Global control of a quantum computing system

Abstract

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

Description

Technical Field

[0001] This disclosure relates to methods and systems for controlling qubits in quantum computing systems. Background Technology

[0002] Quantum computers and quantum simulators promise to revolutionize many aspects of our modern society, from basic scientific and medical research to national security. The implications for the defense of many of these applications will be substantial, such as finding prime factors or breaking cryptography, designing new materials from first principles, artificial intelligence, and machine learning. While some applications are expected to run on medium-sized quantum computers (with 100 to 1000 qubits) without error correction protocols, some of the most destructive algorithms, such as Shor's prime factorization algorithm, will require large and fully fault-tolerant quantum computers with more than a million qubits.

[0003] However, many obstacles need to be overcome before such large-scale quantum computers can be commercially manufactured. One such obstacle is the control of qubits (the basic units of quantum information control). To date, several techniques have been proposed to control the states of qubits, but these techniques either cannot be effectively scaled up or lead to faster decoherence.

[0004] Therefore, a scalable qubit control system is needed that can control multiple qubits simultaneously without adversely affecting their operation. Summary of the Invention

[0005] According to a first aspect, the present invention provides a system for controlling one or more qubits in a quantum processor, the system comprising: a quantum processor including one or more spin-based qubits; and a dielectric resonator located near the quantum processor, the dielectric resonator providing a magnetic field, and the quantum processor being located 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 qubits of the quantum processor.

[0006] In one implementation, multiple spin-based qubits of the quantum processor are operated and controlled by a portion of the magnetic field provided by a dielectric resonator at a cryogenic temperature.

[0007] In some implementations, the cryogenic temperature is less than or equal to 4 Kelvin.

[0008] In another embodiment, the dielectric resonator is made of a dielectric material whose dielectric constant increases at low temperatures relative to at room temperature.

[0009] In some implementations, the dielectric constant of the resonator is in the range of 1,000 to 40,000 at low temperatures.

[0010] In some implementations, a portion of the magnetic field controlling one or more spin-based qubits is a uniform alternating magnetic field.

[0011] In some implementations, this portion of the magnetic field acts as a global magnetic field, used to simultaneously control multiple spin-based qubits of a quantum processor.

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

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

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

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

[0016] In some implementations, the dielectric resonator is derived from a material having a perovskite structure ( It is made from a class of compounds.

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

[0018] In some implementations, the dielectric resonator provides approximately The volume of the resonant mode.

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

[0020] In some implementations, the dielectric resonator is in the form of a solid block of dielectric material, and the quantum processor is placed above or below the dielectric resonator such that one or more spin-based qubits of the quantum processor partially interact with the dielectric resonator to provide an alternating magnetic field.

[0021] In some implementations, the system also includes a tunable coupling element to provide a microwave input signal to the dielectric resonator for generating a magnetic field. The dielectric resonator may require a low-power microwave input signal to minimize any impact on the cryogenic environment of the quantum processor.

[0022] In some implementations, the quality factor Q of the resonator has a value greater than 100 at low temperatures.

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

[0024] In some implementations, the frequency of the magnetic field generated by the resonator is in the microwave frequency range, from 1.0 GHz to 100.0 GHz, and is used to control electron spin.

[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 the system described in the first aspect of the invention.

[0026] As used herein, unless the context otherwise requires, the term “including” and variations thereof, such as “comprising”, are not intended to exclude further additions, components, integers, or steps.

[0027] Further aspects of the invention, as well as other embodiments of the aspects described in the foregoing paragraphs, will become apparent from the examples and with reference to the accompanying drawings. Attached Figure Description

[0028] Figure 1 A prior art quantum computing device is shown, which has donor-based qubits controlled by local on-chip transmission lines;

[0029] Figure 2 A prior art quantum computing device is shown, which has quantum dot qubits controlled by local on-chip transmission lines;

[0030] Figure 3 A schematic architecture of a donor-based quantum computer that is scalable in the prior art is shown, which employs global control of qubits;

[0031] Figure 4 This demonstrates a prior art toroidal resonator capable of separating the magnetic and electric fields and directing them to different regions; and

[0032] Figure 5 A top view of a dielectric resonator made of perovskite material (also known as potassium tantalate, chemical formula KTaO3) and having a fundamental resonant frequency of 4.5 GHz, according to an exemplary embodiment of the present disclosure, is shown.

[0033] Figure 6A and Figure 6B It shows when Figure 5 TE of rectangular dielectric resonator z111 Module (also referred to as TE in this disclosure) 11δ The magnetic and electric field distribution when excited;

[0034] Figure 7An architecture for a scalable donor-based quantum computer according to an exemplary embodiment of the present disclosure is shown, which employs global control of qubits using a uniform magnetic field generated by a dielectric resonator; and

[0035] Figure 8(a) and 8(b) An example of an alternative shape for a dielectric resonator is shown.

[0036] Figure 9 An architecture for a scalable donor-based quantum computer according to another embodiment of the present disclosure is shown, which employs global control of qubits using a uniform magnetic field generated by a dielectric resonator.

[0037] Figure 10 A resonator having electric field lines and magnetic field lines according to some embodiments of the present disclosure is shown.

[0038] Figure 11a A finite element simulation of the magnetic field amplitude of the fundamental mode of a resonator excited with a microwave signal power of 100 μW is shown.

[0039] Figure 11b A finite element simulation of the electric field amplitude of the fundamental mode of a resonator excited with a microwave signal power of 100 μW is shown.

[0040] Figure 12 This is a graph showing the microwave reflection S-parameters of the resonator near the fundamental mode of the dielectric resonator, as detected from a coaxial loop coupler.

[0041] Figure 13a This is a scanning electron micrograph (SEM) of the quantum processor chip used in the experiment.

[0042] Figure 13b Is it through Figure 13a The cross-section of the conduction band distribution in the middle of the quantum processor chip and the device.

[0043] Figure 14a yes Figure 13a Stability diagram of spin qubits in the device.

[0044] Figure 14b It shows the superimposed on Figure 14a The readout pulse sequence is shown as a portion of the stability plot.

[0045] Figure 15a A pulsed scheme for electron spin resonance measurements using the resonator of this disclosure is shown.

[0046] Figure 15b It is a graph showing the triplet probability as a function of the applied microwave frequency.

[0047] Figure 15c The triplet probability is shown as a function of the applied microwave frequency and DC magnetic field.

[0048] Figure 15d It is along Figure 15c The plot, taken diagonally, shows the triplet probability and reflection parameters of the resonator as a function of the microwave drive frequency, demonstrating the enhancement of ESR at the dielectric resonator frequency. Detailed Implementation

[0049] Overview

[0050] This section provides an overview of existing quantum computing systems and the various issues associated with the qubit control techniques implemented in these systems.

[0051] One type of quantum computing system is based on the spin states of individual qubits, where qubits are the electron and nuclear spins located within a silicon quantum chip. These electron and nuclear spins are either confined within artificial quantum dots (e.g., ...) Figure 2 ), or confined to naturally occurring donor atoms (e.g., those implanted in a quantum chip). Figure 1 )middle.

[0052] The applicant's early breakthrough qubit experiments have demonstrated the great promise of these quantum systems, including key quality factors such as qubit coherence time, control, and measurement fidelity that outperform most other types of quantum computing systems. In these small systems (e.g., Figure 1 and Figure 2 In the system shown, on-chip transmission lines are used for local control of each individual qubit. Specifically, each individual qubit is provided with a dedicated on-chip transmission line located a few hundred nanometers from the qubit's position.

[0053] Figure 1 An example of a small silicon quantum chip 10 with a single donor-based qubit is shown. As illustrated in the figure, the quantum chip 10 has a first layer 12 of a silicon substrate and silicon-28 isotope as a purified form of silicon. 28 The second layer 13 is Si. The first layer 12 has a thickness of approximately 500 micrometers, and the second layer 13 has a thickness of approximately 0.9 micrometers. Window 14 shows an enlarged view of the central portion of the upper surface 17 of the quantum chip 10. The qubit 11 is located approximately at the center of the upper surface 17. The qubit 11 includes both electron spin and nuclear spin. The nuclear spin can be phosphorus-31 (Si). 31P) Donor atom. An on-chip transmission line 15 is present to control qubit 11. Located only a few hundred nanometers from qubit 11, the on-chip transmission line 15 transmits 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 spin of qubit 11. The ESR signal can have a frequency of approximately 40 GHz, and the NMR signal can have a frequency of approximately 100 MHz. A single-electron transistor (SET) 16 is used as a charge sensor to read out the state of qubit 11. It is clearly visible in the figure that the SET sensor 16 is located near the on-chip transmission line 15 and qubit 11.

[0054] Figure 2 A plan view of a quantum computing chip 20 is shown, which has a single qubit 21 confined within an artificially formed quantum dot. This system differs from... Figure 1 The system differs in that qubit 21 is located within a silicon quantum dot, rather than in a naturally occurring donor atom (such as...). 31 In P). However, with Figure 1 Similar to quantum chips, Figure 2 The quantum chip 20 uses a dedicated on-chip transmission line 26 for locally controlling the qubits 21. The on-chip transmission line 26 provides ESR and RF signals. Figure 2 (Not shown in the image). The ESR signal generates a microwave magnetic field line B, as shown in reference numeral 24, to control qubit 21. Furthermore, the quantum chip 20 includes one or more SET sensors 25 for measuring the quantum state of qubit 21. Figure 2 It is clear that the SET sensor 25 is located near the on-chip transmission line 26 and the qubit 21.

[0055] exist Figure 1 and Figure 2 In the systems shown, qubits can operate coherently in a microwave magnetic field “locally” generated using on-chip transmission lines (e.g., transmission lines 15 or 26). In these systems, the local microwave magnetic field B operates in “pulse mode,” meaning it is turned on when qubit rotation is required. The reason for operating the local microwave magnetic field B in pulse mode is that the transmission lines (15 or 26) generate a strong alternating electric field, which interferes with SET operation. Therefore, the microwave field is typically turned off at least before qubit measurement.

[0056] The aforementioned local control of qubits (i.e., dedicated transmission lines for each qubit) has been successfully implemented in small quantum computers. However, there may be some complexities and / or drawbacks associated with the local control signals generated by these local transmission lines.

[0057] First, impedance mismatch in the transmission line (e.g., transmission line 15 or 26) can generate stray electric fields that interfere with sensitive SETs used to measure the quantum states of qubits, rendering them unusable, while the control ESR and NMR signals are applied by the transmission line. Figure 1 and Figure 2 It is evident that the SET is located near the transmission lines (e.g., in the nanometer range), and any stray electric fields generated by these transmission lines may affect the operation of adjacent SETs.

[0058] Secondly, the Joule heating generated by the microwave current induced in the transmission line (generated by the control ESR signal) and currents induced elsewhere in the quantum chip increases the chip temperature. This severely affects quantum state measurement and initialization fidelity.

[0059] Third, it has been found that each qubit control transmission line dissipates over 100 nW of heat in a quantum chip. Quantum systems are highly susceptible to thermal noise and therefore typically operate at very low temperatures (approximately tens to hundreds of millikrons). Dilution refrigerators are used to cool the system to these temperatures, but these refrigerators offer limited cooling capacity. For example, some dilution refrigerators have a cooling power of 15 μW at 20 mK. Considering that each qubit dissipates 100 nW of heat, it is difficult to scale up the number of qubits in a quantum chip using currently available cooling capacity; 100 nW of heat is the limit that a typical dilution refrigerator can handle while maintaining a temperature of 20 mK. Greater cooling power of 200–300 µW can be achieved at higher temperatures (approximately 100 mK), but the number of qubits allowed remains fundamentally limited. For example, for 100 qubits, 10 µW of heat will be dissipated, which is the limit that a typical dilution refrigerator can handle.

[0060] When implementing localized transmission lines in medium- or large-scale quantum computers, the aforementioned problems with localized control fields become difficult to manage. First, implementing a transmission line per qubit in a quantum chip containing hundreds, thousands, or even millions of qubits is extremely complex. Even if one transmission line per qubit is successfully implemented in a multi-qubit quantum chip, the amount of Joule heating generated by the transmission lines can disrupt the cryogenic environment (temperatures equal to or below 4K) essential for the operation of the quantum chip. Furthermore, the electric field generated by impedance mismatch in multiple transmission lines will be extremely large and can adversely affect the operation of sensitive SETs. Moreover, in such arrangements, transmission lines will occupy a significant portion of the chip space. For example, the size of a single transmission line can scale from the nanometer scale to hundreds of micrometers. This is a huge amount of space for quantum processors with atomic-level qubits, which can make the architectural design of quantum chips for medium- or large-scale quantum computers extremely complex.

[0061] Due to the aforementioned issues, the quantum computing field generally believes that using a single transmission line to locally control each qubit may not be a feasible solution for scaling up to medium or large-scale quantum computers. Therefore, new models of quantum chip architectures for quantum dot-based quantum computers and donor-based spin quantum computers propose achieving “global” control over multiple qubits in a scalable quantum computer.

[0062] For example, Figure 3 A schematic architecture of a known scalable silicon quantum computing structure 30 is shown, broken down. This structure is formed on isotopically purified silicon 28 (…). 28 In a silicon (Si) substrate. Specifically, multiple donor atoms 31 are embedded in the silicon lattice. Two sets of control lines extend across the architecture. The control lines are disposed on an upper control layer 32 above the qubit layer, and on a lower control layer 34 below the qubit layer. Control lines 33 and 35 are arranged in a cross configuration perpendicular to each other. The control lines in the two planes do not physically intersect, but they define an intersection point 39a, where they pass through two vertically aligned portions of the lattice. With respect to some of these intersection points, control elements 39 are formed, provided in the form of heavily doped silicon islands. Each island forms a single electronic transistor (SET), with respective control elements disposed above and below the island. One pair of these control elements acts as the source and drain of the transistor, and the other pair acts as the gate of the transistor.

[0063] In structure 30, the control line 35 on the bottom plane is divided into two interleaved groups 35a and 35b. Control line 35a acts as the drain (D) of SET, and control line 35b acts as the gate (G) of SET 39. B A similar configuration is shown for the control lines on the top plane (e.g., control lines 33a and 33b), which act as the source (S) and gate (G) of SET 39, respectively. A Each SET 39 interacts with one or more donor atoms 31 through its respective control island 39a.

[0064] The quantum computing structure 30 features a donor-based silicon quantum chip 30 that simultaneously employs global control over multiple qubits. In this system, global microwave (MW) and radio frequency (RF) control signals 36 are in an "always-on" state, and whenever a qubit needs to be rotated / controlled by the "always-on" global control signals, appropriate electrical signals are applied to each qubit.

[0065] Global control in this system is achieved by generating a “global” microwave (MW) and radio frequency (RF) control field 36 that exists across the entire quantum chip 30. During operation, the entire system 30 is cooled to a milliKelvin temperature range. Pulses then applied to control lines 33 and 35 can drive transitions between qubit logic states.

[0066] In one approach, these MW and RF control fields 36 can be generated by embedding a silicon quantum chip 30 in a three-dimensional (3D) microwave resonator (frequency ω and quality factor Q), wherein the resonator is typically made of copper or some other highly conductive metal and probed by a series of microwave pulses.

[0067] However, this arrangement presents several problems. For example, the high conductivity of the metal gate and bonding wires on chip 30 may adversely affect important characteristics such as the resonant frequency ω and quality factor Q of the microwave resonators. Furthermore, these microwave resonators typically generate large alternating electric fields within the cavity, which may interfere with and potentially damage the sensitive SET sensor device 39 on chip 300, thereby significantly affecting the desired operation and detection of the quantum states of the quantum processor.

[0068] A crucial specification for any microwave resonator used in spin resonance applications is the power field conversion factor C, which quantifies the extent to which the microwave input signal is converted into the AC magnetic field required to drive the spin. (Relationship) The accumulated magnetic field B1 within the microwave resonator is correlated with the input microwave signal power P and the conversion factor C. For qubit rotation in quantum processors / chips, a high magnetic field MW is required, which means that C or P, or both, must be quite high to generate a feasible MW magnetic field B1 within the microwave resonator.

[0069] The inventors of this application have learned that conventional metal / copper microwave cavities have a low conversion factor C. Therefore, according to the relationship If a quantum chip were placed inside a conventional metal / copper microwave resonator, a considerably high power P of the input microwave signal would be required (because the conversion factor C of these cavities is very low) to drive the qubits to spin fast enough. However, such a high-power input microwave signal would be incompatible with the low-temperature environment in which quantum chips / processors can exist and operate.

[0070] Therefore, the inventors concluded that conventional metal / copper microwave cavities are not suitable for providing global control signals to the qubits of quantum chips / processors.

[0071] Another experimental technique that provides global control is the use of a toroidal gap resonator. For example... Figure 4 As shown, the annular gap resonator 40 has an inner radius r ,length z Wall thicknessw and the interval extending along the length of the resonator 40 is t The capacitor gap. This annular gap resonator is designed to provide spatial separation between the electric field component (E) and the magnetic field component (H) of the resonant mode. Ideally, resonator 40 should confine the electric field component within the capacitor gap and allow the magnetic field component to circulate in a ring from the upper cross-section to the lower cross-section of resonator 40.

[0072] The resonator 40 exhibits conversion factor and The quality factor. This means that a relatively low power input to the MW signal, such as P = 10 mW (lower than the relatively high power required by a conventional microwave resonator, but still higher than the cooling power of a typical dilution refrigerator), can be used to generate a MW magnetic control signal capable of providing the necessary qubit rotation / control.

[0073] When a qubit is placed within the magnetic field component of the annular resonator 40, it is only affected by the magnetic field component H and the electric field component E, which is confined within the capacitive gap, is not visible. Therefore, the separation of the electric and magnetic field components provided by this annular resonator reduces the adverse effects of the resonator on the qubit (especially SET devices), and vice versa.

[0074] However, actual experimental results show that even at relatively low power (e.g., 0.5 mW, which is insufficient even to provide the necessary qubit control), a high residual stray electric field exists inside the resonator 40. This stray electric field is sufficient to overwhelm the SET device sensor of the quantum chip and thus adversely affect qubit spin measurements.

[0075] Furthermore, although the input power (MW) required by resonator 40 is lower than that required by conventional resonators, at least approximately 10 mW of input power will be needed to achieve a sufficient qubit control frequency (2-3 MHz). This power is at least three orders of magnitude higher than that required for continuous operation of the quantum chip within a millikelvin temperature range. Moreover, this input power range heats the quantum chip and interferes with its normal operation. Therefore, even the toroidal gap resonator cannot successfully demonstrate global control.

[0076] Correspondingly, a method for implementing a global control signal to control multiple qubits in a quantum chip without disrupting the environment in which the qubits can operate to perform quantum computing has not yet been successfully achieved. In other words, for medium and large-scale quantum computers, realizing a global control signal to collectively control multiple qubits without disrupting the delicate environment of the qubits in the quantum chip remains a significant challenge.

[0077] Some requirements of quantum chip environments include, for example, maintaining the quantum chip at the necessary cryogenic temperatures to ensure its intended operation. This cryogenic requirement stems from the fact that quantum phenomena in quantum chips / processors occur only at very low temperatures. Higher temperatures can easily alter certain properties of qubits (e.g., resonant frequency, coherence time, etc.) along with their quantum behavior. Typically, cryogenic constraints require quantum chips / processors to operate within a temperature range of 1 mK to 4 K. Another requirement includes preventing any stray electric fields or electric fields generated by control signals from affecting the SET sensor and qubits. As mentioned earlier, microwave resonators can provide a global control field, but these present several problems when integrated with quantum chips / processors.

[0078] Resonator for global control

[0079] The inventors of this application realized that in order to generate such a global control field, a microwave resonator is needed that can provide a sufficiently high MW magnetic field control field for effectively controlling / rotating qubits without disrupting the fragile environment in which the quantum chip / processor operates.

[0080] This disclosure discloses such a 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 guide the desired magnetic field to control qubits on the quantum chip.

[0081] In some implementations, the resonator is formed of a dielectric, particularly a quantum paradielectric. In one implementation, the quantum paradielectric has a perovskite structure (…). In one specific embodiment, the quantum paraelectric dielectric is potassium tantalate (KTaO3) or strontium titanate (SrTiO3). Quantum paraelectric dielectrics exhibit very high dielectric constants at low temperatures. For example, the dielectric constant of potassium tantalate is [insert value here]. Furthermore, the dielectric constant of strontium titanate is... Such a large dielectric constant Very strict constraints are imposed on the electric field inside the dielectric resonator, thus achieving a clear spatial separation of the electric and magnetic field components. Furthermore, the resonant frequency of the dielectric resonator is related to the dielectric constant of the material. Its modulus volume V is inversely proportional to it, and is given by the following relationship:

[0082]

[0083] Therefore, for a given frequency ω, the mode volume V of the resonator can be used to exhibit a large value at low temperatures. The paraelectric material is used to reduce the charge.

[0084] These materials also exhibit very low microwave loss (e.g., KTaO3). This allows for a very high quality factor (KTaO3). ).

[0085] Furthermore, this resonator has a very high conversion factor C to meet the high MW magnetic field requirements for controlling the qubit spin (according to the relation) According to the relationship The conversion factor C depends on the quality factor Q, the frequency ω, and the mode volume V. Typically, the operating frequency ω is determined by other experimental factors. Therefore, in typical implementations, 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 both. The combination of properties of quantum paradielectrics produces large conversion efficiencies (e.g., for KTaO3, ...). This in itself is sufficient for continuous operation at milliKelvin temperatures. The conversion factor can be further improved by increasing the quality factor of the resulting resonator.

[0086] In one example, the resonator formed according to aspects of this disclosure can operate at a Rabi frequency of 3 MHz and an input power of 15 μW over a milliKelvin temperature range. The Rabi frequency is defined by the following formula: ,in It is the gyromagnetic ratio of the electron spin, and is divided by two to account for the rotating wave approximation. Due to this achievable conversion factor, the disclosed resonator will not overheat the quantum chip / processor placed nearby.

[0087] Figure 5 A plan view of an exemplary solid-state dielectric resonator 50 according to an embodiment of this disclosure is shown. In one example, the dimensions of the cuboid dielectric resonator may be 1 mm x 1 mm x 0.5 mm. Typically, three modes appear in a dielectric resonator: TE mode (electric field transverse to the z-axis), TM mode (magnetic field transverse to the z-axis), and mixed mode (both electric and magnetic fields have components parallel to the z-axis). Cylindrical and ring resonators typically exhibit all three modes.

[0088] TE 11δ Modulo operations are particularly useful for performing ESR. The symbol TE 11δ This mode is used to indicate that the resonator 50 radiates like a dipole along the z-axis and occurs when z is the smallest dimension. In this mode, the alternating magnetic field generated by the resonator 50 is perpendicular to the surface 51 of the resonator 50 and extends outward (or inward) from the surface 51 of the resonator, while the electric field component is transverse to the direction of the magnetic field component and is confined within the resonator 50.

[0089] Figure 6A and Figure 6BA perspective view of the dielectric resonator 50 is shown. Specifically, Figure 6A It shows that when TE is excited 11δ The magnetic field lines in the modal dielectric resonator 50, and Figure 6B It shows that when TE is excited 11δ The electric field lines in the modal-time dielectric resonator 50. For example... Figure 6A As shown, the magnetic field component B1 is perpendicular to surfaces 51 and 52 of the dielectric resonator 50. Similarly, from Figure 6B It can be clearly seen that the electric field component E of the resonator is almost completely confined and circulates within the dielectric resonator 50.

[0090] Example architecture for global control of qubits

[0091] Figure 7 An arrangement 70 for global control of qubits on a quantum computing chip / processor is shown. As shown in the figure, the arrangement includes a quantum chip / processor 75, a dielectric resonator 50, and a coupler 74. In this arrangement, the dielectric resonator 50 is placed on the quantum chip 75 such that one or more qubits of the quantum chip / processor are located below the surface 51 of the dielectric resonator 50. The coupler 74 is positioned above the dielectric resonator 50 to excite the resonator. In one embodiment, the coupler 74 is configured to... 11δ A mode-excited resonator is used, and the resonator 50 is positioned above the quantum chip, with a small gap (smaller than the height of the dielectric resonator) between the bottom of the resonator 50 and the quantum dot qubit chip 75.

[0092] In this embodiment, coupler 74 is a coaxial cable that provides the input MW signal to the dielectric resonator 50. In alternative embodiments, the MW input signal can be provided by couplers of different shapes. In yet other embodiments, the MW input signal can be provided in some way, for example, by using a coupler with photolithographic definition or a printed circuit board coupled via waveguides and apertures.

[0093] When the MW input signal is provided to the resonator 50, an electric field E and a magnetic field B are generated within the resonator. As described above, the electric field component E is tightly confined within the resonator 50, while the magnetic field component B is directed perpendicularly to surfaces 51 and 52 of the resonator 50. Therefore, one or more qubits located on the chip / processor 75 and facing surface 51 interact with the magnetic field component B. This magnetic field acts as a global field to control one or more qubits on the chip 75.

[0094] In one implementation, a single qubit is controlled by a global magnetic field B generated by a dielectric resonator 50. In an alternative implementation, multiple qubits (hundreds, thousands, or millions) can be simultaneously controlled by the global magnetic field B generated by the dielectric resonator 50.

[0095] All components of system 70 can be housed within the custom-designed housing 71, such as Figure 7 As shown. In another embodiment, a printed circuit board can be used.

[0096] In an alternative implementation, if the quantum chip / processor 75 is located above the dielectric resonator 50, the qubits may face the surface 52 of the dielectric resonator 50.

[0097] Although the above implementation describes a cuboid-shaped resonator 50 (see...) Figures 5 to 7 and Figure 9 However, the present invention is not limited to this specific shape of the resonator and alternative resonator shapes can also be used to implement the methods and systems described herein. For example, the resonator can be square, disk-shaped (see disk resonator 80 in FIG. 8(a)), cylindrical, ring-shaped (see ring resonator 82 in FIG. 8(b)), square ring, or rectangular ring, etc.

[0098] For the toroidal geometry of the resonator shown in Figure 8(b), the quantum chip (not shown in the figure) can be held within the central cavity 83 or directly below or above it. The advantage of this geometry is that it potentially allows for higher magnetic field strengths (because the magnetic field in this geometry peaks at the center of the resonator 82).

[0099] In some embodiments of this disclosure, for a given resonator (which has a dielectric constant on the order of thousands), 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 resonators can be adjusted relative to each other to achieve a specific volume and thus a specific operating frequency. For example, a potassium tantalate resonator with a cuboid shape of 0.5 mm x 1 mm x 1 mm can be fabricated. The resonant frequency of such a resonator is approximately 4.5 GHz (the dielectric constant of potassium tantalate is 4300 at mK temperature). The height of this resonator can be reduced by a factor of 4, and the length and width can each be increased by a factor of 2 (i.e., 0.125 mm x 2 mm x 2 mm) to obtain the same volume and a similar resonant frequency.

[0100] In some embodiments of this 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 determined by the resonator mode size, which is in turn limited by the resonator size. Essentially, the spacing between the resonator and the quantum chip is less than the height of the resonator.

[0101] In one embodiment, a low-microwave-loss tangential material, such as a sapphire pad or sapphire plate, can be placed in the gap / spacing between the quantum chip / processor 75 and the dielectric resonator 50. This arrangement 90 in Figure 9 The image depicts a resonator 50 separated from the quantum processor chip 75 by a sapphire plate 92. In an alternative embodiment, the dielectric resonator 50 may be suspended above or below the quantum chip / processor 75, with a vacuum between the two surfaces. The sapphire spacer or vacuum space between the quantum processor and the dielectric resonator helps reduce losses and helps protect the quantum chip / processor 75 from stray electric fields.

[0102] In some embodiments of this disclosure, the resonator preferably operates between 1 GHz and 100 GHz. The electron spin relaxation rate can become quite large at 100 GHz (relative to the electron or nuclear spin coherence time). Furthermore, microwave engineering at frequencies above 100 GHz becomes challenging and costly.

[0103] Although the methods and systems described above in this disclosure represent global control of electron spin using a dielectric resonator, these techniques can also be implemented to control nuclear spin. In this case, the dielectric resonator frequency can be in the range of 1.0 MHz to 1.0 GHz, and can be calculated using the formula... The size of the resonator is scaled accordingly.

[0104] In some embodiments of this disclosure, the input power of the MW signal is less than 100 μW when the operating temperature is in the milliKelvin range. At operating temperatures between 1.5 Kelvin and 4.0 Kelvin, the input power is less than 1.0 W.

[0105] In some embodiments of this disclosure, the conversion factor C of the resonator can be in the range of 0.1-10.0 mT / √(mW) when the operating temperature is in the milliKelvin range. Higher conversion factors can also be achieved at operating temperatures from 1.5 Kelvin to 4.0 Kelvin.

[0106] In some embodiments of this disclosure, the strength of the alternating magnetic field provided by the dielectric resonator can be in the range of 0.01 mT to 100.0 mT.

[0107] Experimental results

[0108] This section presents experimental results achieved using a dielectric resonator 50 suspended above a quantum chip 75, which is formed by one or more spin-based qubits and intercalating sapphire spacers with a width of 200 micrometers (e.g., as shown in the image). Figure 9 (As shown in the settings).

[0109] In the experimental setup, coupler 74 is TE 11δ Mode-excited resonator 50. Specifically, coupler 74 provides an input microwave signal to dielectric resonator 50. When the microwave input signal is provided to resonator 50, an electric field E and a magnetic field B are generated in resonator 50, such as... Figure 10 As shown. Figure 10 As shown, the electric field component E is tightly confined within the resonator 50, while the magnetic field component B is guided perpendicularly to surfaces 51 and 52 of the resonator 50.

[0110] Figure 11a and Figure 11b The diagrams show the effects of the fundamental mode of resonator 50 being excited by a microwave input signal, within the device stack ( Figure 9 Finite element simulations of the electric and magnetic field amplitudes were performed. The input power used in this experiment was 100 microwatts. However, it should be understood that similar magnetic and electric field modes are produced for other input power values, where the magnetic field transformation is provided by (mT / √W) and the electric field transformation by (mT / √W). kV / cm / √W )supply. Figure 11a and Figure 11b The darker areas represent regions with high magnetic and high electric fields, respectively. Figure 11a and Figure 11b The brighter areas represent regions with magnetic fields as low as zero and electric fields as low as zero, respectively. For example... Figure 11b As shown, when an input power signal is applied to the resonator 50, the electric field experienced by the qubit 112 on the surface of the quantum processor 75 is close to zero, while (as shown in the figure) Figure 11a (As shown) Quantum bit 112 experienced a magnetic field of approximately 0.5 mT.

[0111] Figure 12 This shows the reflection parameters (S) of the resonator detected from the coaxial loop coupler 74. 11 A graph showing the frequency relative to its fundamental mode. Reflection parameter S 11 This represents the amount of power reflected from the resonator and is therefore called the reflection coefficient. If Then all power is reflected from the resonator, and none is absorbed. If If the input power is partially absorbed by the resonator, it will generate electric and magnetic fields.

[0112] like Figure 12 As shown, S 11 The amplitude approaches -40 dB at frequencies between 7.653 GHz and 7.6535 GHz. With critical coupling achieved between resonator 50 and coupler 74, S... 11 The amplitude can theoretically decrease to -∞. At the critical coupling frequency, the most efficient power transfer to the resonator occurs.

[0113] As can be clearly seen from the figure, mode 50 of the resonator is excited and generates... Figure 11a and Figure 11b The optimal E and B field distribution is depicted between 7.653 and 7.6535 GHz, and when operating within this frequency range, it can lead to critical coupling with coupler 74.

[0114] Furthermore, while any spin-based quantum processor chip can be used with the resonator 50, the experiments discussed in this section were conducted on singlet and triplet qubits. In a singlet and triplet qubit, two quantum dots (each with one or more electrons) are formed side-by-side and tuned such that they are tunnel-coupled. Information can be stored in the relative spins of the two electrons, further reducing the coupling of the qubit to its environment. Of the four possible relative spin states of an electron (S, T0, T+, and T-), information is typically stored in the singlet state S and the triplet state T0 (the so-called “logic subspace”). This choice is generally for two advantages. First, both qubit states remain unaffected by changes in the magnetic field (they are both m=0), which further decouples them from their environment. Second, due to the Pauli exclusion principle, in the singlet state, an electron has an orbital wavefunction that hybridizes between the two points, while in the triplet state, both electrons are confined to separate points. Therefore, by adjusting the relative chemical potentials of the two points, the charge distribution of the singlet state and the relative energies of the singlet and triplet states can be distributed.

[0115] Figure 13a An example quantum processor chip 75 incorporating two quantum dots is shown. Specifically, Figure 13a This is a scanning electron microscope (SEM) image of the quantum processor chip 75. Figure 13b Depicting Figure 10 A cross-section of the quantum processor chip. The cross-section is cut through the middle of the device (in... Figure 13a (Marked with dashed lines in the middle). The cross-section shows the 3D structure of the quantum processor chip 75 and its conduction band distribution.

[0116] like Figure 13a and Figure 13b As shown, the quantum processor chip 75 includes quantum dots (dot 1 and dot 2), a single-electron transistor (SET) sensor for sensing or reading the states of quantum dots D1 and D2, and a memory (RESG) for loading electrons into the two quantum dots D1 and D2 to form singlet triplet qubits. Furthermore, gate electrodes P1 and P2 are located on top of quantum dots D1 and D2.

[0117] Figure 14aA two-dimensional stability plot of the two quantum dots D1 and D2 is shown, obtained by scanning the gate electrodes (P1, P2) above each point D1 and D2 and monitoring the current ISET through the SET sensor as electrons jump into and out of both quantum dots D1 and D2. The stability plot shows the charge state or occupancy of each point in relation to the bias voltage applied through the gate electrodes. In particular, the horizontal and vertical lines indicate when electrons jump into and out of quantum dots D1 and D2. The portion marked by reference numeral 142 in the appendix shows a singlet / triplet state with three electrons in point 2 and one electron in point 1. The numbers in parentheses in the stability plot represent the charge occupancy of points 1 and 2 in the two-point system: (N1, N2).

[0118] Figure 14b The readout pulse sequence is shown on curve 145, superimposed on the SET current difference between the preparation of mixed states (i.e., mixed spin singlet and triplet states) and singlet spin states, as a function of the voltages on gates P1 and P2. Spin singlet states are prepared by pulses emitted from (4,1) to (4,0), and mixed states are prepared by pulses emitted from (3,0) to (3,1). Pulse sequences A to B prepare separate dual quantum dots with electrons in mixed spin states. Readout is performed in steps B to D. B to C attempt to push electrons from point 2 to point 1. If the electron in point 2 forms a singlet state with the electron in point 1, tunneling occurs. However, if a triplet state is formed, tunneling is prevented. C to D improves the visibility of the readout via an enhanced latching mechanism. E indicates the level used when performing ESR. Solid lines in the graph represent transitions with high tunneling rates, while dashed lines represent transitions with low tunneling rates. Thin lines delineate Pauli spin blocking (PSB) and locked regions.

[0119] Figure 15a A pulsed scheme for electron spin resonance measurements using resonator 50 is shown (e.g., Figure 14b (A through D shown). The two quantum dots D1 and D2 are initialized as a spin triplet state at point A. Microwave power is then applied to the dielectric resonator 50 at point B, thereby generating an alternating magnetic field B, which causes the electrons in quantum dots D1 and D2 to spin. Spin resonance unblocks the spin and leads to a decrease in the triplet probability during readout.

[0120] Figure 15b This is a graph showing the triplet probability of the two quantum dots as a function of the microwave frequency applied under a DC magnetic field of 227.48 mT. The graph shows two electron spin resonance (ESR) peaks. This graph demonstrates the proof-of-principle off-chip control of the quantum dot spin via dielectric resonator 50.

[0121] Figure 15cThe triplet probability is shown as a function of the applied microwave frequency and DC magnetic field. As shown in the figure, the triplet probability decreases at the resonant frequency of resonator 50—indicating that the ESR peak shifts with the magnetic field as expected.

[0122] Figure 15d It is along Figure 15c A diagonal slice is shown, and the triplet probability as a function of the microwave driving frequency is illustrated, measured with a stepping magnetic field such that the spin triplet energy splitting equals the driving frequency. When the microwave frequency is matched to the frequency of the dielectric resonator, the triplet probability decreases, and an enhancement of the spin resonance signal is observed.

[0123] It should be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or clearly seen from the text or drawings. All these different combinations constitute various alternative aspects of the invention.

Claims

1. A system for globally controlling one or more qubits, the system comprising: A quantum processor comprising a plurality of spin-based qubits; and A dielectric resonator, located near the quantum processor, is made of a dielectric material whose dielectric constant increases at low temperatures relative to room temperature, wherein the low temperature is less than or equal to 4 Kelvin. The dielectric resonator is configured to operate at the low temperature and at an operating frequency determined by the dielectric constant and the resonant mode volume of the dielectric resonator. Receive input signal from coupler; and In response to receiving the input signal, a global AC magnetic field extending from the dielectric resonator to the quantum processor at the operating frequency is generated to control the electronic or nuclear spin of one or more of the spin-based qubits.

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

3. The system of claim 1, wherein the global AC magnetic field controls a single qubit of the quantum processor.

4. The system of claim 1, wherein the global AC magnetic field simultaneously controls multiple qubits of the quantum processor.

5. The system of claim 1, wherein the dielectric resonator generates an electric field that is spatially separated from the global AC magnetic field.

6. The system of claim 5, wherein the global AC magnetic field of the dielectric resonator is perpendicular to the surface of the dielectric resonator and oriented outward from the surface of the dielectric resonator.

7. The system of claim 6, wherein the electric field is confined away from the location of the quantum processor to minimize the interaction of the electric field with the one or more spin-based qubits and the on-chip measurement and control electronics of the quantum processor.

8. The system of claim 7, wherein the electric field circulates within the dielectric resonator.

9. The system of claim 1, wherein the dielectric resonator is derived from a material having a perovskite structure ( It is made from a class of compounds.

10. The system of claim 9, wherein the dielectric resonator is made of potassium tantalate (KTaO3) or strontium titanate (SrTiO3).

11. The system of claim 1, wherein each dimension of the dielectric resonator is in the range of 100 micrometers to 10 millimeters.

12. The system of claim 1, wherein the quantum processor is a solid-state semiconductor or a superconducting quantum processor.

13. 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 spin-based qubits of the quantum processor are oriented toward the dielectric resonator to interact with the global AC magnetic field provided by the dielectric resonator.

14. The system of claim 1, wherein the dielectric resonator is separated from the quantum processor by a low-microwave-loss tangential material or a vacuum space.

15. The system of claim 1, wherein the coupler is a coaxial cable, a photolithographically defined coupler, or a waveguide and aperture.

16. The system of claim 1, 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, and is used to control nuclear spin.

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

18. A method for globally controlling a plurality of qubits using the system as described in any one of claims 1 to 17.

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