Charge sensor circuit for sensing spin state in a qubit array

Abstract

The present invention is a novel and useful apparatus and method of sensing spin state to enhance spin-qubit readout in qubit arrays, in particular, a single electron box (SEB) based spin state charge sensing circuit and related control algorithms for quantum charge sensing in a quantum dot array. To overcome limitations of thermal noise and scalability issues, the system utilizes floating lead readout mechanisms to amplify potential shifts and multi-island architectures that leverage Coulomb interactions for higher-temperature operation. An adaptive golden mean control mechanism mitigates nonlinear dynamics and signal drift. By identifying the steepest slope of the sensor signal for maximum sensitivity, the system employs rule-based feedback and reinforcement learning (RL) agents to dynamically tune control gate voltages. These agents maximize the differentiation between charge states by adjusting the step magnitude or autonomously determining the full control gate voltage, ensuring high-fidelity, autonomous sensor stabilization in complex, noisy quantum environments.

Description

[0001] 12485.0118

[0002] CHARGE SENSOR CIRCUIT FOR SENSING SPIN STATE IN A QUBIT ARRAY

[0003] REFERENCE TO PRIORITY APPLICATION

[0004] This application claims the benefit of U.S. Provisional Application No. 63 / 760,880, filed February 20, 2025, entitled “Single Electron Box Charge Sensor for Quantum Sensing In A Qubit Array” incorporated herein by reference in its entirety.

[0005] FIELD OF THE DISCLOSURE

[0006] The subject matter disclosed herein relates to the field of quantum computing and more particularly relates to a charge sensor circuit and related control algorithm for sensing spin state in a qubit array.

[0007] BACKGROUND OF THE INVENTION

[0008] Quantum computing technologies have advanced significantly in recent years, driven by the potential to solve complex problems beyond the capabilities of classical computers, such as factorization of large numbers, simulation of quantum mechanical systems, optimization problems, machine learning tasks, simulating molecular interactions for drug discovery, and optimizing large-scale systems. Practical realization of this promise, however, requires the construction of quantum processors comprising large numbers of physical qubits that can be initialized, manipulated, and measured with extremely high fidelity while maintaining sufficiently long coherence times.

[0009] Among various qubit implementations, spin qubits in semiconductors, particularly silicon-based systems, have emerged as promising candidates due to their long coherence times, high gate fidelities, and compatibility with industrial fabrication processes. These spin qubits leverage the electron spin as the information carrier, enabling dense integration and potential scalability toward fault-tolerant quantum processors.

[0010] A critical aspect of spin qubit operation is the precise detection of spin states, which is essential for readout in quantum computations. This detection typically involves converting spin information into measurable charge signals through spin-to-charge conversion mechanisms, such as Pauli spin blockade or dispersive sensing. Charge sensors play a pivotal role in this process, allowing for the identification of charge transitions that reflect spin state changes in adjacent qubits. As quantum systems become larger and more complex, there is a growing need for better tools to make state detection more precise and efficient.12485.0118

[0011] It is thus desirable to have a quantum charge sensor and related control algorithm that is capable of measuring charge signals through a spin to charge conversion mechanism that is capable of scaling to support large qubit arrays, is efficient, compatible with complex quantum architectures, and which does not suffer from the disadvantages of prior art charge sensors.12485.0118

[0012] SUMMARY OF THE INVENTION

[0013] The present invention is a novel and useful apparatus and method of sensing spin state for spin-qubit readout in quantum computing systems, in particular, a single electron box (SEB) spin state charge sensing circuit and related control algorithms for quantum charge sensing in a qubit array. In one embodiment, the charge sensor in a quantum system uses a single-electron box (SEB), which exploits the Coulomb blockade effect to control and detect individual electron tunneling events. In an SEB, for example, a quantum dot or island is coupled to a reservoir via a tunnel junction, with a gate electrode tuning the electrochemical potential to enable discrete charge states. Such devices can be constructed in various materials, including silicon, and can be used for dispersive readout in spin qubit arrays.

[0014] The charge sensors, based on single electron boxes (SEBs), exploit the Coulomb blockade effect to detect individual electron tunneling events. In an example SEB, a quantum dot or island is coupled to a reservoir via a tunnel junction, with a gate electrode tuning the electrochemical potential for discrete charge states. These devices, demonstrated in materials like silicon, function to provide dispersive readout in spin qubit arrays and integrate with quantum dot architectures, and provide exceptional sensitivity.

[0015] Some sensors, however, have limitations, including sensitivity to thermal fluctuations, necessitating cryogenic operation (typically below 1 K) to maintain charging energy above thermal energy and preserve quantized states. At higher temperatures, thermal broadening reduces sensitivity and precision. Additionally, reliance on bulky resonators or multiple leads increases device footprint, complicates CMOS integration, and limits scalability. Other issues include high output impedance, lack of internal memory, vulnerability to electrostatic discharge, elevated charge noise in silicon systems, and challenges in large-scale arrays, such as interconnect density, crosstalk, heat dissipation, wiring scalability, environmental noise, escalating error rates, and hardware complexity, all exacerbating decoherence and reducing fidelity.

[0016] To address these challenges, the present invention provides advanced SEB-based charge sensors with enhanced performance, thermal robustness, and integration in scalable quantum architectures. One embodiment includes a quantum charge sensor with a floating lead readout mechanism. This circuit comprises a single electron box (SEB) including an island, at least one tunnel junction coupled to the island, and a control gate capacitively coupled to the island. A floating lead is selectively connected to a voltage source via a first switch, coupled to either the tunnel junction or the control gate. A second switch connects the floating lead to a voltage amplifier for measuring potential changes, and an adjacent qubit array is capacitively12485.0118

[0017] coupled to the island. A charge state change in the qubit array induces a tunneling event on the island, resulting in a detectable potential change in the floating lead when in a floating state.

[0018] An alternative embodiment includes coupling the floating lead to the tunnel junction for direct electron tunneling or to the control gate for tuning the island’s electrochemical potential. Deactivation of the first switch places the lead in a floating state, where small capacitance amplifies potential shifts, yielding stepwise outputs from the amplifier. This circuit simplifies integration by eliminating bulky resonators, reduces space requirements, and improves sensitivity and efficiency.

[0019] A corresponding method for reading out spin states (and charge states) involves providing the SEB, coupling the floating lead, activating the first switch to set potentials for tunneling, deactivating it for floating state, coupling the qubit array to induce tunneling events altering the lead potential, and activating the second switch for measurement. Additional steps include adjusting control gate voltage for tuning and leveraging small capacitance for significant potential changes.

[0020] In another embodiment, the invention provides an extended multi-island SEB design for enhanced thermal robustness. This circuit comprises a multi-island SEB with a primary island capacitively coupled to a qubit array, multiple additional islands as intermediary charge reservoirs, at least one tunnel junction coupled to the primary island, a control gate capacitively coupled to the primary island, and a conductive lead capacitively coupled to at least one additional island. Mutual Coulomb interactions among islands create an effective energy gap larger than that of single-island SEBs, enabling operation at higher temperatures by reducing thermal fluctuation sensitivity. Capacitive coupling avoids direct tunnel junctions to the lead, mitigating thermal broadening, while additional islands offer tunability in barriers and couplings for optimized charge states. The sensor may include gate-tuning algorithms to manage island and qubit interactions.

[0021] A related method enhances thermal robustness by providing the multi-island SEB, capacitively coupling the primary island to the qubit array and the lead to additional islands, utilizing Coulomb interactions for larger energy gaps to maintain Coulomb blockade at elevated temperatures, and tuning the control gate to optimize configurations and minimize thermal influences. Gate-tuning algorithms further control interactions.

[0022] The present invention further provides a mechanism for the adaptive control of a charge sensor used in spin qubit readout within a qubit array. The control algorithm is applicable to both SEB and single electron transistor (SET) based charge sensor circuits. The mechanism addresses the challenges of nonlinear dynamics and slow signal drifts by employing automated12485.0118

[0023] feedback loops and machine learning to maintain the sensor at its point of maximum sensitivity. The system first identifies an optimal operating point by locating the steepest slope of the sensor signal curve, typically near the mean value of the signal peak. This process defines initial parameters including a mean signal, signal level difference, and slope direction.

[0024] A rule-based algorithm monitors real-time single-shot readout outcomes. It compares current bimodal signal distributions against historical maximums to detect drift and applies incremental adjustments to the control gate voltage to compensate for environmental noise.

[0025] A reinforcement learning (RL) agent dynamically adjusts the magnitude of the voltage step to ensure the system remains at its most responsive point based on observed deviations. An extension of this technique treats the entire control gate voltage as a learnable parameter, allowing the agent to autonomously determine both the magnitude and sign of adjustments without predefined rules. The RL agents are trained in simulated environments to maximize a reward function proportional to the sensor’s ability to distinguish between distinct charge states.

[0026] These innovations overcome prior art limitations by providing reliable performance at higher temperatures, easier integration without resonators, increased scalability, and sophisticated controls for complex systems. Several advantages of the pattern generator include: (1) simplified integration where the floating lead readout mechanism eliminates the need for traditional bulky resonators, reducing space requirements and facilitating easier integration into larger quantum architectures and dense qubit arrays; (2) enhanced sensitivity is provided with the detection of potential changes due to the small capacitance of the floating lead, providing stepwise outputs that improve the precision of charge state detection in qubits; (3) improved thermal robustness with the multi-island configuration creating larger effective energy gaps through mutual Coulomb interactions, allowing the sensor to operate at higher temperatures while maintaining Coulomb blockade effects and reducing sensitivity to thermal fluctuations; (4) increased tunability is provided from the additional islands in the extended SEB design which offer greater control over tunnel barriers and capacitive couplings, enabling optimized charge states and better mitigation of environmental noise; (5) scalability for large systems is provided by addressing limitations like high output impedance and vulnerability to electrostatic discharge, the sensor supports scaling to thousands of qubits with reduced crosstalk, heat dissipation, and wiring complexity; (6) compatibility with CMOS technology by avoiding reliance on superconducting resonators, making the sensor more compatible with standard CMOS fabrication processes for industrial scalability; and (7) control management12485.0118

[0027] with incorporation of gate-tuning algorithms to handle the complexity of multi-island interactions, ensuring reliable performance in complex quantum systems.

[0028] There is thus provided in accordance with the invention, a spin state charge sensor comprising a single electron box (SEB) including an island, at least one tunnel junction coupled to said island, and a control gate capacitively coupled to said island, a floating lead configured to be selectively connected to a voltage source via a first switch, wherein said floating lead is coupled to either said at least one tunnel junction or said control gate, a second switch configured to connect the floating lead to a voltage amplifier for measuring a potential change in the floating lead, and a qubit array adjacent to the SEB, wherein the qubit array is capacitively coupled to the island such that a charge state change in said qubit array induces a tunneling event on said island, resulting in a detectable potential change in said floating lead when in a floating state.

[0029] There is also provided in accordance with the invention, a charge sensor, comprising a single electron box (SEB) including one or more conductive islands, said island capacitively coupled to a qubit array, a conductive lead coupled to said SEB and a voltage source, an amplifier coupled to said lead which is placed in a floating state after said voltage source is disconnected from said lead, and wherein a tunneling event in said qubit array results in a change in electric potential of said lead that is subsequently detected and amplified by said amplifier.

[0030] There is further provided in accordance with the invention, a spin state charge sensor comprising a multiple island single electron box (SEB) including a primary island capacitively coupled to a qubit array, and a plurality of additional islands acting as intermediary charge reservoirs coupled to each other by tunnel junctions, multiple control gates, each control gate capacitively coupled to an additional island, and a conductive lead capacitively coupled to at least one of the additional islands, wherein mutual Coulomb interactions among said primary island and said additional islands create an effective energy gap larger than a charging energy of a single-island SEB, enabling operation at higher temperatures by reducing sensitivity to thermal fluctuations.

[0031] There is also provided in accordance with the invention, a spin state charge sensing method, comprising the steps of providing a single electron box (SEB) having one or more conductive islands, at least one tunnel junction, and one or more control gates, coupling a floating lead to either said at least one tunnel junction or said one or more control gates, activating a first switch to connect said floating lead to a voltage source, thereby setting a potential to enable tunneling between said floating lead and at least one conductive island,12485.0118

[0032] deactivating said first switch to place said floating lead in a floating state, capacitively coupling a qubit array to said island such that a charge state change in said qubit array induces a tunneling event on said island, altering a potential of said floating lead, and activating a second switch to connect said floating lead to an amplifier to measure the altered potential indicating the occurrence of a charge state change in said qubit array which is detected at an output of said amplifier.12485.0118

[0033] BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention is explained in further detail in the following exemplary embodiments and with reference to the figures, where identical or similar elements may be partly indicated by the same or similar reference numerals, and the features of various exemplary embodiments being combinable. It should be expressly understood that the drawings are included for illustrative purposes and do not represent the scope of the present system. It is to be understood that the figures may not be drawn to scale. Further, the relation between objects in a figure may not be to scale and may have a reverse relationship as to size. In the accompanying drawings, like reference numbers in different drawings may designate identical or similar elements, portions of similar elements and / or elements with similar functionality. The present system is explained in further detail, and by way of example, with reference to the accompanying drawings which show features of various exemplary embodiments that may be combinable and / or severable wherein:

[0035] Fig. 1 is a high level block diagram illustrating a first example quantum computer system constructed in accordance with the present invention;

[0036] Fig. 2 is a diagram illustrating an example single electron box (SEB) charge sensor; Fig. 3 is a diagram illustrating an example RF reflectometry readout circuit for an SEB charge sensor;

[0037] Fig. 4A is a diagram illustrating RF signal sensor response to an electron tunneling event;

[0038] Fig. 4B is a diagram illustrating RF signal sensor response to control gate variations; Fig. 5 is a charge stability diagram illustrating the RF response as plunger gate voltages are swept;

[0039] Fig. 6 is a diagram illustrating a first example floating lead readout using an SEB sensor;

[0040] Fig. 7 is a flow diagram illustrating an example charge sensing method;

[0041] Fig. 8 is a diagram illustrating a second example floating lead readout using an SEB sensor;

[0042] Fig. 9 is a diagram illustrating a third example floating lead readout using an SEB sensor;

[0043] Fig. 10 is a diagram illustrating an example single island SEB charge sensor and its respective energy diagram;12485.0118

[0044] Fig. 11 is a diagram illustrating a first example multiple island SEB charge sensor and its respective energy diagram;

[0045] Fig. 12 is a diagram illustrating a second example multiple island SEB charge sensor; Fig. 13 is a diagram illustrating signal output of an example charge sensor;

[0046] Fig. 14A is a diagram illustrating an example charge stability diagram of a DQD system as detected by the sensor;

[0047] Fig. 14B is a diagram illustrating the interdot transition sweep with two distinct sensor signal levels;

[0048] Fig. 14C is a diagram illustrating a graph of signal level versus control voltage sweep at the high point VH;

[0049] Fig. 14D is a diagram illustrating a graph of signal level versus control voltage sweep at the low point VL;

[0050] Fig. 15 is a flow diagram illustrating an example charge sensor initialization method; Fig. 16A is a diagram illustrating example sensor signal outcome of a single shot measurement when no adjustment is required;

[0051] Fig. 16B is a diagram illustrating example sensor signal outcome of a single shot measurement when an adjustment is necessary;

[0052] Fig. 16C is a diagram illustrating a graph of the sensor signal as a function of control gate voltage;

[0053] Fig. 17 is a flow diagram illustrating an example golden mean control method;

[0054] Fig. 18 is a flow diagram illustrating an example golden mean control method with reinforcement learning;

[0055] Fig. 19 is a flow diagram illustrating an example reinforcement learning (RL) agent training method; and

[0056] Fig. 20 is a flow diagram illustrating an example training procedure portion of the RL agent training method of Figure 19; and

[0057] Fig. 21 is a flow diagram illustrating an example golden mean control method with pure reinforcement learning.12485.0118

[0058] DETAILED DESCRIPTION

[0059] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. It will be understood by those skilled in the art, however, that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the present invention.

[0060] Among those benefits and improvements that have been disclosed, other objects and advantages of this invention will become apparent from the following description taken in conjunction with the accompanying figures. Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely illustrative of the invention that may be embodied in various forms. In addition, each of the examples given in connection with the various embodiments of the invention which are intended to be illustrative, and not restrictive.

[0061] The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings.

[0062] The figures constitute a part of this specification and include illustrative embodiments of the present invention and illustrate various objects and features thereof. Further, the figures are not necessarily to scale, some features may be exaggerated to show details of particular components. In addition, any measurements, specifications and the like shown in the figures are intended to be illustrative, and not restrictive. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.

[0063] Because the illustrated embodiments of the present invention may for the most part, be implemented using electronic components and circuits known to those skilled in the art, details will not be explained in any greater extent than that considered necessary, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention.12485.0118

[0064] Any reference in the specification to a method should be applied mutatis mutandis to a system capable of executing the method. Any reference in the specification to a system should be applied mutatis mutandis to a method that may be executed by the system.

[0065] Throughout the specification and claims, the following terms take the meanings explicitly associated herein, unless the context clearly dictates otherwise. The phrases “in one embodiment,” “in an example embodiment,” and “in some embodiments” as used herein do not necessarily refer to the same embodiment s), though it may. Furthermore, the phrases “in another embodiment,” “in an alternative embodiment,” and “in some other embodiments” as used herein do not necessarily refer to a different embodiment, although it may. Thus, as described below, various embodiments of the invention may be readily combined, without departing from the scope or spirit of the invention.

[0066] In addition, as used herein, the term “or” is an inclusive “or” operator, and is equivalent to the term “and / or,” unless the context clearly dictates otherwise. The term “based on” is not exclusive and allows for being based on additional factors not described, unless the context clearly dictates otherwise. In addition, throughout the specification, the meaning of “a,” “an,” and “the” include plural references. The meaning of “in” includes “in” and “on.”

[0067] Quantum Computer Architecture

[0068] A high-level block diagram illustrating a first example quantum computer system constructed in accordance with the present invention is shown in Figure 1. The quantum computer, generally referenced 10, comprises a conventional (i.e. not a quantum circuit) external support unit 12, software unit 20, cryostat unit 36, quantum processing unit 38, clock generation units 33, 35, and one or more communication busses between the blocks. The external support unit 12 comprises operating system (OS) 18 coupled to communication network 76 such as LAN, WAN, PAN, etc., decision logic 16, and calibration block 14. Software unit 20 comprises control block 22 and digital signal processor (DSP) 24 blocks in communication with the OS 18, calibration engine / data block 26, and application programming interface (API) 28.

[0069] Quantum processing unit 38 comprises a plurality of quantum core circuits 60, high speed interface 58, detectors / samplers / output buffers 62, quantum error correction (QEC) 64, digital block 66, analog block 68, correlated data sampler (CDS) 70 coupled to one or more analog to digital converters (ADCs) 74 as well as one or more digital to analog converters (DACs, not shown), clock / divider / pulse generator circuit 42 coupled to the output of clock generator 35 which comprises high frequency (HF) generator 34. The quantum processing unit12485.0118

[0070] 38 further comprises serial peripheral interface (SPI) low speed interface 44, cryostat software block 46, microcode 48, command decoder 50, software stack 52, memory 54, and pattern generator 56. The clock generator 33 comprises low frequency (LF) generator 30 and power amplifier (PA) 32, the output of which is input to the quantum processing unit (QPU) 38. Clock generator 33 also functions to aid in controlling the spin of the quantum particles in the quantum cores 60.

[0071] The cryostat unit 36 is the mechanical system that cools the QPU down to cryogenic temperatures. Typically, it is made from metal and it can be fashioned to function as a cavity resonator 72. It is controlled by cooling unit control 40 via the external support unit 12. The cooling unit control 40 functions to set and regulate the temperature of the cryostat unit 36. By configuring the metal cavity appropriately, it is made to resonate at a desired frequency. A clock is then driven via a power amplifier which is used to drive the resonator which creates a magnetic field. This magnetic field can function as an auxiliary magnetic field to aid in controlling one or more quantum structures in the quantum core.

[0072] The external support unit / software units may comprise any suitable computing device or platform such as an FPGA / SoC board. In one embodiment, it comprises one or more general purpose CPU cores and optionally one or more special purpose cores (e.g., DSP core, floating point, etc.) that that interact with the software stack that drives the hardware, i.e. the QPU. The one or more general purpose cores execute general purpose opcodes while the special purpose cores execute functions specific to their purpose. Main memory comprises dynamic random access memory (DRAM) or extended data out (EDO) memory, or other types of memory such as ROM, static RAM, flash, and non-volatile static random access memory (NV SRAM), bubble memory, etc. The OS may comprise any suitable OS capable of running on the external support unit and software units, e.g., Windows, MacOS, Linux, QNX, NetBSD, etc. The software stack includes the API, the calibration and management of the data, and all the necessary controls to operate the external support unit itself.

[0073] The clock generated by the high frequency clock generator 35 is input to the clock divider 42 that functions to generate the signals that drive the QPU. Low frequency clock signals are also input to and used by the QPU. A slow serial / parallel interface (SPI) 44 functions to handle the control signals to configure the quantum operation in the QPU. The high speed interface 58 is used to pump data from the classic computer, i.e. the external support unit, to the QPU. The data that the QPU operates on is provided by the external support unit.

[0074] Non-volatile memory may include various removable / non-removable, volatile / nonvolatile computer storage media, such as hard disk drives that reads from or writes12485.0118

[0075] to non-removable, nonvolatile magnetic media, a magnetic disk drive that reads from or writes to a removable, nonvolatile magnetic disk, an optical disk drive that reads from or writes to a removable, nonvolatile optical disk such as a CD ROM or other optical media. Other removable / non-removable, volatile / nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM, and the like.

[0076] The computer may operate in a networked environment via connections to one or more remote computers. The remote computer may comprise a personal computer (PC), server, router, network PC, peer device or other common network node, or another quantum computer, and typically includes many or all of the elements described supra. Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet.

[0077] When used in a LAN networking environment, the computer is connected to the LAN via network interface 76. When used in a WAN networking environment, the computer includes a modem or other means for establishing communications over the WAN, such as the Internet. The modem, which may be internal or external, is connected to the system bus via user input interface, or other appropriate mechanism.

[0078] Computer program code for carrying out operations of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++, C# or the like, conventional procedural programming languages, such as the “C” programming language, and functional programming languages such as Python, MATLAB, Prolog and Lisp, machine code, assembler or any other suitable programming languages.

[0079] Also shown in Figure 1 is the optional data feedback loop between the quantum processing unit 38 and the external support unit 12 provided by the partial quantum data read out. The quantum state is stored in the qubits of the one or more quantum cores 60. The detectors 62 function to measure / collapse / detect some of the qubits and provide a measured signal through appropriate buffering to the output ADC block 74. The resulting digitized signal is sent to the decision logic block 16 of the external support unit 12 which functions to reinject the read out data back into the quantum state through the high speed interface 58 and quantum initialization circuits. In an alternative embodiment, the output of the ADC is fed back to the input of the QPU.12485.0118

[0080] In one embodiment, quantum error correction (QEC) is performed via QEC block 64 to ensure no errors corrupt the read out data that is reinjected into the overall quantum state. Errors may occur in quantum circuits due to noise or inaccuracies similarly to classic circuits. Periodic partial reading of the quantum state function to refresh all the qubits in time such that they maintain their accuracy for relatively long time intervals and allow the complex computations required by a quantum computing machine.

[0081] It is appreciated that the architecture disclosed herein can be implemented in numerous types of quantum computing machines. Examples include semiconductor quantum computers, superconducting quantum computers, magnetic resonance quantum computers, optical quantum computers, etc. Further, the qubits used by the quantum computers can have any nature, including charge qubits, spin qubits, hybrid spin-charge qubits, etc.

[0082] In one embodiment, the quantum structure disclosed herein is operative to process a single particle at a time. In this case, the particle can be in a state of quantum superposition, i.e. distributed between two or more locations or charge qdots. In an alternative embodiment, the quantum structure processes two or more particles at the same time that have related spins. In such a structure, the entanglement between two or more particles could be realized. Complex quantum computations can be realized with such a quantum interaction gate / structure or circuit.

[0083] In alternative embodiments, the quantum structure processes (1) two or more particles at the same time having opposite spin, or (2) two or more particles having opposite spins but in different or alternate operation cycles at different times. In the latter embodiment, detection is performed for each spin type separately.

[0084] Spin State Charge Sensor

[0085] A diagram illustrating an example single electron box (SEB) charge sensor is shown in Figure 2. The charge sensor, generally referenced 80, comprises a conductive island or quantum dot 88 connected to a conductive lead 92 through a tunnel junction 90, coupled capacitively to a control gate 86 as well as to a qubit array 82 via capacitor 84. Note that the qubit array is represented by a double quantum dot (DQD) typically coupled via a tunnel junction (not shown). The electrochemical potential p of this island is highly sensitive to its surrounding electrostatic environment and can be analyzed by monitoring the rate of singleelectron transitions to and from the island. In spin-qubit readout, the SEB leverages the Pauli spin blockade (PSB) effect to convert the spin state of the adjacent qubit array 82 into measurable voltage signals, thereby providing a precise method for detecting spin quantum states.12485.0118

[0086] Note that Pauli spin blockade (PSB) is a phenomenon in double quantum dots where electron transport is restricted by the Pauli exclusion principle, causing current to stop when electrons are trapped in a spin-triplet state. PSB is used to convert spin information into charge signals for qubit readout procedures.

[0087] A diagram illustrating an example RF reflectometry readout circuit for an SEB charge sensor is shown in Figure 3. The RF-reflectometry sensor circuit, generally referenced 100, comprises SEB 116, a superconducting inductor 110, a directional coupler 112, and a cryogenic amplifier 114. The SEB 116 comprises tunnel junction 108, conductive island 104, capacitor 106 and DQD 102 that includes quantum dot (QD) 1 and quantum dot 2 each having a control gate connected to a voltage source, VQD1and VQD2, respectively. The tunneling of an electron onto or out of the SEB island 104 results in a change in impedance, leading to a measurable shift in the reflected RF signal. Detection can be performed using either amplitude or phase response, with phase detection often providing enhanced sensitivity.

[0088] Experimental results from previous studies indicate that electron tunneling events induce measurable amplitude shifts in the RF reflectometry signal, similar to that shown in Figure 4A which illustrates the RF signal response to an electron tunneling event showing a characteristic shift in reflection amplitude. Periodic oscillations (i.e. periodic charge transition signals) in sensor response as a function of control gate voltage similar to that shown in Figure 4B are observed due to Coulomb blockade effects and discrete charge tunneling. A charge stability diagram illustrating the RF response as plunger gate voltages of a double quantum dot (DQD) are swept near the SEB sensor, demonstrating transitions between different charge occupation states in the DQD is shown in Figure 5. Note that the charge stability diagram of double quantum dots exhibit characteristic honeycomb patterns, demonstrating the feasibility of charge state readout.

[0089] RF reflectometry based spin-qubit readout methods that use charge sensors, such as single-electron transistors or quantum point contacts, to detect the state of spin qubits, however, face challenges in achieving reliable performance at higher temperatures and in scalable architectures. Due to their underlying physics and operational principles, these sensors rely on superconducting resonators and RF circuitry which introduces increased spatial requirements, strict operational temperature constraints, and limited scalability within quantum architectures. These sensors typically have narrow operational temperature ranges and require superconducting resonators to achieve the necessary readout fidelity. This reliance on resonators increases space requirements, complicates integration with standard CMOS technology, and further limits operational temperatures.12485.0118

[0090] Floating Lead Charge Readout

[0091] To improve scalability and performance, the present invention includes a charge sensor having a floating lead readout. A diagram illustrating a first example floating lead readout using an SEB sensor is shown in Figure 6. A flow diagram illustrating an example charge sensing method is shown in Figure 7. Building upon the extended SEB design, another improvement incorporates a sensor state readout mechanism using one or more floating leads. This design simplifies the integration of SEBs into larger quantum architectures by reducing the space requirements, as it does not rely on bulky resonators as described supra. In one embodiment, the charge sensor, generally referenced 130, comprises an SEB that includes conductive island 136 coupled to a tunnel junction 140, control gate 138, capacitor 134, and qubit array (DQD) 132. Charge sensor 130 further comprises a first switch 146, voltage source 144, one or more conductive leads 142, second switch 148, amplifier (e.g., voltage or current), and detector 152.

[0092] In operation, the first switch is activated to connect the lead 142 to a voltage source 144 that sets the potential of the lead (step 370). Next, the voltage at the control gate 138 is adjusted to tune the electrochemical potential of the dot and allow the tunneling of an electron from the lead to the island 136 and back (step 372). The first switch 146 is deactivated after this, and the lead 142 is disconnected from the voltage source 144 to place the lead in a “floating” state where a change in the number of electrons will result in a significant change of its electric potential due to its small capacitance (step 374). The second switch 148 is then activated to measure if the electric potential of the lead has changed compared to the original state due to an electron tunneling to the island (step 376). When the adjacent qubit array 132 undergoes a tunneling event, its sudden change in charge state alters the local electrostatic potential, which is capacitively coupled to the SEB island 136 (step 378). This shift in the potential changes the energy alignment of the SEB, modifying its Coulomb blockade conditions. As a result, the energy balance on the SEB island 136 is disturbed, making it energetically favorable for an electron to tunnel onto or off the island through a tunnel junction 140 in order to re-establish equilibrium. This results in a significant change of the lead’s 142 electric potential per transferred electron due to lead’s small capacitance, which in turn is detected as a step at the output (VOUT) of the voltage amplifier 150 and detector 152 (step 380).

[0093] A diagram illustrating a second example floating lead readout using an SEB sensor is shown in Figure 8. In this alternative embodiment of the floating lead method, generally referenced 160, the floating lead 170 is connected to the control gate 168 rather than to a tunnel junction 166 of the SEB. The remaining components, including, qubit array 162, capacitor 164,12485.0118

[0094] conductive island 165, voltage source 172, first switch 174, second switch 176, amplifier 178, and detector 180, function similarly to that of the sensor shown in Figure 6.

[0095] In operation, initially, the first switch 174 connects the lead 170 to the voltage source 172, setting the potential of the control gate 168 which is capacitively coupled to the sensor island 165. This tunes the electrochemical potential of the dot and allows electron tunneling from the lead to the island through a tunnel junction 166 and back. Note that the tunnel junction is connected to a voltage source which may be ground. Afterwards, the first switch 174 is deactivated, placing the lead 170 in a “floating” state, where a change in electron count on the island results in a significant shift in the control gate’s 168 potential due to its small capacitance. The second switch 176 is then activated to measure whether the lead’s potential has shifted compared to its initial state, producing a stepwise change at the output (VOUT) of the voltage amplifier 178 and detector 180 corresponding to the tunneling event.

[0096] A diagram illustrating a third example floating lead readout using an SEB sensor is shown in Figure 9. In this embodiment, the SEB based floating charge sensor, generally referenced 161, comprises qubit array 163, capacitor 165, tunnel junction 169, island 167, control gate 171, voltage source 172, first switch 181, second switch 179, amplifier 175, and detector 177.

[0097] The operation of the charge sensor 161 is similar to that of charge sensor 160 (Figure 8) with the lead 170 replaced by a conductive wire and the tunnel junction 166 connected to ground. In one embodiment, a portion of the control gate 171 functions as the lead.

[0098] To enhance the operational capabilities of SEB sensors, an alternative embodiment introduces a multi -island sensor. This multi-island configuration increases the sensor’s robustness and expands its operational temperature range, addressing one of the significant limitations of traditional SEB designs.

[0099] First, a single island SEB sensor and related energy diagram are described. A diagram illustrating an example single island SEB charge sensor and its respective energy distribution diagram is shown in Figure 10. The single island sensor, generally referenced 190, comprises an SEB that includes qubit array 192, capacitor 194, island 196, tunnel junction 198, and control gate 202, lead 200, voltage source 191, first switch 199, second switch 197, amplifier 193, and detector 195. Note that for the capacitors to operate properly, appropriate bias voltages are applied thereto to create the capacitor in silicon. Normally, an SEB sensor operates based on the Coulomb blockade effect, which requires that the charging energy ECbe significantly larger than the thermal energy kT. As the control gate voltage increases, the energy levels decrease. For the single island SEB sensor 190, when the temperature is too high, thermal12485.0118

[0100] fluctuations can provide enough energy to overcome the charging energy, allowing electrons to tunnel on and off the island through tunnel junction 192 regardless of the applied control, thereby smearing out the distinct quantized charge states 204. This loss of discrete control leads to reduced sensitivity and precision in detecting charge transition events in the qubit array 192. Thus, single island SEB sensors are typically operated at cryogenic temperatures to minimize thermal noise and preserve the clear, stable charge transitions essential for accurate sensing.

[0101] A diagram illustrating a first example multiple island SEB charge sensor and its respective energy diagram is shown in Figure 11. The multiple island sensor, generally referenced 210, comprises an SEB that includes qubit array 212, capacitors 214, 221, dual islands 216 coupled by tunnel junction 218, and control gates 211, 213, conductive lead 222, voltage source 223, first switch 224, second switch 226, amplifier 228, and detector 230.

[0102] The multiple island SEB charge sensor 210 incorporates multiple islands 216 (two in this example sensor) as intermediary charge reservoirs that function to enhance thermal robustness as the sensor can be coupled to the conductive lead 222 only capacitively rather than through a tunnel junction, which makes it less sensitive to the thermal broadening of the carrier gas. In the multi-island configuration, mutual Coulomb interactions and the added capacitances among the islands reshape the energy spectrum 219, leading to larger effective energy gaps between different charge configurations. The barrier 221 is higher than the barrier 198 (Figure 10). This increased gap means that thermal energy kT is less likely to cause unwanted tunneling events, thus preserving the Coulomb blockade effect even at higher temperatures resulting in more temperature independence.

[0103] Moreover, the extra island(s) provide additional tunability in the tunnel barriers 218 and capacitive couplings 221, 214, enabling optimized control over the charge states and further mitigating the influence of thermal fluctuations on device performance. Additionally, the presence of multiple quantum dots creates a more uniform potential landscape, thereby enhancing the overall stability of the sensor-qubit system. This improvement in performance, however, comes with increased complexity in device control, requiring a gate-tuning mehcanism to manage the interactions between multiple islands and the qubit effectively.

[0104] A diagram illustrating a second example multiple island SEB charge sensor is shown in Figure 12. The multiple island sensor, generally referenced 270, comprises an SEB that includes qubit array 272, capacitors 282, 274, three islands 276 coupled by tunnel junctions 278, and control gates 280, conductive lead 284, voltage source 286, first switch 288, second switch 290, amplifier 292, and detector 294.12485.0118

[0105] Operation of the multiple island sensor 270 is similar to that of sensor 210 (Figure 11) whereby multiple intermediary charge reservoirs function to further enhance thermal robustness as the sensor is coupled to the conductive lead 284 capacitively rather than via a tunnel junction, making it less sensitive to thermal broadening of the carrier gas. Similar to sensor 210, an increased gaps in the energy spectrum results in thermal energy less likely to cause unwanted tunneling events thereby preserving the Coulomb blockade effect at higher temperatures.

[0106] Golden Mean Control Mechanism

[0107] A diagram illustrating signal output 360 of an example charge sensor is shown in Figure 13. When charge moves in the coupled qubit array, there is a shift in sensor response due to capacitive coupling. The charge sensor is typically operated within the regime of many electrons, as it facilitates strong tunnel coupling with the reservoirs. These reservoirs consist of accumulated regions of the 2D electron gas (2DEG). The sensor signal is a function of the applied control gate voltage and plunger voltage of the charge sensor. Each peak in the output represents the sequential transport of individual electrons through the sensor, occurring when an electrochemical potential level exists between the Fermi levels of the source and drain. The positioning of each peak is determined by the additional energy and the local electric field. This field is influenced by the potentials applied to the electrostatic gates surrounding the charge sensor and the number of charges in neighboring qubit array. The addition of an electron in an adjacent quantum dot array can be detected by maintaining a fixed source / drain plunger voltage (e.g., on the slope of a peak) and monitoring the source / drain signal. If the number or position of charges in the environment changes there is a shift in the magnitude of the signal. The sensor is capacitively coupled to the qubit array (QDA). If the sensor is isolated from the qubit array, i.e. the barrier between the sensor and the first quantum dot is high, the number of electrons in the array is fixed. In this case, any movement of charge between the quantum dots through capacitive coupling induces a change, denoted as ΔV, in the sensor. Consequently, this alteration in the sensor’s magnitude affects the measured signal.

[0108] Controlling a SEB sensor for spin qubit readout integrated within a qubit array system using PSB is challenging due to the nonlinear dynamics of the system and the sensor’s extreme sensitivity to charge noise, which can cause slow signal drifts. In one embodiment, a reinforcement learning (RL) methodology is employed for precise tuning of the charge sensor. The objective is to identify and maintain optimal operational parameters, including control gate voltages (and / or other sensor parameters such as power, frequency of the reflectometry signal,12485.0118

[0109] etc.), to maximize the differentiation between signals corresponding to distinct charge configurations within the readout window. The sensor’s signal response may undergo random shifts and slow drift during operation, necessitating adjustments to the control gate voltage(s) to maintain optimal readout performance. It is appreciated that the mechanism described infra is applicable to any charge sensor, including single or multiple island SEB sensors and SETs, by adjusting the relevant control gate voltage(s) or other control parameters. Hereafter, we use the terms ‘signal’ and ‘control gate voltage’ without loss of generality, as the methodology applies to any charge sensor, including single and multi-island SEB sensors.

[0110] An example charge stability diagram of a DQD system, as detected by the sensor is shown in Figure 14A. Where solid lines define the charge state boundaries at equilibrium, the dashed line indicates the position of the interdot transition where an electron tunnels between dots, and the diagonal line represents the scan direction used in Figure 14B. A diagram illustrating the interdot transition sweep with two distinct sensor signal levels is shown in Figure 14B. A diagram illustrating a graph of signal level versus control voltage sweep at the high point VH is shown in Figure 14C. A diagram illustrating a graph of signal level versus control voltage sweep at the low point VL is shown in Figure 14D. Note that when charge moves within the quantum dot array, a shift in the sensor signal occurs due to capacitive coupling. Empty circles in Figures 14A and 14B indicate the locations where the measurements in Figures 14C and 14D are performed. Note also the relative offset between the peaks in Figures 14C and 14D, which arises due to the different charge state occupancy of the qubits in the qubit array. A flow diagram illustrating an example charge sensor initialization method is shown in Figure 15. The Algorithm 1 listing below provides an example charge sensor initialization algorithm.

[0111] With reference to Figures 14A, 14B, 14C, 14D, and 15, initially, the charge sensor is set to a regime of maximum sensitivity to external electric field variation. To achieve this, after initialization (step 312), the operating point is adjusted to a point where the signal exhibits the greatest rate of change with respect to variations in control gate voltage Vc. In one embodiment, this corresponds to the region of the steepest slope of the signal curve, as illustrated at point 362 (Figure 13) and in Figure 4B.

[0112] To determine this optimal operating point, the control gate voltage may be swept (step 314) while monitoring the corresponding signal response, thereby identifying the region where the signal variation is maximized. Typically, the control gate voltage corresponding to this steepest slope is positioned near the mean value of the signal. Additionally, the slope of the sensor signal versus control gate voltage curve in Figure 4B is tracked (step 316) for use in the12485.0118

[0113] control phase following initialization. The SLOPE variable is assigned a value of +1 if the slope of the curve is positive, and -1 if it is negative.

[0114] Once the sensor is tuned to maximum sensitivity, it is used to detect a specific charge transition in a neighboring qubit array, which manifests as a characteristic honeycomb pattern in the charge stability diagram, as illustrated in Figure 5 (step 318). As electrons tunnel between quantum dots within the qubit array, the resulting electrostatic potential shifts induce measurable changes in the sensor response. By monitoring variations in the signal, the sensor enables precise identification of charge state boundaries and facilitates the tuning of key qubit array parameters, including interdot coupling, tunneling rates, and charging energies, thereby optimizing charge stability and control within the array. During the qubit readout procedure, the single-shot PSB readout process is relied on. When the qubit array is brought into the PSB region, the sensor signal depends on the charge configuration in the array, exhibiting high or low response levels corresponding to the spin qubit state.

[0115] The primary task is to find the setpoint of the sensor control gate parameters Vc that delivers optimal sensitivity simultaneously to these charge configurations. This is achieved by modifying the relative chemical potentials of the neighboring qubits, also referred to as detuning, by sweeping their plunger gate potentials along the diagonal direction in Figure 14A (step 320). The resulting scan 240 exhibits a distinct step-like feature, as shown in Figure 14B, where the sensor signal transitions between two discrete response levels corresponding to different charge states in the array. The highest and lowest signal values, VH and VL, respectively, represent key operating points (step 322).

[0116] Next, the sensor is tuned at these points, as illustrated in Figures 14C and 14D, following the same procedure as the initial sensor tuning, to maximize sensitivity to the local electric field and enable precise qubit state detection (step 324). The control gate is swept to identify the point of maximum sensitivity, which corresponds to the steepest slope of the sensor signal versus control gate voltage curve. This point is typically located near the mean of the signal peak. Each sweep at the high and low signal levels yields two distinct control gate voltages, denoted as VCH and VCL respectively. These values define the optimized sensitivity points for each individual signal level. The control voltage setpoint, optimized for both signal levels, is then determined as a mean of these values VcsVcs= (VCL+ VCH / 2.

[0117] Next, the control gate voltage is set to Vcs, and the detuning sweep of the interdot transition along the diagonal direction in Figure 14A is repeated, yielding a signal scan similar to Figure 14B again, this time with the sensor tuned to optimum sensitivity for both signal levels and qubit charge states. Following this scan, the high and low signal values, VH and VL,12485.0118

[0118] are recorded at the sensor’ s optimal sensitivity point. These values are then used to compute = VH— VLwhich represents the difference between the high and low signal levels, and fw =(Vh^Vl>representing the mean signal value. With V

[0119]

[0120]

[0121] M, and the SLOPE initialized, the sensor is optimized for maximum sensitivity, enabling single-shot readout experiments.12485.0118

[0122] Algorithm 1 Charge Sensor Initialization Algorithm

[0123] 1: Input:

[0124] 2: Measurement function Measure iqnal()

[0125] 3;

[0126]

[0127] 5ymm v^fsGate sweep ranges 4: Initialize:

[0128] 5:

[0129]

[0130] p’5"',!,r- stop:---l -"

[0131]

[0132] l,;’:!step^l^*"’*’) > Set sensor Control Gate sweep range 6: SLOPE -te O

[0133] 7: Step 1: Sweep Control Gate Voltage

[0134] 8: Signal Afea«ureS'ignal(V<'’-,<1'’'9' )

[0135] 9: Step 2: Set Control Gate Voltage to the optimum point

[0136] 19: Vc - " G, where

[0137] UiSigria / ^i-t:) | | cPuipieK Ifo) |

[0138]

[0139] 11: Step 3: Determine Slope

[0140] 12: if

[0141] dS‘igna / (Vc) |

[0142] . <;Vr. |

[0143]

[0144] vfc

[0145] then

[0146] 13; SLOPE |-1

[0147] .14: else

[0148] 15: SLOPE «. 1

[0149] 16: end if

[0150] 17: Step 4: Find a desired interdot transition in the charge stability diagram

[0151] 1

[0152]

[0153] * C': stop-V^f?ran9e(V^^ stop-V^T, 19: Step 5: Perform interdot transition sweep

[0154] 20: Signal < - A

[0155]

[0156] feammeSignaliV^^ -- V^9*)

[0157] 21: Step 6: Detect High, Low, and Mean Signal levels

[0158] 22: Ph TOw(S'igi'tti)

[0159] 23: V(|‘D1, VQ|J2 <- ^QUI3''QD2’ f°r^Q: J1: VQD2) ’■’■’■ Ill

[0160] 24: VL mln(Signai)

[0161] ~‘i- ^QDl’ ^Qba ^QDl ’ ^ QD2!fof^QD2) ™

[0162] 2

[0163]

[0164] 6: VM *- (i'31 + I'L} / 2

[0165] 27: Step 7: Find sensor optimal setpoint for High, Low, and both signal levels

[0166] 28: Signal < ■ MeasweSignal(V(\*''‘s'’) for VQD: 3'QD2.... I / O TZ«

[0167] "■ ’■ QD1: *' QD2

[0168] 29: VCR <"■ V<'H, where

[0169] | SSignal flfo) | I SSignalOO)

[0170] max i... -

[0171] 30: Signal < - AfetswreSh'gnQl(l'c<lfor VQD ■, VQD2 Km- ’ Ktna

[0172] 31: IZCL <-"• VZ3L; where

[0173] l^ignalfVc) dEignsf(Vc)

[0174] cd'cn

[0175] 3

[0176]

[0177] 2: PQ <"' VGS, where V<is ™;(I’cii 4~ I'C’L) / 2

[0178] 33: Step 8: Retune the Sensor Signal levels of the interdot transition at the sensor optimal setpoint

[0179] 34: Signal «- Metsw'eSigna^Vqg^^ — VQD29R)

[0180] 35: H <— a,x{Signal)

[0181] 36: fojm > Qix> H DI ’QD2: where Sign.a / VQD;. VQD2~ VH

[0182] 37: 'l 3™?n-tnp$’fgnei )

[0183] 6; V^bv ^qm ^QDI 3’QD2: where S?.gnfo(hqDJ;I’QDS)

[0184] 39: AVHL <"'■ (l- l I't); VM (W 4- VjJ / 'ii

[0185] 40: return A VHL. ',

[0186]

[0187] SLOPE12485.0118

[0188] Simple Golden Mean Control Mechanism

[0189] The simple golden mean control algorithm will now be described in more detail. A diagram illustrating example sensor signal outcome of a single shot measurement in the event EV^L— VHL whereby no adjustment is required is shown in Figure 16A. A diagram illustrating example sensor signal outcome of a single shot measurement in the event VHL> whereby an adjustment (indicated in Figure 16C) is necessary is shown in Figure 16B. A diagram illustrating a zoomed view of the sensor signal as a function of control gate voltage is shown in Figure 16C where Vcs is adjusted to maintain operation at the optimal sensitivity point. A flow diagram illustrating an example golden mean control method is shown in Figure 17. The Algorithm 2 listing below provides an example simple golden mean control algorithm.

[0190] In operation of the charge sensor, after initialization (step 330) during the qubit readout procedure, the sensor’s control gate voltage is set to Vcs, and the qubit array is brought to the PSB window near the interdot transition, shown as a dashed line in Figure 14A (step 332). The readout process utilizes single-shot PSB detection, wherein n repetitive measurements are performed, and the measured sensor signal outcomes are categorized into bins (step 334). This procedure yields a bimodal distribution, similar to the one shown in Figures 16A and 16B, which is then fitted to determine AV^L

[0191]

[0192] and the difference between the high and low signal levels and the mean signal value respectively, based on the most recent n single-shot measurements. To compensate for slow drifts occurring during the measurement process, AV^Lis compared with the previously recorded value VHL. If AV^L> AVHL, as illustrated in Figure 16 A, the system remains at its most sensitive operating point, and the values are updated such that VHL= AV^Land AKM= AV^. Under these conditions, no further tuning is required (step 336).

[0193] Otherwise, as illustrated in Figure 16B, the control voltage Vcs is adjusted by a small predefined step 6VCSas shown in Figure 16C:

[0194] v> f vcs+ SLOPE x 3VCSifor < VM

[0195] cs =( Vcs - SLQPE x SVcs for V^ > VM (1)Following this adjustment, the system is ready to perform the next n repetitive measurements using the same algorithm.12485.0118

[0196] Algorithm 2 Simple Golden Mean control Algorithm

[0197] "

[0198]

[0199] 17 Input? M.

[0200] 2: n, t> Number of single-shot measurements 3; MeasureSignalQ Signal Measurement function 4: Initialize:

[0201] 5: Create an empty array Signal^ of size n

[0202] it Create an empty array Histogram^ of size BinsN

[0203] 7: Step 1: Perform Qubit Readout

[0204] 8: for i — 1 to n do

[0205] 9: Signal[i] <- MeasnreSignaI() t> Store measurement result 10: end for

[0206] 11: Step 2: Categorize Sensor Signal outcomes into bins and analyze

[0207] 12: Histogram^ - SignalToBins Signal[]) Categorize Sensor Signal outcomes into bins.

[0208] 13:

[0209] 14: V]'t. <■■■■ Fit.2Gauss(Iiistogram^)

[0210] 15:

[0211]

[0212] (V / }- K), V'4e- (Y£ + V / ) / 2

[0213] 16: Step 3: Check for Drift and Adjust Vos

[0214] 17: if AVflL> AV'H then i> Maintain current Vcs 18: AVJIL e~

[0215] 19:

[0216]

[0217] VM e- 20: else t> Adjust VQS21: if lz< VM then

[0218] 22: ‘ Vos e- I (. + SLOPE x <5VCS

[0219] 23: else

[0220] 24: lzcs t- Vcs “ SLOPE X d'Vos

[0221] 25- end i

[0222]

[0223] f

[0224] 26: end if

[0225] 27: return VCSJ AVIIL, VM

[0226] Simple Golden Mean Control With Reinforcement Learning In one embodiment, the simple golden mean control method described supra is enhanced by employing a machine learning-based approach, in particular, a reinforcement learning (RL) mechanism, to optimize qubit readout performance. A flow diagram illustrating an example golden mean control method with reinforcement learning is shown in Figure 18. The Algorithm 3 listing below provides an example golden mean control algorithm with reinforcement learning.

[0227] Reinforcement learning is a branch of machine learning in which an autonomous ‘agent’ learns to make optimal, sequential decisions by interacting with an environment through trial and error to achieve a defined objective. The agent selects actions, observes the system state, and receives rewards or penalties based on the alignment of its actions with the desired outcome. Through repeated interactions, the agent iteratively refines its control strategy to maximize cumulative rewards over time without explicit supervision, enabling adaptive and optimized sensor tuning for qubit readout.

[0228] Initialization (step 340), qubit readout (step 342), and categorizing sensor signal outcomes (step 344) are performed as in the method of Figure 17 described supra. In this12485.0118

[0229] embodiment, however, rather than using a fixed, predefined 6VCSstep for charge sensor setpoint adjustment in the golden mean control algorithm during the qubit readout procedure, an RL-based optimization method is employed to dynamically adjust its magnitude |<5'lc|. The sensor control system is formulated as an RL agent interacting with the environment, where the system state is defined by the sensor signal response and prior calibration data. The RL agent selects the adjustment magnitude |bl / s-| to the control voltage based on observed deviations in signal level difference

[0230]

[0231] relative to the recorded maximum VHL, ensuring that the system remains at its most responsive operating point (step 346). The problem is structured as an RL framework, where the agent iteratively optimizes sensor control parameters to maintain high-fidelity qubit readout (step 348).

[0232] The components of this RL framework are defined as follows:

[0233] 1. Environment: The environment is the external system with which the agent interacts. In this case, it is the charge sensor measurement signal.

[0234] 2. State Space: The state space is set of all possible situations or configurations of the environment. Here, it represents the sensor signal magnitude within a given range. This should be a continuous bounded space.

[0235] 3. Action Space: The action space is the set of all possible actions the RL agent can take in a given state. In this case, it is defined as adjustments to the control gate voltage 6VCSwithin the range 6VCSG [0,517^], where 6 V^srepresents the maximum permissible adjustment. Note that this can be continuous or discrete. 4. Observation Space: The observation space is the set of parameters accessible to the agent when evaluating a state. In this application, the observation space includes

[0236]

[0237] and AV^L.

[0238] 5. Reward Function: In operation, the RL agent receives a reward proportional to

[0239]

[0240] following an adjustment, which quantifies the sensor’s ability to distinguish charge states within the readout window.

[0241] 6. Learning Algorithm: The learning algorithm is the specific algorithm employed by the agent to update its policy or value function based on interactions with the environment. This algorithm is selected from well-known reinforcement learning methods, such as: Q-learning, SARSA, Deep Q-Networks (DQN), or Policy Gradient methods.

[0242] 7. Policy: This is the control strategy that determines how the agent selects an action based on a given state. The policy may be either deterministic (i.e. directly selecting12485.0118

[0243] the optimal voltage adjustment) or stochastic (i.e. exploring different sensor tuning strategies based on learned probability distributions). Over time, the policy can be refined to minimize drift and maintain qubit readout stability without excessive manual intervention.

[0244] Algorithm 3 Simple Golden Mean control with Reinforcement Learning Algorithm

[0245] i Input: AI-JILS Ki: SLOPE, ^Vcs,

[0246] 2 n. i> Number of single-shot measurements 3 M easureSignal ( ) E> Signal Measurement function 4 FindDelta Vcs () t> RL agent 5 Initialize:

[0247] 6 Create an empty array Signal^ of size n

[0248] Create an empty array Histogram^ of size BinsN

[0249] 8 Step 1: Perform Qubit Readout

[0250] 9 for i — 1 to n do

[0251] 10 Signal^] c- MeasureSignai() i> Store measurement result 11 end for

[0252] 12 Step 2; Categorize Sensor Signal outcomes into bins and analyze

[0253] 13.ffisfogram SignalT oBins(Signal[]) t> Categorize Sensor Signal outcomes into bins.

[0254] 14 Vf3. V - Fit2Gauss(ffistogram )

[0255] 15 A^L (V / j - ), K (K + ) / 2

[0256] 16 Step 3: Use RL agent to Adjust d'V'cs

[0257] 17 tf fes 4~ FindDeUaVcs( AI4IL> F4L) > Let RL agent define.’s 18 Step 4: Check for Drift and Adjust Vos

[0258] 19 if A\(4 > AVHL then i> Maintain current V'cs 20 AV;:| V t;

[0259] 21 ^ 4" Ki

[0260] 22 else c Adjust Vcs 23 if U4 < Hr then

[0261] 24 ' U s Vcs + SLOPE x MUS

[0262] 25 else

[0263] 26 Vcs<■■■■ Vcs - SLOPE x JVC8

[0264] 27 end i

[0265]

[0266] f

[0267] 28 end if

[0268] 29 return

[0269]

[0270] Vi / s- A V'ui ■

[0271] Training the RL Agent

[0272] In one embodiment, the reinforcement learning (RL) agent undergoes a structured training process to optimize its policy for charge sensor set point tuning during qubit readout. A flow diagram illustrating an example reinforcement learning (RL) agent training method is shown in Figure 19 and a training procedure portion is shown in Figure 20. The training procedure consists of the following steps:

[0273] 1. Environment Initialization: The RL environment is initialized to simulate the charge sensor response dynamics, defining the state space, action space, and reward function parameters (step 380).12485.0118

[0274] 2. Selection of RL Algorithm: An appropriate RL algorithm is chosen based on the complexity of the environment, including discrete or continuous action spaces. Several possible implementations include the well-known Proximal Policy Optimization (PPO), Deep Q-Networks (DQN), or other policy -gradient and value-based approaches (step 382).

[0275] 3. Agent Initialization: The RL agent is instantiated using a reinforcement learning framework, such as Stable-Baselines3 or any other suitable implementation. The agent’s neural network architecture is configured to accommodate the dimensions of the observation and action spaces, ensuring efficient state-action mapping (step 384).

[0276] 4. Training Parameter Definition: Hyperparameters critical to learning efficiency are specified, including, for example: learning rate, batch size, number of episodes, steps per episode, and exploration / exploitation balance (step 386).

[0277] 5. Training Procedure: The training procedure includes the following (step 388):

[0278] a. Episode Initialization: At the start of each episode, the environment is reset to obtain an initial state observation (step 400).

[0279] b. Action and Observation Loop: The agent then processes the current observation and selects an action based on its policy. The action is executed in the environment, yielding the next state, a corresponding reward, and an episode termination flag. If experience replay is utilized (e.g., in DQN), the agent stores the transition tuple (state, action, reward, next state) in memory for future updates (step 402).

[0280] c. Policy update: At predefined intervals, the agent refines its policy using collected experience data, leveraging techniques such as gradient-based optimization or Q-learning updates (step 404).

[0281] 6. Performance Evaluation: The agent then undergoes periodic testing without exploration to assess policy effectiveness. Evaluation metrics may include average cumulative reward, convergence stability, and sensitivity to sensor signal drift (step 390).

[0282] 7. Optimization and Fine-Tuning: Hyperparameters, reward functions, and network architectures are iteratively adjusted to improve agent learning efficiency and robustness to environmental variations (step 392).

[0283] 8. Model Deployment: Upon successful training, the final policy and neural network parameters are stored for integration into the charge sensor control system. The trained agent is deployed for real-time charge sensor tuning, adapting dynamically to12485.0118

[0284] environmental fluctuations while maintaining high-fidelity qubit readout conditions (step 394).

[0285] An extension to the golden mean control method will now be described in more detail. A flow diagram illustrating an example golden mean control method with pure reinforcement learning is shown in Figure 21. The Algorithm 4 listing below provides an example simple golden mean control algorithm with pure reinforcement learning. Initialization (step 350), qubit readout (step 352), and categorizing sensor signal outcomes into bins (step 354) are performed as in the method of Figure 18 described supra. In this alternative embodiment, the RL agent directly optimizes the control gate voltage of the charge sensor without relying on predefined heuristics or rule-based corrections. The adjusted control gate voltage Vcs is treated as a learnable parameter, enabling the agent to autonomously determine the optimal tuning strategy based on the full set of accessible parameters when evaluating a state (step 356). In this application, the observation space includes: AVHL, AV / L, AVM, AV^, AVH, AV / , AVL, AV / ,

[0286]

[0287] CH ^VCL- In one embodiment, the system is modeled as a black box, where the RL agent does not rely on an explicit analytical model but instead interacts with the environment to infer optimal control parameters. Depending on the chosen RL algorithm, the agent’s action space may be either discrete, selecting from predefined voltage increments, or continuous, enabling finegrained control over voltage adjustments. At each step, the RL agent determines both the magnitude and sign of the control voltage, ensuring adaptive and optimal sensor tuning.

[0288] The reward function is formulated to maximize the difference AV / Lbetween measured high and low sensor signal levels corresponding to two distinct charge states. This ensures that the agent prioritizes adjustments that enhance the sensor’s sensitivity to charge transitions, thereby maintaining optimal qubit readout conditions over time.12485.0118

[0289] Algorithm 4 Golden. Mean control with Pure Reinforcement Learning

[0290] 1: Input: Vhn, V', AVM, AV", AVH, AV", AI, AV", AVCil;AVCL,

[0291] 2: n. Number of single-shot measurements 3: M easure, Signal{) Signal Measurement function 4: Find Vcs () Pure RL agent 5: Initialize:

[0292] 6: Create an empty array Signal [] of size n

[0293] 7: Create an empty array Histogram] of size BinsN

[0294] 8: Step 1: Perforin Qubit Readout

[0295] 9: for i — 1 to n do

[0296] 10: Signal[i] MeasureSignalQ Store measurement result 11: end for

[0297] 12: Step 2: Categorize Sensor Signal outcomes into bins and analyze

[0298] 13: Histogram] SignalToBins Signal]) Categorize Sensor Signal outcomes into bins.

[0299] 14: I-yi. I" 4- Fit2Gauss(Histogram )

[0300] 15: AI «- (Pi - )< V - (^1 + ) / 2

[0301] 16: Step 3: Use Pure RL agent to Adjust VCs

[0302] 17: V

[0303]

[0304] 'cs FindVcs(AKiLs AIAb AI--"hl, AVJI> AV"t, AVL, AFCH> A VOL) t* Let RL agent define Vcs

[0305] 18: return Ks

[0306] Note that the above algorithms optionally include hysteresis for mitigating chattering effects around the gate control voltage setpoint.

[0307] Those skilled in the art will recognize that the boundaries between logic and circuit blocks are merely illustrative and that alternative embodiments may merge logic blocks or circuit elements or impose an alternate decomposition of functionality upon various logic blocks or circuit elements. Thus, it is to be understood that the architectures depicted herein are merely exemplary, and that in fact many other architectures may be implemented which achieve the same functionality.

[0308] Any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality may be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermediary components. Likewise, any two components so associated can also be viewed as being “operably connected,” or “operably coupled,” to each other to achieve the desired functionality.

[0309] Furthermore, those skilled in the art will recognize that boundaries between the above described operations are merely illustrative. The multiple operations may be combined into a single operation, a single operation may be distributed in additional operations and operations may be executed at least partially overlapping in time. Moreover, alternative embodiments may include multiple instances of a particular operation, and the order of operations may be altered in various other embodiments.12485.0118

[0310] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0311] In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The use of introductory phrases such as “at least one” and “one or more” in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an.” The same holds true for the use of definite articles. Unless stated otherwise, terms such as “first,” “second,” etc. are used to arbitrarily distinguish between the elements such terms describe. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage.

[0312] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. As numerous modifications and changes will readily occur to those skilled in the art, it is intended that the invention not be limited to the limited number of embodiments described herein. Accordingly, it will be appreciated that all suitable variations, modifications and equivalents may be resorted to, falling within the spirit and scope of the present invention. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims

12485.0118CLAIMS1. A spin state charge sensor comprising:a single electron box (SEB) including an island, at least one tunnel junction coupled to said island, and a control gate capacitively coupled to said island; a floating lead configured to be selectively connected to a voltage source via a first switch, wherein said floating lead is coupled to either said at least one tunnel junction or said control gate;a second switch configured to connect the floating lead to a voltage amplifier for measuring a potential change in the floating lead; anda qubit array adjacent to the SEB, wherein the qubit array is capacitively coupled to the island such that a charge state change in said qubit array induces a tunneling event on said island, resulting in a detectable potential change in said floating lead when in a floating state.

2. The charge sensor according to claim 1, wherein said floating lead is coupled to said at least one tunnel junction, and wherein activation of said first switch sets a potential on said floating lead to allow electron tunneling between said floating lead and said island via the tunnel junction.

3. The charge sensor according to claim 1, wherein said floating lead is coupled to said control gate, and wherein activation of said first switch sets a potential on said control gate to tune an electrochemical potential of said island for electron tunneling through said at least one tunnel junction.

4. The charge sensor of claim 1, wherein deactivation of said first switch places said floating lead in the floating state, and wherein the potential change in said floating lead corresponds to a stepwise output from said voltage amplifier indicative of the tunneling event.

5. A charge sensor, comprising:a single electron box (SEB) including one or more conductive islands, said island capacitively coupled to a qubit array;a conductive lead coupled to said SEB and a voltage source;an amplifier coupled to said lead which is placed in a floating state after said voltage source is disconnected from said lead; and12485.0118wherein a tunneling event in said qubit array results in a change in electric potential of said lead that is subsequently detected and amplified by said amplifier.

6. The charge sensor according to claim 5, wherein said SEB comprises a single conductive island coupled to said lead via a tunnel junction.

7. The charge sensor according to claim 6, wherein said island comprises a control gate coupled to a voltage source.

8. The charge sensor according to claim 5, wherein said SEB comprises a single conductive island coupled to said lead via a control gate of said island.

9. The charge sensor according to claim 8, wherein said conductive island is coupled to a voltage source or ground via a tunnel junction.

10. The charge sensor according to claim 5, wherein said SEB comprises a plurality of conductive islands coupled to each other via tunnel junctions.

11. The charge sensor according to claim 10, wherein said plurality of conductive islands are coupled to said lead via a capacitor.

12. The charge sensor according to claim 10, wherein each island comprises a control gate coupled to a voltage source.

13. A spin state charge sensor comprising:a multiple island single electron box (SEB) including a primary island capacitively coupled to a qubit array, and a plurality of additional islands acting as intermediary charge reservoirs coupled to each other by tunnel junctions; multiple control gates, each control gate capacitively coupled to an additional island;anda conductive lead capacitively coupled to at least one of the additional islands, wherein mutual Coulomb interactions among said primary island and said additional islands create an effective energy gap larger than a charging energy of a single-island SEB, enabling operation at higher temperatures by reducing sensitivity to thermal fluctuations.12485.011814. The charge sensor according to claim 13, wherein the capacitive coupling of the conductive lead to the at least one additional island avoids direct tunnel junction coupling to said conductive lead, thereby mitigating thermal broadening effects.

15. The charge sensor according to claim 13, wherein the additional islands provide tunability in tunnel barriers and capacitive couplings for optimizing charge states.

16. The charge sensor according to claim 13, further comprising gate-tuning algorithms configured to manage interactions between said primary island, said additional islands, and said qubit array.

17. A spin state charge sensing method, comprising the steps of:providing a single electron box (SEB) having one or more conductive islands, at least one tunnel junction, and one or more control gates;coupling a floating lead to either said at least one tunnel junction or said one or more control gates;activating a first switch to connect said floating lead to a voltage source, thereby setting a potential to enable tunneling between said floating lead and at least one conductive island;deactivating said first switch to place said floating lead in a floating state; capacitively coupling a qubit array to said island such that a charge state change in said qubit array induces a tunneling event on said island, altering a potential of said floating lead; andactivating a second switch to connect said floating lead to an amplifier to measure the altered potential indicating the occurrence of a charge state change in said qubit array which is detected at an output of said amplifier.

18. The method according to claim 17, further comprising adjusting voltages at each control gate to tune an electrochemical potential of a corresponding island prior to deactivating said first switch.

19. The method according to claim 17, wherein the tunneling event results in a significant potential change due to a small capacitance of said floating lead.

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