High frequency cascode readout

Abstract

A circuit for reading out a state of a quantum bit 100 having a singlet spin state and a triplet spin state, comprising: a double quantum dot 101 forming the quantum bit 100, the double quantum dot 101 comprising a first quantum dot 105 and a second quantum dot 106. The circuit comprises: a cascade quantum dot 102 capacitively coupled to the second quantum dot 106; a charge reservoir 103 tunnel coupled to the cascade quantum dot 102; and a readout circuit 104 coupled to the reservoir 103. When a charge carrier tunnels between the first quantum dot 105 and the second quantum dot 106, the charge carrier tunnels between the cascade quantum dot 102 and the charge reservoir 103. A frequency source connected to a gate electrode or the charge reservoir 103 is configured to apply an alternating electrical potential 111 of a first frequency h, thereby causing a cyclic tunneling of the charge carrier only when the quantum bit is in the singlet state, which is detectable by the resonator circuit 104.

Description

Technical Field

[0001] This invention relates to a circuit for reading out the state of a qubit. The device is suitable for performing measurements or reading out the state of a qubit at a distance from the qubit. Background Technology

[0002] Measuring spin qubits in semiconductor nanostructures is an extremely difficult task. Existing methods typically rely on measuring the charge of the spin-carrying particle, rather than the spin itself. This spin readout method is called spin-charge conversion and is ubiquitous in semiconductor-based quantum computing architectures.

[0003] The preferred spin-charge conversion mechanism is the Pauli spin blockade mechanism because it can be used at higher temperatures (close to a few Kelvin) and lower magnetic fields (B < 1 Tesla).

[0004] Pauli spin blocking requires a double quantum dot, consisting of two quantum dots with two spin-carrying particles (typically electrons or holes). This double quantum dot forms a qubit. The two spin-carrying particles can be in either a singlet spin configuration or a triplet state configuration. These configurations provide the two states of the qubit. When the spin is in a singlet spin configuration, charge can tunnel between the two quantum dots, while tunneling is suppressed when the two quantum dots are in a triplet configuration.

[0005] Charge carrier tunneling between the two quantum dots in a dual quantum dot matrix is ​​typically detected using charge measurements.

[0006] Charge measurements can be performed using dissipative charge sensors located close to the two quantum dots (such as single-electron transistors or quantum dot contacts). These are sensitive sensors, but they occupy a considerable amount of chip space, making it complex to generate highly interconnected qubit architectures. For single-electron transistors, additional quantum dots and two charge banks are required for readout.

[0007] Dispersive charge sensors (such as single-electron cells) occupy less space than single-electron transistors or quantum dot contacts. Therefore, dispersive charge sensors can be used to provide more compact charge measurement methods because they require only an additional quantum dot, a charge reservoir, and the alternating current between them.

[0008] The techniques described above are used to measure charge. Alternatively, charge polarization measurements can be used to detect charge carrier tunneling between two quantum dots. Compared to charge measurements, charge polarization measurements are helpful in detecting Pauli spin blocking.

[0009] Charge polarization measurements can be performed using dispersion readout. This technique involves directly connecting a dual-quantum dot system to an electronic resonator via one of the predefined gates of the dual quantum dots. The presence or absence of charge polarization causes a change in the frequency of the alternating current potential detected by the resonator. This can be observed as a change in the amplitude or phase of the alternating current potential. The absence and presence of charge polarization correspond to the triplet state and singlet state of the dual quantum dots, respectively.

[0010] Dispersion readout methods have an advantage in minimizing on-chip footprint because, unlike charge sensors, they do not require additional on-chip readout infrastructure.

[0011] However, the signal-to-noise ratio of dispersion readouts is typically poor because the measured polarization charge is a small fraction of the total electron charge (i.e., the charge of a single electron). Due to the spacing between the quantum dot and the sensor, it is actually a mirror charge at the quantum dot gate, which is necessarily smaller than that of an electron.

[0012] Furthermore, since charge and charge polarization measurements are governed by Coulomb electrostatic energy, these measurements typically need to be performed locally. This is achieved by placing charge or charge polarization sensors close to the target qubit. This presents a problem for measuring spin qubits in dense arrays, as many sensors need to be locally deployed to sense all qubits.

[0013] To measure charge over long distances, an electronic cascade can be implemented, in which a single charge tunneling event generates a series of charge tunneling events that propagate the charge to the location of the charge readout sensor.

[0014] The aim is to provide improved techniques for performing spin qubit measurements. Summary of the Invention

[0015] A first aspect of the invention provides a circuit for reading out the state of a qubit. The circuit includes: a dual quantum dot forming the qubit, the qubit having a singlet spin state and a triplet spin state, wherein the dual quantum dot comprises a first quantum dot and a second quantum dot, wherein the second quantum dot is tunnel-coupled to the first quantum dot; a gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; a cascade of quantum dots capacitively coupled to the second quantum dot; a charge bank tunneling to the cascade of quantum dots; a readout circuit connected to the charge bank; and a frequency source connected to the gate electrode or the charge bank and configured to apply an alternating current potential thereto. The cascade of quantum dots is tuned to near charge transitions such that when charge carriers tunnel between the first and second quantum dots, charge carriers tunnel between the cascade of quantum dots and the charge bank. A frequency source is configured to apply an alternating current potential at a first frequency, thereby inducing cyclic tunneling of charge carriers from a first quantum dot to a second quantum dot and vice versa only when the qubit is in a singlet spin state, and also inducing cyclic tunneling of charge carriers from cascaded quantum dots to a charge pool and vice versa. The readout circuit is configured to: detect the first alternating current potential; measure one or more properties of the detected first alternating current potential; and infer that the qubit is in a triplet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the triplet spin state; and infer that the qubit is in a singlet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the singlet spin state.

[0016] In this way, a dual quantum dot can be connected to a charge bank and a readout circuit via a cascaded quantum dot array, thereby inferring the state of a qubit at a distance, with the cascaded quantum dots capacitively coupled in the middle. Tunneling between the cascaded quantum dots and the charge bank is due to electrostatic coupling between the systems, specifically between the dual quantum dots (including the first and second quantum dots) and the cascaded quantum dots. Therefore, this circuit can be advantageously used to perform charge polarization measurements at a distance with an improved signal-to-noise ratio. The readout circuit can be advantageously used to infer the state of a qubit without requiring external sensors at the nanostructure. Based on a comparison between one or more measured properties and expected values ​​for singlet and triplet spin configurations, the readout circuit can infer that the qubit is in a triplet spin state, or it can infer that the qubit is in a singlet spin state.

[0017] Therefore, this circuit can utilize a readout sensor from the readout circuit to facilitate the detection of the qubit's state, even if the sensor is located at a certain distance from the qubit. The cascaded Pauli spin blocking process advantageously provides an improved signal-to-noise ratio, where charge carrier tunneling in the two-point system induces tunneling in the neighboring system. Advantageously, this means that charge polarization measurements can be performed at a distance to read out the qubit's state.

[0018] Optionally, the detected first AC potential can be detected on both the real axis (in phase) and the imaginary axis (90 degrees out of phase). These two signals can then be combined to derive the amplitude or phase change between the singlet spin state and the triplet spin state.

[0019] In this way, the qubits in the circuit can be placed further away from the readout sensor, which is advantageous in the context of quantum computing, where readout electronics occupy a lot of space and require connections via classical control circuitry.

[0020] Other techniques for transmitting quantum information are known, including charge shuttle or performing a SWAP operation. However, these techniques are limited by spin relaxation time and the fidelity of the corresponding operations. Therefore, another advantage of this invention is the improved fidelity of readout measurements, since cascaded Pauli spin blocking involves inducing a continuous tunneling process. In this way, the cascaded Pauli spin blocking technique described herein advantageously enhances the charge detected by prior art, similar to that involving latching, DC cascading, and spin-polarized single-electron cells, while preserving the advantageous quantum non-destructive properties of in-situ dispersive readout methods. In this way, the system remains in its eigenstate after readout, rather than the information being destroyed or lost. Therefore, non-destructive readout means that qubit initialization can be accomplished by measurement.

[0021] Another advantage stems from the cyclic nature of tunneling, which results in a readout measurement that is a quantum non-destructive measurement. Cyclic tunneling typically occurs substantially synchronously. When the frequency source is connected to the gate electrode, it is configured to apply an AC potential to the gate electrode; when the frequency source is connected to the charge bank, it is configured to apply an AC potential to the charge bank. Optionally, the frequency source can be connected to both, allowing for flexible circuit configuration. Typically, when an AC potential is applied to the gate electrode, tunneling is induced between the first and second quantum dots, which subsequently induces tunneling in adjacent tunneling coupling systems (i.e., cascaded quantum dots and charge banks). Preferably, in this case, the transmission scattering coefficient, i.e., S, is measured. 21 Alternatively, when an AC potential is applied to the charge pool, tunneling is induced between the cascaded quantum dots and the charge pool, which subsequently induces tunneling in a neighboring tunneling coupling system comprising the first and second quantum dots. Preferably, in this case, the reflection scattering coefficient, i.e., S...11 In both cases, during the application of the AC potential, tunneling occurs continuously at a frequency that matches the driving frequency (i.e., the frequency of the AC potential), and tunneling is substantially synchronized in all tunneling coupling circuit elements capacitively coupled to adjacent tunneling coupling circuit elements.

[0022] Typically, a readout circuit may include one or more resonant circuits having a predetermined resonant frequency. Preferably, the frequency applied by a frequency source to drive the circuit is the resonant frequency of the resonant circuit in the readout circuit. In other examples, other off-chip or on-chip readout sensors may be used as part of the readout circuit. In addition to the readout sensor, the readout circuit preferably includes a processor for measuring the properties of an AC potential and inferring the state of the qubit by comparing the measured properties of the detected AC potential with expected values ​​for singlet spin states and triplet spin states, respectively. When the measured value and the expected value are consistent within a predetermined uncertainty value, it can be determined that the measured value substantially matches the expected value. Furthermore, the expected value may include a range of values, and when the measured value falls within the range of the expected value, it can be determined that the measured value substantially matches the expected value. In each case, one or more measured properties may be compared with corresponding one or more expected values.

[0023] Optionally, the calibration step determines expected values ​​for properties of the triplet spin state and expected values ​​for properties of the singlet spin state. Typically, the calibration step may include determining expected values ​​for properties of the triplet spin state by recording the properties of the AC potential detected by the readout circuit when the two quantum dots are in a (1,1) charge configuration (i.e., each of the first and second quantum dots has charge carriers). The properties recorded from the (1,1) charge configuration can be determined as expected values ​​for properties of the triplet spin state. The calibration step may also include determining expected values ​​for properties of the singlet spin state by recording the properties of the AC potential detected by the readout circuit when the two quantum dots are in a (0,2) charge configuration (i.e., the second quantum dot has two charge carriers). The properties recorded from the (0,2) charge configuration can be determined as expected values ​​for properties of the singlet spin state.

[0024] Optionally, the expected value for the properties of the triplet spin state can include a range of expected values. For example, if the measured frequency of the detected first AC potential is greater than or equal to a first expected frequency value and less than or equal to a second expected frequency value (greater than the first expected frequency value), the readout circuit can determine that the measured frequency matches the expected frequency value for the triplet spin state, thereby inferring that the qubit is in a triplet spin state. Similarly, the expected amplitude value can be between a first expected amplitude value and a second expected amplitude value greater than the first expected amplitude value; and the expected phase value can be between a first expected phase value and a second expected phase value greater than the first expected phase value.

[0025] Optionally, similarly, the expected value for the properties of a singlet spin state can include a range of expected values. For example, if the measured frequency of the detected first AC potential is greater than or equal to a third expected frequency value and less than or equal to a fourth expected frequency value (greater than the third expected frequency value), the readout circuit can determine that the measured frequency matches the expected frequency value for the singlet spin state, thereby inferring that the qubit is in a singlet spin state. Similarly, the expected amplitude value can be between a third expected amplitude value and a fourth expected amplitude value greater than the third expected amplitude value; and the expected phase value can be between a third expected phase value and a fourth expected phase value greater than the third expected phase value.

[0026] Preferably, the expected value range for the properties of the triplet spin state does not overlap with the corresponding expected value range for the properties of the singlet spin state.

[0027] Typically, the expected value may depend on system parameters such as material, temperature, surface factors, circuit variability, and other such experimental factors that deviate from the theoretically determined values ​​of singlet and triplet spin states. Therefore, a confidence interval can be determined around the expected value, within which the readout circuit can infer that one or more measured properties substantially match the expected value of one of the singlet or triplet spin states.

[0028] The circuit may further include one or more intermediate cascaded quantum dots, each intermediate cascaded quantum dot comprising a first intermediate cascaded quantum dot and a second intermediate cascaded quantum dot. The second intermediate cascaded quantum dot is preferably tunnel-coupled to the first intermediate cascaded quantum dot; the second quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of one or more intermediate cascaded quantum dots; the cascaded quantum dot is preferably capacitively coupled to the second intermediate cascaded quantum dot of one or more intermediate cascaded quantum dots. Each intermediate cascaded quantum dot is preferably tuned to near charge transitions such that when charge carriers tunnel between the first and second quantum dots, charge carriers tunnel between the first and second intermediate cascaded quantum dots of the intermediate cascaded quantum dot. The frequency source is preferably configured to apply an alternating potential of a first frequency, thereby causing cyclic tunneling of charge carriers from a first quantum dot to a second quantum dot and vice versa only when the quantum bit is in a singlet spin state, and also causing cyclic tunneling of charge carriers sequentially from a first intermediate cascade quantum dot to a second intermediate cascade quantum dot and vice versa in each of one or more intermediate cascaded quantum dots, and also causing cyclic tunneling of charge carriers from cascaded quantum dots to a charge pool and vice versa.

[0029] Advantageously, the intermediate cascaded dual quantum dots increase the spacing between the qubit and the readout sensor, while simultaneously providing an improved signal-to-noise ratio at the readout sensor. The improved signal-to-noise ratio is achieved because the qubit state information is transmitted using a cascaded Pauli spin blocking process, where charge carrier tunneling in the dual-dot system induces tunneling in neighboring systems. This amplifies the signal detected by the readout circuitry.

[0030] Using a cascaded Pauli spin blocking process to trigger a series of cyclic quantum tunneling events in a two-quantum-dot chain favorably leads to near-perfect electron charge. The charge polarization. In existing dispersive readout methods, the polarization charge is... ,in ,in It is the ratio of the difference in gate capacitance between the first and second quantum dots to the total capacitance of the measured quantum dots. For example, for the first quantum dot, It is the ratio of the gate capacitance of the first quantum dot minus the gate capacitance of the second quantum dot, divided by the total capacitance of the first quantum dot. Advantageously, this technique improves the signal-to-noise ratio by a factor of [missing information]. ,in , It is the ratio of the capacitance from the charge pool to the cascaded quantum dot to the total capacitance of the cascaded quantum dot. The capacitance from the charge pool to the cascaded quantum dot can be engineered to approach zero by increasing the size of the cascaded quantum dot or increasing the spacing between the cascaded quantum dot and the charge pool. In all cases, the spacing between the cascaded quantum dot and the charge pool is within the quantum interaction distance, allowing charge carriers to tunnel between the charge pool and the cascaded quantum dot. Therefore, although the polarization charge is significantly smaller than the intact electron charge, However, according to the present invention, the signal-to-noise ratio is increased by a factor greater than 1. The signal-to-noise ratio (SNR) increases. Therefore, the measured polarization charge is advantageously close to the electron charge. The increase in SNR is partly due to the final tunneling process being closer to the readout sensor, and partly due to the measured charge carrier tunneling directly involving the reservoir rather than merely being adjacent to it.

[0031] Any number of intermediate cascaded quantum dots can be provided to separate the qubits and the readout sensor at arbitrary distances. When the circuit includes only one intermediate cascaded quantum dot, i.e., a first intermediate cascaded quantum dot, the second quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of the first intermediate cascaded quantum dot; the cascaded quantum dot is preferably capacitively coupled to the second intermediate cascaded quantum dot of the first intermediate cascaded quantum dot. In this way, an intermediate cascaded quantum dot is preferably coupled both to the quantum dot forming the qubit and to the cascaded quantum dot.

[0032] When the circuit comprises only two intermediate cascaded quantum dots, namely a first intermediate cascaded quantum dot and a second intermediate cascaded quantum dot, the second quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of the first intermediate cascaded quantum dot; the cascaded quantum dot is preferably capacitively coupled to the second intermediate cascaded quantum dot of the second intermediate cascaded quantum dot. The second intermediate cascaded quantum dot of the first intermediate cascaded quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of the second intermediate cascaded quantum dot. In this way, one intermediate cascaded quantum dot is coupled to the quantum dot forming the qubit, the other intermediate cascaded quantum dot is coupled to the cascaded quantum dot, and the first and second intermediate cascaded quantum dots are mutually coupled.

[0033] When a circuit includes three or more intermediate cascaded quantum dots, i.e., a first intermediate cascaded quantum dot, a second intermediate cascaded quantum dot, a third intermediate cascaded quantum dot, ..., the nth intermediate cascaded quantum dot, the second quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of the first intermediate cascaded quantum dot; the cascaded quantum dot is preferably capacitively coupled to the second intermediate cascaded quantum dot of the nth intermediate cascaded quantum dot. The second intermediate cascaded quantum dot of the kth intermediate cascaded quantum dot is preferably capacitively coupled to the first intermediate cascaded quantum dot of the (k+1)th intermediate cascaded quantum dot, where... In this way, the first intermediate cascaded quantum dot is coupled to the quantum dot forming the qubit and the second intermediate cascaded quantum dot; the nth intermediate cascaded quantum dot is coupled to the cascaded quantum dot and the (n-1)th intermediate cascaded quantum dot; and the remaining intermediate cascaded quantum dots are each coupled to two adjacent intermediate cascaded quantum dots.

[0034] In this way, the cascaded Pauli spin blocking process proceeds sequentially from the two quantum dots forming the qubit to each of one or more intermediate cascaded two quantum dots, and then to the cascaded quantum dots and the library. This advantageously improves the signal-to-noise ratio at the readout sensor, which can be advantageously separated from the qubit by an arbitrary distance. The ability to separate the qubit and the readout sensor provides a further advantage: the qubits in the circuit can be arranged in a dense array because there is no need to reserve space near the qubit for the library and readout circuitry. Alternatively, the cascaded Pauli spin blocking process can be initiated by driving the charge library at a first frequency. In this case, the initial order of tunneling events is reversed. However, once all charge carriers tunnel (or do not tunnel) within the tunneling coupling system (depending on the spin state of the qubit), tunneling will continue substantially synchronously during the application of the applied AC potential.

[0035] Optionally, the circuit may further include: a second dual quantum dot forming a second quantum bit, the second quantum bit having a singlet spin state and a triplet spin state, wherein the second dual quantum dot includes a second first quantum dot and a second second quantum dot, wherein the second second quantum dot tunnels to the second first quantum dot; a second gate electrode configured to control the energy state of the second first quantum dot or the energy state of the second second quantum dot; and a second cascaded quantum dot capacitively coupled to the second second quantum dot and tunneling to a charge bank. A frequency source is preferably connected to the second gate electrode or the charge bank and is preferably configured to apply an AC potential thereto. The frequency source is preferably further configured to apply an AC potential of a second frequency, thereby inducing cyclic tunneling of charge carriers from the second first quantum dot to the second second quantum dot and vice versa only when the second quantum bit is in a singlet spin state, and also inducing cyclic tunneling of charge carriers from the second cascaded quantum dot to the bank and vice versa. The readout circuit is preferably further configured to: detect a second AC potential; measure one or more properties of the detected second AC potential; and infer that the second qubit is in a triplet spin state when one or more measured properties of the detected second AC potential substantially match the expected values ​​of the properties of the triplet spin state; and infer that the second qubit is in a singlet spin state when one or more measured properties of the detected second AC potential substantially match the expected values ​​of the properties of the singlet spin state.

[0036] Advantageously, in this example, the first and second qubits utilize a shared charge bank and readout circuitry. More qubits can also share the same charge bank and readout circuitry. Using this arrangement, the same readout circuitry can be used to infer the state of multiple qubits. This advantageously reduces the amount of circuitry required to determine the state of multiple qubits. Fewer banks and fewer readout circuits are needed. Reducing circuitry requirements in this way advantageously enables denser qubit arrangements.

[0037] Optionally, when the readout circuit includes resonant circuits, the readout circuit may include n resonant circuits connected in parallel, each used to measure the state of the n qubits. Each resonant circuit preferably has a different resonant frequency. Advantageously, using different resonant frequencies makes it possible to distinguish them even when the signals are combined. Typically, the outputs of the n resonant circuits are combined using capacitive coupling.

[0038] Furthermore, compared to other techniques for transmitting quantum information, such as charge shuttle or SWAP operation, this circuit can be advantageously used to read out the states of multiple qubits substantially simultaneously.

[0039] Optionally, alternatively, or additionally, the circuit may further include: a third dual quantum dot forming a third quantum bit, the third quantum bit having a singlet spin state and a triplet spin state, wherein the third dual quantum dot comprises a third first quantum dot and a third second quantum dot, wherein the third second quantum dot tunnels to the third first quantum dot; and a third gate electrode configured to control the energy state of the third first quantum dot or the energy state of the third second quantum dot. The cascaded quantum dots are preferably further capacitively coupled to the third second quantum dot. A frequency source is preferably connected to the third gate electrode or a charge bank and is preferably configured to apply an AC potential thereto. The frequency source is preferably further configured to apply an AC potential at a third frequency, thereby inducing cyclic tunneling of charge carriers from the third first quantum dot to the third second quantum dot and vice versa only when the third quantum bit is in a singlet spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dots to the charge bank and vice versa. The readout circuit is preferably further configured to: detect a third AC potential; measure one or more properties of the detected third AC potential; and infer that the third qubit is in a triplet spin state when one or more of the measured properties of the detected third AC potential substantially match the expected values ​​of the properties of the triplet spin state; and infer that the third qubit is in a singlet spin state when one or more of the measured properties of the detected third AC potential substantially match the expected values ​​of the properties of the singlet spin state.

[0040] Advantageously, the first and third qubits utilize a shared charge bank, readout circuitry, and cascaded quantum dots. More qubits can also share the charge bank, readout circuitry, and cascaded quantum dots. In some cases, multiple qubits can share the charge bank and readout circuitry. In some cases, multiple qubits can share the charge bank, readout circuitry, and cascaded quantum dots. In some cases, the first set of multiple qubits can share the charge bank and readout circuitry; the second set of multiple qubits can share the charge bank, readout circuitry, and cascaded quantum dots.

[0041] Sharing charge banks, readout circuits, and cascaded quantum dots among multiple qubits advantageously reduces the circuitry required to determine the state of multiple qubits. Fewer banks, fewer readout circuits, and fewer cascaded quantum dots are needed. This reduction in circuitry advantageously enables denser qubit arrangements. Specifically, sharing cascaded quantum dots among qubits advantageously reduces the area occupied by the bank: fewer cascaded quantum dots are needed to couple the same number of qubits to the bank while arranging them adjacent to the bank.

[0042] Furthermore, compared to other techniques for transmitting quantum information, such as charge shuttle or SWAP operation, this circuit can be advantageously used to read out the states of multiple qubits substantially simultaneously.

[0043] Optionally, one or more of the intermediate cascaded dual quantum dots are shared by the first, second, and / or third dual quantum dots. Compared to other techniques for transmitting quantum information, such as charge shuttle or swap operation, this circuit can be advantageously used to read out the states of multiple qubits substantially simultaneously. The intermediate cascaded dual quantum dots can be used to simultaneously transmit quantum information associated with the first, second, and / or third qubits.

[0044] Optionally, one or more of the intermediate cascaded quantum dots are shared by the first and second quantum dots. Optionally, one or more of the intermediate cascaded quantum dots are shared by the first and third quantum dots. Optionally, one or more of the intermediate cascaded quantum dots are shared by the second and third quantum dots. Optionally, one or more of the intermediate cascaded quantum dots are shared by the first, second, and third quantum dots.

[0045] Advantageously, the area occupied by the circuit can be reduced when one or more of the two quantum dots forming qubits in the circuit share one or more intermediate cascaded two quantum dots. By using shared intermediate cascaded two quantum dots, the paths between each qubit and the library partially overlap, which advantageously saves space. For example, qubits can be arranged in a nested architecture, advantageously realizing dense qubit arrays.

[0046] The first frequency, second frequency, and third frequency can be the same. In this case, the states of the first qubit, second qubit, and third qubit can be deduced sequentially. However, preferably, the second frequency and / or the third frequency is different from the first frequency.

[0047] Optionally, the second frequency is different from the first frequency, and the third frequency is different from the first frequency. Typically, the first, second, and third frequencies are different from each other.

[0048] Optionally, for a circuit comprising m two quantum dots forming m qubits, the frequency source can be configured to apply f alternating potentials of different frequencies, where Alternatively, the circuit may include multiple frequency sources configured to apply alternating potentials of one or more different frequencies.

[0049] Advantageously, frequency division multiplexing readout technology is achieved by applying alternating current potentials of different frequencies to different qubits (where the frequencies are applied to the corresponding gate electrodes of the first quantum dot of the dual quantum dots forming the respective qubits). This means that the states of multiple qubits can be advantageously read out simultaneously because the different frequencies can be distinguished by the readout circuitry. Typically, different frequencies are distinguished by utilizing different resonator circuits, each with a different resonant frequency. The frequency source is preferably configured to drive the circuitry at one or more frequencies corresponding to the resonant frequencies of the multiple resonator circuits. Typically, the one or more frequencies are mutually orthogonal.

[0050] Therefore, advantageously, the readout circuit can be used to read the states of multiple qubits substantially simultaneously. This can be achieved by applying different alternating current potentials (i.e., alternating current potentials with different frequencies) to different qubits. Thus, by comparing the properties of the detected alternating current potentials with determined expected values ​​of properties for different spin configurations of the qubits, the state of each qubit can be inferred. By using several different frequencies, frequency multiplexing can be used to infer the states of different qubits. The determined expected values ​​can be determined by measuring the circuit under known charge configurations corresponding to singlet and triplet spin configurations, respectively, and recording the measured properties as reference values ​​for subsequent inference of the spin state of the qubit to be measured. Typically, confidence intervals can be applied such that when the measured value of the alternating current potential property falls within a certain range, the measured value is considered to match the reference value (expected value).

[0051] A second aspect of the invention provides a circuit for reading out the state of a qubit. The circuit includes: a dual quantum dot comprising a first quantum dot having a first spin state and a second spin state, and a second quantum dot having a first spin state and a second spin state, wherein the second quantum dot is tunnel-coupled to the first quantum dot; wherein the first quantum dot forms a data qubit and the second quantum dot forms an auxiliary qubit; or the first quantum dot forms an auxiliary qubit and the second quantum dot forms a data qubit; a gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; a control circuit connected to the auxiliary qubit, the control circuit being configured to initialize the auxiliary qubit to the first spin state; a cascaded quantum dot capacitively coupled to the second quantum dot; a charge bank tunneling to the cascaded quantum dot; a readout circuit connected to the charge bank; and a frequency source connected to the gate electrode or the charge bank and configured to apply an alternating current potential thereto. The cascaded quantum dot is tuned to near charge transitions such that when charge carriers tunnel between the first and second quantum dots, charge carriers tunnel between the cascaded quantum dot and the charge bank. A frequency source is configured to apply an alternating current potential at a first frequency, thereby inducing cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa only when the data qubit is in the second spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dot to the charge pool and vice versa. A readout circuit is configured to: detect the first alternating current potential; measure one or more properties of the detected first alternating current potential; and infer that the data qubit is in the first spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the first spin state; and infer that the data qubit is in the second spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the second spin state.

[0052] Similar to the first aspect, the state of a qubit can be inferred at a distance by connecting a charge bank and a readout circuit via cascaded quantum dots, with the cascaded quantum dots capacitively coupled in the middle. Tunneling between the cascaded quantum dots and the charge bank is due to electrostatic coupling between the systems. Therefore, this circuit can be advantageously used to perform charge polarization measurements at a distance with an improved signal-to-noise ratio. The readout circuit can be advantageously used to infer the state of the qubit without requiring external sensors at the nanostructure. Based on a comparison between one or more measured properties and the expected values ​​of spin states that are parallel and antiparallel to the spin states of the auxiliary qubit, respectively, the readout circuit can infer that the data qubit is in a first spin state, or the readout circuit can infer that the data qubit is in a second spin state.

[0053] The advantageous features of the first aspect also apply to the second aspect. In the first aspect, the circuit is suitable for reading out the state of a singlet-triple qubit in a dual quantum dot; in the second aspect, the circuit is suitable for reading out the state of a single-spin qubit in one of the quantum dots in a dual quantum dot. Thus, in the first aspect, the measured state is a singlet spin state or a triplet spin state, while in the second aspect, the measured state is a first spin state or a second spin state corresponding to spin-up and spin-down. A cascaded process involving substantially synchronous cyclic tunneling in a capacitively coupled neighboring dual quantum dot system is utilized in both the first and second aspects of the invention.

[0054] The expected value of the property of the first spin state corresponds to the expected value of the property of the first AC potential detected when the data qubit and the auxiliary qubit have the same spin state. Typically, the method may include a calibration step that determines the expected value of the property for the first spin state by recording the property of the AC potential detected by a readout circuit when the two quantum dots are in a (1,1) charge configuration (i.e., each of the first and second quantum dots has charge carriers). The property recorded from the (1,1) charge configuration can be determined as the expected value of the property for the first spin state (i.e., when the data qubit and the auxiliary qubit have the same parallel spin state).

[0055] The expected value of the property of the second spin state corresponds to the expected value of the property of the first AC potential detected when the data qubit and the auxiliary qubit have opposite spin states. Typically, the method may include a calibration step that involves determining the expected value of the property for the second spin state by recording the property of the AC potential detected by a readout circuit when the two quantum dots are in a (0,2) charge configuration (i.e., the second quantum dot has two charge carriers). The property recorded from the (0,2) charge configuration can be determined as the expected value of the property for the second spin state (i.e., when the data qubit and the auxiliary qubit have opposite antiparallel spin states relative to each other).

[0056] A third aspect of the invention provides a method for reading the state of a quantum bit, wherein the quantum bit is a dual-quantum-dot quantum bit comprising a first tunneling-coupled quantum dot and a second tunneling-coupled quantum dot, the quantum bit having a singlet spin state and a triplet spin state, wherein a cascaded quantum dot is capacitively coupled to the dual-quantum-dot quantum bit, tunneling-coupled to a charge pool and tuned to near-charge transitions, and wherein a frequency source is connected to the charge pool or a gate electrode, the gate electrode being configured to control the energy state of the first quantum dot or the energy state of the second quantum dot, and the frequency source being configured to apply an alternating current potential to the charge pool or the gate electrode. The method includes: applying an alternating current potential of a first frequency to a gate electrode or a charge bank using a frequency source; detecting the first alternating current potential using a readout circuit coupled to the charge bank; measuring one or more properties of the detected first alternating current potential using the readout circuit; and inferring that the qubit is in a triplet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of a triplet spin state; or inferring that the qubit is in a singlet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of a singlet spin state. The dual-quantum-dot qubit is configured such that when an alternating current potential of the first frequency is applied, cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa occurs only when the qubit is in a singlet spin state, and also cyclic tunneling of charge carriers from cascaded quantum dots to the charge bank and vice versa.

[0057] Advantageously, this method can be used to infer the state of a qubit at a distance. The state of the qubit can be read out using charge polarization measurement techniques. Cascaded Pauli spin blocking processes advantageously provide an improved signal-to-noise ratio, where charge carrier tunneling in a two-point system induces tunneling processes in neighboring systems.

[0058] In this way, the method can be used to infer the state of qubits located further away from the readout sensor, which is advantageous in the context of quantum computing, where readout electronics occupy a lot of space and require connection via classical control circuitry.

[0059] A fourth aspect of the invention provides a method for reading out the state of a data qubit, wherein the data qubit is a quantum dot having a first spin state and a second spin state, the data qubit is tunneled coupled to another quantum dot having a first spin state and a second spin state, the other quantum dot forming an auxiliary qubit, wherein the data qubit and the auxiliary qubit form a dual quantum dot, wherein a cascaded quantum dot is capacitively coupled to the dual quantum dot, tunneled coupled to a charge pool and tuned to near charge transitions, and wherein a frequency source is connected to the charge pool or a gate electrode configured to control the energy state of the quantum dot or the energy state of the other quantum dot, the frequency source being configured to apply an alternating current potential to the charge pool or the gate electrode. The method includes: initializing an auxiliary qubit to a first spin state using a control circuit connected to the auxiliary qubit; applying an alternating current potential of a first frequency to a gate electrode or a charge bank using a frequency source; detecting the first alternating current potential using a readout circuit connected to the charge bank; measuring one or more properties of the detected first alternating current potential using the readout circuit; and inferring that the data qubit is in the first spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the first spin state; or inferring that the data qubit is in the second spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the second spin state; wherein the dual quantum dots are configured such that when an alternating current potential of the first frequency is applied, cyclic tunneling of charge carriers from one quantum dot to another quantum dot and vice versa occurs only when the data qubit is in the second spin state, and also cyclic tunneling of charge carriers from cascaded quantum dots to the charge bank and vice versa.

[0060] Advantageously, this method can be used to infer the state of a qubit at a distance. The state of the qubit can be read out using charge polarization measurement techniques. Cascaded Pauli spin blocking processes advantageously provide an improved signal-to-noise ratio, where charge carrier tunneling in a two-point system induces tunneling processes in neighboring systems.

[0061] In this way, the method can be used to infer the state of qubits located further away from the readout sensor in the readout circuit, which is advantageous in the context of quantum computers, where readout electronics occupy a lot of space and require connection via classical control lines.

[0062] The third and fourth aspects of the present invention correspond to the first and second aspects, respectively, and have corresponding advantageous features.

[0063] Another aspect of the present invention provides a circuit for reading out the state of a qubit. The circuit includes: a dual quantum dot forming the qubit, the qubit having a singlet spin state and a triplet spin state, wherein the dual quantum dot comprises a first quantum dot and a second quantum dot, wherein the second quantum dot is tunnel-coupled to the first quantum dot; a gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; a cascaded quantum dot capacitively coupled to the second quantum dot; a charge bank tunnel-coupled to the cascaded quantum dot; a readout circuit connected to the charge bank; and a frequency source connected to the gate electrode or the charge bank and configured to apply an alternating current potential thereto. The cascaded quantum dot is arranged such that when charge carriers tunnel between the first and second quantum dots, charge carriers tunnel between the cascaded quantum dot and the charge bank. A frequency source is configured to apply an alternating current potential at a first frequency, thereby inducing cyclic tunneling of charge carriers from a first quantum dot to a second quantum dot and vice versa only when the qubit is in a singlet spin state, and also inducing cyclic tunneling of charge carriers from cascaded quantum dots to a charge pool and vice versa. A readout circuit is configured to: detect the first alternating current potential; measure one or more properties of the detected first alternating current potential; and infer that the qubit is in a triplet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the triplet spin state; and infer that the qubit is in a singlet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the singlet spin state.

[0064] Another aspect of the present invention provides a circuit for reading out the state of a quantum bit. The circuit includes: a dual quantum dot comprising a first quantum dot having a first spin state and a second spin state, and a second quantum dot having a first spin state and a second spin state, wherein the second quantum dot is tunnel-coupled to the first quantum dot; wherein the first quantum dot forms a data quantum bit and the second quantum dot forms an auxiliary quantum bit; or the first quantum dot forms an auxiliary quantum bit and the second quantum dot forms a data quantum bit; a gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; a control circuit connected to the auxiliary quantum bit, the control circuit being configured to initialize the auxiliary quantum bit to the first spin state; a cascaded quantum dot capacitively coupled to the second quantum dot; a charge bank tunnel-coupled to the cascaded quantum dot; a readout circuit connected to the charge bank; and a frequency source connected to the gate electrode or the charge bank and configured to apply an alternating current potential thereto. The cascaded quantum dot is arranged such that when charge carriers tunnel between the first and second quantum dots, charge carriers tunnel between the cascaded quantum dot and the charge bank. A frequency source is configured to apply an alternating current potential at a first frequency, thereby inducing cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa only when the data qubit is in the second spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dot to the charge pool and vice versa. A readout circuit is configured to: detect the first alternating current potential; measure one or more properties of the detected first alternating current potential; and infer that the data qubit is in the first spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the first spin state; and infer that the data qubit is in the second spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the second spin state.

[0065] Another aspect of the present invention provides a method for reading the state of a quantum bit, wherein the quantum bit is a dual quantum dot quantum bit comprising a first tunneling coupled quantum dot and a second tunneling coupled quantum dot, the quantum bit having a singlet spin state and a triplet spin state, wherein cascaded quantum dot capacitors are coupled to the dual quantum dot quantum bit and tunnel coupled to a charge bank, and wherein a frequency source is connected to the charge bank or a gate electrode, the gate electrode being configured to control the energy state of the first quantum dot or the energy state of the second quantum dot, and the frequency source being configured to apply an alternating potential to the charge bank or the gate electrode. The method includes: applying an alternating current potential of a first frequency to a gate electrode or a charge bank using a frequency source; detecting the first alternating current potential using a readout circuit coupled to the charge bank; measuring one or more properties of the detected first alternating current potential using the readout circuit; and inferring that the qubit is in a triplet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of a triplet spin state; or inferring that the qubit is in a singlet spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of a singlet spin state. The dual-quantum-dot qubit is configured such that when an alternating current potential of the first frequency is applied, cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa occurs only when the qubit is in a singlet spin state, and also cyclic tunneling of charge carriers from cascaded quantum dots to the charge bank and vice versa.

[0066] Another aspect of the present invention provides a method for reading out the state of a data qubit, wherein the data qubit is a quantum dot having a first spin state and a second spin state, the data qubit is tunneled coupled to another quantum dot having a first spin state and a second spin state, the other quantum dot forming an auxiliary qubit, wherein the data qubit and the auxiliary qubit form a dual quantum dot, wherein a cascaded quantum dot is capacitively coupled to the dual quantum dot and tunneled coupled to a charge bank, and wherein a frequency source is connected to the charge bank or a gate electrode, the gate electrode being configured to control the energy state of the quantum dot or the energy state of the other quantum dot, and the frequency source being configured to apply an alternating current potential to the charge bank or the gate electrode. The method includes: initializing an auxiliary qubit to a first spin state using a control circuit connected to the auxiliary qubit; applying an alternating current potential of a first frequency to a gate electrode or a charge bank using a frequency source; detecting the first alternating current potential using a readout circuit connected to the charge bank; measuring one or more properties of the detected first alternating current potential using the readout circuit; and inferring that the data qubit is in the first spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the first spin state; or inferring that the data qubit is in the second spin state when one or more of the measured properties of the detected first alternating current potential substantially match the expected values ​​of the properties of the second spin state; wherein the dual quantum dots are configured such that when an alternating current potential of the first frequency is applied, cyclic tunneling of charge carriers from one quantum dot to another quantum dot and vice versa occurs only when the data qubit is in the second spin state, and also cyclic tunneling of charge carriers from cascaded quantum dots to the charge bank and vice versa. Attached Figure Description

[0067] Embodiments of the present invention will now be described with reference to the accompanying drawings, in which:

[0068] Figure 1 This is a schematic diagram of the circuit;

[0069] Figure 2A It is a schematic diagram of a circuit that includes multiple intermediate cascaded double quantum dots;

[0070] Figure 2B It is a schematic diagram of a circuit that includes multiple intermediate cascaded double quantum dots;

[0071] Figure 3 This is a schematic diagram of a circuit involving frequency reuse;

[0072] Figure 4 It is a schematic diagram of a circuit involving frequency reuse, including a shared intermediate cascaded dual quantum dot.

[0073] Figure 5A , Figure 5B and Figure 5C This is a schematic diagram of the circuit;

[0074] Figure 6A , Figure 6B and Figure 6C This is a schematic diagram of measurements at different layers in the circuit;

[0075] Figure 7A and Figure 7B This is a schematic diagram illustrating robustness to errors;

[0076] Figure 8 This is a schematic diagram of the circuit;

[0077] Figure 9 This is a flowchart of a method for reading the state of a quantum bit;

[0078] Figure 10 It is a flowchart of the method for reading the state of a quantum bit; and

[0079] Figure 11 This is a schematic diagram of the frequency response of the singlet spin state and the triplet spin state. Detailed Implementation

[0080] These figures schematically illustrate circuits and methods for reading out the state of one or more qubits in a quantum device. A qubit is either a two-quantum-dot spin qubit or a single-quantum-dot spin qubit, typically implemented in semiconductor nanostructures. The readout mechanism utilizes a form of spin-charge conversion called Pauli spin blocking. Pauli spin blocking can be used at temperatures above millikelvin, approaching a few Kelvin, and at low magnetic fields (where the magnetic field strength is below about 1 Tesla). To achieve Pauli spin blocking, two quantum dots are required, each containing two spin-carrying particles (typically electrons or holes). For two-quantum-dot qubits, tunneling of the spin-carrying particles or charge-carrying particles between the quantum dots separated by a tunneling barrier is possible when the spin is in a singlet configuration, while tunneling is suppressed when they are in a triplet configuration. In the singlet state, the spin of the two quantum dots is 0, and in the triplet state, the spin of the two quantum dots is 1. Similarly, for single quantum dot qubits, tunneling of spin-carrying particles between quantum dots separated by a tunneling barrier is possible when the spins are opposite (i.e., antiparallel), while tunneling is suppressed when the spins are the same (i.e., parallel).

[0081] Figure 1 A circuit suitable for reading the state of a qubit is schematically shown. The circuit includes a dual quantum dot 101, a cascaded quantum dot 102, a charge bank 103, and a resonator circuit 104. The resonator circuit forms part of the readout circuit used to infer the state of the qubit. The readout circuit typically also includes a processor for processing the received signal. Figure 1A step diagram of the dual quantum dot 101, cascaded quantum dot 102, and coulomb 103 is shown. The step diagram illustrates the relative alignment of the electrochemical potentials of the quantum dots in the circuit before performing readout measurements of the state of the quantum bit 100. According to the step diagram, electrons can tunnel from higher electrochemical potentials to lower electrochemical potentials separated by tunneling barriers. The step diagram only indicates the selection of electrochemical potential levels near the Fermi level; generally, there are higher unoccupied levels above the Fermi level and lower occupied levels below the Fermi level.

[0082] The electrochemical potential can be tuned (i.e., increased or decreased) by applying a potential to the corresponding gate electrode (not shown). In this way, the corresponding gate electrode can be used to control the energy state of the quantum dot.

[0083] The dual quantum dot 101 is formed by two quantum dots: a first quantum dot 105 and a second quantum dot 106. The first quantum dot 105 and the second quantum dot 106 are separated by a first tunneling barrier 107. Charge carriers (i.e., electrons or holes) can tunnel from the first quantum dot 105 through the first tunneling barrier 107 to the second quantum dot 106, and vice versa, from the second quantum dot 106 through the first tunneling barrier 107 to the first quantum dot 105. The dual quantum dot 101 is defined by a first electrostatic barrier 109 and a second electrostatic barrier 110. The first electrostatic barrier 109 and the second electrostatic barrier 110 strongly suppress quantum tunneling, thereby confining charge carriers within the dual quantum dot 101. The second electrostatic barrier 110 separates the dual quantum dot 101 from the cascaded quantum dot 102, thereby capacitively coupling the dual quantum dot 101 and the cascaded quantum dot 102.

[0084] The cascaded quantum dot 102 and the coulomb 103 are separated by a second tunneling barrier 108. Therefore, charge carriers can travel from the cascaded quantum dot 102 through the second tunneling barrier 108 to the coulomb 103 during quantum tunneling, and vice versa. The coulomb 103 is typically an electron coulomb.

[0085] Figure 1 The electrostatic and tunneling barriers shown are provided by applying a bias potential to the gate electrode. The height of the barrier is determined by the magnitude of the bias potential, thus defining the tunneling barrier for a smaller bias potential and the electrostatic barrier for a larger bias potential.

[0086] In this way, the first quantum dot 105, the second quantum dot 106, the cascaded quantum dot 102, the coulomb 103, the first tunneling barrier 107 and the second tunneling barrier 108, and the first electrostatic barrier 109 and the second electrostatic barrier 110 are all controlled using corresponding gate electrodes (not shown). Therefore, the occupancy rate of quantum dots 105, 106, and 102 and the height of barriers 107-110 can be modified by controlling the potential applied to the relevant gate electrodes.

[0087] like Figure 1 As shown in the step diagram, the first quantum dot 105, the second quantum dot 106, and the cascaded quantum dot 102 have discrete energy levels. This is due to the confinement of electrons in the quasi-zero-dimensional structure. In contrast, the energy levels of Coulomb 103 are continuous and not discrete.

[0088] exist Figure 1 In this configuration, the first quantum dot 105 and the second quantum dot 106 are each occupied by a single electron. In this configuration, the quantum bit 100 can be in a singlet or triplet state. In the singlet state, the spin of the two quantum dots is 0. In the triplet state, the spin of the two quantum dots is 1. In other examples, the first quantum dot 105 and the second quantum dot 106 may be occupied by more than a single electron; however, the circuit typically operates in an isolated state. This means that only one charge transition is detected. In other examples, the charge carrier can be a hole. When the charge carrier is a hole, the description of the electron applies accordingly.

[0089] The plunger gate electrode of the first quantum dot 105 controls the energy states of the first quantum dot 105, causing the electrochemical potential level to rise or fall depending on the sign of the potential. Typically, applying a positive bias to the plunger gate electrode lowers the electrochemical potential level, while applying a negative bias raises it. Therefore, in this case, when a negative potential is applied to the plunger gate electrode of the first quantum dot 105, the electrochemical potential level of the first quantum dot 105 is raised to a level higher than that of the second quantum dot 106 corresponding to the second quantum dot 106 being occupied by two opposite spin states.

[0090] This means that the electrochemical potential in the second quantum dot 106 is tuned such that when a negative potential is applied to the plunger gate electrode of the first quantum dot 105, due to Pauli spin blocking, electrons in the first quantum dot 105 can only tunnel to the second quantum dot 106 when the qubit 100 is in a singlet state. This tunneling process occurs in... Figure 1The potential applied to the plunger gate electrode is such that if quantum bit 100 is in a triplet state, electrons on the first quantum dot 105 will not tunnel to the second quantum dot 106 when the potential is applied, because there is Coulomb repulsion between the charge carrier spins.

[0091] The cascaded quantum dot 102 is tuned to near charge transitions using a plunger gate electrode. This means that, due to the electrostatic barrier 110 providing capacitive coupling between the cascaded quantum dot 102 and the second quantum dot 106, a change in the charge carrier occupancy of the second quantum dot 106 induces a change in the charge carrier occupancy of the cascaded quantum dot 102. This is because, when electron tunneling occurs as shown at 1a, the cascaded quantum dot 102 enters a higher energy state, such as... Figure 1 As shown at point 1b. The cascaded quantum dot 102 is further tuned so that, from this higher energy state, electrons tunnel from the cascaded quantum dot 102 through the second tunneling barrier 108 to the coulomb 103, as shown. Figure 1 As shown at position 1c in the diagram.

[0092] In this example, the frequency source is configured to apply an alternating current potential 111 of a first frequency f1 to the plunger gate electrode of the first quantum dot 105. The first alternating current potential typically has a sinusoidal form. ,in The frequency source can be any commercially available frequency source capable of applying one or more frequencies to multiple gate electrodes. An alternating current potential (AC) is used to drive the circuitry. In this example, the AC potential is applied to the plunger gate electrode of the first quantum dot. In other examples, the AC potential may be applied to the plunger gate electrode of the second quantum dot, or to a charge bank.

[0093] An alternating current potential is applied to alternately raise and lower the electrochemical potential level of the first quantum dot 105. When the electrochemical potential is raised, charge carriers move as described above, as indicated by arrows 1a, 1b, and 1c. When the electrochemical potential is lowered, the charge carriers move in the opposite direction, as shown by arrows 2a, 2b, and 2c. First, at 2a, electrons tunnel from the second quantum dot 106 through the first tunneling barrier 107 to the first quantum dot 105. This change in the occupancy rate of the second quantum dot 106 induces a change in the neighboring cascaded quantum dot 102 because the energy state decreases, as shown at 2b. Finally, at 2c, electrons tunnel from Coulomb 103 to the cascaded quantum dot 102 because the electrochemical potential is lower than the Fermi level of Coulomb 103.

[0094] In this way, the AC potential applied to the gate electrode of the first quantum dot 105 causes cyclic tunneling of charge carriers from the first quantum dot 105 to the second quantum dot 106 (1a) and vice versa (2a) only when the qubit is in a singlet state. Cyclic tunneling involves charge carriers tunneling back and forth, here between the first quantum dot 105 and the second quantum dot 106. Tunneling depends on the spin state of the qubit 100. As described above, the cascaded quantum dot 102 is tuned such that this tunneling also causes cyclic tunneling of charge carriers from the cascaded quantum dot 102 to the coulomb 103 (1c) and vice versa (2c). This is achieved by tuning the cascaded quantum dot 102 such that the electrochemical potential when there are no charge carriers in the neighboring second quantum dot 106 is lower than the Fermi level of the coulomb 103, and the electrochemical potential when there are charge carriers in the neighboring second quantum dot 106 is higher than the Fermi level of the coulomb 103.

[0095] Figure 1 A resonator circuit 104 coupled to library 103 is shown. Resonator circuit 104 is an LC resonator, typically comprising capacitors and inductors connected in parallel or series to form a resonant circuit with a resonant frequency for radio-frequency (RF) measurements. That is, resonator circuit 104 has RF readout capability. Resonator circuit 104 provides a readout sensor that can be used to infer the state of qubit 100. In this example, qubit 100 is a two-quantum-dot qubit, therefore qubit 100 has two states: (1) a singlet state or (2) a triplet state. In other examples, the first or second quantum dot can form a single-spin qubit to be measured: a data qubit. The circuit operates in the same manner, except that the unmeasured quantum dot forms an auxiliary qubit whose spin state is prepared before the state of the data qubit is measured.

[0096] The resonator circuit 104 is configured to detect a first AC potential 112 near a first frequency f1 using a zero-difference detection method commonly used in RF measurements. The first frequency f1 is the same as the frequency applied by the frequency source to the plunger gate electrode of the first quantum dot 105. The RF output detected by the readout circuit 104 has the form... The output properties will change depending on whether the singlet-triple qubit is in a singlet or triplet state. When the qubit is in a singlet spin state, the RF output is... When the qubit is in the triplet spin state, the RF output is: . Unlike ,and Unlike Therefore, the properties of the detected first AC potential 112 vary depending on the spin state of the qubit. Thus, based on the measured properties of the detected first AC potential (such as frequency, amplitude, and / or phase), it can be inferred whether the qubit 100 is in a triplet or singlet state.

[0097] The desired RF output value is calibrated by recording the properties of the AC potential detected by the readout circuit in the (1,1) charge configuration and the (0,2) charge configuration to determine the desired values ​​of the properties for the triplet spin state and the singlet spin state, respectively.

[0098] In other examples involving single-spin data qubits, the properties of the RF output will vary in a similar manner to those described above, depending on whether the spin state of the data qubit is antiparallel or parallel to the spin state of the auxiliary qubit. Due to the presence and absence of cyclic tunneling, the RF outputs of antiparallel and parallel spin states roughly correspond to the RF outputs of singlet and triplet spin states as described above. When the spin state of the data qubit is opposite to the spin state of the auxiliary qubit, the RF output is... When the spin state of the data qubit is the same as the spin state of the auxiliary qubit, the RF output is: . Unlike ,and Unlike Therefore, the properties of the detected first AC potential vary depending on the spin state of the qubit. Thus, based on the measured properties of the detected first AC potential (such as frequency, amplitude, and / or phase), using the expected value of the RF output and the known spin state of the auxiliary qubit, it is possible to infer whether the data qubit is in the first or second spin state.

[0099] The desired RF output value is calibrated by recording the properties of the AC potential detected by the readout circuit in the (1,1) charge configuration and the (0,2) charge configuration to determine the desired values ​​of the properties for the parallel data-auxiliary qubit spin configuration and the antiparallel data-auxiliary qubit spin configuration, respectively.

[0100] therefore, Figure 1 The circuit shown operates to perform charge polarization measurements to infer the state of qubit 100.

[0101] Figure 2A and Figure 2B A one-dimensional chain is schematically shown, with each chain connecting the qubit 200 to be read out and a library 203 coupled to the readout sensor 204 (in the form of a resonator circuit).

[0102] and Figure 1 similar, Figure 2A and Figure 2B A staircase diagram of the circuit assembly is shown. It should be noted that these diagrams are schematic and there may typically be many more electrochemical potential levels. For simplicity, only the electrochemical potential levels associated with the cascaded Pauli spin blocking process are shown. In practice, quantum dots can be occupied by any number of electrons. Figure 2A and Figure 2B In this embodiment, the dual quantum dot 201 forming the quantum bit 200 includes a first quantum dot 205 and a second quantum dot 206, which are separated by a tunneling barrier 207. The dual quantum dot 201 is defined by electrostatic barriers 209 and 210, which confine charge carriers within the dual quantum dot 201.

[0103] Similarly, with Figure 1 similar, Figure 2A and Figure 2B The circuit includes cascaded quantum dots 202, which are separated from the library 203 by a tunneling barrier 208. The library 203 is coupled to a resonator circuit 204, which includes... Figure 1 Inductors and capacitors in the process.

[0104] and Figure 1 compared to, Figure 2A and Figure 2B The illustrated embodiment also includes intermediate cascaded dual quantum dots 220, 230 arranged between qubit 200 and cascaded quantum dots 202. In the prior art, charge polarization measurements are performed locally due to the small amount of electrostatic energy detected. This means that the readout sensor (i.e., the charge polarization sensor) needs to be placed close to the target qubit (whose state will be measured). However, as previously mentioned, this is incompatible with measuring the state of multiple qubits arranged in a dense array.

[0105] Each intermediate cascaded quantum dot 220, 230 includes a first intermediate cascaded quantum dot 221, 231 and a second intermediate cascaded quantum dot 222, 232, separated by tunneling barriers 223, 233. Adjacent intermediate cascaded quantum dots are separated by electrostatic barriers 218, 224, 234, thereby forming capacitive coupling between adjacent intermediate cascaded quantum dots.

[0106] therefore, Figure 2A and Figure 2B A one-dimensional bi-quantum dot chain is shown, in which charge carriers can tunnel between the two quantum dots within each bi-quantum dot, and capacitive coupling exists between other nearest neighbors, i.e., capacitive coupling exists between adjacent quantum dots of adjacent bi-quantum dots. Furthermore, spin-dependent tunneling events between adjacent bi-quantum dots are suppressed.

[0107] A first intermediate cascaded quantum dot 220, defined by a left electrostatic barrier 210 and a right electrostatic barrier 224, includes a first intermediate cascaded quantum dot 221 tunneled to a first and second intermediate cascaded quantum dot 222 via a tunneling barrier 223. The first intermediate cascaded quantum dot 221 is capacitively coupled to a second quantum dot 206 via the left electrostatic barrier 210. The right electrostatic barrier 224 provides capacitive coupling between the first and second intermediate cascaded quantum dots 222 and the second intermediate cascaded quantum dot 230. In another example, including only one intermediate cascaded quantum dot, the first and second intermediate cascaded quantum dots are adjacent to the cascaded quantum dots, thus being directly capacitively coupled to the cascaded quantum dots.

[0108] A second intermediate cascaded quantum dot 230, defined by a left electrostatic barrier 224 and a right electrostatic barrier 234, includes a second first intermediate cascaded quantum dot 231 tunneled to a second second intermediate cascaded quantum dot 232 via a tunneling barrier 233. The left electrostatic barrier 224 capacitively couples the second first intermediate cascaded quantum dot 231 to the first second intermediate cascaded quantum dot 222. The right electrostatic barrier 234 capacitively couples the second second intermediate cascaded quantum dot 232 to another intermediate cascaded quantum dot (not shown). In another example, including only two intermediate cascaded quantum dots, the second second intermediate cascaded quantum dot is adjacent to the cascaded quantum dot, thus being directly capacitively coupled to the cascaded quantum dot.

[0109] More intermediate cascaded quantum dots are indicated between the second intermediate cascaded quantum dot 230 and the cascaded quantum dot 202. A final intermediate cascaded quantum dot (not shown) is arranged between another intermediate cascaded quantum dot (either the second intermediate cascaded quantum dot 230 or another intermediate cascaded quantum dot not shown) and the cascaded quantum dot 202. In this way, the final first intermediate cascaded quantum dot is capacitively coupled to another second intermediate cascaded quantum dot; and the final second intermediate cascaded quantum dot is capacitively coupled to the cascaded quantum dots. The final second intermediate cascaded quantum dot is separated from the cascaded quantum dots by an electrostatic barrier 218.

[0110] In an example including three or more intermediate cascaded dual quantum dots, the circuit comprises a first intermediate cascaded dual quantum dot arranged as described above, a final intermediate cascaded dual quantum dot arranged as described above, and one or more second intermediate cascaded dual quantum dots arranged as described above. Thus, a one-dimensional chain is defined by the sequential arrangement of qubit 200, the first (and optionally the second, third, ... nth) intermediate cascaded dual quantum dots 220, 230, and cascaded quantum dot 202. Cascaded quantum dot 202 is directly coupled to library 203 via tunneling barrier 208.

[0111] exist Figure 2A and Figure 2BIn this example, an alternating current potential 211 with a first frequency f1 is applied to the gate electrode of the first quantum dot 205 using a frequency source. In other examples, the frequency source may be used to apply an alternating current potential to the gate electrode of a second quantum dot, or to a charge pool. The resonator circuit 204 is configured to detect the first alternating current potential 212 and measure the properties of the detected alternating current potential to infer the state of the quantum bit 200. These properties include the frequency, amplitude, and / or phase of the alternating current potential.

[0112] Each intermediate cascaded dual quantum dot 220, 230 is tuned to near charge transition. In this way, a change in the charge carrier occupancy of the second quantum dot 206 induces a change in the charge carrier occupancy of the first intermediate cascaded dual quantum dot 220, which in turn induces a change in the charge carrier occupancy of the second intermediate cascaded dual quantum dot 230, and so on, until a change in the charge carrier occupancy of the cascaded quantum dot 202 is induced, which is detected by the resonator circuit 204.

[0113] when Figure 2A When qubit 200 is in the triplet state, tunneling does not occur. Theoretically, in this case, the RF output detected by resonator circuit 204 could be the same as the RF input. However, due to circuit imperfections, the detected AC potential 212 is usually different. Therefore, to determine the spin state of the qubit, one or more properties of the detected AC potential 212 are compared with expected values ​​for properties of the triplet spin state and the singlet spin state. When qubit 200 is in the triplet state, the readout circuit determines that one or more measured values ​​substantially match the corresponding expected values ​​for properties of the triplet spin state. In this way, it can be inferred that qubit 200 is in the triplet state.

[0114] When qubit 200 is in a singlet state Figure 2A The cascaded Pauli spin blocking shown proceeds as follows. Electrons tunnel through tunneling barrier 207 from first quantum dot 205 to second quantum dot 206. Due to the capacitive coupling between the dual quantum dot 201 and the first intermediate cascaded dual quantum dot 220, the first intermediate cascaded quantum dot 221 enters a higher energy state. Electrons tunnel through tunneling barrier 223 from the first intermediate cascade quantum dot 221 to the first second intermediate cascade quantum dot 222. Due to the capacitive coupling between the first intermediate cascaded quantum dot 220 and the second intermediate cascaded quantum dot 230, the second first intermediate cascaded quantum dot 231 enters a higher energy state. Electrons tunnel through tunneling barrier 233 from the second intermediate cascade quantum dot 231 to the second intermediate cascade quantum dot 232. ).

[0115] Due to the capacitive coupling between adjacent intermediate cascaded quantum dots, a higher energy state is entered through the kth first intermediate cascaded quantum dot. And electrons tunnel through the tunneling barrier from the k-th first intermediate cascade quantum dot to the k-th second intermediate cascade quantum dot. ) to perform the cascade Pauli spin blocking process.

[0116] The cascading process continues until cascaded quantum dot 202 is reached. At this point, the process is similar. Due to the capacitive coupling between the final intermediate cascaded dual quantum dots and cascaded quantum dot 202, the cascaded quantum dot enters a higher energy state ( Electrons tunnel from cascaded quantum dot 202 through tunneling barrier 208 to Coulomb 203.

[0117] Such as about Figure 1 The electrochemical potential level of the first quantum dot 205 is alternately raised and lowered by applying an alternating current potential through a frequency source. When the electrochemical potential increases, charge carriers move as described above, as indicated by the arrow. As shown.

[0118] When the electrochemical potential decreases, the charge carriers move in the opposite direction. This is in Figure 2A The middle arrow As shown. In At this point, electrons tunnel from the second quantum dot 206 through the tunneling barrier 207 to the first quantum dot 205. This change in the charge carrier occupancy of the second quantum dot 206 causes the energy state of the first intermediate cascade quantum dot 221 to change. The position decreases, allowing electrons to... The charge carriers tunnel from the first and second intermediate cascade quantum dot 222 to the first intermediate cascade quantum dot 221. The corresponding charge carrier motion occurs... The second intermediate cascaded double quantum dot at the location, and not in All the more intermediate cascaded dual quantum dots are shown here. Finally, the energy states of cascaded quantum dot 202 are shown in... The point is caused to drop, thus allowing electrons to... The tunnel from the reservoir 203 tunnel to the cascaded quantum dot 202.

[0119] In this way, the AC potential applied to the gate electrode of the first quantum dot 205, when the qubit is in a singlet state, causes a cascading effect of synchronous cyclic tunneling to be initiated in the chain of coupled circuit elements. This cascading involves quantum tunneling processes in each dual-quantum-dot system. The application of the AC potential leads to cyclic tunneling processes (A, B) in each dual-quantum-dot system. The cascading of charge carriers is triggered by the first quantum tunneling process in the dual quantum dots, which induces further quantum tunneling processes in each intermediate cascaded dual quantum dots. Finally, charge carriers tunnel from the cascaded quantum dots into a library coupled to a resonator circuit configured to detect the first AC potential 212, measure the properties of the detected first AC potential (i.e., frequency, amplitude, and / or phase), and infer that the dual-quantum-dot qubit 200 is in a singlet state if the properties of the detected first AC potential substantially match the expected values ​​of the properties of the singlet spin state. In this way, even if the qubit may be separated from the cascaded quantum dots (and thus from the library and readout device) by any number of intermediate cascaded double quantum dots, the state of the qubit 200 can be determined using charge polarization measurements.

[0120] Figure 2B It shows the relationship with Figure 2A A similar cascaded process is shown. Figure 2A In this process, the cascade is initiated by charge carriers tunneling from the first quantum dot 205 to the second quantum dot 206. Figure 2B In this process, the cascade is initiated by charge carriers tunneling from the second quantum dot 206 to the first quantum dot 205.

[0121] when Figure 2B When the qubit 200 is in the triplet state, tunneling does not occur. In this way, the resonator circuit 204 detects a first AC potential 212 that has properties that substantially match the expected value of the properties of the triplet spin state, and can infer that the qubit 200 is in the triplet state.

[0122] When qubit 200 is in a singlet state, such as Figure 2B The cascaded Pauli spin blocking shown proceeds as follows. Electrons tunnel through tunneling barrier 207 from the second quantum dot 206 to the first quantum dot 205. Due to the capacitive coupling between the dual quantum dot 201 and the first intermediate cascaded dual quantum dot 220, the first intermediate cascaded quantum dot 221 enters a lower energy state. Electrons tunnel through tunneling barrier 223 from the first and second intermediate cascade quantum dots 222 to the first intermediate cascade quantum dot 221. Due to the capacitive coupling between the first intermediate cascaded quantum dot 220 and the second intermediate cascaded quantum dot 230, the second first intermediate cascaded quantum dot 231 enters a lower energy state. Electrons tunnel through tunneling barrier 233 from the second intermediate cascade quantum dot 232 to the second intermediate cascade quantum dot 231. ).

[0123] Due to the capacitive coupling between adjacent intermediate cascaded quantum dots, a lower energy state is entered through the kth first intermediate cascaded quantum dot. And electrons tunnel through the tunneling barrier from the kth second intermediate cascade quantum dot to the kth first intermediate cascade quantum dot. ) to perform the cascade Pauli spin blocking process.

[0124] The cascading process continues until cascaded quantum dot 202 is reached. At this point, the process is similar. Due to the capacitive coupling between the final intermediate cascaded dual quantum dots and cascaded quantum dot 202, the cascaded quantum dot enters a lower energy state ( Electrons tunnel through tunneling barrier 208 from library 203 to cascaded quantum dot 202.

[0125] Such as about Figure 1 The electrochemical potential level of the first quantum dot 205 is alternately raised and lowered by applying an alternating current potential through a frequency source. When the electrochemical potential decreases, charge carriers move as described above, as indicated by the arrow. As shown.

[0126] As the electrochemical potential increases, the movement of charge carriers reverses. This is in Figure 2B The middle arrow As shown. In At this point, electrons tunnel from the first quantum dot 205 through the tunneling barrier 207 to the second quantum dot 206. This change in the charge carrier occupancy of the second quantum dot 206 causes the energy state of the first intermediate cascade quantum dot 221 to change. The rise in altitude allows electrons to... The charge carriers tunnel from the first intermediate cascade quantum dot 221 to the first second intermediate cascade quantum dot 222. The corresponding charge carrier motion occurs... The second intermediate cascaded double quantum dot at the location, and not in All the more intermediate cascaded dual quantum dots are shown here. Finally, the energy states of cascaded quantum dot 202 are shown in... The area is caused to rise, thus enabling electrons to... The quantum dot 202 tunnels from the cascaded quantum dot 202 to the Ku 203.

[0127] In this way, the AC potential applied to the gate electrode of the first quantum dot 205 causes a cascading effect when the qubit is in a singlet state. This cascading involves a quantum tunneling process in each of the two-quantum-dot systems. The application of the AC potential causes a cyclic tunneling process in each of the two-quantum-dot systems. The cascading of charge carriers is triggered by the first quantum tunneling process in the two quantum dots, which initiates a further quantum tunneling process in each intermediate cascaded two quantum dots. Finally, charge carriers tunnel from the cascaded quantum dots into a library coupled to a resonator circuit configured to detect a first AC potential 212 having properties that substantially match the expected value of the properties of the singlet spin state. In this way, the state of the qubit 200 can be determined using charge polarization measurements, even if the qubit may be isolated from the cascaded quantum dots (and thus from the library and readout device) by any number of intermediate cascaded two quantum dots.

[0128] Figure 2A and Figure 2B The examples in the text are described using electrons as charge carriers. However, it is understood that in different examples, holes could be used as charge carriers to achieve the same process. Similarly, although already discussed... Figure 2A and Figure 2B The measurement of a two-quantum-dot qubit is described, but if the other qubit in the two-quantum-dot is prepared in a known spin state (e.g., spin-down), the same circuit can be used to measure a single-spin qubit.

[0129] Figure 3 A circuit comprising a first qubit 301 and a second qubit 311 formed by two dual quantum dots is schematically shown. Each qubit has a singlet and a triplet state. The circuit includes a shared charge pool 303 shared by the first qubit 301 and the second qubit 311. In this way, a readout sensor 304 coupled to the pool is configured to measure the state of both the first qubit 301 and the second qubit 311. The readout sensor in this example includes two resonator circuits connected in parallel, each resonator circuit including an inductor and a capacitor, in the form of an LC resonator. The first resonator circuit has a first resonant frequency, and the second resonator circuit has a second resonant frequency. The outputs of the two resonator circuits can be combined to produce a single output signal containing multiple frequency components.

[0130] exist Figure 3In this configuration, the first qubit 301 and the second qubit 311 are capacitively coupled to their respective first intermediate cascaded quantum dots 321 and 331, respectively. Each first intermediate cascaded quantum dot is further capacitively coupled to its corresponding second intermediate cascaded quantum dot 322 and 332. One or more intermediate cascaded quantum dots are arranged between each second intermediate cascaded quantum dot and its corresponding cascaded quantum dot 302 and 312. The total number of intermediate cascaded quantum dots separating qubits 301 and 311 from cascaded quantum dots 302 and 312 can be the same or different.

[0131] Each intermediate cascaded dual quantum dot is separated from its neighboring quantum dots by electrostatic barriers 307, 308, 309, 310, 317, 318, 319, and 320, forming capacitive coupling between adjacent circuit elements. The corresponding final intermediate cascaded dual quantum dots are capacitively coupled to their respective cascaded quantum dots 302 and 312, which tunnel to the same library 303. In this case, the circuit elements between the first quantum bit 301 and the first cascaded quantum dot 302 are electrically isolated from the circuit elements between the second quantum bit 302 and the second cascaded quantum dot 312. In some cases, two or more libraries may be provided. In each case, a readout sensor is provided for each library. In this way, the readout sensor coupled to each library is configured to infer the state of all (possibly one or more) qubits coupled to that library.

[0132] Each intermediate cascaded dual quantum dot 321, 322, 331, 332 includes a tunneling barrier ( Figure 3 A first intermediate cascaded quantum dot and a second intermediate cascaded quantum dot are separated by a tunneling barrier (not shown). The dual quantum dots forming the first quantum bit 301 and the second quantum bit 311 each include a tunneling barrier (not shown). Figure 3 The first quantum dots 305 and 315 and the second quantum dots 306 and 316 are separated by a potential barrier (not shown in the image).

[0133] As described above, when an AC potential is applied to the gate electrodes of the first quantum dots 305 and 315 of the frequency source vector quantum bits 301 and 311, this triggers a series of charge carrier tunneling.

[0134] exist Figure 3 In this process, an alternating current potential 341 at a first frequency f1 is applied to the gate electrode of the first quantum dot 305 of the first quantum bit 301. Similarly, an alternating current potential 342 at a second frequency f2 is applied to the gate electrode of the first quantum dot 315 of the second quantum bit 311.

[0135] When the first quantum bit 301 is in the triplet state, tunneling does not occur. In this way, the first AC potential 351 detected by the first resonator circuit of the readout circuit 304 has properties similar to the applied AC potential 341. Due to the non-ideal characteristics of the circuit, the expected value of the properties of the AC potential detected for the triplet state is usually different from the applied AC potential. Therefore, although theoretically the detected AC potential may match the applied AC potential when the quantum bit is in the triplet state, in practice, due to the non-ideal characteristics of the circuit (such as impedance mismatch or environmental factors), the circuit usually absorbs or reflects voltage. When the dual quantum dots are in the (1,1) charge configuration, the expected RF output when the first quantum bit is in the triplet state can be determined by monitoring the RF output signal. In this way, the expected value of the properties of the detected first AC potential can be determined, and when one or more measured properties of the detected first AC potential substantially match the corresponding expected value, the readout circuit can infer that the first quantum bit 301 is in the triplet state. The expected value can be a range of expected values, and when the measured attribute falls within the range of expected values, the readout circuit can determine that the measured attribute is basically matched.

[0136] When the second qubit 311 is in the triplet state, tunneling does not occur. In this way, the second AC potential 352 detected by the second resonator circuit of the readout circuit 304 has properties similar to the applied AC potential 342, differing slightly due to experimental factors similar to those of the first qubit. Similar to the first qubit, the second qubit 311 can be inferred to be in the triplet state when one or more measured properties of the detected second AC potential substantially match known expected values ​​for these properties for the triplet state.

[0137] When the first quantum bit 301 is in a singlet state, as regarding Figure 2A or Figure 2B As described above, applying an alternating current potential 341 to the gate electrode of the first quantum dot 305 of the first quantum bit 301 induces a series of quantum tunneling processes. Therefore, the readout circuit 304 detects a first alternating current potential 351, which has properties modified relative to the applied alternating current potential 341 due to tunneling. Specifically, the properties of the first alternating current potential detected when the first quantum bit 301 is in a singlet state substantially match the properties of the alternating current potential detected by the readout circuit when the dual quantum dot is in a (0,2) charge configuration. In this way, by determining whether one or more measured properties of the detected first alternating current potential substantially match a desired value, it can be inferred that the first quantum bit 301 is in a singlet state, where the desired value corresponds to the value of the properties of the alternating current potential detected by the readout circuit when the dual quantum dot is in a (0,2) charge configuration.

[0138] When the second quantum bit 311 is in a singlet state, as regarding Figure 2A or Figure 2B As described above, applying an alternating current potential 342 to the gate electrode of the first quantum dot 315 of the second quantum bit 311 induces a series of quantum tunneling processes. Therefore, the readout circuit 304 detects a second alternating current potential 352 that has properties substantially matching the expected value for singlet properties, thereby inferring that the second quantum bit 311 is in a singlet state.

[0139] When measuring multiple qubits using a single library and connected resonator circuitry, the state of the qubits can be determined using multiplexing methods. In some examples, time-division multiplexing can be used. In time-division multiplexing, multiple qubits sharing a single library and resonator circuitry can be measured sequentially. In time-division multiplexing, a first frequency f1 is applied to the gate electrode of the first quantum dot 305 of the first qubit 301 at a first time, and a second frequency f2 is applied to the gate electrode of the second quantum dot 315 of the second qubit 311 at a second time, later than the first time. In this case, the first frequency f1 and the second frequency f2 can be the same or different. The measurements can be distinguished at the resonator circuitry by being time-separated.

[0140] In a preferred example, frequency division multiplexing (FDM) can be used. In FDM, multiple qubits sharing a single library and connected resonator circuits can be measured simultaneously. Alternating current potentials at first frequencies f1 and f2 are typically applied substantially simultaneously to the first quantum dots 305, 315 of the first qubit 301 and the second qubit 311. In this case, the first frequencies f1 and f2 are different from each other and correspond to the resonant frequencies of the first and second resonant circuits, respectively. Therefore, measurements can be distinguished at the resonator circuits by frequency separation. Thus, for FDM, the readout circuit 304 is configured to use multiple different resonant circuits to detect multiple different frequencies.

[0141] In multiplexing techniques, the readout circuit (including resonator circuit 304) typically also includes a mapping relationship between each qubit and its corresponding time and / or frequency. In this way, when the resonator circuit detects a specific time and / or frequency, the readout circuit determines the corresponding qubit based on the mapping relationship. Preferably, the mapping relationship is one-to-one.

[0142] Figure 3Two qubits, 301 and 311, are shown. In a circuit, any number of qubits can share a common library and resonator circuit. For time-division multiplexing, there is no limit to the number of qubits in a shared library, and having more qubits per library has the advantage of saving space. However, measuring the state of more qubits using time-division multiplexing requires more time, which affects efficiency. For frequency-division multiplexing, increasing the number of qubits per library has the advantage of saving space without sacrificing efficiency, because the state of each of the multiple qubits sharing the library can be inferred substantially simultaneously. The total number of qubits per library is limited only by bandwidth capability and spectral resolution.

[0143] Typically, the frequency source applies frequencies between 20 kHz and 300 GHz, and usually between 1 MHz and 10 GHz, with a spectral resolution between 1 and 50 MHz. This spectral resolution avoids overlap between adjacent frequencies. The frequency source can be any commercially available unit capable of outputting alternating current at one or more selected frequencies. Preferably, the frequency source is capable of outputting multiple selected frequencies to facilitate frequency division multiplexing.

[0144] Figure 4 A two-dimensional qubit array is schematically illustrated. Within the two-dimensional array, adjacent quantum dots are arranged within a quantum interaction distance, allowing the potential barriers between adjacent quantum dots to be tuned to facilitate or suppress tunneling between them. The qubit array includes quantum dots 426 and 427 configured to function as data qubits or auxiliary qubits. When used as data qubits, quantum dots 426 and 427 store quantum information related to quantum computing. The state of the data qubits is measured to record the results of the quantum computing. Therefore, the circuitry is used to read out the state of the data qubits. When used as auxiliary qubits, quantum dots 426 and 427 indirectly relay quantum information. For example, intermediate cascaded quantum dots include auxiliary qubits.

[0145] exist Figure 4 In this configuration, the first subset of quantum dots 427 can be addressed by a frequency source. Addressing a quantum dot in the first subset of quantum dots 427 involves applying an alternating current potential to the plunger electrode of that quantum dot in the first subset of quantum dots 427 using the frequency source. The same frequency source can be used to address each quantum dot in the first subset of quantum dots 427. Alternatively, multiple frequency sources can be provided, each configured to address one or more quantum dots in the first subset of quantum dots 427.

[0146] In this example, the first subset of quantum dots 427 comprises approximately half of the total number of quantum dots 426 and 427 in the array. In this example, quantum dots 427 that can be addressed by the frequency source alternate with quantum dots 426 that cannot be addressed by the frequency source. In this way, vertically or horizontally adjacent quantum dots can form a pair of quantum dots, where one quantum dot 427 is addressable. It is not necessary to be able to address every quantum dot in the array, thus this arrangement reduces the control circuitry required to connect the quantum dots and the frequency source, while maximizing the flexibility of routing quantum information from data qubits to readout circuitry. In this example, one quantum dot (surrounded by quantum dots in the first subset of quantum dots 427) is replaced by a library 424. In other examples, multiple quantum dots can be replaced by one or more libraries.

[0147] The states of multiple data qubits can be measured using readout circuitry 425. Readout circuitry 425 is coupled to library 424. In this example, the wiring connecting library 424 and readout circuitry 425 is out of plane. This means that no space needs to be reserved within the quantum dot array for wiring, which is beneficial for dense quantum dot arrays. Using readout circuitry 425 in this way results in minimal on-chip footprint because no additional infrastructure is required to read out the states of the qubits. Readout circuitry 425 includes multiple readout sensors, such as LC resonators.

[0148] Figure 4 Two quantum information paths 40 and 41 are schematically illustrated. The first path 40 connects the first qubit 401 to the library 424. The second path 41 connects the second qubit 411 to the same library 424. The first qubit 401 and the second qubit 411 are data qubits. The first qubit 401 and the second qubit 411 comprise a first tunneling-coupled quantum dot and a second tunneling-coupled quantum dot forming a dual-quantum-dot qubit with two states (single-state and triplet-state), as described above. In this example, the first path 40 and the second path 41 overlap, as described below.

[0149] In the first path 40, the first quantum bit 401 is capacitively coupled to the first intermediate cascaded quantum dot 402; the first intermediate cascaded quantum dot 402 is capacitively coupled to the first second intermediate cascaded quantum dot 403; the first second intermediate cascaded quantum dot 403 is capacitively coupled to the first third intermediate cascaded quantum dot 404; the first third intermediate cascaded quantum dot 404 is capacitively coupled to the first shared intermediate cascaded quantum dot 421; the first shared intermediate cascaded quantum dot 421 is capacitively coupled to the second shared intermediate cascaded quantum dot 422; the second shared intermediate cascaded quantum dot 422 is capacitively coupled to the shared cascaded quantum dot 423; and the shared cascaded quantum dot 423 is tunneled to the library 424.

[0150] In the second path 41, the second quantum bit 411 is capacitively coupled to the second first intermediate cascaded quantum dot 412; the second first intermediate cascaded quantum dot 412 is capacitively coupled to the first shared intermediate cascaded quantum dot 421; the first shared intermediate cascaded quantum dot 421 is capacitively coupled to the second shared intermediate cascaded quantum dot 422; the second shared intermediate cascaded quantum dot 422 is capacitively coupled to the shared cascaded quantum dot 423; and the shared cascaded quantum dot 423 is tunneled to the library 424.

[0151] It can be seen that the first shared intermediate cascaded dual quantum dot 421, the second shared intermediate cascaded dual quantum dot 422, and the cascaded quantum dot 423 exist in both the first path 40 and the second path 41. Sharing portions of the cascaded chain in this way increases the circuit's robustness to faulty nanostructures.

[0152] In other examples, other path shapes and lengths can be implemented. Different paths within the same circuit can have different or the same shape and length. The number of overlapping circuit elements varies depending on circuit requirements (such as the relative positions of the data qubits to be measured and the library). In other examples, some intermediate cascaded dual quantum dots can be shared by two paths, but the cascaded quantum dots and libraries of these two paths are not shared.

[0153] Such as about Figure 3 The states of each of a plurality of qubits can be measured using frequency division multiplexing or time division multiplexing. In this example, an AC potential 441 at a first frequency f1 is applied to the plunger gate of the first quantum dot of the first qubit 401, and an AC potential 442 at a second frequency f2, different from the first frequency f1, is applied to the plunger gate of the first quantum dot of the second qubit 411. Each plunger gate is configured to control the energy state of the corresponding first quantum dot by raising and lowering the electrochemical potential level according to the potential applied to the plunger gate.

[0154] Therefore, the readout circuit 425 is configured to detect a first AC potential 451 and a second AC potential 452, measure one or more properties of the AC potentials, and compare the detected first AC potential and one or more measured properties of the second AC potentials with expected values ​​for the properties of the AC potentials for singlet and triplet states. The expected values ​​vary depending on the frequency of the applied AC potential and the spin state of the qubit. Therefore, frequency division multiplexing can be used to measure the states of the first qubit 401 and the second qubit 411 substantially simultaneously. Any shared circuit elements (i.e., the first shared intermediate cascaded dual quantum dot 421 and the second shared intermediate cascaded dual quantum dot 422 and cascaded quantum dot 423 in this example) can simultaneously relay the quantum information of the first qubit 401 and the second qubit 411 by addressing the first qubit 401 and the second qubit 411 using different frequencies.

[0155] Figures 5A-5C A possible circuit architecture for reading the state of multiple qubits is schematically illustrated, including exemplary paths for transmitting quantum information and an example of frequency multiplexing using this circuit architecture. This circuit architecture defines gate-defined silicon metal oxide semiconductor (Si-MOS) quantum dots in a two-dimensional array. Within the two-dimensional array, adjacent quantum dots are arranged within a quantum interaction distance, such that the potential barriers between adjacent quantum dots can be tuned to facilitate or inhibit tunneling between adjacent quantum dots. Each quantum dot is defined by multiple gate electrodes that can be individually controlled. Therefore, by applying a voltage to the gate electrodes, a state can be defined as follows: Figures 5A-5C The potential energy landscape is illustrated schematically. For each quantum dot, a plunger gate is provided to control the electrochemical potential of that quantum dot, and a barrier gate is provided to control the tunneling coupling between adjacent quantum dots or between a quantum dot and a pool. The potential applied to each gate can be controlled according to the capacitance matrix. In this way, the potential energy landscape can be flexibly defined to include the desired paths, couplings, and barriers.

[0156] This circuit architecture forms a unit cell, which can be repeated multiple times on the chip of a quantum device. Each unit cell includes a charge pool 505 located at the center of the quantum dot array. This pool is an n-doped electron pool. A readout circuit 506 is out-of-plane coupled to the charge pool 505. In this example, the readout circuit includes multiple LC resonators (i.e., resonator circuits or tank circuits).

[0157] exist Figures 5A-5C In the exemplary unit cell shown, 40 quantum dots 501, 502, 503, and 504 surround a library 505. Of these 40 quantum dots, 16 quantum dots 502 and 504 are coupled to a frequency source. This means that the frequency source can apply an alternating current potential of a selected frequency to these 16 quantum dots 502 and 504. The quantum dots are arranged in concentric layers around the library 505, with each subsequent layer surrounding the previous one. This arrangement allows vertically or horizontally adjacent quantum dots to form a pair of quantum dots, as shown in the diagram. Figure 4 The nearly centered position of the Ku505 within the unit cell enables denser qubit arrangements because fewer Kus are needed to address the same number of qubits. This also allows for a reduction in the length of the one-dimensional chain.

[0158] Figure 5BExemplary paths for quantum information are illustrated using double-headed arrows. To create each path, vertically or horizontally adjacent quantum dots can form a pair of quantum dots, using a cascaded Pauli spin blocking process to transfer quantum information associated with the state of the data qubit to the charge pool. Other paths involving vertically or horizontally adjacent quantum dots can also be easily defined by modifying the gate potential of the quantum dots in the unit cell.

[0159] The initial zeroth layer L0, arranged next to the library 505, comprises four auxiliary quantum dots 504, each coupled to the library 505. The quantum dots 504 in the zeroth layer are coupled to a frequency source.

[0160] Quantum dots 503, 502, and 501 in layers L1, L2, and L3 can be used to form data qubits. Each data qubit can be a single-spin data qubit tunneled to an adjacent qubit forming an auxiliary qubit, or it can be a two-quantum-dot qubit. In both cases, a two-quantum-dot qubit is formed, with one of the two qubits coupled to a frequency source. This means that 36 out of 41 elements can be used to form data qubits: the space occupied by the quantum dots used to form data qubits is 87.8% of the total area. This achieves a dense arrangement of data qubits.

[0161] Quantum dots 503 and 502 in the first layer L1 and the second layer L2 are also used as auxiliary qubits when measuring the state of data qubits in layers farther from the charge bank 505, as shown in the relevant section. Figure 6B and Figure 6C As stated above.

[0162] In other examples, additional quantum dot layers may exist within the unit cell. In each case, the outermost layer of quantum dots can only be used to form data qubits. The quantum dots in the middle layers can be used as data qubits or auxiliary qubits, depending on the qubit to be measured. The number of quantum dots N in a layer is [number] when the library occupies the space of one quantum dot in the array. d for , where d is the number of layers.

[0163] The number N of different RF frequencies required for different quantum dots in the addressing array M It depends on the number of quantum dots in the highest layer with RF connections, i.e. Where d is the layer number. In this case, the highest layer of quantum dots coupled to the frequency source is the second layer L2, which comprises twelve quantum dots. Accordingly, twelve different resonator circuits with twelve different resonant frequencies are required in this example. Alternatively, the resonator circuits used to detect the AC potential applied to the quantum dots in the second layer L2 can also be used to detect the AC potential applied to the quantum dots in the zeroth layer L0. This reduces the total number of resonator circuits required, thereby reducing the requirements for the readout circuitry.

[0164] Figure 5C The method of measuring data qubits in the third layer L3 using two different RF frequencies applied to quantum dots in the second layer L2 is described. First frequency An alternating current potential of 541 is applied to the first auxiliary qubit in the second layer L2, which is adjacent to the first data qubit in the third layer L3; and a second frequency different from the first frequency. An alternating current potential 542 is applied to the second auxiliary qubit in the second layer L2, which is adjacent to the second data qubit in the third layer L3. Tunneling of charge carriers between the first and second data qubits and the charge pool is indicated by double-headed arrows. The readout circuit 506 is configured to use a frequency corresponding to the first frequency... A first LC resonator with a fundamentally matched resonant frequency is used to detect the first AC potential 551; and a second frequency is used... A second LC resonator with a basically matched resonant frequency is used to detect the second AC potential 552. The first and second LC resonators (not shown) are connected in parallel in the readout circuit. The outputs of the resonant circuit can be combined to form a signal containing the first and second AC potentials.

[0165] exist Figures 5A-5C In the arrangement shown, there are more quantum dots in the third layer L3 than in the second layer L2. Therefore, to measure the state of all qubits in the third layer L3, two measurement steps are required. In the first measurement step, the state of up to twelve different data qubits in the third layer L3 can be measured by applying an AC potential of a different frequency to each of the twelve quantum dots in the second layer L2. In the second measurement step, the state of the remaining data qubits in the third layer L3 can be measured by applying an AC potential of a different frequency to a corresponding number of adjacent quantum dots in the second layer L2.

[0166] exist Figure 5B In the diagram, the path for the first measurement step of each layer is indicated by a solid double-headed arrow, and the path for the second measurement step of each layer is indicated by a dashed double-headed arrow.

[0167] Unit cells can be placed adjacent to each other, such that the outermost layer of a unit cell is adjacent to the outermost layer of multiple additional unit cells.

[0168] In other examples, alternative arrangements of the circuit elements are possible. In each case, capacitive coupling exists between nearest neighbors, and RF readout capability is available. Tunneling coupling between these adjacent quantum dots can be selectively formed by reducing the barrier height by modifying the potential applied to the barrier electrodes (separating adjacent quantum dots). In this way, a path between each data qubit to be measured and the charge pool can be defined. To define the path, the bias potential applied to every other barrier gate along the path to be defined is reduced to lower the barrier height, thus forming two quantum dots. The bias potential applied to the plunger gate is then modified so that the quantum dots approach charge transitions. The barriers between quantum dots in the path to be defined and those not in the path are tuned so that the charge carrier occupancy of quantum dots outside the path remains constant. In this way, the relationship between the plunger gates of the quantum dots in the array and all other circuit elements can be characterized as a capacitance matrix to determine the path of quantum information. Furthermore, based on the values ​​in this matrix, a set of potentials can be applied to the gate electrodes of quantum dots adjacent to the path but not part of it. This means that any impact on other circuit elements that are not part of the path will be reduced.

[0169] Figures 6A-6C The diagram illustrates the use of cascading processes for... Figures 5A-5C Measurements were performed on the data qubits of each of the three layers L1-L3 in the unit cell shown. Figures 6A-6C In the diagram, a one-dimensional chain is shown along a line; however, in a circuit, each coupling between adjacent quantum dots can be formed vertically or horizontally in a quantum dot array.

[0170] Figure 6A The measurement involving the first layer L1 of the unit cell is shown. This measurement is similar to existing charge polarization measurements. The measurement circuitry for reading out the spin states includes a first-layer quantum dot 603, a zero-layer quantum dot 604, and a charge bank 605. A frequency source is connected to the gate electrode of the zero-layer quantum dot 604.

[0171] exist Figure 6A In this configuration, the first-layer quantum dot 603 tunnels to the zeroth-layer quantum dot 604, and the zeroth-layer quantum dot capacitively couples to the charge pool 605. A frequency source is configured to apply a first frequency to the zeroth-layer quantum dot 604. The alternating current potential is 641. Based on the spin states of the two quantum dots 603 and 604, this can lead to cyclic tunneling of charge carriers from the zeroth-layer quantum dot 604 to the first-layer quantum dot 603 and vice versa. When cyclic tunneling occurs, a readout circuit connected to the charge bank 605 detects charge carriers. (or mirror charge, or mirror image charge). The readout circuit is in Figures 6A-6C Not shown in the image.

[0172] use Figure 6A The first type of measurement in the circuit shown is a single-spin qubit measurement. In this example, a first-layer quantum dot 603 forms a single-spin data qubit, and a zero-layer quantum dot 604 forms an auxiliary qubit. The readout spin state of the first-layer quantum dot 603 can be spin-up or spin-down. Before the readout measurement, the zero-layer quantum dot 604 is initialized to a known spin state, typically spin-down. The readout circuit is used to infer when the data qubit is in a spin-up or spin-down state. This can be inferred because the aforementioned cyclic tunneling will occur when the spin state of the data qubit is antiparallel (i.e., opposite) to the spin state of the auxiliary qubit; while the aforementioned cyclic tunneling will not occur when the spin state of the data qubit is parallel (i.e., identical) to the spin state of the auxiliary qubit. Therefore, the expected values ​​of the properties of the first and second spin states will differ due to the presence or absence of tunneling, which can be used to infer the state of the qubit.

[0173] When a cyclic tunneling process occurs in response to an AC potential applied to the zero-layer quantum dot 604 by a frequency source, the properties of the AC potential detected by the readout circuit will substantially match the expected value for the antiparallel spin configuration; while when the cyclic tunneling process does not occur, the properties of the detected AC potential will substantially match the expected value for the parallel spin configuration. Therefore, if the auxiliary qubit is initialized to a spin-down state, the readout circuit will infer that the data qubit is in a spin-down state if the measured properties of the detected AC potential substantially match the expected value for the spin-down state. Alternatively, the readout circuit will infer that the data qubit is in a spin-up state if the measured properties of the detected AC potential substantially match the expected value for the spin-up state.

[0174] use Figure 6A The second type of measurement for the circuit shown is a two-quantum-dot qubit measurement. In this example, the first-layer quantum dot 603 forms the first quantum dot of the two-quantum-dot system, and the zeroth-layer quantum dot 604 forms the second quantum dot. The readout state of the two quantum dots can be either a singlet spin configuration or a triplet spin configuration. Before the readout measurement, the zeroth-layer quantum dot 604 can optionally be initialized to a random spin state.

[0175] The readout circuit is used to infer whether a two-quantum-dot qubit is in a singlet spin state or a triplet spin state. This can be inferred because the aforementioned cyclic tunneling will occur when the qubit is in a singlet spin state, while it will not occur when the qubit is in a triplet spin state.

[0176] Similar to the first type of measurement, when a cyclic tunneling process occurs in response to an AC potential applied to the zero-layer quantum dot 604 by a frequency source, the properties of the AC potential detected by the readout circuit will substantially match the expected values ​​for the properties of the singlet spin state; while when the cyclic tunneling process does not occur, the properties of the detected AC potential will substantially match the expected values ​​for the properties of the triplet spin state. Therefore, the readout circuit will infer whether the qubit is in a triplet spin state or a singlet spin state based on the expected values ​​for the properties of the triplet spin state and the singlet spin state, respectively. Thus, the expected values ​​are used as reference values, and the detected AC potential can be compared with these reference values ​​to infer the spin state of the qubit.

[0177] Figure 6B It shows the involvement Figures 5A-5C Measurements of the second layer L2 of the unit cell shown. The circuit layout is similar to... Figure 1 As shown. In Figure 6B In this configuration, the second quantum dot 602 tunnels to the first quantum dot 603, forming a dual quantum dot array, and the zeroth quantum dot 604 tunnels to the charge pool 605. The first quantum dot 603 is capacitively coupled to the zeroth quantum dot 604. A frequency source is connected to the gate electrode of the second quantum dot 602. A frequency source is also connected to the gate electrode of the zeroth quantum dot 604, but is not used in this example.

[0178] The frequency source is configured to apply a first frequency to the second-layer quantum dot 602. The alternating current potential is 641. Based on the spin states of the first quantum dot 603 and the second quantum dot 602, this can cause charge carriers to circulate and tunnel back and forth between the first and second quantum dots 603 and 602. This circulatory tunneling of charge carriers between the first and second quantum dots 603 induces a circulatory tunneling process between the zeroth quantum dot 604 and the charge bank 605. In this way, when the cascaded circulatory tunneling process occurs, charge carriers tunnel into the charge bank. In this way, the readout circuit connected to the charge bank 605 detects a complete electron charge. This amplifies the signal detected by the readout circuit, and relative to... Figure 6A The measurement improved the signal-to-noise ratio.

[0179] and Figure 6A similar, Figure 6BThe circuit shown can be used for both the first and second measurement types, depending on the initial state of the first-layer quantum dot 603. For the first measurement type, if the first-layer quantum dot 603 is initialized with a known spin state, a single-quantum-dot qubit measurement can be performed to determine the spin state of the second-layer quantum dot 602, i.e., spin-up or spin-down. As mentioned above, due to Pauli spin blocking and Coulomb repulsion, cyclic tunneling only occurs when the spins are antiparallel; therefore, the spin state of the qubit can be inferred by using a readout circuit to determine whether cyclic tunneling occurs in response to an applied AC potential. The detected AC potential will have different properties depending on whether cyclic tunneling occurs; therefore, by measuring the properties of the detected AC potential and comparing them with a reference value, the spin state of the qubit can be measured.

[0180] For the second type of measurement, if the first layer quantum dot 603 can be initialized with a random spin state, then the first layer quantum dot 603 and the second layer quantum dot 602 will form a dual quantum dot, whose state can be determined as a singlet spin state or a triplet spin state, as described above.

[0181] Figure 6C It shows the involvement Figures 5A-5C Measurements of the third layer L3 of the unit cell shown. Figure 6C In this configuration, the third-layer quantum dot 601 tunnels to the second-layer quantum dot 602; the first-layer quantum dot 603 tunnels to the zeroth-layer quantum dot 604. In this way, the second-layer quantum dot 602 and the third-layer quantum dot 601 form a first dual quantum dot; the zeroth-layer quantum dot 604 and the first-layer quantum dot 603 form a second dual quantum dot. The first dual quantum dot is capacitively coupled to the second dual quantum dot; the second dual quantum dot is capacitively coupled to the charge pool 605. Specifically, the first-layer quantum dot 603 and the second-layer quantum dot 602 are capacitively coupled; the zeroth-layer quantum dot 604 is capacitively coupled to the charge pool 605. A frequency source is connected to the gate electrodes of the second-layer quantum dot 602 and the zeroth-layer quantum dot 604. In this example, the same frequency source is connected to both quantum dots 602 and 604, but this is not necessary.

[0182] The frequency source is configured to apply a first frequency to the second-layer quantum dot 602. The alternating current potential is 641. Based on the spin states of the second-layer quantum dot 602 and the third-layer quantum dot 601, this can cause charge carriers to circulate and tunnel back and forth between the second-layer and third-layer quantum dots 602 and 601. This circulatory tunneling of charge carriers between the second-layer and third-layer quantum dots 602 and 601 induces a circulatory tunneling process between the zeroth-layer quantum dot 604 and the first-layer quantum dot 603. In this way, when the cascaded circulatory tunneling process occurs, charge carriers tunnel to the vicinity of the charge reservoir, and the readout circuit connected to the charge reservoir 605 detects the mirror charge. In this configuration, the cascaded process transfers quantum information associated with the third-layer L3 quantum dot to a location closer to the library 605, thereby improving the signal-to-noise ratio (SNR) compared to a circuit that omits the zeroth-layer quantum dot 604 and the first-layer quantum dot 603. This improved SNR is due to the tunneling of charge carriers closer to the library.

[0183] and Figure 6A and Figure 6B similar, Figure 6C The circuit shown can be used for both the first and second measurement types, depending on the initial state of the second-layer quantum dot 602. For the first measurement type, the second-layer quantum dot 602 is initialized with a known spin state, allowing a single-quantum-dot qubit measurement to determine the spin state of the third-layer quantum dot 601, i.e., spin-up or spin-down. As described above, due to Pauli spin blocking and Coulomb repulsion, cyclic tunneling occurs only when the spins in adjacent second and third-layer quantum dots are antiparallel. Therefore, the spin state of a single-quantum-dot qubit can be inferred by using a readout circuit to determine whether cyclic tunneling occurs in response to an applied AC potential.

[0184] For the second type of measurement, the first layer quantum dot 603 may optionally be initialized with a random spin state, and the second layer quantum dot 602 and the third layer quantum dot 601 form a dual quantum dot whose state can be determined as a singlet spin state or a triplet spin state, as described above.

[0185] exist Figures 6A-6C In the circuit arrangements shown, the coupling between adjacent quantum dots is designed by modifying the electrostatic barrier between them. Furthermore, in these circuit arrangements, an AC potential for stimulating cyclic tunneling is applied to the gate electrode of the quantum dots. In this way, S is measured by the readout circuit. 21 Transmitted scattering component. In other examples, an alternating current potential used to stimulate cyclic tunneling can be applied to the charge pool. In these examples, S is measured by a readout circuit. 11 Reflected scattering component.

[0186] Figure 7A and Figure 7B schematically shown Figures 5A-5C The circuit architecture shown is robust to faults. The same principle applies to different circuit architectures involving quantum dot arrays. Figures 5A-5C Similarly, the unit cell includes a zero-layer quantum dot 704, a first-layer quantum dot 703, a second-layer quantum dot 702, and a third-layer quantum dot 701. Quantum dots 701, 702, 703, and 704 are arranged concentrically around a charge reservoir 705; in this example, the charge reservoir occupies the same space as a single quantum dot in the array. A readout circuit 706 is connected to the charge reservoir 705.

[0187] exist Figure 7AIn the diagram, the first layer quantum dot 7031 is faulty and therefore considered a "dead" qubit, unmeasurable and unusable in the path between the other qubit to be measured and the charge pool. The dashed double-headed arrows indicate the path between the charge pool 705 and the third layer quantum dot 701 involving the first layer quantum dot 7031; this path might be used if the first layer quantum dot 7031 were not a dead qubit. However, because the path can be flexibly determined and coupling can be formed between vertically and horizontally adjacent quantum dots in the array, the path used to transfer quantum information can be easily rerouted to the non-dead second layer quantum dot 7032. The solid double-headed arrows indicate alternative paths that can be used to transfer quantum information from the second layer quantum dot 702 and the third layer quantum dot 701 to the charge pool 705 without involving the dead qubit 7031. Of course, any of several paths involving different combinations of vertical and / or horizontal couplings can be defined according to experimental requirements. Typically, a short path is chosen, optionally the shortest possible one.

[0188] Figure 7B Two adjacent unit cells are shown: a first unit cell 710 and a second unit cell 720. Each unit cell 710, 720 has a zero-layer quantum dot 704, a first-layer quantum dot 703, a second-layer quantum dot 702, and a third-layer quantum dot 701 arranged around their respective charge banks 715, 725. In this example, the first bank 715 in the first unit cell 710 is functioning normally, while the second bank 725 in the second unit cell 720 is not functioning, or is "dead". In this example, quantum dots 701-704 in the second unit cell 720 cannot be read out by the readout circuit connected to the second bank 725. However, as indicated by the double-headed arrows, the state of the qubits can be read out by forming paths to the charge banks in different unit cells. Figure 7B This indicates the path between the first layer of quantum dots 703 in the second unit cell 720 and the first charge pool 715 in the first unit cell 710. Typically, a short path is chosen, optionally the shortest possible one. Therefore, quantum information from other measurable subqubits in the second unit cell 720 can be routed to the charge pools in other adjacent unit cells. Typically, the circuit architecture comprises multiple unit cells, with outer layers such as… Figure 7B The adjacent ones are shown.

[0189] Figure 8 This is a schematic diagram of the circuit. Figure 8The circuitry includes a first quantum dot 801, a second quantum dot 802, a third quantum dot 803, a charge reservoir 804, a resonator circuit 805, and an RF output 806. The first quantum dot 801, the second quantum dot 802, and the third quantum dot 803 are each capacitively coupled to their respective first gate electrode 811, second gate electrode 812, and third gate electrode 813. An RF input signal 821 is applied to the first gate electrode 811 of the first quantum dot 801, thereby alternately raising and lowering the energy levels within the first quantum dot 801 as described above, initiating the tunneling process. In other examples, the RF input signal may be applied to the second gate electrode 812 of the second quantum dot 802. Since the first quantum dot 801 and the second quantum dot 802 are tunneling coupled, the application of the RF input signal 821 forces charge carriers to tunnel from the first quantum dot 801 to the second quantum dot 802 or from the second quantum dot 802 to the first quantum dot 801, depending on the relative energy states of the two quantum dots. The third quantum dot 803 is capacitively coupled to the second quantum dot 802 and tunnels to the charge pool 803. Therefore, when cyclic tunneling occurs between the first quantum dot 801 and the second quantum dot 802, the capacitive coupling between the second quantum dot 802 and the third quantum dot 803 will generate synchronous cyclic tunneling between the third quantum dot 803 and the charge pool 804. The transmitted signal is picked up at the output of the resonant circuit (here, the resonator circuit 805, also referred to as an LC resonator).

[0190] The resonator circuit 805 connected to the charge bank 804 includes an inductor 815 and a capacitor 825. The resonator circuit 805 has a resonant frequency. To measure the state of a qubit, a frequency source connected to the first gate electrode 811 is configured to apply an alternating current potential at the resonant frequency of the resonator circuit 805. Typically, the readout mechanism involves zero-difference detection, where the alternating current potential applied to the gate electrode 811 is simultaneously applied to the resonator circuit 805. In this way, if no tunneling occurs between the tunneling-coupled qubits, the RF output 806 is substantially the same as the RF input 821. Conversely, if tunneling does occur, the RF output 806 differs from the RF input 821. Typically, the frequency of the RF output 806 shifts negatively when tunneling occurs. In the frequency domain, this is considered a direct negative frequency shift. In the time domain, at a specific frequency (typically the resonant frequency)... This means that the amplitude and / or phase of the RF output 806 are lower when the cascaded cyclic tunneling process occurs.

[0191] Figure 8The arrangement shown can be used to measure (a) the spin state of a first quantum dot 801, (b) the spin state of a second quantum dot 802, or (c) the spin state of a dual quantum dot comprising the first quantum dot 801 and the second quantum dot 802. To measure the spin state of the first quantum dot 801, the second quantum dot 802 is initialized with a known spin state (e.g., spin-down). To measure the spin state of the second quantum dot 802, the first quantum dot 801 is initialized with a known spin state. When measuring the spin state of a dual quantum dot, optionally, the quantum dots can be initialized with a random spin state, or the measurement can be performed without an initialization step.

[0192] In other examples, additional qubits (not shown) can be measured simultaneously using frequency multiplexing as described above. In these examples, additional resonator circuits arranged in parallel with the illustrated resonator circuit 805 will exist, each with a different resonant frequency. The resonant frequency is determined by the inductive reactance L and capacitive reactance C, or by an inductor and a capacitor. Specifically, the resonant frequency is... The outputs of each resonant circuit can be combined to provide a single RF output signal with multiple frequency components.

[0193] exist Figure 8 In the example shown, transmission scattering parameters are measured. In alternative examples, the RF input can be applied to a charge bank. In these examples, the reflection and scattering parameters are measured. The remaining details of this setup are as described above.

[0194] Figure 9 This is a flowchart of a method for reading the state of a qubit. Step S91 involves applying an alternating current potential of a first frequency to the gate electrode of a first quantum dot, the gate electrode of a second quantum dot, or a charge bank using a frequency source. The first and second quantum dots form a dual-quantum-dot array of the qubit to be measured.

[0195] Gate electrodes are typically plunger gate electrodes used to raise and lower the electrochemical potential level within the associated quantum dot. For multiple qubits, a frequency source can be further used to apply additional AC potentials at corresponding frequencies to the gate electrode or charge bank of the quantum dot forming each qubit.

[0196] The dual quantum dot qubit is configured such that when an alternating potential of a first frequency is applied, cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa occurs only when the qubit is in a singlet state, and thus cyclic tunneling of charge carriers from the cascaded quantum dot to the coulomb and vice versa.

[0197] Therefore, in order to infer the state of the qubit, the method further includes in step S92: detecting a first AC potential using a readout circuit connected to a charge bank. The detected first AC potential is detected by a resonator circuit having a first frequency as its resonant frequency.

[0198] Step S93 involves measuring one or more properties of the detected first AC potential using a readout circuit. The one or more properties include frequency, amplitude, and phase. For example, in the frequency domain, only the frequency may be measured, or in the time domain, only the amplitude may be measured. Of course, two or more properties can be measured.

[0199] Step S94 involves inferring that the qubit is in a triplet spin state when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the triplet spin state; or inferring that the qubit is in a singlet spin state when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the singlet spin state. In other words, if the frequency, amplitude, and / or phase of the detected AC potential substantially match or fall within the expected values ​​for the triplet spin state or the singlet spin state, the dual-quantum-dot qubit can be inferred to be in a triplet spin configuration or a singlet spin configuration, respectively. Typically, a singlet spin configuration is reflected as a negative frequency shift relative to a triplet spin configuration, which results in a decrease in amplitude and phase at the resonant frequency.

[0200] Figure 9 This method can be applied to qubit arrays. For Figures 5A-5C The example readout method for the illustrated unit cell is described below. The first set of qubits comprises a bi-qubit array consisting of four of the eight first-layer quantum dots 503 and a zero-layer quantum dot 504. The state of the first set of qubits is measured by applying alternating current potentials at first, second, third, and fourth frequencies to the four zero-layer quantum dots 504, respectively (see [link to documentation]). Figure 9 Step S91 and Figure 6A For each of the four dual-quantum-dot qubits, four AC potentials are detected using four parallel-connected resonant circuits to perform steps S92-S94 in parallel. Subsequently, the zeroth-layer quantum dot 504 is loaded with a random spin. Then, the second set of qubits comprises dual-quantum-dot qubits formed by the remaining four of the eight first-layer quantum dots 503 (tunneled to the zeroth-layer quantum dot 504). The state of each qubit in the second set is measured in the same manner as the first set. Subsequently, the first-layer quantum dots 503 are initialized with random spins.

[0201] The third set of qubits comprises eight dual-dot qubits, formed by eight of the twelve second-layer quantum dots 502 (each tunneled to one of the first-layer quantum dots 503). The state of each qubit in the third set of qubits is determined in parallel using the frequency division multiplexing technique described above (see [link]). Figure 9 Steps S91-S94 and Figure 6B Therefore, eight alternating current potentials, each with a different frequency, are applied to the corresponding second-layer quantum dots 502. The fourth set of qubits comprises a bi-qubit formed by the remaining four of the twelve second-layer quantum dots 502 (each tunneled-coupled to four of the first-layer quantum dots 503). Before measuring the fourth set of qubits, the first-layer quantum dots 503, which constitute at least a portion of the bi-qubit to be measured, are prepared into a random spin state. Subsequently, the second-layer quantum dots 502 are initialized with random spins.

[0202] The fifth set of qubits comprises twelve dual-quantum-dot qubits, formed by twelve of the sixteen third-layer quantum dots 501, each tunneled to one of the second-layer quantum dots 502. Using the frequency division multiplexing technique described above, an AC potential is applied to the second-layer quantum dot 602 to infer the state of each qubit in the fifth set of qubits in parallel (see [link to relevant documentation]). Figure 9 Steps S91-S94 and Figure 6C The sixth set of qubits comprises a bi-qubit formed by the remaining four of the third-layer quantum dots 501 (each tunneled to one of the four in the second-layer quantum dots 502). Before measuring the state of each qubit in the sixth set of qubits, the second-layer quantum dots 502, which constitute at least a portion of the bi-qubit to be measured, are prepared in a random spin state.

[0203] In each case, the maximum number of qubits in each group is determined by the total number of quantum dots in the (normally functioning) inner adjacent layers. The number of readout cycles (i.e., the number of qubit groups that need to be measured separately in time) is logarithmically related to the number of qubits in the unit cell.

[0204] Figure 10 This is a flowchart of a method for reading the state of a single-spin data qubit. The data qubit being measured tunnels to an auxiliary qubit (ancillary qubit or ancilla qubit). Therefore, the data qubit and the auxiliary qubit form a two-quantum-dot pair. Each of the data qubit and the auxiliary qubit has a first spin state and a second spin state. For example, the first spin state can be spin-down and the second spin state can be spin-up. Alternatively, the first spin state can be spin-up and the second spin state can be spin-down. The first and second spin states are antiparallel.

[0205] Step S100 involves initializing the auxiliary qubit to a first spin state using a control circuit connected to the auxiliary qubit. The spin state of the auxiliary qubit can be prepared using any well-known initialization technique (e.g., by tuning the energy level to exclude the spin-up state in terms of energy). In this way, the spin state will necessarily be spin-down.

[0206] Steps S101, S102, and S103 are similar Figure 9 The corresponding steps S91-S93 are shown. Step S101 involves applying an alternating current potential of a first frequency to the gate electrode or charge bank of the data qubit or auxiliary qubit using a frequency source. Figure 9 Similarly, the frequency source can be further used to apply multiple alternating potentials to measure the corresponding multiple data qubits.

[0207] The dual quantum dots are configured such that when an AC potential of a first frequency is applied, charge carrier cyclic tunneling between the data qubit and the auxiliary qubit occurs only when the data qubit is in a second spin state (i.e., in a spin state antiparallel to the spin state of the auxiliary qubit). Cyclic tunneling of charge carriers between the cascaded quantum dots and the charge pool also occurs when the data qubit is in the second spin state.

[0208] Step S102 involves detecting a first AC potential using a readout circuit connected to a charge bank. The detected first AC potential is detected by a resonator circuit having a first frequency as its resonant frequency.

[0209] Step S103 involves using a readout circuit to measure one or more properties of the detected first AC potential, such as frequency, amplitude, and / or phase.

[0210] Step S104 involves: inferring that the data qubit is in a first spin state when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the first spin state; or inferring that the data qubit is in a second spin state when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the second spin state. The expected values ​​of the properties of the first spin state and the second spin state are different because cascaded cyclic tunneling occurs when the data qubit is in an antiparallel spin state relative to the auxiliary qubit, but does not occur when the data qubit is in a parallel spin state relative to the auxiliary qubit.

[0211] Figure 10 This method can be applied to qubit arrays. For Figures 5A-5CThe example readout method for the illustrated unit cell is described below. First, the zeroth-layer quantum dot 504 is initialized to a first known spin state (step S100). The first set of qubits comprises single-spin qubits formed by four of the eight first-layer quantum dots 503. The zeroth-layer quantum dots 504 form auxiliary qubits. The state of the first set of qubits is measured by applying alternating current potentials at first, second, third, and fourth frequencies, respectively, to the four zeroth-layer quantum dots 504 (see [link to documentation]). Figure 10 Step S101 and Figure 6A For each of the four single-spin qubits, four AC potentials are detected using four parallel resonant circuits to perform steps S102-S104 in parallel. Subsequently, the zero-layer quantum dot 504 is again initialized with the first spin state. Then, the state of each qubit in the second group of qubits, comprising single-spin qubits formed by the remaining four of the eight first-layer quantum dots 503, is measured in the same manner as the first group. The first-layer quantum dots 503 are then prepared into the first spin state (S100).

[0212] The third set of qubits comprises eight single-spin qubits formed by eight of the twelve second-layer quantum dots 502. The state of each qubit in the third set of qubits is determined in parallel using the frequency division multiplexing technique described above (see [link]). Figure 10 Steps S101-S104 and Figure 6B Following this measurement, the first layer of quantum dots 503 is again prepared into the first spin state (S100). The fourth set of qubits comprises single-spin qubits formed by the remaining four of the twelve second-layer quantum dots 502. Once the second-layer quantum dots 502 are measured, each of them is loaded with charge carriers having a known spin state (here, the first spin state) (S100).

[0213] The fifth group of qubits comprises twelve single-spin qubits formed by twelve of the sixteen third-layer quantum dots 501. The state of each qubit in the fifth group is determined in parallel using the frequency division multiplexing technique described above (see [link]). Figure 10 Steps S101-S104 and Figure 6C Following this measurement, the second-layer quantum dot 502 was again prepared into the first spin state (S100). The sixth set of qubits consists of single-spin qubits formed by the remaining four qubits in the third-layer quantum dot 501.

[0214] In each case, the maximum number of qubits in each group is determined by the total number of quantum dots in the (normally functioning) inner adjacent layers. The number of readout cycles (i.e., the number of qubit groups that need to be measured separately in time) is logarithmically related to the number of qubits in the unit cell.

[0215] Figure 11This illustrates a possible S-mode operation on two two-quantum-dot qubits in the frequency domain. 21 Example of scattering parameter measurement. Detection of AC potential for singlet and triplet states of the first and second qubits. Figure 11 As shown in the image.

[0216] The readout circuit for reading out measurements includes circuits each having a first resonant frequency. Second resonant frequency Two resonant circuits. A frequency source is configured to apply a first frequency to the first and second qubits, respectively. Second frequency The figure schematically illustrates the detected first and second AC potentials corresponding to the first and second qubits, respectively.

[0217] If the first qubit is in a triplet spin state T, the frequency, amplitude, and phase of the detected first AC potential substantially match the expected values ​​of the properties of the AC potential for a triplet spin state. These properties include one or more of the frequency, amplitude, and phase. A schematic diagram of an example measurement is shown in the first qubit triplet spin state response 11. If the first qubit is in a singlet spin state S, the frequency undergoes a negative shift due to the change in circuit impedance. This is schematically illustrated by the first qubit singlet spin state response 12. At the first frequency At (only the resonant frequency of the first resonant circuit), the negative frequency shift causes the detected first AC potential to be at the first frequency. The amplitude and / or phase at that point decreases.

[0218] exist Figure 11 In the middle, the second frequency Higher than the first frequency Second frequency It is only the resonant frequency of the second resonant circuit. Figure 11 The triplet spin state response 21 and the singlet spin state response 22 of the second qubit are shown. Similar to the first qubit, when the second qubit is in the triplet spin state T, the properties of the detected second AC potential essentially match the expected values ​​of the AC potential properties for the triplet spin state; when the second qubit is in the singlet spin state S, the properties of the detected second AC potential essentially match the expected values ​​of the AC potential properties for the singlet spin state. For the singlet spin state, the frequency undergoes a negative shift relative to the triplet spin state due to the change in circuit impedance. Figure 11 In the diagram, the triplet spin-state responses 11 and 21 are essentially aligned with their respective resonant frequencies. However, in practice, due to the characteristics of non-ideal circuits, these frequencies may shift.

[0219] Figure 11 S was displayed 21 Response, but S 11 The response is similar. Figure 11 The singlet and triplet states measured when the qubit is a two-quantum-dot qubit are described. For the example involving the measurement of a single-quantum-dot qubit, when the data qubit has a spin state parallel to the known spin of the auxiliary qubit, the properties of the detected AC potential will substantially match the expected values ​​for the properties of the parallel spin state (e.g., ...). Figure 11 The triplet spin state response is shown in Figures 11 and 21. When the data qubit has a spin state antiparallel to the known spin of the auxiliary qubit, the detected AC potential property will basically match the expected value for the property of the antiparallel spin state (e.g., ...). Figure 11 (The singlet spin state responses are shown in Figures 12 and 22). Typically, the antiparallel spin state response has a lower frequency than the parallel spin state response.

[0220] The examples above differ in the arrangement of circuit elements (including the position of the data qubits relative to the library (and thus the number of intermediate circuit elements required)) and the arrangement of intermediate circuit elements. In each case, charge polarization measurements driven by a high-frequency AC potential applied by a frequency source are detected at a distance using a cascaded process, where quantum information is successively transferred from one circuit element to the next. Charge carriers can be electrons or holes; for examples involving multiple qubits, the qubits can be driven by the same or different frequencies; the qubits can be single-quantum-dot qubits or dual-quantum-dot qubits; the paths of different qubits can be partially shared or separate; one or more frequency sources, libraries, and resonator circuits can be provided for multiple qubits.

[0221] It should be understood that a circuit that implements a series of cyclic tunneling events provides a method for reading out the cascaded radio-frequency charge carriers of a semiconductor spin qubit at arbitrary distances from the qubit. This circuit is driven by a high-frequency sinusoidal excitation that induces cyclic tunneling of charge carriers when the dual-qubit qubit is in a single-state or when the single-qubit qubit has a spin antiparallel to its adjacent auxiliary qubit. This tunneling subsequently induces tunneling events in adjacent capacitively coupled qubits. The cascade terminates with charge carriers tunneling into and from the library, which can be measured using a readout circuit including a resonant circuit. This cascade can be used to transmit quantum information any distance within a quantum dot array.

Claims

1. A circuit for reading the state of a quantum bit, the circuit comprising: A dual quantum dot, which forms a qubit, wherein the qubit has a singlet spin state and a triplet spin state, wherein the dual quantum dot includes a first quantum dot and a second quantum dot, wherein the second quantum dot is tunneled coupled to the first quantum dot; A gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; Cascaded quantum dots, whose capacitive coupling is to the second quantum dot; A charge pool that tunnels to the cascaded quantum dots; Readout circuitry, which is connected to the charge bank; and A frequency source, connected to the gate electrode or the charge bank, and configured to apply an alternating potential to the gate electrode or the charge bank; The cascaded quantum dots are tuned to near charge transitions such that when charge carriers tunnel between the first quantum dot and the second quantum dot, the charge carriers tunnel between the cascaded quantum dots and the charge pool. The frequency source is configured to apply an alternating current potential of a first frequency, thereby inducing cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa only when the quantum bit is in the singlet spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dots to the charge pool and vice versa; and The readout circuit is configured as follows: Detect the first alternating current potential; Measuring one or more properties of the first detected alternating current potential; and When one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the triplet spin state, it is inferred that the qubit is in the triplet spin state; and when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the singlet spin state, it is inferred that the qubit is in the singlet spin state.

2. The circuit according to claim 1, further comprising: One or more intermediate cascaded quantum dots, each intermediate cascaded quantum dot comprising a first intermediate cascaded quantum dot and a second intermediate cascaded quantum dot, wherein: The second intermediate cascaded quantum dot tunnels and couples to the first intermediate cascaded quantum dot; The second quantum dot is capacitively coupled to the first intermediate cascaded quantum dot of one of the one or more intermediate cascaded dual quantum dots; and The cascaded quantum dot is capacitively coupled to a second intermediate cascaded quantum dot, which is one of the one or more intermediate cascaded dual quantum dots. Each intermediate cascaded quantum dot is tuned to near charge transitions such that when charge carriers tunnel between the first and second quantum dots, charge carriers also tunnel between the first and second intermediate cascaded quantum dots within the intermediate cascaded quantum dot; and The frequency source is configured to apply an alternating potential of a first frequency, thereby causing cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa only when the quantum bit is in the singlet spin state, and also causing cyclic tunneling of charge carriers sequentially from the first intermediate cascade quantum dot to the second intermediate cascade quantum dot and vice versa in each of the one or more intermediate cascaded quantum dots, and also causing cyclic tunneling of charge carriers from the cascaded quantum dots to the charge pool and vice versa.

3. The circuit according to claim 1 or 2, further comprising: The second dual quantum dot forms a second quantum bit, which has a singlet spin state and a triplet spin state. The second dual quantum dot includes a second first quantum dot and a second second quantum dot, wherein the second second quantum dot is tunneled coupled to the second first quantum dot. A second gate electrode, configured to control the energy state of the second first quantum dot or the energy state of the second second quantum dot; and The second cascaded quantum dot is capacitively coupled to the second quantum dot and tunnel-coupled to the charge pool; The frequency source is connected to the second gate electrode or the charge bank and is configured to apply an alternating potential to the second gate electrode or the charge bank. The frequency source is further configured to apply an alternating potential of a second frequency, thereby inducing cyclic tunneling of charge carriers from the second first quantum dot to the second second quantum dot and vice versa only when the second quantum bit is in the singlet spin state, and also inducing cyclic tunneling of charge carriers from the second cascaded quantum dot to the charge pool and vice versa; and The readout circuit is further configured as follows: Detecting the second alternating current potential; Measuring one or more properties of the detected second AC potential; and When one or more measured properties of the detected second AC potential substantially match the expected values ​​of the properties of the triplet spin state, it is inferred that the second qubit is in the triplet spin state; and when one or more measured properties of the detected second AC potential substantially match the expected values ​​of the properties of the singlet spin state, it is inferred that the second qubit is in the singlet spin state.

4. The circuit according to claim 1 or 2, further comprising: A third dual quantum dot, forming a third qubit, the third qubit having a singlet spin state and a triplet spin state, wherein the third dual quantum dot comprises a third first quantum dot and a third second quantum dot, wherein the third second quantum dot tunnels coupled to the third first quantum dot; and The third gate electrode is configured to control the energy state of the third first quantum dot or the energy state of the third second quantum dot; The cascaded quantum dots are further capacitively coupled to the third and second quantum dots; The frequency source is connected to the third gate electrode or the charge bank and is configured to apply an alternating potential to the third gate electrode or the charge bank. The frequency source is further configured to apply an alternating potential at a third frequency, thereby inducing cyclic tunneling of charge carriers from the third first quantum dot to the third second quantum dot and vice versa only when the third quantum bit is in the singlet spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dots to the charge pool and vice versa; and The readout circuit is further configured as follows: Detecting the third alternating current potential; Measuring one or more properties of the detected third AC potential; and When one or more measured properties of the detected third AC potential substantially match the expected values ​​of the properties of the triplet spin state, it is inferred that the third qubit is in the triplet spin state; and when one or more measured properties of the detected third AC potential substantially match the expected values ​​of the properties of the singlet spin state, it is inferred that the third qubit is in the singlet spin state.

5. The circuit according to claim 3 or 4, which is dependent on claim 2, wherein, One or more of the intermediate cascaded dual quantum dots are shared by the dual quantum dot and the second dual quantum dot and / or the third dual quantum dot.

6. The circuit according to any one of claims 3-5, wherein, The second frequency and / or the third frequency are different from the first frequency.

7. A circuit for reading the state of a qubit, the circuit comprising: A dual quantum dot, comprising: a first quantum dot having a first spin state and a second spin state, and a second quantum dot having the first spin state and the second spin state, wherein the second quantum dot is tunnel-coupled to the first quantum dot; wherein the first quantum dot forms a data qubit, and the second quantum dot forms an auxiliary qubit; or the first quantum dot forms an auxiliary qubit, and the second quantum dot forms a data qubit; A gate electrode configured to control the energy state of the first quantum dot or the energy state of the second quantum dot; A control circuit connected to the auxiliary qubit, the control circuit being configured to initialize the auxiliary qubit to the first spin state; Cascaded quantum dots, whose capacitive coupling is to the second quantum dot; A charge pool that tunnels to the cascaded quantum dots; Readout circuitry, which is connected to the charge bank; and A frequency source, connected to the gate electrode or the charge bank, and configured to apply an alternating potential to the gate electrode or the charge bank; The cascaded quantum dots are tuned to near charge transitions such that when charge carriers tunnel between the first quantum dot and the second quantum dot, the charge carriers tunnel between the cascaded quantum dots and the charge pool. The frequency source is configured to apply an alternating current potential of a first frequency, thereby inducing cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa only when the data qubit is in the second spin state, and also inducing cyclic tunneling of charge carriers from the cascaded quantum dot to the charge pool and vice versa; and The readout circuit is configured as follows: Detect the first alternating current potential; Measuring one or more properties of the first detected alternating current potential; and When one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the first spin state, it is inferred that the data qubit is in the first spin state; and when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the second spin state, it is inferred that the data qubit is in the second spin state.

8. A method for reading the state of a qubit, wherein, The qubit is a dual-quantum-dot qubit comprising a first tunneling-coupled quantum dot and a second tunneling-coupled quantum dot. The qubit has a singlet spin state and a triplet spin state. A cascaded quantum dot is capacitively coupled to the dual-quantum-dot qubit, tunneling-coupled to a charge pool, and tuned to near-charge transitions. A frequency source is connected to the charge pool or a gate electrode, the gate electrode being configured to control the energy state of the first quantum dot or the second quantum dot. The frequency source is configured to apply an alternating current potential to the charge pool or the gate electrode. The method includes: Applying an alternating potential of a first frequency to the gate electrode or the charge bank using the frequency source; and The first AC potential is detected using a readout circuit connected to the charge bank; The readout circuit is used to measure one or more properties of the detected first AC potential; and When one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the triplet spin state, it is inferred that the qubit is in the triplet spin state; or when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the singlet spin state, it is inferred that the qubit is in the singlet spin state. The dual quantum dot qubit is configured such that when an AC potential of the first frequency is applied, cyclic tunneling of charge carriers from the first quantum dot to the second quantum dot and vice versa occurs only when the qubit is in the singlet spin state, and also cyclic tunneling of charge carriers from the cascaded quantum dot to the charge pool and vice versa.

9. A method for reading out the state of a data qubit, wherein, The data qubit is a quantum dot having a first spin state and a second spin state. The data qubit is tunneled coupled to another quantum dot having the first spin state and the second spin state, the other quantum dot forming an auxiliary qubit. The data qubit and the auxiliary qubit form a dual quantum dot. A cascaded quantum dot is capacitively coupled to the dual quantum dot, tunneled coupled to a charge pool, and tuned to near-charge transitions. A frequency source is connected to the charge pool or a gate electrode, the gate electrode being configured to control the energy state of the quantum dot or the other quantum dot. The frequency source is configured to apply an alternating current potential to the charge pool or the gate electrode. The method includes: Using a control circuit connected to the auxiliary qubit, the auxiliary qubit is initialized to the first spin state; Applying an alternating potential of a first frequency to the gate electrode or the charge bank using the frequency source; and The first AC potential is detected using a readout circuit connected to the charge bank; The readout circuit is used to measure one or more properties of the detected first AC potential; and When one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the first spin state, it is inferred that the data qubit is in the first spin state; or when one or more measured properties of the detected first AC potential substantially match the expected values ​​of the properties of the second spin state, it is inferred that the data qubit is in the second spin state. The dual quantum dots are configured such that when an AC potential of the first frequency is applied, charge carrier cyclic tunneling from the quantum dot to the other quantum dot and vice versa occurs only when the data qubit is in the second spin state, and also causes charge carrier cyclic tunneling from the cascaded quantum dots to the charge pool and vice versa.

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