Global control of quantum computing systems

Abstract

A system and method for controlling one or more qubits in a quantum processor is disclosed. The system includes a quantum processor including one or more spin-based qubits and a dielectric resonator disposed near the quantum processor. The dielectric resonator provides a magnetic field. The quantum processor is disposed in a portion of the magnetic field provided by the resonator such that the portion of the magnetic field controls the spin transitions of one or more spin-based qubits in the quantum processor.

Description

[Technical Field]

[0001] Aspects of the present disclosure relate to methods and systems for controlling qubits in quantum computing systems. [Background technology]

[0002] Quantum computers and quantum simulators are poised to revolutionize many aspects of modern society, from basic science and medical research to national security. The defense implications of many of these applications, including discoveries in prime factorization and cryptography, the design of new materials from first principles, artificial intelligence, and machine learning, will be significant. While some applications are expected to be feasible on medium-scale quantum computers (100-1000 qubits) without error-correction protocols, some of the most disruptive algorithms, such as Shor's algorithm for prime factorization, will require large-scale, fully fault-tolerant quantum computers of over 1 million qubits.

[0003] However, before such large-scale quantum computers can be commercially manufactured, several hurdles must be overcome. One such hurdle is the control of qubits (the basic units of quantum information control). To date, several techniques have been proposed to control the state of qubits, but these techniques either cannot be scaled up effectively or result in faster decoherence. Summary of the Invention [Problem to be solved by the invention]

[0004] Therefore, there is a need for a scalable qubit control system that can simultaneously control multiple qubits without adversely affecting the operation of the qubits.

[0005] According to a first aspect, the present invention provides a system for controlling one or more quantum bits in a quantum processor, the system comprising: a quantum processor including one or more spin-based quantum bits; and a dielectric resonator positioned proximate to the quantum processor, the dielectric resonator providing a magnetic field, the quantum processor being positioned in a portion of the magnetic field provided by the dielectric resonator such that the portion of the magnetic field controls spin transitions of one or more spin-based quantum bits of the quantum processor.

[0006] In one embodiment, multiple spin-based qubits of a quantum processor are manipulated and controlled in part by a magnetic field provided by a dielectric resonator at cryogenic temperatures.

[0007] In some embodiments, the cryogenic temperature is 4 Kelvin or less.

[0008] In a further embodiment, the dielectric resonator is made of a dielectric material that has a dielectric constant that increases at cryogenic temperatures compared to room temperature.

[0009] In some embodiments, the dielectric constant of the resonator is in the range of 1000 to 40,000 at cryogenic temperatures.

[0010] In some embodiments, the portion of the magnetic field that controls one or more spin-based qubits is a uniform AC magnetic field.

[0011] In some embodiments, a portion of the magnetic field serves as a global magnetic field for simultaneously controlling multiple spin-based qubits of a quantum processor.

[0012] In some embodiments, the dielectric resonator generates an electric field that is spatially separated from the magnetic field.

[0013] In some embodiments, the magnetic field of the dielectric resonator is perpendicular to the surface of the resonator.

[0014] In some embodiments, the electric field is confined away from the location of the quantum processor to minimize interaction of the electric field with one or more spin-based qubits and the on-chip measurement and control electronics of the quantum processor.

[0015] In some embodiments, the electric field circulates within the resonator.

[0016] In some embodiments, the dielectric resonator is a perovskite structure ( XII A 2+VI B 4+ X 2- 3) is made of a material from a class of compounds having the following properties:

[0017] In some embodiments, the dielectric resonator is made of potassium tantalate (KTaO3) or strontium titanate (SrTiO3).

[0018] In some embodiments, the dielectric resonator has a capacitance of about 5×10 -7 m 3 provides a resonant mode volume of

[0019] In some embodiments, the quantum processor is a solid-state semiconductor or superconducting quantum processor.

[0020] In some embodiments, the dielectric resonator is in the form of a solid block of dielectric material, and the quantum processor is positioned above or below the dielectric resonator such that one or more spin-based qubits of the quantum processor face the dielectric resonator and interact with a portion of the AC magnetic field provided by the dielectric resonator.

[0021] In some embodiments, the system further includes an adjustable coupling element for providing a microwave input signal to the dielectric resonator to generate the magnetic field. The dielectric resonator may require a low-power microwave input signal that minimizes impact on the cryogenic environment of the quantum processor.

[0022] In some embodiments, the resonator has a quality factor Q having a value greater than 100 at cryogenic temperatures.

[0023] In some embodiments, the frequency of the magnetic field generated by the resonator is in the radio frequency range of 1.0 MHz to 1.0 GHz to control nuclear spins.

[0024] In some embodiments, the frequency of the magnetic field generated by the resonator is in the microwave frequency range, which is in the range of 1.0 GHz to 100.0 GHz for controlling electron spins.

[0025] According to a second aspect, the present invention provides a method for controlling one or more spin-based qubits in a quantum processor using a system described in the first aspect of the invention.

[0026] As used herein, unless the context requires otherwise, the term "comprise" and variations of the term such as "comprising," "comprises," and "comprised" are not intended to exclude additional additives, ingredients, integers, or steps.

[0027] Further aspects of the invention and further embodiments of the aspects described in the preceding paragraphs will become apparent from the following description, given by way of example and with reference to the accompanying drawings, in which: [Brief explanation of the drawings]

[0028] [Figure 1] 1 illustrates a prior art quantum computing device having a donor-based qubit controlled by a local on-chip transmission line. [Figure 2] 1 shows a prior art quantum computing device having quantum dot qubits controlled by local on-chip transmission lines. [Figure 3]1 shows a schematic architecture of a prior art scalable donor-based quantum computer that employs global control of qubits. [Figure 4] 1 shows a prior art loop gap resonator that can separate magnetic and electric fields and direct them to different regions. [Figure 5] 1 illustrates a top view of a dielectric resonator made of perovskite material (also known as potassium tantalate, having the chemical formula KTaO 3 ) and having a fundamental resonant frequency of 4.5 GHz, according to an exemplary embodiment of the present disclosure. [Figure 6A] 6 shows the magnetic and electric field profiles when the TEz111 mode (also referred to as TE11δ in this disclosure) of the rectangular dielectric resonator of FIG. 5 is excited. [Figure 6B] 6 shows the magnetic and electric field profiles when the TEz111 mode (also referred to as TE11δ in this disclosure) of the rectangular dielectric resonator of FIG. 5 is excited. [Figure 7] 1 illustrates an architecture for a scalable donor-based quantum computer employing global control of qubits using a uniform magnetic field generated by a dielectric resonator, according to an exemplary embodiment of the present disclosure. [Figure 8a] 10A-10C illustrate examples of alternative geometries for dielectric resonators. [Figure 8b] 10A-10C illustrate examples of alternative geometries for dielectric resonators. [Figure 9] 10 illustrates a scalable donor-based quantum computer architecture employing global control of qubits using a uniform magnetic field generated by a dielectric resonator, according to another embodiment of the present disclosure. [Figure 10] 1 illustrates a resonator according to some embodiments of the present disclosure having electric and magnetic field lines. [Figure 11A] A finite element simulation of the magnetic field magnitude of the fundamental mode of the resonator excited with a microwave signal power of 100 μW is shown. [Figure 11B] A finite element simulation of the electric field magnitude of the fundamental mode of the resonator excited with a microwave signal power of 100 μW is shown. [Figure 12] 1 is a plot showing microwave reflection S-parameters of a dielectric resonator near its fundamental mode, probed from a coaxial loop coupler. [Figure 13A] A scanning electron microscope (SEM) photograph of the quantum processor chip used in the experiment. [Figure 13B] 13B is a cross section through the center of the conduction band profile of the quantum processor chip and device of FIG. 13A. [Figure 14A] FIG. 13B is a stability diagram for the spin qubit in the device of FIG. 13A. [Figure 14B] 14B shows a readout pulse sequence superimposed on a portion of the stability diagram shown in FIG. 14A. [Figure 15A] 1 illustrates a pulse scheme for electron spin resonance measurements using the resonator of the present disclosure. [Figure 15B] 1 is a chart showing triplet probability as a function of applied microwave frequency. [Figure 15C] 1 shows the triplet probability as a function of applied microwave frequency and DC magnetic field. [Figure 15D] 15C is a plot taken along the diagonal of FIG. 15C showing the triplet probability and reflection parameters of the resonator as a function of microwave drive frequency, demonstrating the enhancement of ESR at the dielectric resonator frequency. DETAILED DESCRIPTION OF THE INVENTION

[0029] overview This section provides an overview of prior art quantum computing systems and various issues associated with the qubit control techniques implemented in these systems.

[0030] One type of quantum computing system is based on the spin states of individual qubits, which are electron and nuclear spins localized within a silicon quantum chip. These electron and nuclear spins are confined in artificial quantum dots (e.g., Figure 2) or on naturally occurring donor atoms embedded in the quantum chip (e.g., Figure 1).

[0031] Early groundbreaking qubit experiments conducted by applicant have shown the great promise of these quantum systems, with key figures of merit, including qubit coherence time, control, and measurement fidelity, exceeding most other types of quantum computing systems. In these small-scale systems (e.g., the systems shown in Figures 1 and 2), on-chip transmission lines are used for local control of each individual qubit. In particular, each individual qubit is provided with a dedicated on-chip transmission line located several hundred nanometers away from the qubit's location.

[0032] FIG. 1 shows an example of a small-scale silicon quantum chip 10 with a single donor-based qubit. As shown in this figure, quantum chip 10 includes a first layer 12 of silicon substrate and a silicon-28 isotope ( 28 The first layer 12 has a thickness of about 500 micrometers, and the second layer 13 has a thickness of about 0.9 micrometers. The window 14 shows an enlarged view of the central portion of the top surface 17 of the quantum chip 10. The qubit 11 is located approximately in the center of the top surface 17. The qubit 11 includes an electron spin and a nuclear spin. The nuclear spin is determined by the phosphorus-31 ( 31P) donor atom. There is an on-chip transmission line 15 for controlling the qubit 11. The on-chip transmission line 15 is located just a few hundred nanometers away from the qubit 11 and provides a strong magnetic microwave signal B (also known as an electron spin resonance signal, or ESR signal) and an RF signal (also known as a nuclear magnetic resonance signal, or NMR signal) to control the electron and nuclear spins of the qubit 11. The frequency of the ESR signal can be about 40 GHz, and the frequency of the NMR signal can be about 100 MHz. A single-electron transistor (SET) 16 is used as a charge sensor to read the state of the qubit 11. As can be seen from this figure, the SET sensor 16 is located in close proximity to the on-chip transmission line 15 and the qubit 11.

[0033] Figure 2 shows a top view of a quantum computing chip 20 with a single qubit 21 confined in an artificially formed quantum dot. 31 2 differs from the system of FIG. 1 in that the quantum chip 20 of FIG. 2 is localized in a silicon quantum dot rather than a naturally occurring donor atom such as P. However, like the quantum chip of FIG. 1, the quantum chip 20 of FIG. 2 uses a dedicated on-chip transmission line 26 to locally control the qubit 21. The on-chip transmission line 26 provides an ESR signal and an RF signal (not shown in FIG. 2). The ESR signal generates microwave magnetic field lines B, as indicated by reference numeral 24, to control the qubit 21. Additionally, the quantum chip 20 includes one or more SET sensors 25 for measuring the quantum state of the qubit 21. As can be seen in FIG. 2, the SET sensors 25 are positioned in close proximity to the on-chip transmission line 26 and the qubit 21.

[0034] In the systems shown in Figures 1 and 2, qubits can operate coherently in a microwave magnetic field that is generated "locally" using an on-chip transmission line (e.g., transmission line 15 or 26). In these systems, the local microwave magnetic field B operates in "pulsed mode," that is, it is turned on when qubit rotation is desired. The reason for operating the local microwave magnetic field B in pulsed mode is that the transmission line (15 or 26) generates a strong AC electric field that interferes with SET operation. Therefore, the microwave field is typically turned off at least prior to qubit measurement.

[0035] The above-described local control of qubits (i.e., dedicated transmission lines per qubit) has been successfully implemented in small-scale quantum computers, however, there may be some complications and / or drawbacks associated with the local control signals generated by these local transmission lines.

[0036] First, impedance mismatches in transmission lines (e.g., transmission lines 15 or 26) create spurious electric fields that can interfere with the sensitive SETs used to measure the quantum states of the qubits, rendering the SETs unusable while the control ESR and NMR signals are applied by the transmission lines. As is evident from Figures 1 and 2, SETs are placed in close proximity (e.g., in the nanometer range) from transmission lines, and spurious electric fields generated by these transmission lines can affect the operation of adjacent SETs.

[0037] Second, Joule heating from microwave currents induced in the transmission lines (generated by the controlled ESR signal) and currents induced elsewhere in the quantum chip increases the chip temperature, which severely impacts the fidelity of measurements and initialization of qubit states.

[0038] Third, we found that quantum chips dissipate more than 100 nW of heat per qubit control transmission line. Because quantum systems are highly susceptible to thermal noise, they typically operate at very low temperatures (on the order of tens to hundreds of millikelvins). Dilution refrigerators are used to bring systems down to these temperatures, but these dilution refrigerators offer a finite amount of cooling power. For example, some dilution refrigerators have a cooling power of 15 μW at 20 mK. Given that 100 nW of heat is dissipated per qubit, it is difficult to increase the number of qubits on a quantum chip with currently available cooling power, which is the limit that typical dilution refrigerators can handle while maintaining a temperature of 20 mK. Greater cooling power of 200–300 μW is available at higher temperatures (around 100 mK), but the number of qubits allowed is still fundamentally limited. For example, for 100 qubits, 10 μW of heat is dissipated, which is the limit that typical dilution refrigerators can handle.

[0039] When local transmission lines are implemented in medium- or large-scale quantum computers, the above problems of local control fields become unmanageable. First, implementing one transmission line per qubit on a quantum chip containing hundreds, thousands, or even millions of qubits is extremely complex. Even if a single transmission line per qubit on a multi-qubit quantum chip were successfully implemented, the amount of Joule heating generated by the transmission line could disrupt the cryogenic temperature environment (temperatures below 4 K) essential for the operation of the quantum chip. Furthermore, the electric fields generated by impedance mismatches in multiple transmission lines could be very large and adversely affect the operation of sensitive SETs. Furthermore, such an arrangement would result in the transmission lines occupying a large portion of the chip area. For example, the size of a single transmission line could extend from nanometer size to hundreds of micrometers. This is a significant amount of space for a quantum processor with atomic-sized qubits, which could seriously complicate the architecture design of quantum chips for medium- or large-scale quantum computers.

[0040] Due to the above issues, the field of quantum computing acknowledges that local control of qubits using a single transmission line per qubit may not be a viable solution for scaling to medium- or large-scale quantum computers. Therefore, emerging models of quantum chip architectures for both quantum dot-based quantum computers and donor-based spin quantum computers propose implementing "global" control of multiple qubits for scalable quantum computers.

[0041] For example, FIG. 3 shows a decomposed schematic architecture of a known scalable silicon quantum computing structure 30. The structure is made of isotopically purified silicon 28 ( 28 The architecture is formed of a silicon (Si) substrate. Specifically, a plurality of donor atoms 31 are embedded in the silicon lattice. Two sets of control lines span the entire architecture. The control lines are disposed on an upper control layer 32 above the qubit layer, and the control lines are disposed on a lower control layer 34 below the qubit layer. The control lines 33 and 35 are disposed perpendicular to each other in a cross-shaped configuration. The two planar control lines do not physically intersect, but define intersections 39a that pass through two vertically aligned portions of the lattice. Control elements 39, provided in the form of heavily doped silicon islands, are formed around some of these intersections. Each island forms a single-electron transistor (SET) with respective control members disposed above and below the island. One pair of these control members functions as the transistor's source and drain, and the other pair functions as the transistor gate.

[0042] In structure 30, the control lines 35 on the bottom surface are separated into two interleaved groups 35a and 35b. Control line 35a serves as the drain (D) of the SET, and control line 35b serves as the gate (G) of the SET 39. B ) function as the source (S) and gate (G) of SET39. A) are shown for the top surface control lines (e.g., control lines 33a and 33b), which each function as a control island. Each SET 39 interacts with one or more donor atoms 31 via a respective control island 39a.

[0043] The quantum computing structure 30 includes a donor-based silicon quantum chip 30 that employs global control of multiple qubits simultaneously. In this system, global microwave (MW) and radio frequency (RF) control signals 36 are in an "always on" state, but appropriate electrical signals are applied to individual qubits whenever the qubits need to be rotated / controlled by the "always on" global control signals.

[0044] Global control is implemented in this system by generating a "global" microwave (MW) and radio frequency (RF) control field 36 that exists throughout the quantum chip 30. During operation, the entire system 30 is cooled to the millikelvin temperature range. Pulses applied to control lines 33 and 35 can then drive transitions between qubit logic states.

[0045] In one approach, these MW and RF control fields 36 can be generated by embedding the silicon quantum chip 30 in a three-dimensional (3D) microwave resonator (frequency ω and quality factor Q), where the resonator is typically constructed from copper or some other highly conductive metal and is probed with a series of microwave pulses.

[0046] However, this arrangement presents several problems. For example, the high conductivity of the metal gates and bond wires on chip 30 can adversely affect important characteristics of the microwave resonators, such as their resonant frequency ω and quality factor Q. Furthermore, these microwave resonators typically generate large AC electric fields within the cavity, which can interfere with and potentially damage the sensitive SET sensor devices 39 on chip 300, thereby significantly affecting the desired operation and detection of the quantum processor's qubit states.

[0047] A key metric for any microwave resonator used in spin resonance applications is the power-to-magnetic field conversion factor, C, which quantifies how well a microwave input signal is converted into the AC magnetic field needed to drive spin rotation. The relationship B1 = C√P relates the magnetic field, B1, stored in the microwave resonator to the input microwave signal power, P, and the conversion factor, C. Qubit rotation in quantum processors / chips requires high magnetic MW fields, which means that C and / or P must be reasonably high to generate a viable MW magnetic field, B1, in the microwave resonator.

[0048] The inventors of the present application have realized that conventional metal / copper microwave cavities have a low conversion factor C. Therefore, according to the relationship B1=C√P, if a quantum chip were placed inside a conventional metal / copper microwave resonator, a substantially high power P of the input microwave signal would be required to drive sufficiently fast spin rotation of the qubits (because the conversion factor C of these cavities is very low). However, such a high power of the input microwave signal would be incompatible with the cryogenic environment in which the quantum chip / processor may reside and operate.

[0049] Therefore, the inventors have concluded that conventional metal / copper microwave cavities cannot adequately provide global control signals to the qubits of a quantum chip / processor.

[0050] Another experimental technique for providing global control has been proposed. This technique employs a loop-gap resonator. As shown in FIG. 4, a loop-gap resonator 40 has an inner radius r, a length z, a wall thickness w, and a separating capacitive gap t extending along the length of the resonator 40. This loop-gap resonator is designed to provide spatial separation between the electric (E) and magnetic (H) components of a resonant mode. Ideally, the resonator 40 would confine the electric field component within the capacitive gap and allow the magnetic field component to circulate in a loop from the top cross-section of the resonator 40 to the bottom cross-section.

[0051] This resonator 40 exhibited a conversion coefficient of C≈0.03 mT / √(mW) and a quality factor of Q≈200. This means that a relatively low-power input MW signal, e.g., P=10 mW (which is low compared to the relatively high power required for conventional microwave resonators, but still high compared to the cooling power of a typical dilution refrigerator), can be used to generate a MW magnetic control signal capable of providing the required qubit rotation / control.

[0052] When a qubit is placed within the magnetic field component of loop gap resonator 40, it is affected only by the magnetic field component H and does not see the electric field component E confined within the capacitive gap. Thus, the separation of the electric and magnetic field components provided by this loop gap resonator reduces the adverse effects of the resonator on the qubit (and particularly the SET device), and vice versa.

[0053] However, actual experimental results show that even at fairly low powers (e.g., 0.5 mW, which is not even sufficient to provide the necessary qubit control), there is a high residual stray electric field inside the resonator 40. This stray field is sufficient to overwhelm the SET device sensors of the quantum chip, thus adversely affecting the qubit spin measurements.

[0054] Furthermore, although resonator 40 requires a lower input power MW signal than that required by conventional resonators, an input power of at least approximately 10 mW is required to achieve sufficient quantum bit control frequencies (2-3 MHz). This power is at least three orders of magnitude too high to enable continuous operation of the quantum chip in the millikelvin temperature range. Furthermore, this input power range heats the quantum chip and disrupts its normal operation. Therefore, even loop-gap resonators cannot successfully demonstrate global control.

[0055] Thus, the implementation of global control signals for controlling multiple qubits within a quantum chip without disrupting the environment in which the qubits can operate to perform quantum computing has not been successfully implemented. In other words, for medium- and large-scale quantum computers, the implementation of global control signals for collectively controlling multiple qubits without disturbing the delicate environment of the qubits within a quantum chip remains an open challenge.

[0056] Some of the requirements for the quantum chip environment include, for example, maintaining the quantum chip at the cryogenic temperatures necessary to ensure the expected functionality of the quantum chip. The cryogenic requirement arises from the fact that quantum phenomena in quantum chips / processors only occur at very low temperatures. Higher temperatures can easily alter certain characteristics of the qubits (e.g., resonant frequency, coherence time, etc.) and their quantum behavior overall. Typically, cryogenic constraints require the quantum chip / processor to operate at temperatures ranging from 1 mK to 4 K. Other requirements include ensuring that any stray electric fields or electric fields generated by control signals do not affect the SET sensor and qubits. As already discussed, microwave resonators can provide a global control field, but when integrated with a quantum chip / processor, these pose multiple challenges.

[0057] Global control resonator The inventors of the present application have recognized that to generate such a global control field, a microwave resonator is needed that can provide a MW magnetic control field that is high enough to effectively control / rotate the qubits, while at the same time not destroying the fragile environment in which the quantum chip / processor operates.

[0058] The present disclosure describes one such resonator. In particular, the resonator disclosed herein is a high-dielectric-constant solid-state microwave resonator that can be placed near a spin-based quantum chip / processor to direct the magnetic fields necessary to control the qubits on the quantum chip.

[0059] In a particular embodiment, the resonator is formed of a dielectric medium, in particular a quantum paraelectric medium. In one embodiment, the quantum paraelectric medium is a perovskite structure ( XII A 2+VI B 4+ X 2- In a specific embodiment, the quantum paraelectric medium is potassium tantalate (KTaO3) or strontium titanate (SrTiO3). Quantum paraelectric media exhibit very large dielectric constants at cryogenic temperatures. For example, potassium tantalate has an ε r strontium titanate has a dielectric constant of ε r This large dielectric constant ε r provides very tight confinement of the electric field within the dielectric resonator, allowing a clear spatial separation of the electric and magnetic field components. Furthermore, the resonant frequency of a dielectric resonator is determined by the dielectric constant ε of the material. r and its modal volume V, which is given by the following relation: ω∝1 / (ε r 1 / 2 V 1 / 3 )

[0060] Therefore, for a given frequency ω, a large ε r By using these paraelectric materials, which exhibit

[0061] This class of materials also has very low microwave loss (e.g., tanδ ~ 10 for KTaO3). -4 ~10 -5 ), which allows for very high quality factors (Q~30,000 for KTaO3).

[0062] Furthermore, this resonator has a very high conversion factor C (according to the relationship B1 = C√P) to meet the high MW magnetic field requirements for controlling the spin of the qubit. The conversion factor C is given by the relationship

number

[10] . Typically, the operating frequency ω is fixed by other experimental considerations. Therefore, in typical embodiments, a high conversion factor C is achieved by providing a high quality factor Q, or by providing a low mode volume V, or by providing a combination of a high quality factor Q and a low mode volume V. The combination of properties of the quantum paraelectric medium produces a large conversion efficiency (e.g., C≈1 mT / √(mW) for KTaO), which is sufficient by itself for continuous operation at millikelvin temperatures. This conversion factor can be further improved by increasing the quality factor of the formed resonator.

[0063] In one example, a resonator formed in accordance with aspects of the present disclosure can operate at a Rabi frequency of 3 MHz at an input power of 15 μW in the millikelvin temperature range. The Rabi frequency is calculated using the following equation: Ω R =γ e B1 / 2, where γ e = 28 GHz / T is the gyromagnetic ratio of electron spin, which when divided by 2 gives the rotating wave approximation. Due to this achievable conversion factor, the disclosed resonator will not overheat a quantum chip / processor placed adjacent to it.

[0064] 5 shows a plan view of an exemplary solid dielectric resonator 50 according to an embodiment of the present disclosure. In one example, the dimensions of a rectangular dielectric resonator may be 1 mm x 1 mm x 0.5 mm. Typically, there are three types of modes that appear in a dielectric resonator: TE mode (electric field transverse to the z-axis), TM mode (magnetic field transverse to the z-axis), and hybrid mode (both electric and magnetic fields have components parallel to the z-axis). Cylindrical and ring resonators typically exhibit all three modes.

[0065] TE 11δ This mode is particularly useful for performing ESR. 11δ is used to indicate that the resonator 50 radiates like a dipole in the z-axis, occurring when z is the smallest dimension. In this mode, the AC magnetic field generated by the resonator 50 is perpendicular to the surface 51 of the resonator 50 and extends outward (or inward) from the resonator surface 51, while the electric field component is transverse to the direction of the magnetic field component and is confined within the resonator 50.

[0066] 6A and 6B show perspective views of a dielectric resonator 50. In particular, FIG. 11δ 6B shows the magnetic field lines in the dielectric resonator 50 when the mode is excited. 11δ 6A shows the electric field lines of the dielectric resonator 50 when the mode is excited. As can be seen in FIG. 6A, the magnetic field component B1 is perpendicular to the surfaces 51 and 52 of the dielectric resonator 50. Similarly, it is clear from FIG. 6B that the electric field component E of this resonator is almost completely confined and circulates within the dielectric resonator 50.

[0067] Example architecture for global control of qubits 7 illustrates an arrangement 70 for globally controlling qubits on a quantum computing chip / processor. As shown in this figure, the arrangement includes a quantum chip / processor 75, a dielectric resonator 50, and a coupler 74. The dielectric resonator 50 in this arrangement is positioned above the quantum chip 75 such that one or more qubits of the quantum chip / processor are below the surface 51 of the dielectric resonator 50. A coupler 74 is positioned above the dielectric resonator 50 to excite the resonator. In one embodiment, the coupler 74 is a TE 11δ The resonator 50 is configured to excite the resonator in a mode, and is positioned on top of a quantum chip with a small gap (less than the height of the dielectric resonator) between the bottom of the resonator 50 and the quantum dot qubit chip 75.

[0068] In this embodiment, coupler 74 is a coaxial cable that provides the input MW signal to dielectric resonator 50. In alternative embodiments, the MW input signal may be provided by a differently shaped coupler. In still other embodiments, the MW input signal may be provided by several means, such as using a printed circuit board with a lithographically defined coupler or coupling through a waveguide and iris.

[0069] When a MW input signal is provided to resonator 50, an electric field E and a magnetic field B are generated within the resonator. As noted above, electric field component E is tightly confined within resonator 50, while magnetic field component B is in a direction perpendicular to surfaces 51 and 52 of resonator 50. Thus, one or more qubits located on chip / processor 75 and facing surface 51 interact with magnetic field component B. This magnetic field serves as a global magnetic field for controlling one or more qubits on chip 75.

[0070] In one embodiment, a single qubit is controlled by the global magnetic field B generated by the dielectric resonator 50. In an alternative embodiment, multiple qubits (hundreds, thousands, or millions) can be simultaneously controlled by the global magnetic field B generated by the dielectric resonator 50.

[0071] All components of system 70 may be housed within a custom device enclosure 71, as shown in Figure 7. In further embodiments, printed circuit boards may be utilized.

[0072] In an alternative embodiment, if quantum chip / processor 75 is positioned above dielectric resonator 50 , the qubits may face surface 52 of dielectric resonator 50 .

[0073] Although the above embodiment describes a rectangular parallelepiped-shaped resonator 50 (see FIGS. 5-7 and 9), the present invention is not limited to this particular shape of the resonator, and alternative resonator shapes may also be employed to implement the methods and systems described herein. For example, the resonator may be square, disk-shaped (see disk-shaped resonator 80 in FIG. 8a), cylindrical, annular (see annular resonator 82 in FIG. 8b), square annular, or rectangular annular, etc.

[0074] In the case of an annular shape of the resonator as shown in Figure 8b, the quantum chip (not shown in this figure) may be held inside the central cavity 83, or directly below or above the cavity 83. The advantage of this type of shape is that it potentially allows access to higher magnetic field strengths (as the magnetic field in this shape peaks at the center of the resonator 82).

[0075] In some embodiments of the present disclosure, for a given resonator (with a dielectric constant on the order of several thousand), each dimension (e.g., length, height, width, thickness, or diameter) can range from 100 micrometers to 10 millimeters. For a given dielectric constant, the operating frequency of the resonator depends on its volume. Therefore, the dimensions of the resonator can be adjusted to achieve a specific volume and therefore a specific operating frequency. For example, a rectangular parallelepiped potassium tantalate resonator can be fabricated with a volume of 0.5 mm x 1 mm x 1 mm. Such a resonator provides a resonant frequency of approximately 4.5 GHz (the dielectric constant of potassium tantalate is 4300 at mK). The height of this resonator can be reduced by a factor of four and the length and width doubled (i.e., 0.125 mm x 2 mm x 2 mm) to achieve the same volume and a similar resonant frequency.

[0076] In some embodiments of the present disclosure, the operating distance between the resonator and the chip ranges from 50 micrometers to 5 millimeters. The operating distance between the resonator and the quantum chip is set by the mode size of the resonator, which in turn is limited by the dimensions of the resonator. Essentially, the separation between the resonator and the quantum chip is less than the height of the resonator.

[0077] In one embodiment, a low microwave loss tangent material, such as a sapphire spacer or plate, may be placed in the gap / separation between the quantum chip / processor 75 and the dielectric resonator 50. This arrangement 90 is shown in FIG. 9, where the resonator 50 is spaced from the quantum processor chip 75 by a sapphire plate 92. In an alternative embodiment, the dielectric resonator 50 can be suspended above or below the quantum chip / processor 75, using a vacuum between the two surfaces. The sapphire spacer or vacuum space between the quantum processor and the dielectric resonator helps to reduce losses and protect the quantum chip / processor 75 from stray electric fields.

[0078] In some embodiments of the present disclosure, the operating frequency of the resonator is preferably between 1 GHz and 100 GHz. Electron spin relaxation rates can be significant (compared to electron or nuclear spin coherence times) above 100 GHz. Furthermore, microwave engineering at frequencies above 100 GHz becomes difficult and expensive.

[0079] Although the foregoing methods and systems of this disclosure describe global control of electron spin using a dielectric resonator, these techniques can also be implemented to control nuclear spin. In that case, the frequency of the dielectric resonator can be in the range of 1.0 MHz to 1.0 GHz, and the size of the resonator can be determined by the formula ω∝1 / (ε r 1 / 2 V 1 / 3 )) can be used to scale accordingly.

[0080] In some embodiments of the present disclosure, the input power of the MW signal is less than 100 μW when the operating temperature is in the millikelvin range. For operating temperatures within 1.5 Kelvin to 4.0 Kelvin, the input power is less than 1.0 W.

[0081] In some embodiments of the present disclosure, the resonator's conversion coefficient C can be in the range of 0.1 to 10.0 mT / √(mW) when the operating temperature is in the millikelvin range. Higher conversion coefficients can also be achieved at operating temperatures within 1.5 Kelvin to 4.0 Kelvin.

[0082] In some embodiments of the present disclosure, the strength of the AC magnetic field provided by the dielectric resonator may range from 0.01 mT to 100.0 mT.

[0083] Experimental results In this section, we present experimental results achieved using a dielectric resonator 50 suspended above a quantum chip 75 formed of one or more spin-based qubits with a 200 micron wide sapphire spacer in between (e.g., as shown in the device of Figure 9).

[0084] In the experimental setup, coupler 74 is 11δ 10. As can be seen in FIG. 10, the electric field component E is tightly confined within the resonator 50, while the magnetic field component B is in a direction perpendicular to the surfaces 51 and 52 of the resonator 50.

[0085] 11A and 11B show finite element simulations of the magnitude of the electric and magnetic fields, respectively, in the device stack (of FIG. 9) when the fundamental mode of resonator 50 is excited with a microwave input signal. The input power used in this experiment was 100 microwatts. However, it will be understood that other input power values ​​will produce similar magnetic and electric field patterns, with the magnetic field conversion being given by (mT / √W) and the electric field conversion being given by (kV / cm / √W). The darker regions in FIGS. 11A and 11B represent regions with high magnetic and electric fields, respectively, and the lighter regions in FIGS. 11A and 11B represent regions with low to zero magnetic and electric fields, respectively. As can be seen in FIG. 11B, when an input power signal is applied to resonator 50, qubit 112 on the surface of quantum processor 75 experiences a near-zero electric field, while (as seen in FIG. 11A) qubit 112 experiences a magnetic field approaching 0.5 mT.

[0086] FIG. 12 shows the reflection parameters (S 11 ) is a chart showing the reflection parameter S 11 is known as the reflection coefficient because it represents the amount of power reflected from the resonator. 11 If S11 = 0 dB, all the power is reflected from the resonator and nothing is absorbed. If S11 < 0 dB, some of the input power is absorbed by the resonator, generating electric and magnetic fields.

[0087] As shown in Figure 12, S 11The amplitude of S approaches -40 dB at frequencies between 7.653 and 7.6535 GHz. If critical coupling is achieved between resonator 50 and coupler 74, the S amplitude can theoretically drop to -∞. At the critical coupling frequency, the most efficient power transfer to the resonator occurs.

[0088] From this plot, it becomes clear that the resonator 50 modes are excited to produce the E electric and B magnetic field profiles shown in Figures 11a and 11b, which are best between 7.653 and 7.6535 GHz, and that operating in this frequency range can result in achieving critical coupling with coupler 74.

[0089] Furthermore, while any spin-based quantum processor chip may be utilized with the resonator 50, the experiments discussed in this section are performed with a singlet-triplet qubit. In a singlet-triplet qubit, two quantum dots, each with one or more electrons, are formed side-by-side and arranged to tunnel-couple. Information can be stored in the relative spin of the two electrons, further reducing the qubit's coupling to its environment. Of the four possible relative spin states of the electrons (S, T, T, and T), information is typically stored in the singlet state S and the triplet state T (the so-called "logical subspace"). This choice is generally motivated by two advantages. First, these two qubit states remain unaffected by changes in magnetic fields (both m = 0), further decoupling them from their environment. Second, due to the Pauli exclusion principle, in the singlet state, one electron has an orbital wave function hybridized between the two dots, while in the triplet state, both electrons are confined to separate dots. Therefore, by tuning the relative chemical potentials of the two dots, the charge distribution of the singlet state and the relative energies of the singlet and triplet states can be dispersed.

[0090] Figure 13A shows an exemplary quantum processor chip 75 including double quantum dots. In particular, Figure 13A is a scanning electron microscope (SEM) image 130 of quantum processor chip 75. Figure 13B shows a cross section 132 of the quantum processor chip of Figure 10A. Cross section 132 was taken through the center of the device (marked by a dashed line in Figure 13A). Cross section 132 shows the 3D structure of quantum processor chip 75 and its conduction band profile.

[0091] 13A and 13B, the quantum processor chip 75 includes quantum dots (Dot 1 and Dot 2), single-electron transistor (SET) sensors for sensing or reading the states of the quantum dots D1 and D2, and a reservoir (RESG) for loading electrons into the double quantum dots D1 and D2 to form singlet-triplet qubits. Additionally, gate electrodes P1 and P2 are disposed on top of the quantum dots D1 and D2.

[0092] FIG. 14A shows the current I passing through the SET sensor as the gate electrodes (P1, P2) above each dot D1 and D2 are scanned and electrons jump into and out of the two quantum dots D1 and D2. SET 1 shows a two-dimensional stability map 140 of double quantum dots D1 and D2 obtained by monitoring the charge state or occupancy of each dot relative to the bias applied through the gate electrode. In particular, the horizontal and vertical lines indicate the timing of electron jumps into and out of quantum dots D1 and D2. The section marked with reference number 142 shows a singlet-triplet state with three electrons in dot2 and one electron in dot1. The numbers in parentheses in stability map 140 are the charge occupancies (N1, N2) of the double-dot systems D1 and D2.

[0093] Figure 14B shows a readout pulse sequence superimposed on a plot 145 of the difference in SET current between mixed (i.e., mixed spin singlet and triplet) and singlet spin state preparation as a function of gate P1 and P2 voltage. The spin singlet state is prepared by pulsing from (4,1) to (4,0) occupancy, and the mixed state is prepared by pulsing from (3,0) to (3,1) occupancy. Pulse sequence A through B prepares a double quantum dot separated by electrons in a mixed spin state. Readout is performed in steps B through D. Steps B through C attempt to push electrons from Dot2 to Dot1. When an electron from Dot2 forms a singlet with an electron from Dot1, tunneling occurs. However, when a triplet state is formed, tunneling is blocked. Steps C through D improve the visibility of the readout via an enhanced latching mechanism. Also, E represents the level used when performing ESR. The solid lines in the plot indicate the transitions with high tunneling rates, the dashed lines in the plot indicate the transitions with low tunneling rates, and the thin lines delineate the Pauli spin blockade (PSB) and latching regions.

[0094] FIG. 15A shows a pulsed scheme (A-D shown in FIG. 14B) for electron spin resonance measurements using resonator 50. Double quantum dots D1 and D2 are initialized in a spin triplet state at A. Microwave power is then applied to dielectric resonator 50 at B, generating an AC magnetic field B, which rotates the spins of electrons in quantum dots D1 and D2. Spin resonance raises spin blockade, resulting in a reduction in triplet probability during readout.

[0095] 15B is a plot showing the triplet state probability of a double quantum dot as a function of applied microwave frequency in a DC magnetic field of 227.48 mT. The plot shows two electron spin resonance (ESR) peaks. This plot demonstrates proof-of-principle off-chip control of quantum dot spins through a dielectric resonator 50.

[0096] 15C shows the triplet probability as a function of applied microwave frequency and DC magnetic field. As can be seen in this figure, the triplet probability drops off at the resonant frequency of resonator 50. This shows that the ESR peak shifts with magnetic field, as expected.

[0097] Figure 15D, a slice taken along the diagonal of Figure 15C, shows the triplet probability as a function of microwave drive frequency, measured while stepping the magnetic field so that the spin triplet energy splitting is equal to the drive frequency. When the microwave frequency matches the dielectric resonator frequency, the triplet probability decreases and an enhancement of the spin resonance signal is observed.

[0098] It will be understood that the invention disclosed and defined herein extends to all alternative combinations of two or more individual features mentioned or apparent from the text or drawings, all of these different combinations constituting various alternative aspects of the invention.

Claims

1. 1. A system for global control of one or more qubits, comprising: a quantum processor including a plurality of spin-based qubits; a dielectric resonator disposed adjacent to the quantum processor, the dielectric resonator being formed from a dielectric material whose dielectric constant increases at cryogenic temperatures compared to room temperature; Equipped with the dielectric resonator is operated at the cryogenic temperature at an operating frequency determined by the dielectric constant and resonant mode volume of the dielectric resonator, Receives the input signal from the coupler, and in response to receiving the input signal, generating a global AC magnetic field at the operating frequency extending from the dielectric resonator to the quantum processor to control electron spin or nuclear spin of one or more qubits of the spin-based qubits. The system.

2. The system of claim 1 , wherein the cryogenic temperature is 4 Kelvin or less.

3. 3. The system of claim 1, wherein the dielectric constant of the dielectric resonator is in the range of 1000 to 40,000 at the cryogenic temperature.

4. The system of any one of claims 1 to 3, wherein the global AC magnetic field controls one qubit of the quantum processor.

5. The system of any one of claims 1 to 3, wherein the global AC magnetic field simultaneously controls multiple qubits of the quantum processor.

6. The system of any one of claims 1 to 5, wherein the dielectric resonator generates an electric field that is spatially separated from the global AC magnetic field.

7. 7. The system of claim 6, wherein the global AC magnetic field of the dielectric resonator is perpendicular to a surface of the dielectric resonator and directed outward from the surface of the dielectric resonator.

8. 8. The system of claim 7, wherein the electric field is confined away from the location of the quantum processor to minimize interaction of the electric field with one or more of the spin-based qubits and the on-chip measurement and control electronics of the quantum processor.

9. The system of claim 8 , wherein the electric field circulates within the dielectric resonator.

10. The dielectric resonator has a perovskite structure ( ＸＩＩ A ２＋ＶＩ B ４＋ X ２－ ３ 10. The system according to claim 1, made of a material from the class of compounds having the formula:

11. The dielectric resonator is made of potassium tantalate (KTaO ３ ) or strontium titanate (SrTiO ３ 11. The system of claim 10, wherein the system is made of

12. The resonant mode volume of the dielectric resonator is about 5×10 －７ m ３ The system according to any one of claims 1 to 11,

13. The system of any one of claims 1 to 12, wherein the quantum processor is a solid-state semiconductor or superconducting quantum processor.

14. 14. The system of claim 1, wherein the dielectric resonator is in the form of a solid block of dielectric material, and the quantum processor is positioned above or below the dielectric resonator such that one or more of the spin-based qubits of the quantum processor face the dielectric resonator to interact with the global AC magnetic field provided by the dielectric resonator.

15. The system of any preceding claim, wherein the dielectric resonator is separated from the quantum processor by a low microwave loss tangent material or a vacuum space.

16. The coupler is Coaxial cable, a lithographically defined coupler, or Waveguide and Iris The system according to any one of claims 1 to 15,

17. 17. The system of any one of claims 1 to 16, wherein the frequency of the global AC magnetic field generated by the dielectric resonator is in the radio frequency range of 1.0 MHz to 1.0 GHz for controlling nuclear spins.

18. 17. The system of claim 1, wherein a frequency of the global AC magnetic field generated by the dielectric resonator is in a microwave frequency range ranging from 1.0 GHz to 100.0 GHz for controlling electron spins.

19. A method for global control of multiple qubits in a quantum processor using a system according to any one of claims 1 to 18.

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