lived qubit 16 and the short-lived qubit 12 to a known quantum state, turning on the coupling for a time “tau,” turning off the coupling, and later measuring both qubits 12 and 16 independently. By repeating this measurement sequence for various values ​​of tau, a plot such as that shown in FIG. 2 can be obtained, from which the Rabi frequencies can be easily determined. The Rabi frequencies determined by the calibration step can be saved in a data store for future use. For example, the data store can include memory locations accessible to control circuitry connected to control the coupling of the long-lived qubit 16 and the short-lived qubit 12 using any of the mechanisms described herein.

[0123] FIG. 2 is a graph showing the probability density of short-lived quantum bit 12 being in the higher energy level of two non-degenerate binary quantum states (curve 22A) and the probability of long-lived quantum bit 16 being in the higher energy level of two non-degenerate binary quantum states (curve 22B).

[0124] 2, at time 0, short-lived qubit 12 is in a high-energy quantum state and long-lived qubit 16 is in a low-energy quantum state. This can occur by performing a quantum measurement at time 0 or by manipulating the states of qubits 12, 16. At time 0, system 10 is configured to couple the states of short-lived qubit 12 and long-lived qubit 16.

[0125] The probability density represented by curve 22A varies periodically with period T. At time T / 2, the long-lived qubit 16 has a high probability of being in a high-energy state, and the short-lived qubit 12 has a low probability of being in a low-energy quantum state. In effect, the quantum state of the short-lived qubit 12 is transferred to the long-lived qubit 16, and vice versa.

[0126] The principles illustrated in FIG. 2 also apply to other quantum states and superpositions of short-lived qubits 12 and long-lived qubits 16.

[0127] transferring the state of the short-lived qubit 12 (which may be a superconducting qubit) to the long-lived qubit 16 (which may be, for example, a spin qubit), as described above; short lifespan qubit 12 Longevity It can be stored in the long-lived qubit 16 for longer than a lifetime and later returned to the short-lived qubit 12 for further processing.

[0128] 3 shows 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 high-energy state and a low-energy state. Block 32A may include, for example, performing a quantum computation on a quantum computer of which the short-lived qubit is a part.

[0129] In block 32B, the short-lived qubit is coupled to the long-lived qubit 16, e.g., by coupler 18 as described above. Block 32B may be implemented, for example, by coupling ΔE S = ΔE L To realize the energy difference ΔE between the high-energy quantum state and the low-energy quantum state of the long-lived qubit 16, L and / or adjusting the energy difference ΔE between the high-energy quantum state and the low-energy quantum state of the short-lived qubit 12. S This can include adjusting:

[0130] In block 32C, the coupling of the short-lived qubit 12 and the long-lived qubit 16 is maintained for a time τ equal to an odd number N (N=1, 3, 5, . . .) of half periods T / 2 of the Rabi period (e.g., one half period), and then discontinued (e.g., ΔE S ≠ΔE L ΔE S and ΔE L(The coupling can be stopped by adjusting one or both of τ and τ and / or by changing the resonant frequency of resonator 20.) The time τ is significantly shorter than the decoherence time of short-lived qubit 12.

[0131] The time τ for which the coupling between the short-lived qubit 12 and the long-lived qubit 6 is maintained can be controlled by a timer that uses a conserved value equal to or derived from the two-qubit Rabi frequency of a particular pair of short-lived qubit 12 and long-lived qubit 16 determined in a calibration step to set the time for which the coupling is maintained.

[0132] At the end of block 32C, the desired quantum state of short-lived qubit 12 is transferred to long-lived qubit 16.

[0133] In block 32D, a time passes. The time may be longer than the decoherence time of short-lived qubit 12. The time is shorter than the decoherence time of long-lived qubit 16. In some embodiments, the time is greater than 10 microseconds, or greater than 100 microseconds, or greater than 1 second, or greater than 1 minute.

[0134] In block 32E, short-lived qubit 12 is again coupled to long-lived qubit 16, e.g., by coupler 18 as described above. Block 32E may, for example, operate in the same manner as described herein for block 32B.

[0135] 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, ...) of half periods T / 2 of the Rabi period and then discontinued. Block 32F can be performed, for example, as described above for block 32C.

[0136] At the end of block 32F, short-lived qubit 12 has been returned to the desired quantum state.

[0137] 4 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 28 that is greater than 92.23% silicon). In some embodiments, the material of substrate 42 is at least 96%, or 99%, or 99.5%, or 99.9% (by atomic number) silicon 28.

[0138] The long-lived qubit 16 is provided by a luminescent center 43 in the substrate 42. For example, the luminescent center can include a luminescent center selected from a T center, an I center, or an M center, or a nitrogen carbon center, or an Al or Ga center, or a defect such as a radiation damage center with an unpaired ground state spin, or an impurity such as an atom of selenium or tellurium or sulfur, or other double donor impurity.

[0139] The short-lived qubit 12 may be provided by a superconducting structure 44 supported on a substrate 42. The structure 44 may include a patterned layer of a metal that is superconducting at low temperatures deposited on the substrate 42. The layer may include, for example, a superconducting loop that includes a Josephson junction. An electrically insulating layer 45 may be present between the superconducting structure 44 and the main body of the substrate 42 in which the luminescent center 43 is located.

[0140] The coupler (which performs the function described above for coupler 18) may be provided by portion 44A of superconducting structure 44, which has an energy difference ΔE S and ΔE L The portion 44A may be designed to provide a resonance at a frequency corresponding to an energy that can equalize both the radiative energy and the radiative energy. The portion 44A may comprise, for example, a tab of superconducting material in a circuit having a resonant frequency in the microwave range. The portion 44A may physically overlap the radiative center 43.

[0141] The luminescent center 43 must be spaced sufficiently close to the portion 44A to couple to the electric or magnetic field components of the photons in the portion 44A. To couple to the electric field, the luminescent center 43 must have a non-negligible capacitance with the portion 44A. In some embodiments, Illumination Center 43 is spaced from portion 44A by a distance on the order of about 1 μm or less, or on the order of 100 nm or less. Preferably, portion 44A is aligned with the crystallographic axes of substrate 42 so that the electric or magnetic field of the photon mode in portion 44A couples well to light-emitting center 43. In some embodiments, the magnetic field of the photon mode is non-parallel (e.g., perpendicular) to the external magnetic field applied to light-emitting center 43.

[0142] 4 also shows a tunable magnet 46 that is operable to vary the magnitude of the magnetic field at the location of the luminescence center 43 (and thus vary the energy difference between the spin-up and spin-down states of a spin, such as an electron spin, used to provide the long-lived qubit 16). Control circuitry A controls the tunable magnet 46 (e.g., to vary the energy difference between the spin-up and spin-down states of the long-lived qubit 16 and the short-lived qubit 16). 12 One or more permanent magnets 46B near the light-emitting center 43 can augment the magnetic field from the adjustable magnet 46. The magnets 46B can be deposited on, in, or near the substrate 42.

[0143] It is generally beneficial to minimize the component of the magnetic field generated by magnets 46 and 46B that is transverse to the plane of 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 is no longer superconducting) is generally much lower for a transverse magnetic field (perpendicular magnetic field) than for a magnetic field whose field lines are parallel to superconducting structure 44.

[0144] 4 also shows a coil 47 that can be driven by an RF signal source 47A to manipulate the quantum state of long-lived qubit 16 through resonance effects (e.g., electron spin resonance—"ESR"), as known to those skilled in the art. The RF signal source can be controlled to generate pulses of radiation, such as π pulses or π / 2 pulses, that, when applied, manipulate the quantum state of long-lived qubit 16.

[0145] FIG. 4 also shows an optional light source 48 positioned to illuminate the location of the long-lived qubit 16. The light source 48 can emit light having a wavelength corresponding to an optical transition of the long-lived qubit 16, e.g., the generation of an exciton. For example, the long-lived qubit 16 can include an exciton in a crystal defect such as a T-center. The light source 48 can be operated to generate the exciton by emitting a pulse of light at an appropriate wavelength. Quantum information can later be stored in the exciton, e.g., in its spin state. The light source 48 can include, for example, a laser. The laser can be tunable to emit light having wavelengths corresponding to various optical transitions of the long-lived qubit 16.

[0146] Substrate 42 is contained within a cooling device 49 that can reach cryogenic temperatures at which structure 44 becomes superconducting. In some embodiments, the operating temperature of structure 44 can be very low (e.g., a few mK or a few Kelvin).

[0147] In addition to or as an alternative to storing quantum information, the systems described herein can be used as a pathway for transferring quantum information to and from a quantum information processing system of which short-lived qubit 12 is a part, and / or as a mechanism for generating optical photons that represent the quantum state of short-lived qubit 12.

[0148] FIG. 5 shows a schematic diagram of an apparatus 50 according to an exemplary embodiment in which a quantum communication pathway 52 connects long-lived qubit 16 to an external system 54 .

[0149] Quantum information pathway 52 may, for example, carry quantum information in the form of optical photons. Quantum information storage quantum information pathway 52 may, for example, include waveguide 53 capable of carrying photons carrying quantum information. In some advantageous embodiments, the optical photons have wavelengths in the range of about 1.3 to about 1.7 μm or about 1 μm to about 3 μm.

[0150] Quantum information channel 52 may be coupled to long-lived qubit 16 by an optical resonator 55 placed in close proximity to long-lived qubit 16. To facilitate coupling of long-lived qubit 16 to an optical photon in optical resonator 55, long-lived qubit 16 must have available quantum states with energy levels that can be separated by an energy difference equivalent to the energy of the optical photon. In this case, long-lived qubit 16 can undergo allowable transitions that cause long-lived qubit 16 to either emit or absorb an optical photon.

[0151] In some cases, photons that may be emitted or absorbed at different allowed transitions of long-lived qubit 16 have different polarizations. In such cases, the polarization of the emitted photon can encode the quantum state of long-lived qubit 16 from which the photon is emitted. In some cases, long-lived qubit 16 becomes entangled with photons having particular polarization states, such that the quantum information represented by the spin state of qubit 16 can be accessed via the polarization states of the entangled photons.

[0152] 6 shows a simplified exemplary structure of the energy levels of long-lived qubit 16. Levels 16H and 16L can correspond, for example, to spin-up and spin-down states of an unpaired spin (e.g., of an electron or hole); for example, levels 16H and 16L can be the result of hyperfine splitting caused by the interaction of the nuclear spin and the electron spin at the location of long-lived qubit 16. The energy difference between levels 16H and 16L can correspond to the energy of a photon at microwave wavelengths.

[0153] Long-lived qubit 16 also has states 17H and 17L, which may correspond to spin-up and spin-down states, respectively, of an unpaired spin (e.g., of an electron or hole). States 17H and 17L may be related to states 16H and 16L, respectively, by orbital or exciton transitions. The energy difference between states 17H and 16H or between states 17L and 16L may correspond to the energy of a photon at an optical wavelength.

[0154] As shown in FIG. 6, 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 -28 J). This creates an opportunity to provide optical photons that will either interact with high probability or not interact with long-lived qubit 16 depending on whether the unpaired spin is spin up or spin down.

[0155] For example, when provided with optical photons 66 having a wavelength corresponding to an energy equal to ΔE1, long-lived qubit 16 can absorb one of the photons 66 and transition from state 16H to state 17H. Long-lived qubit 16 can later transition from state 17H ​​to state 16H and emit a photon 66 with the same energy ΔE1.

[0156] However, because long-lived qubit 16 is a quantum system, it is not necessarily the case that long-lived qubit 16 is in a distinct quantum state. Instead, long-lived qubit 16 may be in a superposition of states. Also, long-lived qubit 16 and optical photon 66 may both be in a superposition of states in which long-lived qubit 16 is either interacting with the photon or not. In general, the quantum state of a quantum system consisting of long-lived qubit 16 and optical photon 66 includes a wide variety of possible interactions between long-lived qubit 16 and optical photon 66. As a result, the quantum states of long-lived qubit 16 and optical photon 66 can be entangled.

[0157] It can be seen that an energy structure such as that shown in Figure 6 can be used to couple long-lived qubit 16 to other quantum objects either by microwave photons or by optical photons. This property can be used to store quantum information in long-lived qubit 16 from a selected one of multiple sources and / or to transfer quantum information from long-lived qubit 16 to a selected one or more of multiple destinations. This property can be used to convert quantum information from microwave photons to optical photons by long-lived qubit 16 and / or to convert quantum information from optical photons to microwave photons by long-lived qubit 16.

[0158] Long-lived qubits 16 can be coupled to microwave photons and / or short-lived qubits 12 by a variety of mechanisms. These include: Electric field mediated bonding and Magnetic field coupling Includes: Some embodiments have physical structures that optimize one or more of these coupling mechanisms. In some embodiments, the bond facilitates electron dipole spin resonance ("EDSR") interactions.

[0159] The long-lived qubit 16 can couple to the electric field component of the microwave photon. To optimize the electrical coupling, the microwave photon can exist as a standing wave mode within the resonator, with the standing wave mode having one or more antinodes of maximum electric field strength. The long-lived qubit 16 can be placed close to (e.g., within a few microns of) the antinode of maximum electric field strength.

[0160] In device 60 according to the exemplary embodiment shown in Figure 6A, microwave photons may be present in a metallic resonator structure 61 on a silicon layer 63. An electrically insulating layer 62, e.g., a layer of silicon dioxide, separates resonator structure 61 from layer 63. The microwave photons in resonator structure 61 have a standing wave mode in which the electric field strength is greatest at antinodes 64. Long-lived qubit 16-1 is located on or in silicon substrate 63 proximate to nodes 64.

[0161] The electric field interaction has a long enough range in some embodiments that the long-lived qubit couples to the electric field of photons that are not in the resonant cavity (e.g., photons in an optical waveguide close to the long-lived qubit 16).

[0162] The long-lived qubit 16 can couple to the magnetic field component of microwave photons. To optimize electromagnetic coupling, the microwave photons can exist within the resonator as a standing wave mode, with the standing wave mode having one or more antinodes of maximum magnetic field strength and / or one or more antinodes of maximum electric field strength. For example, the long-lived qubit 16 can be positioned proximate (e.g., within a few micrometers) to an antinode of maximum magnetic field strength. For example, FIG. 6A shows a long-lived qubit 16-2 positioned on or in a silicon substrate 63 proximate to an antinode 65 where the magnetic field strength of the standing wave mode is greatest.

[0163] In some embodiments, the resonator structure 61 comprises a coplanar waveguide ("CPW") resonator. A CPW resonator may comprise a coplanar waveguide with a signal pin segmented into a stub that is capacitively coupled to a signal feed line. The CPW resonator can support standing wave resonance at a frequency determined by the length of the stub. The electric field antinodes are at the ends of the stub.

[0164] In some embodiments, the resonator structure 61 has a high 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 5 Or at least 10 6 It has a Q factor of

[0165]

number

[0166] Spin transitions can occur in systems where bound excitons can be created. A quantum number of 0 indicates the absence of bound excitons, and a quantum number of 1 indicates the presence of one bound exciton. In notation for the quantum state of a system that can include an exciton state, an electron (or hole) spin state, and a nuclear spin state, the exciton quantum number can be followed by the electron (hole) spin, which can then be followed by the nuclear spin. For example,

number

[0167] In the system shown in Figure 6B, the energy ΔE A When a photon with ΔE is absorbed, a bound exciton can be generated. A corresponds to a photon wavelength of approximately 1326 nm. A bound exciton can be generated by directing light with this wavelength at a T-center. When a bound exciton is present, a system of upper energy levels 67A, 67B, 67C, and 67D, shown on the right side of Figure 6B, is available. When a bound exciton is not present, only the lower energy levels 66A, 66B, 66C, and 66D are available. The T-center can exist in a superposition of states, including one state in which a bound exciton is present and another state in which a bound exciton is not present.

[0168] Transitions are possible between any of the energy levels on the right side of Figure 6B. These transitions can be classified as follows: Transitions that flip the electron or hole spin but not the nuclear spin (e.g., electron paramagnetic resonance (EPR) transitions). Transitions 69C1, 69C2, 69D1, and 69D2 are examples of transitions in which only the electron or hole spin flips. Transitions that flip the nuclear spin but not the electron spin (e.g., nuclear magnetic resonance (NMR) transitions). Transitions 69C3, 69C4, 69D3, and 69D4 are examples of transitions in which only the nuclear spin flips. Crossing transitions in which both the electron or hole spin and the nuclear spin are inverted (e.g., EDSR transitions). Transitions 69C5, 69C6, 69D5, and 69D6 are examples of crossing transitions. 。 · Transitions between states with and without bound excitons are also possible (eg, transitions from one of states 66A, 66B, 66C, 66D to one of states 67A, 67B, 67C, 67D).

[0169] In quantum systems such as T-centers that contain multiple nuclear spins, the energy levels of the transitions are generally different for different nuclear spins. By coupling nuclear spins to other qubits as described herein, a particular available nuclear spin can be selected for quantum interaction with the other qubit through a selected one of the transitions, such that the transition between the quantum states of the other qubit involves an energy difference that matches the energy difference of the selected transition.

[0170] In quantum systems such as T-centers that have unpaired electrons and support bound exciton states, quantum information is stored in the unpaired electrons. to or the hole of a bound exciton. As described below, the energy difference of the transitions involving the hole is different from the energy difference of the transitions involving the electron. By coupling a system containing an electron or a hole to another qubit as described herein, the electron or hole spin can be selected for quantum interaction with the other qubit through a selected one of the above transitions, such that the transition between quantum states of the other qubit involves an energy difference that matches the energy difference of the selected transition for the electron or hole.

[0171] Any of transitions 69C1, 69C2, 69C3, 69C4, 69C5, 69C6, 69D1, 69D2, 69D3, 69D4, 69D5, and 69D6 can be used to encode quantum information in electron or hole spin, in nuclear spin, or in a combination of two or more of these. Each of these transitions has an energy ΔE C1 , ΔE C2 , ΔE C3 , ΔEC4 , ΔE C5 , ΔE C6 , ΔE D1 , ΔE D2 , ΔE D3 , ΔE D4 , ΔE D5 , and ΔE D6 In the case of the T center, these energies correspond to ΔE C5 , ΔE C6 , ΔE D5 , and ΔE D6 corresponds to photons with frequencies from about 1 MHz to 100 MHz, and ΔE C1 , ΔE C2 , ΔEC3, ΔE C4 , ΔE D1 , ΔE D2 , ΔE D3 , and ΔE D4 corresponds to photons having frequencies from about 1 GHz to about 100 GHz.

[0172] In some embodiments, the nuclear spin and electron or hole spin of the T-center are initialized to a known quantum state. The spin can be set to a desired state, for example, by optically pumping the spin to a desired energy level and / or by applying a pulse to flip the spin (a "π pulse"). For example, the initial state is

number

[0173] Photons are in the state

number

number

number

number

[0174] In another example, driven transitions are used to store quantum states in the nuclear spins of T centers or in other crystal defects involving nuclear spins and electron or hole spins. In this example, the electron or hole spins are initially in a particular quantum state (e.g., spin-up, spin-down, or a superposition of spin-up and spin-down). The quantum state of the electron or hole spin can be set by inducing quantum state transfer between a short-lived qubit and the electron or hole spin, for example, as described elsewhere herein.

[0175] If necessary, the available nuclear spins can be initialized to a known state, e.g., spin-down or spin-up. The T-center can be illuminated with photons from an external source (e.g., a laser) having a wavelength matching the energy of the spin transition that will subsequently involve the nuclear spin. In some cases, the transition is a crossing transition that also involves an electron or hole. In T-centers or other crystal defects where multiple nuclear spins exist, which of the nuclear spins undergoes quantum interactions with the electron or hole spin can be selected by the energy of the photon illuminating the T-center. The photons can be provided in the form of a coherent π pulse. Using a π-pulse-induced transition is an efficient way to store the electron or hole spin state in the nuclear spin.

[0176] In EDSR, a transition occurs in which both the electron spin and the nuclear spin are flipped.

number

number

[0177] This specification describes various ways of using electron spin by coupling the quantum state of electron spin with the quantum state of nuclear spin. In general, when a bound exciton containing a hole spin is present, the hole spin can be coupled to the nuclear spin in the same ways as described herein, except that the energy levels of the hole spin of the bound exciton are generally different from the energy levels of the electron spin.

[0178] The primary reason for the difference in energy levels between electron and hole spins is that the g-factor of a hole can differ from that of an electron by at least a factor of two, depending on the hole's environment (e.g., the electron g-factor is 2, while the hole g-factor can range from about 1 to 4, depending on the hole's environment). Energy levels typically vary approximately proportionally to the g-factor. The same mechanisms described herein for varying ΔE to flip the electron spin can also be used to vary ΔE to flip the hole spin.

[0179] As another example, the energy ΔE C5 Using photons with

number

[0180] Figures 7A and 7B show a schematic diagram of a system 70 in which a long-lived qubit 16 is arranged to couple to an optical photon 66. System 70 has elements in common with system 40 of Figure 4. These elements are labeled in Figure 7 with the same reference numerals as in Figure 4.

[0181] In system 70, long-lived qubit 16 is provided by luminescent center 43 located within or in close proximity to optical resonator 72. Optical resonator 72 is designed to have a resonant frequency corresponding to the frequency of photons having energy ΔE1 or ΔE2 (see FIG. 6). Advantageously, long-lived qubit 16 can be located inside the optical resonator at a mode maximum of the optical electric field.

[0182] 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. In FIG. 7A, the optical resonator 72 comprises a ring resonator. The resonator 72 can be fabricated, for example, as described in Tait et al., arXiv:2001.05100, incorporated herein by reference for all purposes. The microring resonator can be fabricated, for example, on a silicon-on-insulator (SOI) platform including a thin (e.g., approximately 200-500 nm thick) silicon layer (ideally silicon 28). The silicon 28 layer can be formed on a thicker (e.g., approximately 3 μm thick) silicon oxide layer on a host silicon wafer (the silicon wafer can have a natural isotope concentration of silicon). In some embodiments, photons at or very near the resonant frequency of the resonator 72 have whispering gallery modes.

[0183] The optical resonator 72 is optically coupled to an optical waveguide 74 by which optical photons 66 can be introduced into the resonator 72 or carried out of the resonator 72 to other locations.

[0184] 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 that corresponds to the center of the micro-ring resonator and extends 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 in the silicon-on-insulator device layer that is about half the depth of the silicon-on-insulator device layer.

[0185] The coupling between the long-lived quantum bit 16 and the photon 66 in the optical resonator 72 can be tuned 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 closely matches one of ΔE1 and ΔE2.

[0186] ΔE1 and ΔE2 can be adjusted, for example, by varying the strength of the electromagnetic field at the location of long-lived qubit 16. In the illustrated embodiment, this is done by controlling power supply 75 to 44A This is achieved by applying a potential difference between conductor 75A and conductor 75B.

[0187] The resonant frequency of the resonator 72 is, for example, Changing the optical properties of the boundaries of the resonator 72, for example by manipulating a microelectromechanical system (MEMS); Modifying the structural properties, such as introducing a gas that adheres to the boundaries of the resonator 72 and changes its interaction with the photons 66; ·substrate 42 or by applying a force to the resonator 72 itself, thereby distorting the resonator 72; Varying the drive strength and / or coupling of long-lived qubits 16 to resonator 72 to take advantage of nonlinear effects in resonator 72; and applying an electromagnetic field to the resonator 72; Varying the temperature of the resonator 72 can be adjusted by

[0188] In some embodiments, the resonant frequency of optical resonator 72 is swept over a range of frequencies that includes ΔE1 or ΔE2.

[0189] System 70 uses quantum transitions with energy differences corresponding to frequencies in the optical domain to couple to optical photons 66. These transitions include, for example, orbital transitions or transitions that create excitons. The transitions affect the quantum state of the quantum system (e.g., electron spin, hole spin, nuclear spin, spin combinations, excitons) in which quantum information is stored. The transitions can entangle the quantum state of long-lived qubit 16 with the photon state in optical resonator 72. In some embodiments, a long-lived qubit 16includes multiple quantum particles that can individually or collectively store quantum information. For example, 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. It may be desirable to store the quantum state of superconducting qubit 12 as the quantum state of the nuclear spins.

[0190] In some embodiments, quantum state transfer is used to transfer the state of the superconducting qubit to the quantum state of the nuclear spins. An exemplary way to do this is to transfer the quantum state of the superconducting qubit 12 to the quantum state of the electron or hole spins, for example, as described above, and then later transfer the quantum state of the electron or hole to the quantum state of the nuclear spins.

[0191] A similar method to the state transfer process described above can be used to induce quantum interactions such as state transfer or entanglement between a long-lived spin qubit and a short-lived superconducting qubit. For example, both the spin qubit and the superconducting qubit can be prepared in appropriate eigenstates. The spin qubit and the superconducting qubit can then be coherently interacted in the manner described above to generate two-qubit Rabi oscillations similar to those shown in Figure 2. If this interaction ceases after an odd number of half-Rabi periods, state transfer is achieved. Alternatively, if the interaction ceases after (N / 2 + 1 / 4) Rabi periods, where N is an integer, an entangled state is generated between the two qubits.

[0192] Superconducting qubits using electron spin or hole spin qubits 12The quantum state of the superconducting qubit 12 can be teleported to an optical photon. For example, the electron spin of a long-lived qubit can be entangled with an incoming photon by initializing the electron to a spin-up state and allowing it to interact with one of the two photons of the entangled pair. This interaction transfers the entanglement to the electron spin, creating a spin-photon entangled state. The electron spin can later be entangled with the superconducting qubit 12 in the manner described above. After this entanglement is established, the superconducting qubit 12 and the electron spin qubit can be jointly measured in a Bell state (entanglement) basis. The results of these measurements can be used to select an operation to perform on the second photon from the original entangled pair, resulting in the superconducting qubit 12 The state of a photonic qubit can be "feedforward" to the photon qubit. For example, the measurement result can be fed to classical control electronics, which can look up the feedforward operation in a lookup table and later control electrical circuitry to perform the feedforward operation. The photonic qubit can later transfer its quantum information to a distant electron spin qubit, which in turn can transfer its quantum state to a distant superconducting qubit.

[0193] The entanglement of the state of the long-lived qubit 16 with an optical photon 66 facilitates a mechanism for coupling the long-lived qubit 16 to an external system. The optical photon carries thermal energy (approximately 26 meV kJ at room temperature). B is given by T, and k B The optical photons 66 have energies significantly higher than the thermal energy of the long-lived qubits 16 (where T is the Boltzmann constant and T is the temperature in Kelvin). For example, the energy of near-infrared optical photons at a wavelength of 1 μm is approximately 1.2 eV. In this example, the optical photons have more than 40 times more energy than the thermal energy at room temperature. This allows optical photons 66 to be transported outside of the cooling system in which long-lived qubits 16 are located without being unduly affected by thermal noise. Using suitable optical fibers or other known photon transport mechanisms, photons 66 can be transported over long distances.

[0194] This mechanism can be used to identify long-lived qubits 16 and potentially located at a distance from qubit 16. One, Two or more other Entanglement can be generated between the long-lived qubit 16 and the other qubit. In some embodiments, the other qubit with which the long-lived qubit 16 is entangled is another long-lived qubit 16 described herein. The long-lived qubits 16 may be the same. For example, the entangled long-lived qubit 16 may be a T-center.

[0195] In the above description, the long-lived qubit 16 has been described as being provided by a single luminescent center, such as an impurity atom or a crystal defect. This is possible, but not necessary. In any embodiment, the long-lived qubit may be provided by multiple identical or nearly identical luminescent centers. Some advantages of this include improved coupling with photons and less need for precise placement of individual luminescent centers. A collection of long-lived qubits 16 can effectively operate as a single, more strongly coupled long-lived qubit 16.

[0196] As an example of the use of an ensemble of long-lived qubits that effectively function as a single long-lived qubit, in some embodiments, multiple long-lived qubits 16 are placed within or adjacent to optical resonator 72. The multiple long-lived qubits 16 may include, for example, T-centers. The multiple long-lived qubits 16 may be placed inside the ring of an optical ring resonator at a mode maximum of the optical electric field of photons at the resonant frequency of the ring resonator.

[0197] In some embodiments, the long-lived qubit has a 5, or about 1 to 2000, or about 40 to 1000. Coupling of photons into an ensemble of N identical long-lived qubits tends to increase proportionally to √N. However, the larger the number N, the more difficult it becomes to make the long-lived qubits behave similarly or nearly similarly. If the long-lived qubits do not behave similarly, the coherence time of the ensemble can be shortened. For large values ​​of N, the larger the number of widely spaced long-lived qubits, the wider the range of environments in which the long-lived qubits may be exposed to the field of the coupling photons in locations where the field strength differs from that of the fewer long-lived qubits. As a result, N can be chosen large enough to achieve the desired strength of coupling to photons (microwave or optical photons) while still providing the ensemble with a coherence time long enough for the intended application.

[0198] If it is desired to use a collection of luminescent centers for a long-lived qubit, it is beneficial to arrange the luminescent centers so that they are identical to one another and so that the strength of the magnetic or electric field through which they couple to photons is similar for all luminescent centers included in long-lived qubit 16.

[0199] Defect centers, e.g., T-centers, can have any of a number of orientations relative to the crystal lattice in which they are located. For example, T-centers can have any of 12 orientations. In some embodiments, defect centers with multiple different orientations are included in an ensemble that provides a long-lived qubit. In some embodiments, defect centers with specific, selected orientations are excluded from participating in an ensemble that provides a long-lived qubit. This can be done, for example, by selectively shifting the energy levels of defect centers with selected orientations to prevent them from coupling to photons that defect centers included in the ensemble can couple to. The energy levels can be shifted for selected orientations of the defect centers, for example, by distorting the crystal lattice in a selected direction.

[0200] FIG. 8 schematically illustrates an exemplary structure of a quantum computer system 80 comprised of multiple modules 82 (modules 82-1, 82-2, through 82-N are shown). Each module 82 includes a cooling device 82A for cooling a quantum computing subsystem 82B, which includes one or more short-lived qubits 12, each coupled to a corresponding long-lived qubit 16, according to any embodiment described herein. The modules 82 may include other environmental control systems, such as a high-vacuum system, electromagnetic radiation shielding, vibration isolation, etc., as needed. The short-lived qubits 12 may be part of a quantum information processing system 13 that 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 qubits 16 are coupled to the short-lived qubits 12 by microwave resonators 20.

[0201] Photon carrier 84 extends between the long-lived qubit 16 of one module 82-1 and the long-lived qubit of another module 82-2. Photon carrier 84 may include an optical system composed of optical elements such as mirrors, lenses, refractive elements, etc. that direct photons 56 through, for example, optical fibers, optical waveguides, free space, etc. Photon carrier 84 provides a path along which photons 56 travel from near one long-lived qubit 16, exit a cooling device 82A housing the one long-lived qubit 16, travel to a cooling device 82A housing a second long-lived qubit 16, enter a cooling device 82A housing the second long-lived qubit 16, and interact with the second long-lived qubit 16. By this mechanism, the quantum states of the first and second long-lived qubits 16 can be entangled. Photon carrier 84 may optionally be connected to carry the photon state to multiple destinations that collectively host multiple remote qubits, such that long-lived qubit 16 can be simultaneously entangled with multiple remote qubits by the optical photon state within photon carrier 84.

[0202] In some embodiments, any module 82 may include two or more long-lived qubits 16 coupled to corresponding long-lived qubits 16 in one or more other modules 82. In such embodiments, one photon may entangle two, three, four, or more long-lived qubits 16, and some or all of the long-lived qubits 16 may be in different modules 82.

[0203] The overall structure of system 80 is advantageous because it allows the quantum computer's qubits (e.g., short-lived qubits 12) to be distributed across multiple cooling devices 82A. This is beneficial because cooling quantum computer components to the required low temperatures while simultaneously making the cooling devices large enough to accommodate large quantum computers is extremely difficult and presents operational challenges. Furthermore, the possibility of creating system 80 with photon carriers 84 having extended lengths can be used to widely distribute modules 82. System 80 may be applied, for example, to securely distribute quantum information among widely distributed modules 82.

[0204] In the above embodiment, it was found that a T-center can be advantageous for use as the long-lived quantum bit 16. Figure 9 shows the structure of a T-center 90. The T-center is a position in a silicon crystal where a silicon atom is replaced by two carbon atoms 91A and 91B and a hydrogen atom 92 bonded to carbon atom 91B. Carbon atom 91A has one unpaired electron. The spin state of the unpaired electron of carbon atom 91A can be used as the long-lived quantum bit 16.

[0205] T-centers can also host bound excitons, the number of which (e.g., 0 or 1) can be used as long-lived qubits 16. Also, the spin state of the hole in the bound exciton can be used as a long-lived qubit 16 or as an intermediate state used to encode quantum information in nuclear spin.

[0206] Bound excitons can be created and destroyed so that they exist only when needed. Excitons can be used to receive quantum information from an external source (such as an optical or microwave photon) and transfer that quantum information to a spin manifold, such as a nuclear spin, which has a very long coherence time for the quantum information. The wave function of the hole in a bound exciton has a relatively large spatial extent that facilitates coupling of the hole spin with the photon, as described elsewhere herein.

[0207] T-centers have the following properties that make them particularly well suited for use as long-lived qubits 16: ·T centers exhibit long spin coherence times (>2.1 ms for electron spin and >1 s for nuclear spin). ·T centers have narrow optical linewidths (<30MHz). ·T centers can bind to photons in the O band (wavelengths including about 1326 nm). ·T-centers can provide multiple (e.g., four) accessible spin manifolds. ·T centers weakly but controllably couple to lattice distortion. ·T-centers couple weakly but controllably to electric fields. ·T centers can support excitons that can be used to store quantum information (e.g., in hole spins).

[0208] T-centers can be formed in a silicon body by irradiating the silicon body with high-energy carbon and high-energy hydrogen. This irradiation is followed by a high-temperature anneal to activate the T-center formation. In some embodiments, T-centers are formed at desired locations in a silicon body by applying a hard mask to the silicon body and irradiating the desired locations through openings in the hard mask.

[0209] As mentioned above, the T-center has several accessible spin manifolds. These are: one unpaired electron spin, One exciton-hole spin (if an exciton is present), one hydrogen nuclear spin, and Two carbon nuclear spins Includes: It is possible to store quantum information in the quantum state of any of these spins.

[0210] Quantum information can be stored in any of the nuclear spin manifolds. This can be done in a variety of ways. Using these methods, the same or different quantum information can be stored in each of two or more nuclear spin manifolds. In some embodiments, the quantum information from microwave or optical photons is encoded in the quantum state of the electron or hole spin state, as described elsewhere herein. The quantum information is later encoded in the spin state of one of the nuclear spins. In some embodiments, the quantum information from microwave or optical photons is simultaneously encoded in the spin state of the electron or hole spin and one or more nuclear spins.

[0211] In general, in a quantum system containing an electron or hole spin and several different nuclear spins (a T-center is an example of such a system), various spin transitions can be selected depending on the frequency of the photon involved in the interaction. A set of energy levels is available for each pair of electron or hole spin and nuclear spin. These energy levels can be identified, for example, as follows:

number

[0212] The individual nuclear spins are optically cycled through the spin-down electronic state while simultaneously stimulating the electron flip transition with an RF tone (e.g., having a frequency corresponding to the energy EPR2,

number

number

number

number

[0213] Another way to initialize the nuclear spins to the desired state is to measure the nuclear spins and, if they are not already in the desired spin state, apply a π pulse to bring the nuclear spins to the desired spin state.

[0214] As an exemplary application of the techniques described herein, a superconducting qubit can be driven into a particular state. This can be done, for example, by performing a quantum computation on a quantum computer of which the superconducting qubit is a part. The quantum state of the superconducting qubit can then be stored in the electron spin of the T-center, and then that quantum state can be transferred to the longer-lived hydrogen nuclear spin of the T-center. This process can be repeated for each of the carbon nuclear spins of the T-center. This process allows up to three states of the superconducting qubit to be stored, manipulated as needed in the stored states as spins, and later retrieved as needed any of the three states into the superconducting qubit. Furthermore, any of the three states can be transferred to optical photons and transported anywhere.

[0215] In some embodiments, multiple nuclear spins at T-centers or other crystalline defects are used for quantum error correction. For example, using the techniques described herein, multiple nuclear spins can be used for majority local error correction. The qubit state of interest can be stored in one nuclear spin according to any of the examples described herein. Two or more other nuclear spins can be used as ancillaries to encode the state of interest into a logical qubit for later error correction or error detection. Error correction can operate, for example, as described in Waldherr et al., "Quantum error correction in a solid-state hybrid spin register," Nature 506, 204-207 (2014), incorporated herein by reference.

[0216] In some embodiments, long-lived qubits 16, such as T-centers, are used to refine entanglement. In such embodiments, electron or hole spins can be used as operation qubits, and nuclear spins can be used as memory qubits. For example, consider the case where it is desired to generate entanglement between quantum states at two or more nodes that may be distant from one another. Each node may include a long-lived qubit 16 that includes an electron or hole spin and at least one nuclear spin. Entanglement can be established between the operation qubits (e.g., using optical photons as described herein). The resulting entanglement is then transferred to the memory qubits by state transfer, as described later herein. The operation qubits are later re-entangled, but this time the entanglement is mapped to each memory qubit by conditional operations at each node. By repeating this sequence and taking appropriate measurements, memory qubits at different nodes can be entangled with very high purity. The entanglement can be mapped back to the operation qubits as needed. A reference that describes the basic principles of quantum purification that can be applied using long-lived qubits 16 as described herein is Kalb et al., Science 356, 928-932 (2017), which is incorporated herein by reference.

[0217] In some of the above examples, the short-lived qubit is a superconducting qubit. The present techniques can also be used when the short-lived qubit is another type of qubit, such as a quantum dot or an ion trap. When the short-lived qubit is provided by a quantum dot, the quantum dot can be positioned relative to other structures as described herein (e.g., a resonator, an optical structure, a long-lived qubit, a silicon substrate on which the long-lived qubit is disposed, etc.). When the short-lived qubit includes an ion trapped by a magnetic field (i.e., an ion trap qubit), the magnetic field can be configured to trap the ion adjacent to a surface of the device including the long-lived qubit in proximity to the resonator and / or the long-lived qubit, such that the ion trap qubit can be coupled to the long-lived qubit as described herein.

[0218] The methods and systems described herein may be applied to any quantum information processing system, for example, short-lived qubits 12 may be part of any quantum information processing system now known or developed in the future.

[0219] Systems incorporating the techniques described herein also include: Setting the state of the qubits, Manipulating the state of qubits, Entangle the quantum states of different qubits with each other, and / or · Performing quantum measurements The present invention may include a non-quantum computer system configured to control a set of qubits to perform a quantum computation by performing a function such as

[0220] Such non-quantum computer systems can be configured to perform the above functions to implement commands in a programming language suitable for quantum computing. Non-quantum computer systems can be implemented using specially designed hardware, configurable hardware, programmable data processors configured by providing software (which may optionally include "firmware") executable on the data processor, special-purpose computers, or data processors specially programmed, configured, or constructed to perform one or more steps of the methods detailed herein and / or combinations of two or more thereof. 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"), field-programmable gate arrays ("FPGAs"), etc. Examples of programmable data processors are microprocessors, digital signal processors ("DSPs"), embedded processors, graphics processors, mathematical coprocessors, general-purpose computers, server computers, cloud computers, mainframe computers, computer workstations, etc. For example, one or more data processors in the control circuitry of the device may perform the methods described herein by executing software instructions in program memory accessible to the processors.

[0221] Non-quantum computer systems can be centralized or distributed. When processing is distributed, information, including software and / or data, can be held centrally or distributed. Such information can be exchanged between different functional units by means of a communications network, such as a local area network (LAN), a wide area network (WAN), the Internet, wired or wireless data links, electromagnetic signals, or other data communications channels.

[0222] Those skilled in the art, upon reading this disclosure, will appreciate that the above techniques have many embodiments and applications, including but not limited to the following: A. Apparatus and methods operative to convert 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 an optical frequency. The method induces a quantum interaction between the first and second qubits mediated by microwave photon states at microwave frequencies, entangling the first and second qubits and / or transferring all or a portion of the quantum state of the first qubit to the second qubit. The method subsequently induces a quantum interaction between the second qubit and one or more third qubits mediated by optical photon states at optical frequencies, entangling the second and third qubits and / or transferring the quantum state of the second qubit to the third qubit. The first qubit may be provided, for example, by a superconducting circuit, a quantum dot, or an ion trap. In some embodiments, the second qubit is provided by a defect center in silicon, such as a T-center. The first pair of quantum states may include, for example, up and down spin states of an unpaired electron at a T-center, up and down spin states of a nuclear spin at a T-center, or spin states of a multi-particle spin system (e.g., spin states of an unpaired electron spin and a nuclear spin) separated by a spin-flip transition. The second pair of quantum states may include, for example, states separated by an orbital transition or a transition that creates an exciton, where the transition has a different energy when the second qubit is in one of the first pair of quantum states than when the second qubit is in the other of the first pair of quantum states. In some embodiments, the first, second, and third qubits are part of a quantum computer. B. Apparatus and methods for storing quantum information at defect centers in silicon. In some embodiments, the defect center is a T-center. In some embodiments, quantum information is received from a first qubit, stored at the defect center, and later returned to the first qubit. In some embodiments, the quantum information is stored at 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 stored at the defect center. C. Apparatus and Method for Storing Quantum Information at a T-Center in Silicon. In some embodiments, quantum information is stored in the spin state of the unpaired electron at the T-center. In some embodiments, quantum information is stored in the spin state of the nuclear spin at the T-center. In some such embodiments, quantum information is transferred directly from the first qubit to the nuclear spin. In some embodiments, quantum information is transferred from the first qubit to the spin state of the unpaired electron at the T-center, and later transferred from the unpaired electron spin state to the nuclear spin state. 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 two or more of the spin states are used for quantum error correction. D. Apparatus and method for storing quantum information using a collection of atomically identical crystalline defects in silicon. In some embodiments, the crystalline defects are T-centers. E. Apparatus and methods for quantum computing in a quantum computer system having multiple qubits distributed across multiple physically separate controlled environments. The controlled environments may include, for example, ultra-low temperature and / or high vacuum environments. Quantum information can be transferred between qubits in different of the separate controlled environments using the techniques described herein. F. Apparatus and methods for entanglement and transfer of quantum interactions between physically separated qubits that store quantum information in quantum states separated by an energy of 1.3 meV or less. The method includes converting some or all of the quantum information from a first qubit into optical photons by coupling the first qubit to a second qubit with microwave photons and subsequently coupling the second qubit with optical photons. In some embodiments, the second qubit is a luminescent center in silicon. For example, the second qubit may include an impurity atom, a defect center (e.g., a T-center), or a collection of atoms or defect centers.

[0223] Interpretation of terms Unless the context clearly requires otherwise, throughout the specification and claims: "Including" and similar words should be construed in an inclusive sense, rather than an exclusive or exhaustive sense, i.e., "including but not limited to." "Connected," "coupled," or variations thereof means a direct or indirect connection or coupling between two or more elements, where the coupling or connection between the elements can be physical, logical, or a combination thereof. The words "herein," "above," "below," and words of similar import, when used to describe this specification, shall refer to this specification as a whole and not to any particular portions of this specification. "Or", in relation to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. · The singular forms "a", "an" and "the" include all appropriate plural references.

[0224] Directional terms such as "longitudinal," "lateral," "horizontal," "upper," "lower," "forward," "rearward," "inward," "outward," "left," "right," "front," "rear," "top," "bottom," "lower," "above," and "below," as used in this specification and the appended claims (if any), are dependent on the particular orientation of the device being described and illustrated. The subject matter described herein can assume various alternative orientations. Accordingly, these directional terms are not precisely defined and should not be construed narrowly.

[0225] Where a component (e.g., a software module, processor, assembly, device, circuit, etc.) is referred to above, unless otherwise indicated, the reference to that component (including the reference to "means") should be interpreted to include any component that performs the function of (i.e., is functionally equivalent to) the described component as an equivalent of that component, including components that are not structurally equivalent to the disclosed structures that perform the function in the illustrated exemplary embodiments of the invention.

[0226] Where methods are described herein that include a series of steps and / or actions, alternative embodiments may perform the steps and / or actions in a different order. Some processes or blocks may be deleted, moved, added, subdivided, combined, or otherwise modified to provide alternative embodiments. and / or may be modified and / or incorporated into subcombinations. Also, each step or action may be performed in a variety of different ways. Also, while steps or actions may be shown as occurring in sequence, these steps or actions may instead be performed in parallel or may occur at different times.

[0227] Specific examples of systems, methods, and apparatus have been described herein for illustrative purposes. These are examples only. The techniques provided herein may be applied to systems other than the exemplary systems described above. Many changes, modifications, additions, omissions, and substitutions are possible within the scope of the present invention. The present invention includes variations of the described embodiments that would be apparent to one skilled in the art, resulting from replacing features, elements, and / or operations with equivalent features, elements, and / or operations, mixing and matching features, elements, and / or operations from different embodiments, combining features, elements, and / or operations from the embodiments described herein with features, elements, and / or operations from other technologies, and / or omitting to combine features, elements, and / or operations from the described embodiments.

[0228] Various features are described herein as being present in "some embodiments." Such features are not required and may not be present in all embodiments. Embodiments of the invention may include none, any one, or a combination of two or more of such features. This is limited in the sense that if a particular one of such features is incompatible with another of such features, it would be impossible for one of ordinary skill in the art to construct a working embodiment combining such incompatible features. Consequently, a statement that "some embodiments" have feature A and "some embodiments" have feature B should be interpreted as explicitly indicating that the inventors also contemplate embodiments combining features A and B (unless the description states otherwise or features A and B are fundamentally incompatible).

[0229] It is therefore intended that the following appended claims and any claims introduced hereafter be construed to include all such modifications, permutations, additions, omissions, and subcombinations that may reasonably be inferred. The scope of the claims should not be limited by the preferred embodiments set forth in the examples, but rather should be accorded the broadest interpretation consistent with the description as a whole.

Claims

1. 1. A method for storing quantum information, comprising: a first qubit in a first quantum state encoding first quantum information, the first qubit having an energy ΔE corresponding to the microwave frequency; SQ providing a first qubit having first and second quantized energy levels separated by coupling the first quantum bit to a first luminescent center in silicon by a microwave photon state, such that the quantum states of the first quantum bit and the first luminescent center undergo a quantum interaction, and such that the quantum state of the first luminescent center encodes the first quantum information; decoupling the first quantum bit from the first luminescent center; Including, the first quantum bit is coupled to the first luminescent center for a time period substantially equal to n half periods of the Rabi frequency of the two quantum bits, the first quantum bit and the first luminescent center, where n is an odd integer.

2. The first luminescence center has an energy ΔE LC1 and coupling the first quantum bit to the first luminescent center reduces the energy ΔE LC1 and the energy ΔE SQ Adjust one or both of ΔE LC1 and ΔE SQ The method of claim 1 , comprising causing:

3. The energy ΔE LC1 The method of claim 2 , comprising adjusting:

4. The first luminescence center has an energy difference ΔE LC2 and a third quantized energy level of the first luminescent center separated from the first quantized energy level of the first luminescent center by ΔE LC2 2. The method of claim 1, comprising coupling a quantum state of the first luminescent center to an optical photon state in a first resonator having a resonant frequency corresponding to

5. 5. The method of claim 4, comprising delivering photons of the optical photon state to a second resonator and coupling the second resonator to a second luminescent center such that a quantum state of the second luminescent center encodes the first quantum information.

6. 5. The method of claim 4, wherein an optical photon state in the first resonator is entangled with another photon state in a second resonator, the method comprising coupling the second resonator to a second luminescent center such that a quantum state of the second luminescent center encodes the first quantum information.

7. 6. The method of claim 5, comprising encoding the first quantum information into a quantum state of a second matter qubit by coupling a second luminescent center to the second matter qubit by another microwave photon state, the quantum states of the second matter qubit and the second luminescent center quantum interacting such that the quantum state of the second matter qubit encodes the first quantum information.

8. 8. The method of claim 7, wherein the first qubit is in a first cooling device and the second matter qubit is in a second cooling device, and the first and second resonators are connected by an optical path that passes outside the first and second cooling devices.

9. At least a portion of the optical path that is outside the first and second cooling devices has a ΔE SQ / k B at a temperature higher than k B The method of claim 8 , wherein is Boltzmann's constant.

10. 10. The method of claim 1, comprising transferring the first quantum information back to the first quantum bit by coupling the first luminescent center to the first quantum bit with another microwave photon state such that the quantum states of the first luminescent center and the first quantum bit undergo a quantum state transfer interaction, and the quantum state of the first quantum bit encodes the first quantum information.

11. The method of claim 1 , wherein the first luminescence center comprises a crystal defect in a silicon crystal.

12. The method of claim 11 , wherein the crystal defects include T centers.

13. The method of claim 1 , wherein the first luminescent center comprises a cluster of luminescent centers, and each of the luminescent centers in the cluster comprises a crystal defect in a silicon crystal.

14. The method of claim 13 , wherein the crystal defects include T centers.

15. 12. The method of claim 11, 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 and second quantized energy levels of the first luminescence center include a spin-down state and a spin-up state of the electron or hole, respectively.

16. 16. The method of claim 15, wherein the crystalline defect comprises at least one nuclear spin, the method further comprising encoding a quantum state of the electron or hole into a quantum state of the nuclear spin, such that the nuclear spin encodes the first quantum information.

17. The crystal defects include a plurality of nuclear spins, and the method further comprises: encoding the first quantum information onto a first one of the nuclear spins; encoding second quantum information into the first quantum bit; coupling the first quantum bit to the first luminescent center by a second microwave photon state such that the quantum states of the first quantum bit and the electron or hole of the first luminescent center undergo a quantum interaction, and the quantum state of the electron or hole of the first luminescent center encodes the second quantum information; decoupling the first quantum bit from the first luminescent center; encoding the quantum state of the electron or hole into the quantum state of a second one of the nuclear spins, such that the second one of the nuclear spins encodes the second quantum information; 16. The method of claim 15, comprising:

18. 10. The method of claim 1, wherein the first qubit is a superconducting qubit.

19. The method of claim 1 , wherein the first quantum bit comprises a quantum dot or an ion trap.

20. 1. A device for storing quantum information, comprising: Energy ΔE equivalent to microwave frequency SQ a first qubit having first and second quantized energy levels separated by a first luminescence center in silicon; means for coupling the first quantum bit to the first luminescent center by a microwave photon state for a time period substantially equal to n half periods of the Rabi frequency of two qubits, the first quantum bit and the first luminescent center, where n is an odd number, such that quantum states of the first quantum bit and the first luminescent center undergo a quantum interaction and the quantum state of the first luminescent center encodes first quantum information; An apparatus comprising:

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