Qubit Hardware for Electrons on Helium

Abstract

To provide a technique of a realistic qubit and a readout method.SOLUTION: A system includes: a substrate to support a film of liquid helium; and an electron subsystem. In the system, the electron subsystem is confined by: image forces in a direction perpendicular to the surface of the film; a side gate to electrostatically define a boundary of the electron subsystem; a trap gate to electrostatically define an electron trap located outside the boundary of the electron subsystem; and a load gate to selectively open and close access from the electron subsystem to the electron trap. In the system, to open access to the electron trap is to apply a first load gate voltage to the load gate to allow the electrons to access the electron trap; and to close access to the electron trap is to apply a second load gate voltage to the load gate to prevent the electrons from accessing the electron trap.The present invention discloses the system and a method of using the system.SELECTED DRAWING: Figure 5

Description

Technical Field

[0001] This specification generally relates to systems and methods for fabricating qubit hardware and qubit control and readout mechanisms for quantum computing. More particularly, this specification relates to generating qubits by confining electrons present near the surface of liquid helium within an electrostatic trap, and to quantum control and readout of such qubits by probing the quantum state of the trapped electrons with electromagnetic wave signals.

Background Art

[0002] Quantum computing is a technology that uses a quantum system capable of taking a superposition state α|0〉 + β|1〉 of two quantum states |0〉 and |1〉, where parameters α and β vary continuously, different from classical bits that always remain in one of two classical states, either 0 or 1. The operation of a quantum computer can include preparation of qubit states, quantum entanglement of two or more separate qubits, quantum transitions of an entangled qubit system according to a quantum algorithm (code) created for a specific task to be solved, quantum readout of the final state of the entangled qubits, and an error correction mechanism taking into account the essentially probabilistic nature of the quantum system. Quantum computers can outperform classical computers in some cases (such as prime factorization) where problems are impossible to implement on classical computers or would require exponentially large resources. Despite various proposed realizations of qubits and readout methods, reliable implementation of quantum computing presents unresolved technical challenges. For practical quantum computing, qubits need to have no additional degrees of freedom that could affect the coherence of the qubit's quantum state. At the same time, external coupling to individual qubits is necessary for preparation of the initial state of the qubit and for readout of its final state. Qubits need to be able to maintain their quantum coherence for a sufficiently long time for preparation of the initial state, execution of the quantum algorithm, and readout of the final state. The ease and reliability of the readout method remain a major bottleneck in current quantum computing efforts. For the reasons above, the development of practical qubits and readout methods is of extremely important technically. Summary of the Invention

[0003] Aspects and implementations of the present disclosure will be better understood from the following detailed description and the accompanying drawings showing various aspects and implementations of the present disclosure. However, these should not be construed as limiting the present disclosure to specific aspects or implementations, but are shown for purposes of illustration and understanding only.

[0004] Aspects of the present disclosure relate to implementations of qubits based on surface state electrons, associated readout and control systems, and methods of quantum computing. In some cases, surface state electrons can be implemented using electrons that exist near the surface of liquid helium and are held near its surface by the electrostatic image force on helium. Electrostatic gates can be used to confine electrons in a bounded region and, further, to implement an electron trap outside that bounded region for trapping a small number of electrons therein. The number of electrons thus trapped can be controlled by electrostatic gating and, in some implementations, can be one. Such individual electrons can be used as qubits. The quantum states |0〉 and |1〉 of the qubit can be realized, for example, as the ground state and the excited state of the electron in the trap. In some implementations, the quantum state of the qubit may be the vertical Rydberg motion state of an electron floating on the surface of liquid helium. In other implementations, the quantum state of the qubit may be due to the quantized lateral motion of an electron inside a designed electrostatic trap. In yet other implementations, a hybrid double qubit can be formed by coupling the out-of-plane and in-plane motions of the electron in the trap. In these implementations, two qubits with a large frequency separation are formed from each trapped electron.

[0005] Aspects of the present disclosure also relate to various components (and assemblies thereof) of a system for implementing quantum computing, such as a single electron qubit, an electrostatic trap, associated microwave and radio frequency (RF) control, and a readout electronics component by post-processing using a classical digital computer. Depending on the implementation, the RF readout of a system including one or more qubits may be performed by preparing an input RF signal having a frequency tuned to the energy difference between two quantum states of the qubit, transmitting the input signal to a microwave resonator circuit including a system in which the qubit is included as a capacitive element, and detecting the response of the microwave resonator circuit. The components described herein can be used to perform single qubit and two qubit gate operations for universal quantum computing. The systems and components described herein can be used for noisy intermediate scale quantum (NISQ) computing when scaled up to multiple qubits (e.g., about 100 qubits). The systems and components described herein can be used for further development in noise reduction, qubit entanglement, and improved qubit coherence for the realization of a fully fault-tolerant quantum computing platform.

Brief Description of the Drawings

[0006]

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[0007] FIG. 1 schematically shows an exemplary system that can serve as an electron reservoir for a qubit and uses liquid helium and electrostatic gates to facilitate electron confinement, according to one implementation. The liquid helium in system 100 can be supported by substrate 102. In some implementations, substrate 102 may be a dielectric, such as silicon or sapphire. Substrate 102 can support a film of liquid helium 104. The film of liquid helium can be laterally restricted by banks 106 so as not to leak from substrate 102. In some implementations, banks 106 may be made of a dielectric material that may be the same as or different from the material of substrate 102. For example, the banks may be SiO xOr it may be made of SiO2. The bank can be deposited by thermal evaporation or sputtering. The thickness (height) of the bank 106 can be used to determine the level of the liquid film. Depending on the implementation form, the bank can have a thickness of 0.2 μm to 1 μm, but in other implementation forms, the thickness may be below or above this range. Depending on the implementation form, the bank 106 can be arranged to form microchannels of liquid helium as shown in FIG. 1. The microchannels (or any other configuration of the helium film 104) can be filled with helium by capillary action using a source of helium (not shown explicitly in FIG. 1). The source of helium may be a low-level bulk storage tank of helium.

[0008] The helium film 104 can serve as a substrate for supporting electrons 108 that float above the surface of helium. The electrons 108 can be attracted to the surface of helium by long-range image forces generated by the interaction between the electronic charge and the dielectric polarization of helium. On the other hand, the electrons 108 are repelled by helium atoms at short distances. As a result, the electrons 108 can be confined near the surface of liquid helium at a distance of about 50 Å to 100 Å from the surface of the liquid helium and can have a binding energy of about 1 meV. The spectrum of electrons due to image force binding can be of the Rydberg type. A lower gate (electrode) 110 can be disposed on the substrate 102. The lower gate 110 may extend over the entire width and length of the system depending on the implementation form. In other implementation forms, the lower gate may be under only a part of the system. The lower gate 110 can be made of a conductive material so that the entire lower gate 110 obtains the same potential when a direct current (DC) voltage signal is applied to the lower gate 110. Depending on the implementation form, the electrons 108 can first be deposited on the surface of helium by thermionic emission from a filament (e.g., a tungsten filament) disposed in the vicinity (e.g., above the helium film). In other implementation forms, electrons can be generated by field emission or by photon emission. The lower gate 110 can also be used to control the density of electrons. By varying the potential of the lower gate 110, the optimal density of electrons 108 on the surface of helium can be realized. For example, by lowering the potential of the lower gate 110, some of the electrons 108 can be pushed away. Conversely, increasing the potential of the lower gate 110 may enable the system 100 to hold more of the electrons 108. When the electrons 108 are in a high-density state, the electrons 108 can be in the state of a Wigner solid having a regular spatial arrangement as schematically shown in FIG. 1. At low density, the electrons 108 can form an electron liquid state.

[0009] Further control of electrons 108 can be achieved by one or more upper gates (electrodes) 112 that can be fabricated on the insulating bank 106. The upper gates 112 can regulate the movement of electrons along the surface of liquid helium 104 by lateral electrostatic confinement. For example, by applying a lower (e.g., negative) voltage to a pair of upper gates 112, it may be possible to squeeze the electron channel laterally. Conversely, by increasing the voltage applied to the upper gates 112, the lateral spread of the electron channel can be increased. Additional gates (not shown in FIG. 1) may be used to control the lateral spread and movement of electrons 108 (e.g., along the channel). The upper gates 112 (and lower gates 110 and / or other gates) can be formed from various conductive materials. For example, in one implementation, the gate may be formed from 5 nm of Ti and 45 nm of Au, but in other implementations, other designs of the gate are possible. As illustrated in FIG. 1, the gate can be thermally evaporated or sputtered onto the underlying substrate (e.g., silicon or sapphire) bank 106.

[0010] The system 100 shown in FIG. 1 can be designed and manufactured in various implementations. Some of the components shown in FIG. 1 may be omitted. Depending on the implementation, the system 100 may always be implemented within a cryostat (not shown) to maintain a low temperature. The system 100 within the cryostat may be maintained at a temperature lower than 4.2 K, which is the boiling point of helium. Depending on the implementation, the system 100 4 may be maintained at a temperature lower than 2.17 K, which is the superfluid transition temperature of He. Depending on the implementation, the system may be maintained at an extremely low temperature, e.g., 3 lower than 0.0025 K, which is the superfluid transition temperature of He. Depending on the implementation, a cryogen-free 3 He- 4A He dilution refrigerator may be used. At such temperatures, the natural thermal transitions between different Rydberg electronic states of vertical confinement can be almost frozen out. The surface tension of the liquid helium film 104 serves to stabilize and can maintain the electrons 108 at a fixed distance from various additional readout and control electrodes (see below) that can be fabricated within the system. The stability of the surface of the helium film 104 can be further controlled, for example, 4 by introducing a controlled amount of 3 He isotope that has a relatively high viscosity compared to the

[0011] Figure 2 schematically shows an exemplary system 200 that can implement an electron trap according to one implementation form and uses liquid helium and an electrostatic gate to facilitate electron confinement. System 200 may use part of the concept shown in Figure 1. Some of the components of system 200 may correspond to the components of system 100. Specifically, components indicated by numbers with different leading digits (e.g., 1XY and 2XY) may be the same or similar in the two systems. The liquid helium in system 200 may be supported by a substrate 202. A lower gate 210 can be attached on the substrate 202. Liquid helium (not shown) can be disposed on the substrate 202 and / or the lower gate 210 to form a film similar to that in Figure 1. The liquid helium film can be laterally supported by a set of (e.g., dielectric) banks similar to the bank 106 in Figure 1. Depending on the implementation form, the banks can divide the liquid helium into separate reservoirs. The reservoirs may extend over most of the lateral dimension of system 200 depending on the implementation form. In other implementation forms, the reservoirs may extend only over a part of system 200. Depending on the implementation form, the reservoirs may be divided into several parallel microchannels. The liquid helium can support an electron subsystem of electrons confined in the vertical direction (a direction perpendicular to the surface of helium) by an electrostatic image force as described above with respect to Figure 1. A conductive guard electrode 212 may be attached above the insulating bank. Depending on the implementation form, the guard electrode 212 may reproduce the shape of the underlying insulating bank. Depending on the implementation form, the geometry of the guard electrode 212 may be different from the geometry of the insulating bank. The guard electrode 212 may be formed by an upper gate. Depending on the implementation form, the guard electrode 212 may be at an equipotential. In other implementation forms, the guard electrode 112 may consist of a plurality of separated elements so that different potentials (voltages) can be applied separately to its various parts.

[0012] In a particular implementation form schematically shown in FIG. 2 (left figure), the system 200 has a left storage tank 214 and a right storage tank 216, which are two relatively large areas, each including 20 to 25 microchannel structures. For example, the microchannel structure may have a relatively long length (e.g., about 700 μm in one embodiment). The left storage tank 214 and the right storage tank 216 can define a plurality of electronic microchannels as described above. The storage tanks 214 and 216 can ultimately function as an electron reservoir for loading electrons into the electron trap. The system 200 may further include a plurality of side gates such as a side gate 218 and a side gate 220. The side gates 218 and 220 may be electrically separated from the guard electrodes 212 and each other. In some implementation forms, different potentials may be applied to the side gates separately. As shown in the exploded view of FIG. 2 (central figure), the side gates can define a central microchannel 222. The central microchannel may have a short length compared to the dimensions of the storage tanks 214 and 216. In some implementation forms, the length of the central microchannel 222 can be 100 μm to 200 μm. The density of electrons in the central microchannel 216 can be controlled by capacitive coupling due to the voltage applied to the lower gate 224, while the effective width of the electrons occupied by the electrons in the central microchannel 222 can be further controlled by the voltage applied to the side gates 218 and 220. In order to characterize the characteristics of the obtained electron subsystem, electrical conduction measurements (such as low audible frequency conductivity and compressibility measurements, current-voltage characteristics, measurements for obtaining electron density, etc.) are performed in combination with finite element simulations to obtain the electrochemical potential φ e , the surface electron density n sand / or other quantities may be determined. In some implementations, the conduction measurement may be performed by applying a voltage bias between the left and right portions of the reservoir electrode 210 such that an electron current is generated only in the central microchannel 222. In other implementations, depending on the particular geometry of the drive electrodes, a voltage bias may be applied to the microchannels of the left reservoir 214 (or right reservoir 216) with a current flowing through some or all of the microchannels. The drive electrodes may include the guard electrode 212 or a separate additional electrode (not shown explicitly in FIG. 2).

[0013] Electrons floating above the surface of helium within the central microchannel 222 can function as a source of electrons for the electron trap 226 shown in FIG. 2 (enlarged view, right figure). An electric field generated by the side gates 218 (and side gate 220) (with a voltage bias applied) can create one or more boundaries for the electrons 108 within the central microchannel 222. The boundary can demarcate the limit of the lateral movement of the electrons 108 floating above the surface of helium within the central microchannel 222. One or more additional control gates 228 may be disposed outside this boundary. A positive voltage applied to the control gate 228 can energetically favor the movement of electrons from the central microchannel 222 to the vicinity of the control gate 228. Since the control gate 228 can have an opposite (e.g., positive) voltage compared to the potential of the side gate 218 (e.g., negative), in some implementations, it may be advantageous to notch the side gate 218 to reduce the counteracting effect of the negative side gate potential. In some implementations, a charge sensor may be disposed inside the electron trap 226. In some implementations, the charge sensor may be a quantum charge sensor capable of detecting the presence of individual electrons. For example, the charge sensor may be a radio frequency single electron transistor sensor (RF-SET sensor) 230.

[0014] Additional side microchannels extending from the central microchannel 222 to the electron trap 226 can be formed by the load gate 232. The load gate 232 can selectively open and close the entry of electrons floating above the surface of liquid helium into the electron trap 226. For example, when a positive potential is applied to the load gate 232, the side microchannels can be opened to electrons from the central microchannel 222 due to the electrostatic attraction of electrons to the load gate, allowing the electrons to fill the electron trap 226. Subsequently, when a negative voltage is applied to the load gate, this negative voltage can cut off the side microchannels by building a potential barrier between the central microchannel 222 and the electron trap 226, trapping the electrons inside the electron trap 226. Depending on the implementation, the control gate 228, the RF-SET sensor 230, and the load gate 232 may be disposed below the surface of helium. In an embodiment, as shown in FIG. 2, the control gate 228, the RF-SET sensor 230, and the load gate 232 may be disposed in the plane of the lower gate 224, while being electrically separated from the lower gate 224 and each other by the insulating insert 234. In other implementations, at least a portion of the control gate 228, the RF-SET sensor 230, the load gate 232, the lower gate 224, and the reservoir electrode 210 may be disposed in different planes.

[0015] After the connection between the central microchannel 222 and the electron trap 226 is disconnected, the number of electrons trapped inside the electron trap 226 can be adjusted as needed by controlling the voltage V g applied to the control gate 228. For example, the gate voltage V gWhen it is decreased, the potential energy of the electrons in the electron trap 226 increases (since the electronic charge is negative). As a result, some of the electrons are pushed out of the electron trap 226. This process can be continued until the number of electrons in the electron trap 226 reaches a predetermined value. In some embodiments related to quantum computing, the predetermined value may be equal to 1, which is the situation where a single-electron quantum qubit is realized. FIG. 3 shows an exemplary electron loading method for adjusting the number of electrons in the electron trap 226. For a specific implementation of the system 200 and the electron trap 226, the dependence 300 of the charge Q inside the electron trap 226 on the applied control gate 228 voltage V g is shown (in units of electronic charge). The dependence 300 shown in FIG. 3 is calculated using finite element modeling. The dependence 300 shows a characteristic Coulomb blockade electron staircase with a sharp transition between the states having n electrons and n + 1 electrons that occurs at a specific value of the voltage V g . By adjusting the voltage V g , the number of electrons in the electron trap 226 can be controlled so that a predetermined number of electrons (e.g., 1, 2, 3, etc.) remain in the electron trap 226, as indicated by the Coulomb blockade staircase.

[0016] Depending on the implementation form, it is also possible to perform the process of loading a single electron into the trap region in different ways by cutting the loading microchannel following the adjustment of the number of electrons inside the trap 226. For example, the loading process may be performed as follows. First, the electrostatic potential of the electrons in the electron trap 226 and the loading microchannel can be tuned to be positive relative to the electrochemical potential of the electrons in the storage tanks 214 and 216 and in the central microchannel 222. Under such conditions, electrons can move along the loading microchannel into the electron trap 226. The number of electrons loaded into the electron trap 226 can be estimated from the finite element modeling as described above. Then, the control gate voltage V g can be swept to a negative (or lower positive) value. As a result, as shown in FIG. 3, the electrostatic potential inside the electron trap 226 will decrease such that electrons decrease one by one from the electron trap 226. According to the finite element modeling calculation, the voltage difference ΔV g required to unload one electron from the electron trap 226 can vary from 1 mV to several tens of mV depending on the geometric size and shape of the electron trap 226 and its electrostatic environment. In addition to the mathematical modeling, as will be detailed below, the RF-SET sensor 230 can monitor the electron unloading process. After the number of electrons in the electron trap 226 has decreased to one (or other predetermined value), the electrostatic potential of the loading microchannel can be set to a negative value by lowering the voltage of the loading gate 232. Depending on the implementation form, in order to build an electric potential barrier high enough to prevent electrons from escaping from the formed qubit and returning to the central microchannel 222, the electric potential inside the loading microchannel may be made sufficiently more negative compared to the electric potential inside the electron trap 226.

[0017] The RF-SET sensor 230 (or any other quantum charge sensor) may be a highly sensitive high-frequency single-electron transistor microfabricated on an insulating substrate (e.g., substrate 202) and submerged beneath the surface of liquid helium. Depending on the implementation form, a high-speed quantum charge sensor may be used as an RF-SET for measuring the vertical motion quantum state of electrons trapped above it (e.g., inside the electron trap 226). In the full quantum computing system disclosed herein, the RF-SET sensor 230 can facilitate the readout of qubit states. To achieve the high operating speed of the RF-SET sensor 230, in some implementation forms, a conventional SET may be incorporated as a capacitive component of a high-frequency microwave resonance circuit. The latest RF-SET-based charge sensors have a demonstrated sensitivity of up to 1×10 6 μC / √Hz and a measurement speed exceeding 100 MHz. Such high frequencies are fast enough to read out the Bloch sphere oscillations of the qubits and high enough to ensure that the low-frequency 1 / f noise from background charges is negligible for the readout performance of the quantum charge sensor. Depending on the implementation form, the charge sensor may be different from the RF-SET-based sensor. For example, the charge sensor may be an offset charge-sensitive superconducting qubit or a similar device capable of detecting individual electron charges.

[0018] Electrons trapped inside a finite region (e.g., electron trap 226) can have a discrete spectrum of energy. In one implementation of a qubit, the ground state of the electron can represent the qubit state |0〉, while one of the excited states, e.g., the first excited state, can represent the qubit state |1〉. In various implementations, the first excited state can correspond to various quantum motions of the electron. In such a trap, the first excited state |1〉 of the qubit can be the first excited Rydberg state of the vertical (i.e., perpendicular to the surface of helium) motion of the trapped electron. This can represent an exemplary implementation of a qubit. In such an implementation, the frequency difference between the first excited state |1〉 and the ground state |0〉 of the qubit can be about 120 GHz (which corresponds to an energy difference of about 0.5 meV). Conversely, in an electron trap where the lateral dimension is larger than the Bohr radius of the Rydberg state, the spacing between the energy levels corresponding to the lateral motion can be smaller than the spacing between the energy levels corresponding to the vertical motion of the trapped electron. In such a trap, the first excited state |1〉 of the qubit can be the first excitation of the lateral motion (e.g., the "particle in a box" quantum motion) of the trapped electron. This can represent another exemplary implementation of a qubit. Depending on the degree of confinement of the electrons in the electron trap 226, which can be controlled by, for example, the geometry and potential of the control gate 228, the energy difference between the states of the qubit can vary significantly from one implementation to another. For example, in one non-limiting exemplary implementation, the frequency difference between the first lateral excited state |1〉 and the ground state |0〉 of the qubit can be about 10 GHz. For example, by causing Rabi oscillations with amplitudes α and β, a superposition α|0〉 + β|1〉 of the two states of the qubit with quantum amplitudes α and β can be prepared and controlled using a high-frequency or microwave signal (as detailed below).

[0019] Depending on the implementation form, a two - qubit system using single electrons can be implemented by using both the vertical and lateral motions of the trapped electrons. In such an implementation form, the trapped electrons can have at least four eigenstates such as |↓0〉, |↓1〉, |↑0〉, and |↑1〉, where |↓〉 is the ground state related to the vertical Rydberg motion of the trapped electron, |↑〉 is the excited state, |0〉 is the ground state related to the lateral motion of the trapped electron, and |1〉 is the excited state. Thus, the state |↓0〉 is the ground state of the trapped electron with energy E0. The state |↓1〉 can have an energy E0 + E1 that is higher by only the first energy difference E1 corresponding to the excited state related to the lateral motion. The state |↑0〉 can have an energy E0+E2 that is higher by only the second energy difference E2 corresponding to the excited state related to the vertical motion. Finally, the state |↑1〉 can have an energy E0 + E1+E2 corresponding to the excited state related to both motions. The state of such a two - qubit system can be a superposition of four states A|↓0〉+B|↓1〉+C|↑0〉+D|↑1〉 with quantum amplitudes A, B, C, and D, which can be prepared and controlled using a plurality of high - frequency or microwave signals such as a first signal with frequency E1 / h and a second signal with frequency E2 / h.

[0020] Note that the quantum state of such an implementation form of the qubit can have a quantum coherence time long enough for quantum computing applications, and that the in - situ placement of electrons on the surface of liquid helium is achievable. For example, even in an implementation form where the energy difference between the qubit states is as low as 10 GHz corresponding to about 0.5 K on the temperature scale, the temperature decoherence of the qubit can be negligible at about 10 mK, which is a typical temperature of the latest dilution refrigerators.

[0021] It should be noted that the main problem when using the quantized vertical or transverse motion of electrons trapped on helium as qubits is how to implement in an integrated system that will enable single or multi-qubit gate operations, both a sufficiently fast control of qubit dynamics and the integration of readout electronics to the qubits. In aspects of the present disclosure, such implementations for a complete and integrated system that can utilize quantized motion for NISQ or fully fault-tolerant quantum computing will be described.

[0022] As described above, individual qubits (electrons) can be placed above an RF-SET sensor 230 disposed near an electron trap 226 defined by a control gate 228. In other implementations, instead of the RF-SET sensor 230, a similar quantum charge sensor (e.g., an offset charge sensitive superconducting qubit or a similar device) may be used for qubit readout. Electrons can be loaded from the central microchannel 222. As shown in FIG. 2 (central figure), a single microchannel can correspond to multiple electron traps 226, with each electron trap 226 functioning as a separate qubit. Depending on the implementation, individual qubits can be controlled separately. For example, different control gate voltages can be applied to the control gates 228 of different electron traps 226. As a result, the electron spectra in different traps may not be the same. For example, adjacent traps may be tuned to have different frequencies corresponding to the energies that split the qubit into two states, such as 12.0 GHz, 12.1 GHz, 12.2 GHz. Thus, the response of the target qubit can be resonantly probed by a specific qubit. That is, the first qubit can be resonantly probed at a drive frequency of 12.0 GHz, a signal having a frequency of 12.2 GHz can resonantly probe the state of the second qubit, and so on. Correspondingly, the quantum states of various qubits can be probed by a single variable RF source. In other implementations, the control gate 228 is at the same voltage V greceives, although the geometry and layout of the control gate and / or side gate 218 may vary from trap to trap. In some implementations, both the voltage of the control gate 228 and the geometry / layout of different traps may be different. In some implementations, the layout of the trap and the voltage of the control gate 228 may be the same, but different DC voltages may be applied to the RF-SET sensors 230 disposed near (e.g., below) the corresponding electron trap 226. Using such different RF-SET voltages for each trap, the resonance frequency of each qubit can be individually Stark-tuned. In some implementations, the individual qubits can be selectively tuned to resonate with each other in order to promote the quantum entanglement of various qubits. In this way, two or more qubits can be entangled. In some implementations, the applied control gate voltage and / or RF-SET voltage may vary with time. For example, such voltages can be adiabatically varied to tune the energy of the electron state in the trap without causing a quantum transition between the quantum states of the trap. In some implementations, the entanglement between different qubits (e.g., between the nearest neighboring qubit and the next nearest neighboring qubit) can occur due to the interaction between their respective charge degrees of freedom. Specifically, such an interaction can occur due to the electric dipole-dipole coupling. The parameters of such a coupling (e.g., strength and distance) can be controlled by electrostatic gating and / or the Stark shift of the quantum energy levels as disclosed above. In some implementations, long-range entanglement between distant qubits can be realized by coupling the electrons in the electron trap 226 to the underlying resonator bus (e.g., by capacitive coupling). In some implementations, collective charge oscillations (e.g., plasma oscillations) of a plurality of qubits may be used to establish long-range coupling and entanglement of distant qubits.

[0023] The components disclosed with reference to FIGS. 2 and 3 can be implemented on a single chip. Depending on the implementation form, various components may be implemented on separate chips. For example, a first plurality of qubits may be implemented on a first chip, and a second plurality of qubits may be implemented on a second chip. Depending on the implementation form, the first and / or second plurality of qubits may have a linear spatial arrangement. Depending on the implementation form, the first and / or second plurality of qubits may have a planar spatial arrangement.

[0024] FIG. 4 is a circuit block diagram showing an exemplary embodiment capable of implementing microwave and radio frequency single electron transistor based readout and control of qubits, and components of system 400. System 400 can include a cryostat and an RF circuit that sends one or more RF signals to the cryostat. System 400 includes components for preparing RF signals and microwave signals (e.g., one or more signal generators, mixers, amplifiers, multipliers, etc.), and a signal guide for sending signals prepared in a container (e.g., a cryostat) that includes a microwave resonator circuit coupled (e.g., capacitively) to a system of electronic qubits, and components for detecting the response of the microwave circuit to the prepared signals (e.g., an RF-SET sensor, a tank circuit, a directional coupler, an analog-to-digital converter, etc.). These elements are exemplary components that can be used to prepare and then read out the state of an electronic qubit. In some embodiments, the preparation of the qubit may begin with a signal generator 402 that generates a continuous wave radio frequency signal (e.g., a sine signal). Signal generator 402 may be a variable frequency signal generator that generates a time-varying signal tuned to the resonance frequency of the qubit. Signal generator 402 may be an analog synthesizer, a crystal oscillator, a fast enough digital signal source, etc. In some embodiments, the signal generated by signal generator 402 may be phase shifted by a phase shifter 404 to correct for uncontrolled time delays and spurious phase shifts of the transmitted signal during propagation. These control signals may be appropriately shaped to produce one and / or two qubit states controlled by the signal generated by signal generator 402. In some embodiments, the control signals may be shaped into a pulse waveform. These pulse signals can have an accurately controlled duration, phase, and amplitude. In some embodiments, this can be achieved by single sideband modulation and mixing. For example, the signal can be supplied to the local oscillator input of a microwave mixer 406. Mixer 406 may be an IQ mixer in some embodiments, and a 3-port mixer may be used in other embodiments.The mixer 406 may have an LO input coupled to the phase shifter 404 and / or the signal generator 402. The mixer 406 may further have an in-phase input and a quadrature input that receive signals at a frequency lower than the qubit resonance frequency (e.g., 10 MHz to 1 GHz), such as a signal (e.g., a pulse), so that when the signal is mixed with the signal generated by the signal generator 402, a signal having a frequency at the qubit resonance frequency is obtained. Depending on the implementation, the in-phase input of the mixer 406 can receive a first signal from the waveform generator 408, and the quadrature input of the mixer 406 can receive a second signal from the waveform generator 408. Depending on the implementation, the waveform generator 408 may be an arbitrary waveform generator (AWG) or a field programmable gate array (FPGA) board signal source. The mixer 406 may mix the local oscillator input with a signal (e.g., a phase-stable pulse) generated by the waveform generator (AWG) 408. The mixer output can be one or more high-frequency signals (e.g., pulses) with a predetermined duration, phase, and amplitude, controlled by the generator 408. Depending on the implementation, the signal generated by the signal generator 402 may be a 5 GHz to 20 GHz signal corresponding to the difference in the transverse kinetic energy levels of the qubits whose motion is intended to be controlled and read out. Depending on the implementation, the frequency can be further tuned by the mixer 406, for example, using appropriate pulses from the AWG 408, to the frequency of a specific (e.g., Stark-tuned) qubit (or qubits). To compensate for spurious losses during signal transmission, the mixed signal may be amplified by the amplifier 410 before being fed into the cryostat 420. For example, the amplifier 410 may convert the amplifier input RF signal to a signal at the same frequency but with a larger amplitude, and then output the amplified RF signal to the cryostat 420. Depending on the implementation, the prepared and amplified RF output signal may be sent directly through the signal guide 412 to the cryostat 420, which includes the qubit system (e.g., system 200 depending on the implementation). The signal guide 412 may be a tapered waveguide with a filter or a coaxial cable such as a coaxial semi-rigid cable with a filter and attenuation.In some implementations where both the lateral and vertical motions of trapped electrons are used to implement a two - qubit system, both waveguides and coaxial cables may be used to simultaneously feed signals into the cryostat 420. Depending on the implementation, the qubit resonance frequency may be significantly higher than the frequency of the signal output by the mixer 406 (and amplifier 410). For example, this can be the case when the qubit uses the lateral Rydberg state of the vertical motion of the trapped electron. In such an implementation, the signal output by the mixer 406 (and amplifier 410) may be processed by a frequency multiplier 416 to up - convert the frequency to a target frequency (the target frequency corresponds to the energy difference between the qubit's eigenstates). Depending on the implementation, the up - converted frequency can be at least 10 times the frequency of the signal output by the mixer 406 and / or amplifier 410. For example, as shown as an example but not limited in FIG. 4, a 12× multiplier can up - convert an initial frequency of 10 GHz to a 120 GHz signal. The frequency multiplier 416 may be based on a standard frequency extender module in some implementations. In other implementations, the frequency multiplier may operate using mixer - based up - conversion. The resulting up - converted high - frequency signal (e.g., a pulse) can then be transmitted to the cryostat 420 via the signal guide 418. The signal guide may be a tapered waveguide. The signal guide 418 may include additional filters to filter out spurious signals that may have been generated during up - conversion or emitted from regions of the system that have a higher temperature than the section of the cryostat that can be maintained at 10 mK.

[0025] Depending on the implementation form, only one of the signal guides 412 and 418 may be used. For example, when the vertical movement of the trapped electrons is used as a qubit, only the signal guide 418 may be used, and there is no signal transmitted through the signal guide 412. Depending on the implementation form, both a high-frequency signal (e.g., a 120 GHz signal as shown in the figure) and a low-frequency signal (e.g., a 10 GHz signal as shown in the figure) may be simultaneously transmitted through the signal guides 418 and 412, respectively. For example, this can be done when the qubit system includes different types of qubits, one using the vertical movement of the trapped electrons and the other using the lateral movement of the trapped electrons, and it is necessary to simultaneously read out (or prepare) both types of qubits.

[0026] A signal (whether upconverted or not) sent to a cryostat 420 that can include a qubit system can be used to probe the quantum state of one or more qubits. The quantum state of one or more qubits can represent the result of a previous execution of a quantum code by the qubit system. At the end of the code, it may be necessary to read out the quantum state of the qubit system for subsequent processing on a conventional (classical) computer. The state of a multi-qubit system may be a entangled combination of the quantum states of individual qubits. To determine the properties of such an entangled combination, one or more pulses of microwave radiation (prepared as disclosed above) can be applied to the qubit system, and the state of the qubit system at the end of the quantum code execution can be determined from the qubit's response to the microwave radiation. Depending on the implementation, such a response may include Rabi oscillations, i.e., time-dependent transitions of the quantum amplitude that show a superposition of the qubit's quantum states |1〉 and |0〉. Such Rabi oscillations can, depending on the implementation, be measured by the attenuation and frequency shift of a microwave resonance circuit that includes an RF-SET sensor 430 (e.g., the RF-SET sensor 230 of system 200) as a probe of the electron trap 226 as disclosed above. Depending on the implementation, the RF-SET sensor 430 may have two tunnel junctions connected via a central island, as schematically shown by the components within the dashed rectangle SET of FIG. 4. The central island may be made of metal or semiconductor. Depending on the implementation, the central island may be made of a superconducting material. Depending on the implementation, the central island may be a quantum dot. The central island of the RF-SET sensor 430 can be capacitively coupled to a gate, and a gate voltage 431 can be applied therein. For example, the gate voltage 431 may be used to tune the state of the RF-SET sensor 430 such that a single conduction electron is present in the central island. As shown in FIG. 4, a bias voltage 433 may further be applied to the RF-SET sensor 430.

[0027] The response detected by the RF-SET430 can pass through a sufficiently fast analog-to-digital converter (ADC) 432, where the response can be sampled and digitized. Depending on the implementation, the ADC 432 can have a speed of about 0.5 GS / s to 6.4 GS / s or higher. By synchronizing the control and measurement methods, the operation of the qubit system can be improved. For example, the synchronization may be facilitated by a master clock 434. Further, the signal from the RF-SET430 can be monitored for reflection or transmission at the resonant frequency of the resonant circuit 436 using a two-port vector network analyzer (VNA) 441. In one embodiment, the resonant circuit is an LC tank circuit in which an inductor is serially coupled between the RF-SET sensor 430 and a capacitor, and a capacitor is parallely coupled between the RF-SET sensor 430 and ground (or ground potential). The measurement circuit may include additional elements such as a directional coupler 438 for directing the readout signal from the generator 440. Depending on the implementation, this coupler may be replaced with a three-port isolator or circulator. The signal generator 440 can generate RF signals within a wide frequency range (10 MHz to 100 MHz) for interrogation of the tank circuit 436 including the RF-SET, depending on the specific implementation. The master clock 434 can be coupled to both the ADC 432 and the waveform generator 408 and the RF signal source 440 for synchronization of qubit preparation and readout. Depending on the implementation, the master clock 434 may relate the pulses generated by the signal generator 402 and the mixer 406 to the output received by the ADC 432.

[0028] Referring to the implementation form of qubits by the vertical Rydberg state of trapped electrons, depending on the implementation form, the characteristic time scale of the Rabi oscillation of such qubits can be in the range of about 100 MHz to 1 GHz. Considering the coherence time known in the art, this can enable more than 100 quantum gate operations by these qubits. Thereby, the readout mechanism disclosed herein becomes a feasible component of a comprehensive quantum computing system.

[0029] In an implementation form where the qubit is realized by the quantized lateral motion of electrons within the electron trap 226, the frequency difference between the ground state |0〉 and the first excited state |1〉 of such motion (which is the resonance frequency of the qubit) can be designed to be on the order of 1 GHz to 10 GHz (by the geometry of the trap 226 and its control gate 228). Depending on the implementation form, by using RF-SET technology together with a microwave circuit similar to the circuit developed for circuit quantum electrodynamics measurement of superconducting circuit-based qubits (in addition to the readout mechanism disclosed above), it is also possible to realize the readout of such lateral motion states of the qubit. The novelty of the concept disclosed herein regarding the incorporation of such circuit-based implementation forms lies in the use of a specific reservoir and trap design that ensures the formation of a clear qubit state and the integration of the microwave control and RF-SET readout methods of these features.

[0030] Although the above disclosure with reference to FIG. 4 described the qubit readout technology, the same technology can also be used for qubit control. More specifically, by causing Rabi oscillation in the qubit when applying a pulsed microwave signal to the qubit by the technology described in relation to FIG. 4, the qubit, which is initially in the ground state |0〉, can be changed to the desired superposition state α|0〉 + β|1〉 (required by the quantum computing code implemented in the qubit system).

[0031] FIG. 5 schematically shows an exemplary implementation 500 of an electron trap (e.g., electron trap 226) for creating a qubit using the lateral motion of trapped electrons. In one non-limiting exemplary implementation, the electron trap 500 may have an asymmetric shape. For example, the trap may be 4 μm in length and 1 μm in width. The asymmetry of the trap can resolve the degeneracy of the excited states corresponding to the lateral motion of the electrons, and thus can serve to suppress the decoherence of state |1〉 due to virtual transitions to / from another excited state by the proximity energy. FIG. 6 exemplifies the energy difference E n -E m between the energy levels of the qubit as a function of the voltage applied to the control gate 228. The energy difference shown in FIG. 6 was calculated by numerically solving the Schrödinger equation for the eigenstates and eigenenergies of the motion of the trapped electrons. As shown by the data 600, by varying the potential of the control gate 228, the qubit transition frequency for the transition |0〉→|1〉 from the ground state to the first excited state can be tuned over a wide range within approximately 4 GHz to 8 GHz.

[0032] The qubit implementation shown in FIG. 6 exhibits anharmonicity. That is, the energy (or equivalently the transition frequency) difference E1 - E0 between the first excited state and the ground state is different from the difference E2 - E1 between the second excited state and the first excited state. In the specific exemplary implementation shown in FIG. 6, the range of such anharmonicity is on the order of 0.1 GHz to 0.4 GHz. Depending on the implementation, such anharmonicity may be advantageous. For example, when the frequency of the readout microwave signal is tuned near E1 - E0, the Rabi oscillations can be limited to transitions between states |0〉 and |1〉. Thus, the same readout microwave signal is less likely to cause transitions between states |1〉→|2〉. This can prevent spurious mixing of higher excited states |2〉, |3〉... that would cause qubit decoherence. Depending on the implementation, the degree of anharmonicity may be controlled by the geometry of the electron trap so as to reliably prevent qubit excitation to higher excited states.

[0033] During qubit operation, as disclosed above, when electrons are injected into the microchannel and the electron trap, the initialization of the qubit to the motional ground state |0〉 inevitably occurs. This can happen because the typical operating temperature of the system (about 10 mK) can be significantly lower than the qubit transition energy E1 - E0. During subsequent qubit control operations (e.g., gate operations), an excitation of the qubit to the state |1〉 can be achieved using a pulsed microwave field tuned to the qubit transition frequency as disclosed above with respect to FIG. 4.

[0034] FIG. 7 is a flow diagram illustrating an exemplary implementation of a method 700 for forming an electron trap and injecting electrons from an electron subsystem that floats on the surface of a helium film into the electron trap, in one exemplary implementation. Depending on the implementation, method 700 can be performed using the systems and components disclosed above in connection with FIGS. 1-6. Method 700 can begin by providing a film of liquid helium that can support an electron subsystem of electrons that float near the surface of the film (710). For example, method 700 can include providing a substrate with microchannels filled with liquid (e.g., superfluid) helium using capillary action of helium. Providing the film can include injecting electrons from an electron source into the electron subsystem, e.g., by thermionic emission from the electron source. Providing the film can also include evaluating the characteristics of the electron subsystem, e.g., by making measurements to determine the electrochemical potential, density (e.g., the concentration of electrons in air), and / or other quantities of the electron subsystem. Providing the film can also include placing various gates in the vicinity of the liquid helium. Some of the gates may be electrically isolated from the helium and from the electron subsystem, but capacitively coupled to the electron subsystem. Some of the gates may be in direct electrical contact with the helium film. Some of the gates may be voltage biased. Some of the gates may be used to form the boundary of the electron subsystem. Some of the gates may be used to define one or more electron traps outside the boundary such that electrons in the electron trap are spatially (e.g., laterally) separated from electrons that may be present in other parts of the electron subsystem and / or other electron traps.

[0035] Method 700 can then apply a first side gate voltage to the side gate to form the boundary of the electronic subsystem (720). In some implementations, the magnitude of the first side gate voltage can be used to control the position and shape of the boundary. In some implementations, the side gate may have a plurality of electrically connected portions such that a microchannel of liquid helium is formed between portions of the side gate. In some implementations, the side gate may include a plurality of electrically isolated portions. Thus, the term "side gate voltage" can include a plurality of voltages applied to different portions of the side gate. Method 700 can then apply a first trap gate voltage to the trap gate to form an electronic trap located outside the boundary of the electronic subsystem (730). The term "trap gate" includes the control gate 228 of FIG. 2. The electronic trap can be defined by an electrostatic potential having a maximum value at or near the trap position (such that the potential energy of the negatively charged trapped electrons can have a minimum value at that position). In some implementations, as shown in FIG. 5, the trap gate may be a single electrode surrounding the trap. In some implementations, as shown in FIG. 2 (right figure), the trap gate may include a plurality of electrodes, and a plurality of different trap gate voltages may be applied to different electrodes (e.g., control gate 228). In some implementations, no first trap gate voltage may be applied at all, for example, the electronic trap may be defined by a particular shape of the side gate such that a region of elevated electrostatic potential is formed outside the boundary of the electronic subsystem.

[0036] Method 700 can then apply a first load gate voltage to the load gate to open the electron access path of the electronic subsystem (740). For example, the first load gate voltage can change the spatial profile of the electrostatic potential to enable the entry of electrons from the boundary of the electronic subsystem to the electron trap (e.g., by forming a microchannel between two regions). In some implementations, the first load gate voltage may not be applied at all. For example, a microchannel may be formed by a particular shape of the side gate such that a region of increased electrostatic potential exists all the way from the boundary of the electronic subsystem to the trap region. Method 700 can then apply a second load gate voltage to the load gate to close the entry of electrons from the electronic subsystem to the electron trap (750). For example, the second load gate voltage may not be more positive than the first load gate voltage. Thus, the previously formed microchannel between the electron trap and the boundary of the electronic subsystem can be cut off so that electrons are trapped within the electron trap.

[0037] Method 700 can then apply a second trap gate voltage to the trap gate to adjust the number of electrons within the electron trap (760). More specifically, after the macrochannel leading to the electron trap is severed, the trap may contain a number of electrons different from the required number. Depending on the implementation, the second trap gate voltage can be lower than the first trap gate voltage. This raises the potential energy of the electrons within the trap and can push some of the electrons back into the electron subsystem over the potential barrier. Specifically, by lowering the voltage of the trap gate, the system can be made to "descend" a Coulomb blockade staircase (as illustrated in FIG. 3). The second trap gate voltage may be selected to maintain a predetermined number of electrons within the trap, such as one, two, three, etc. Depending on the implementation, for forming a single electron qubit, the second trap gate voltage may be selected such that only one electron (e.g., corresponding to step Q = 1 of the Coulomb blockade staircase) remains within the trap. Depending on the implementation, the required second trap voltage may be known from prior calibration measurements. Depending on the implementation, the application of the second trap gate voltage may not be performed at all, and the required number of remaining electrons (e.g., Q = 1) may be achieved by appropriate selection of the first trap gate voltage at block 730 and / or the first side gate voltage at block 720. Depending on the implementation, after the application of the second trap gate voltage and the adjustment of the number of trapped electrons, a third trap gate voltage may be applied (not shown in FIG. 7). The third trap gate voltage can be made higher (e.g., more positive) than the second trap gate voltage such that the depth of the potential well of the remaining electrons within the trap increases to prevent the remaining electrons from escaping the trap.

[0038] Some of the operations of method 700 may not be used every time method 700 is performed. For example, the preparation of the helium film at block 710 may be performed only once for a plurality of situations in which a gate voltage is applied for trapping electrons. Depending on the implementation, no additional preparation may be required as long as the helium film maintains a stable state (or is replenished from a reservoir).

[0039] FIG. 8 is a flow diagram illustrating an exemplary implementation of a method 800 for reading the state of a qubit capacitively coupled to a microwave resonator circuit using a high-frequency input signal. Method 800 can begin by preparing a first input signal having a frequency corresponding to a first energy difference between the eigenstates of the qubit (810). The eigenstates of the qubit can correspond to the vertical (perpendicular to the surface of the liquid helium) or lateral (parallel to the surface of the liquid helium) motion of the trapped electrons. Depending on the implementation, the first input signal can be prepared by some or all of the high-frequency circuit components 402, 404, 406, 408, 410, 412, 416, 418 shown in FIG. 4. Method 800 can subsequently apply the first input signal to the qubit by sending the prepared first input signal to a microwave resonator circuit that includes the qubit as a capacitive component (820). Depending on the energy difference between the eigenstates of the qubit, the transmission of the first input signal may utilize sending the first input signal to the holder of the qubit (e.g., within a cryostat) via a coaxial high-frequency cable or a tapered waveguide. The qubit may be part of the microwave resonator circuit. For example, the trapped electrons of the qubit may be capacitively coupled to an RF-SET disposed in the vicinity of the trapped electrons, as shown in FIGS. 2, 4, and 5. The RF-SET may be included in the microwave resonator circuit as shown in FIG. 4 in one exemplary implementation.

[0040] Method 800 can subsequently detect a first response of the microwave resonator circuit to the first input signal (830). In some implementations, this can be done by measuring the impedance response of the microwave resonator circuit, such as the frequency shift and attenuation of the circuit. Method 800 can then determine the state of the qubit from the measured response of the microwave resonator circuit (840). The first response of the microwave resonator circuit can be processed by an analog-to-digital converter, and subsequent processing on a classical computer can be used to obtain the Rabi oscillations of the qubit. As a result, the state of the excited qubit before the input microwave signal is applied (e.g., at the completion of quantum code execution) can be determined.

[0041] In some implementations, method 800 may use multiple signals simultaneously. For example, the first input signal may have a frequency corresponding to one of the vertical or lateral motions of the trapped electron, and the second input signal may have a frequency corresponding to the other (e.g., lateral or vertical) motion of the trapped electron. In some implementations, the second input signal can be obtained by a multiplier 416 that upconverts the RF signal output by the amplifier 410 and / or the mixer 406. Thus, two input signals can be prepared at block 810. Similarly, at block 820, the first input signal and the second input signal may be applied to the qubit simultaneously (or at different times, e.g., consecutive times). In some implementations, the first input signal may be sent to the microwave resonator circuit via a coaxial cable, and the second input signal may be sent to the microwave resonator circuit via a waveguide (e.g., a tapered waveguide). At block 830, a second response of the microwave resonator to the second input signal may be detected together with the first response of the microwave resonator to the first input signal. In some implementations, at block 840, the state of the qubit may be determined based on both the first response and the second response. As a result of performing method 800, the 4-bit state of the qubit, such as the state of the qubit that is a superposition of the eigenstates |↓0〉, |↓1〉, |↑0〉, and |↑1〉, can be determined.

[0042] Prior to the execution of the quantum code, a method similar to method 800 can also be used to prepare the state of the qubits. For example, after being loaded into an electron trap (e.g., according to method 700 or some other equivalent method), the corresponding qubit can be in the ground state |0>. To prepare a superposition state α|0〉 + β|1〉 (which may be required by a specific quantum computing code implemented in the qubit system), a microwave signal appropriately prepared for the qubit may be applied to generate Rabi oscillations with an amplitude and duration that drive the qubit to the required superposition state.

[0043] A method similar to method 800 may be performed using multiple qubits. For example, a device including multiple qubits and multiple control gates can be capacitively coupled to a microwave resonator circuit. The various qubits (and / or) control gates may have a linear spatial arrangement (e.g., arranged along the same line) or a planar spatial arrangement (e.g., arranged in the same plane). In some implementations, each of the multiple qubits may be associated with each of the multiple control gates. In some implementations, an instruction to read out a target qubit may be received from a processing device (e.g., a computing system). To perform Stark tuning of the energy difference between the eigenstates of the target qubit, a control voltage may be applied to each control gate associated with the target qubit. The Stark tuning can be performed such that the energy difference Δτ between the eigenstates of the target qubit is separated from the corresponding difference Δ in the eigenstate energies of the other qubits (e.g., such that the quantity |Δτ - Δ| exceeds the inverse (radiative or non-radiative) lifetime of the qubit). This method then continues by preparing an input signal having a frequency corresponding to the energy difference Δτ, applying the input signal to the device by sending the input signal to the microwave resonator circuit, detecting the response of the microwave resonator circuit to the input signal, and determining the state of the target qubit from the response of the microwave resonator circuit.

[0044] Methods 700 and 800, and other methods similar to methods 700 and / or 800, can be performed by processing logic that may include hardware (e.g., circuits, dedicated logic, programmable logic, microcode, etc.), software, firmware, or any combination thereof. Methods 700 and 800 and / or their individual functions, routines, subroutines, or operations may be performed by one or more processing units of a conventional computer. In certain implementations, methods 700 and 800 may be performed by a single processing thread. Alternatively, methods 700 and 800 may be performed by two or more processing threads, where each thread executes one or more individual functions, routines, subroutines, or operations of the method. In an exemplary embodiment, the processing threads implementing methods 700 and 800 may be synchronized. Alternatively, the processing threads implementing methods 700 and 800 may execute asynchronously with respect to each other. The various steps of methods 700 and 800 may be performed in an order different from that shown in FIGS. 7 and 8. Some steps may be performed in parallel with other steps.

[0045] FIG. 9 shows a block diagram of a classical computer system 900 operating according to one or more aspects of the present disclosure. For example, the classical computing system 900 can implement classical computing code used to prepare and control the initial states of one or more of the qubits, depending on the implementation. The computing system 900 may implement some of the operations shown in FIG. 4, depending on the implementation. The computing system 900 can process response data received from the microwave resonator circuit and determine the final state of the qubit to be read out. In certain implementations, the computer system 900 can be connected to other computer systems (e.g., via a network such as a local area network (LAN), intranet, extranet, or the Internet). The computer system 900 can operate as a server or client computer in a client-server environment, or as a peer computer in a peer-to-peer or distributed network environment. The computer system 900 can be provided by a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web device, server, network router, switch or bridge, or any device capable of executing a set of instructions (sequential or other instructions) that specify actions to be performed by the device. Also, the term "computer" shall include any collection of computers that individually or jointly execute a set of instructions (or multiple sets) to perform any one or more of the methods described herein.

[0046] In a further aspect, computer system 900 can include a processing device 902, a volatile memory 904 (e.g., random access memory (RAM)), a non-volatile memory 906 (e.g., read-only memory (ROM) or electrically erasable programmable ROM (EEPROM)), and a data storage device 916, which can communicate with each other via a bus 908.

[0047] The processing device 902 can be provided by one or more processors such as a general-purpose processor (e.g., a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a microprocessor implementing other types of instruction sets, or a microprocessor implementing a combination of multiple types of instruction sets), or a dedicated processor (e.g., an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), or a network processor, etc.).

[0048] The computer system 900 may further include a network interface device 922. The computer system 900 may also include a video display unit 910 (e.g., an LCD), an alphanumeric input device 912 (e.g., a keyboard), a cursor control device 914 (e.g., a mouse), and a signal generation device 920.

[0049] The data storage device 916 can include a non-transitory computer-readable storage medium 924 that can store instructions 926 encoding any one or more of the methods or functions described herein, particularly instructions for implementing methods 700 and 800, in order to implement a model for detecting unfavorable employee relationships and the likelihood of termination.

[0050] Instruction 926 may be stored entirely or partially in volatile memory 504 and / or in processing device 902 when the instruction is executed by computer system 500, and thus, volatile memory 904 and processing device 902 may also constitute a machine-readable storage medium.

[0051] In the illustrated embodiment, computer-readable storage medium 924 is shown as a single medium, but the term "computer-readable storage medium" shall include a single medium or multiple media (e.g., centralized or distributed databases and / or associated caches and servers) that store one or more sets of executable instructions. The term "computer-readable storage medium" shall also include any tangible medium that can store or encode a set of instructions for causing a computer to perform any one or more of the methods described herein. The term "computer-readable storage medium" shall include, but not be limited to, solid-state memory, optical media, and magnetic media.

[0052] The methods, components, and mechanisms described herein may be implemented by individual hardware components or integrated into the functionality of other hardware components such as ASICs, FPGAs, DSPs, or similar devices. Additionally, the methods, components, and mechanisms may be implemented by firmware modules or functional circuits within a hardware device. Further, the methods, components, and mechanisms may be implemented in any combination of a hardware device and computer program components or in a computer program.

[0053] It should be understood that the above description is intended to be illustrative and not restrictive. Many other implementation examples will be apparent to those skilled in the art upon reading and understanding the above description. Although the present disclosure describes specific embodiments, it will be understood that the systems and methods of the present disclosure are not limited to the embodiments described herein and can be implemented with modifications within the scope of the appended claims. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense. Therefore, the scope of the present disclosure should be determined by reference to the appended claims, along with the full scope of equivalents to which the appended claims are entitled.

[0054] The above method, hardware, software, firmware, or code implementation can be implemented by instructions or code stored on a machine-accessible medium, machine-readable medium, computer-accessible medium, or computer-readable medium executable by a processing element coupled to a memory. "Memory" includes any mechanism that provides (i.e., stores and / or transmits) information in a form readable by a machine such as a computer or an electronic system. For example, "memory" includes random access memory (RAM) such as static RAM (SRAM) or dynamic RAM (DRAM), ROM, magnetic or optical storage media, flash memory devices, electrical storage devices, optical storage devices, acoustic storage devices, and any kind of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer).

[0055] Throughout this specification, when we refer to "one implementation" or "an implementation", it means that the specific mechanisms, structures, or features described in relation to that implementation are included in at least one implementation of the present disclosure. Thus, when the phrases "in one implementation" or "in an implementation" are described in various places throughout this specification, they do not necessarily all refer to the same implementation. Also, the specific mechanisms, structures, or features can be combined in any suitable manner in one or more implementations.

[0056] As described above, in this specification, detailed descriptions have been provided with reference to specific exemplary implementations. However, it will be apparent that various modifications and changes can be made to these implementations without departing from the broader ideas and scope of the present disclosure as described in the appended claims. Therefore, this specification and the drawings should be construed in an illustrative rather than a restrictive sense. Also, the use of the above-mentioned implementations, embodiments, and / or other exemplary expressions does not necessarily refer to the same implementation or the same example of implementation, and may refer to different, clearly distinguishable implementations, and in some cases, implementations that may be the same.

[0057] As used herein, the terms "example" or "exemplary" are used to mean an example, instance, or illustration. Any aspect or design described herein as an "example" or "exemplary" should not necessarily be construed as preferred or advantageous over other aspects or designs. Conversely, the use of the terms "example" or "exemplary" is intended to present concepts in a concrete form. The term "or" as used in this application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X includes A or B" is intended to mean any of the natural inclusive substitutions. That is, "X includes A or B" is satisfied in any of these instances when X includes A, X includes B, or X includes both A and B. Further, the articles "a" and "an" as used in this application and the appended claims should generally be construed to mean "one or more" unless otherwise specified or it is clear from the context that the singular form is indicated. Also, throughout, the use of the terms "embodiment" or "an embodiment" or "implementation" or "an implementation" is not intended to mean the same embodiment or implementation unless described as the same embodiment or implementation. Also, the terms "first", "second", "third", "fourth", etc. as used herein are intended to be labels for distinguishing different elements and may not necessarily have an ordinal meaning based on their numerical representation in some cases.

Claims

1. A system comprising: a liquid helium film supporting an electronic subsystem, the electronic subsystem including electrons confined near the surface of the liquid helium film by electrostatic attraction; a plurality of gates, each of the plurality of gates receiving each of a plurality of voltages; a first region of the electronic subsystem; a plurality of gates that electrostatically define a second region of the electronic subsystem; wherein, in a first configuration of the plurality of voltages, the electrons in the first region have access to the second region; and wherein, in a second configuration of the plurality of voltages, the electrons in the first region are prevented from accessing the second region.

2. The system of claim 1, wherein the liquid helium film supporting the electronic subsystem and the plurality of gates are located within a cryostat.

3. One or more electronic circuits for generating an electromagnetic wave signal; and a communication channel for transmitting the electromagnetic wave signal to at least the second region of the electronic subsystem.

4. The system of claim 3, wherein the communication channel includes at least one of a waveguide or a coaxial cable.

5. The system of claim 3, wherein the electromagnetic wave signal is configured to change the state of one or more electrons within the second region of the electronic subsystem.

6. The system of claim 1, further comprising a substrate supporting the liquid helium film; wherein the liquid helium film contains a liquid substance.

7. The plurality of gates further electrostatically define a third region of the electronic subsystem; and wherein, in the second configuration of the plurality of voltages, the electrons in the first region have access to the third region.

8. The system of claim 7, wherein, in a third configuration of the plurality of voltages, the electrons in the first region are prevented from accessing the second region and the third region.

9. The system of claim 1, further comprising a charge sensor capacitively coupled to the second region of the electronic subsystem.

10. The system of claim 9, wherein the charge sensor includes a single electron transistor.

11. The plurality of gates include: side gates that electrostatically define the boundary of the first region of the electronic subsystem; A trap gate that electrostatically defines the second region of the electronic subsystem; The system according to claim 1, further comprising a load gate that selectively opens and closes the entry of electrons in the first region of the electronic subsystem into the second region of the electronic subsystem.

12. A method for implementing a qubit, comprising: Providing a liquid helium film that supports an electronic subsystem, the electronic subsystem including electrons confined near the surface of the liquid helium film by electrostatic attraction; Applying each of a plurality of voltages to each of a plurality of gates, the plurality of voltages electrostatically defining a first region and a second region of the electronic subsystem; Applying a first configuration of the plurality of voltages to enable the electrons in the first region to enter the second region; Applying a second configuration of the plurality of voltages to prevent the electrons in the first region from entering the second region.

13. The method according to claim 12, further comprising applying a third configuration of the plurality of voltages to adjust the number of electrons in the second region to a predetermined number.

14. The method according to claim 13, wherein the predetermined number is one or two.

15. Generating an electromagnetic wave signal; Transmitting the electromagnetic wave signal at least to the second region of the electronic subsystem; The method according to claim 12, further comprising using the electromagnetic wave signal to change the state of one or more electrons in the second region of the electronic subsystem.

16. A method for determining the state of a qubit, comprising: Generating the qubit by trapping one or more electrons from an electronic subsystem electrostatically confined near the surface of liquid helium; Providing a first signal having a frequency corresponding to a first energy of the qubit; Transmitting the first signal to an electronic circuit capacitively coupled to the qubit so that the qubit receives the first signal; Detecting a first response of the electronic circuit to the first signal; Determining the state of the qubit based on the first response of the electronic circuit to the first signal.

17. The method according to claim 16, wherein causing the qubit to receive the first signal includes transmitting the first signal via a waveguide or a coaxial cable. **Claim 18** providing a second signal having a second frequency corresponding to a second energy of the qubit; causing the qubit to receive the second signal by transmitting the second signal to the electronic circuit; further comprising detecting a second reaction of the electronic circuit to the second signal; The method according to claim 16, wherein determining the state of the qubit further includes determining the state of the qubit based on the second reaction of the electronic circuit to the second signal. **Claim 19** The first energy of the qubit is associated with (i) a vertical movement of the qubit, or (ii) a lateral movement of the qubit; The method according to claim 18, wherein the second energy of the qubit is associated with the other of (i) a vertical movement of the qubit, or (ii) a lateral movement of the qubit.

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