Methods for calibrating and / or assisting the design of spin qubits or two-level quantum systems and quantum components

Abstract

The invention relates to a method for calibrating a two-level spin quantum system in the form of a double quantum dot comprising a left dot and a right dot, coupled to a microwave cavity by symmetric and antisymmetric magnetic fields, the system being subjected to a bias voltage, the method being characterized by the steps of: - setting the bias voltage (ε) to zero volts, - determining the wave function φp of each of the quantum dots, - calculating and / or setting the antisymmetric magnetic coupling constant αas and the symmetric magnetic coupling constant αs, calculating and / or setting the tunnel coupling constant and / or the symmetric magnetic coupling constant αs and / or the antisymmetric magnetic coupling constant αas.

Description

[Technical field]

[0001] The present invention relates to methods for assisting in the design of qubits and / or for calibrating qubits in order to perform quantum computations using quantum components.

[0002] The quantum components are particularly, but not exclusively, intended for producing quantum computers. [Background technology]

[0003] Semiconductor-hosted qubits have recently attracted much interest in the development of large-scale quantum computers.

[0004] This is especially true due to the demonstration of good coherence times and quantum gate fidelity enabled by coupling via a microwave resonator, which is higher than purely magnetic coupling.

[0005] A spin qubit, also known as a spin quantum bit, is represented by an electron whose spin, an eigenvector in two-dimensional space, encodes quantum information.

[0006] In all quantum systems, including spin qubits, quantum decoherence arises when the qubit interacts with its external environment.

[0007] To model a qubit, the two quantum dots are considered to correspond to the capture of a single electron in the two dots / wells, thus creating a qubit.

[0008] In the paper M. Benito, JR Petta, and G. Burkard, Physical Review B 100 081412 (2019), "Optimized cavity-mediated dispersive two-qubit gates between spin qubits", an interface between a single electron in a silicon dot / quantum dot and a single photon trapped in a superconducting cavity is known. This interface allows the implementation of a photon-mediated two-qubit entanglement gate. To couple the spin to the cavity electric field, some type of spin-charge hybridization is required, which affects the spin control and coherence. A two-qubit cavity-mediated gate is proposed and the fidelity of the cavity-mediated entanglement gate in the dispersive regime is calculated taking into account the errors due to spin-charge hybridization as well as photon- and phonon-induced damping. It is planned to optimize the degree of spin-charge hybridization with the aim of proposing a cavity-photon-mediated two-qubit gate that can achieve a fidelity of more than 90% in the current device architecture. High fidelity of the iSWAP gate is achievable even in the presence of 2 μeV level charge noise.

[0009] Also known from the document A. Cottet and T. Kontos, Physical Review Letters 105:160502, 2010 "A spin quantum bit with ferromagnetic contacts for circuit QED" is a scheme for a spin qubit based on a double quantum dot in contact with a ferromagnetic element. The interface exchange effect allows all-electrical manipulation of the spins and strong switchable coupling into a superconducting coplanar waveguide cavity for on-chip single spin manipulation and readout using cavity QED techniques.

[0010] There are several problems with the prior art. 1. There are no well-defined tunable parameters that allow experimental physicists to control the operating regime of spin photon qubits. For example, in the Cottet and Kontos disclosure, the inhomogeneous magnetic fields that form the magnetic field gradient are highly specific and not related to any tunable parameters. 2. Because of the above problems, there is no systematic way to define a good operating regime, i.e., to design qubits that are resistant to charge noise, which is the most significant noise source causing qubit decoherence. 3. There is no way to find a good compromise between immunity to charge noise while having good coupling to the cavity, which allows better qubit control and therefore shorter gate times.

[0011] The gates are quantum gates that correspond to logical operations that can change the state of a superposition of quantum bits, for example, a quantum bit can have a one-half chance of being in one or the other of two states.

[0012] One object of the present invention is to provide a method to aid in the design and / or optimal calibration of physical systems involving qubit spin photons with limited quantum decoherence, limited gating times, and improved gate fidelity or reliability. Summary of the Invention

[0013] To this end, according to a first aspect, the invention proposes a method for calibrating, or aiding in the design of, a two-level spin quantum system or spin qubit coupled to a microwave cavity by a symmetric and an antisymmetric magnetic field, said quantum system being in the form of a double quantum dot comprising a left dot and a right dot, and being subjected to a bias voltage, - setting the bias voltage (ε) to zero volts; - determining the wave function φ of each of the quantum dots; The following formula:

[0014]

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[0018] The spin and photon parts of a spin-photon qubit can be coupled in two ways: 1. by applying symmetric and antisymmetric magnetic fields, and 2. by using a microwave cavity.

[0019] The present invention solves the above-mentioned problems by proposing a design for a good qubit operating regime that leads to a series of steps that enable experimental physicists to gain access to low-noise, highly controllable spin-photon qubits.

[0020] For purposes of the foregoing and the remainder of the description, calibration means preparing or setting a qubit to an optimal operating state.

[0021] Furthermore, for purposes of this description, a symmetric magnetic field means a magnetic field that is symmetric between two quantum dots, or a symmetric magnetic field between two quantum dots means a magnetic field of the same orientation, value, and direction.

[0022] Furthermore, for purposes of this description, an antisymmetric magnetic field means a magnetic field that is antisymmetric between two quantum dots, or an antisymmetric magnetic field between two quantum dots means a magnetic field of the same orientation, same value, and opposite direction.

[0023] Additionally, the following expressions, ie, wave functions or electron orbitals, are used interchangeably and are represented interchangeably by the mathematical symbols phi φ or psi ψ.

[0024] Likewise, the expressions antisymmetric magnetic coupling or asymmetric magnetic coupling are used interchangeably.

[0025] In addition, in the following the expressions double dot and double quantum dot are used interchangeably.

[0026] In one embodiment, the wave function is found by solving the Schrödinger equation, preferably a single Schrödinger equation, based on the assumption that the system is in a double-well electrostatic potential.

[0027] Preferably, for each wavefunction, the method comprises the steps of: - solving the Schrödinger equation assuming that the system is in a double-well electrostatic potential, - calculating the wave function in the absence of a magnetic field, - calculating the tunnel coupling constant γ, - applying a symmetric magnetic field Bs(x) and an antisymmetric magnetic field Ba(x) to the electrons, - calculating the asymmetric magnetic coupling constant αas and the symmetric magnetic coupling constant αs.

[0028] Preferably, the symmetric and / or antisymmetric magnetic field is adjustable.

[0029] For example, a symmetric magnetic field Bs(x) and an antisymmetric magnetic field Ba s (x) are generated by a magnet.

[0030] For example, the symmetric magnetic field Bs(x) is generated by a solenoid and the antisymmetric magnetic field Ba s (x) is generated by at least one magnetic polarizing electrode, preferably at least one grid electrode.

[0031] Preferably, the bias voltage is adjustable, for example via an electrostatic potential, preferably via the gate electrode of the quantum component.

[0032] According to a second aspect, the invention proposes a quantum component comprising a two-level spin quantum system or spin qubit coupled to a microwave cavity by a symmetric magnetic field and an antisymmetric magnetic field, the quantum system being in the form of a double quantum dot comprising a left dot and a right dot, the component comprising: - means for applying an electrostatic potential to apply a bias voltage (ε) to said double quantum dot; means for applying a symmetric magnetic field and an antisymmetric magnetic field between the left dot and the right dot, respectively; further comprising a bias voltage (ε) maintained at zero volts, and a tunnel coupling constant, and / or a symmetric magnetic coupling constant α and / or an antisymmetric magnetic coupling constant α, such that: 2γαs=αs 2 +αas 2 and / or

[0033]

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[0037] Preferably, the quantum component comprises one or more of the features of the first aspect.

[0038] There are multiple ways to construct a qubit.

[0039] A key factor that distinguishes good qubits from bad qubits is their susceptibility to decoherence.

[0040] This affects not only the qubit lifetime and therefore the maximum depth of quantum circuits that can be implemented on a processor, but also the error rate of individual quantum gates.

[0041] Therefore, to identify whether carbon nanotubes are good hosts for the construction of quantum information devices, it is important to identify the processes that lead to qubit decoherence.

[0042] In order to have a somewhat realistic description of a qubit and the quantum operations one wishes to perform on it, one needs to take into account the anomalies associated with the qubit's external environment, such as charge noise.

[0043] However, this is not the only cause of qubit decoherence.

[0044] We separate them into two categories according to their effect on the qubits.

[0045] Relaxation refers to the process by which a qubit relaxes towards its ground state over time, and phase shift refers to the process by which the two qubit states acquire different phases over time. [Brief description of the drawings]

[0046] Other features and advantages of the present invention will become apparent from the following detailed description of the invention which refers to the accompanying drawings. [Figure 1] FIG. 1 shows one representation of a double quantum dot. [Diagram 2] FIG. 1 shows a schematic diagram of a quantum component including a nanotube disposed on electrodes, specifically non-collinear magnetic electrodes. [Diagram 3] FIG. 1 shows a schematic diagram of a quantum component with a nanotube positioned above an electrode and displaying a dipole fringing field. [Figure 4]Two graphs are shown, one above the other: the upper graph shows, on the one hand, the electrostatic potential in the nanotube as a function of distance in nanometers (solid grey line), on the other hand, the two coupled (solid black line) and anti-coupled (dotted black line) states of electrons in a double quantum dot (solid black line), and the lower graph shows the profiles of the two magnetic flux leakage components. [Diagram 5] 1 is a graph illustrating four qubit energy levels and showing the reduction in charge noise. [Figure 6] 1 shows the curves of the magnetic field components along a carbon nanotube, in particular the magnetic field distribution along the carbon nanotube obtained using a micro-magnet.

[0047] For greater clarity, identical or similar elements of the various embodiments are designated by the same reference numerals in all figures. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0048] With reference to FIG. 1 , in one embodiment, the method steps are described to calibrate or aid in the design of a two-level spin quantum system or spin qubit, where the quantum system is in the form of a double quantum dot.

[0049] Figures 1, 2 and 3 show charge-controlled spin states. In particular, Figure 1 shows electron spin S=1 / 2 in a double quantum dot in a uniform magnetic field. Figure 2 shows the presence of a non-uniform magnetic field represented by the diagonal arrows on the suspension electrodes known as source and drain electrodes. Figure 3 shows the presence of a non-uniform magnetic field represented by the arc-shaped arrows generated by magnets or magnetic electrodes forming a magnetic dipole, generating a fringing field outside the magnetic electrodes.

[0050] Define tunable variables for simulation and design. For a physical system hosting spin qubits in a double quantum dot (DQD), coupled to a magnetic field with symmetric and antisymmetric components, it is possible to model the physical behavior of the system using the following Hamiltonian:

[0051]

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[0053] Calculate and set the four spin qubit variables Physically, it is possible to manipulate these four variables by controlling any of the following: - Magnetic field applied to the DQD: (Bs(x), Ba(x), where x is the direction along the DQD.

[0054] This representation allows an applied magnetic field to couple the spin of an electron to its location on the spin qubit.

[0055] For example, by adjusting the current through a solenoid, which is the physical embodiment of a magnet, it is possible to control the magnetic field strength in both directions in real time.

[0056] The magnetic field can be adjusted. - the applied electrostatic potential V(x), which depends on the design of the physical system hosting the double quantum dot (DQD) and, for example, the voltage applied to the electrodes controlling the qubit.

[0057] One way to arrive at V(x) is to use a numerical method, such as the finite element method, to solve Maxwell's equations.

[0058] The electrostatic potential V(x) can be set. There are several embodiments to perform this setting.

[0059] According to one embodiment, the Schrödinger equation for electrons in the DQD is solved with a fixed electrostatic potential V(x) and bias voltage ε=0.

[0060]

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[0061] This equation can be solved numerically, for example using the finite element method.

[0062] The solution to this equation is an infinite dimensional vector space.

[0063] We retain only the vector subspace associated with the first two eigenvalues ​​of the Hamiltonian, call this (E+, E-), with their associated wavefunctions (ψ+(x), ψ-(x)).

[0064] The tunnel coupling constant γ can be calculated numerically based on the eigenvalues ​​calculated above, with the bias voltage set to zero, as follows:

[0065]

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[0066] The left and right eigenstates ψL(x) and ψR(x) can then be calculated based on the numerical values ​​of the previously calculated wavefunctions ψ+(x) and ψ−(x).

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[0068] The magnetic coupling constant can then be calculated numerically by calculating the integral:

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[0070] Optimal qubit operating point: Based on the tunable parameters defined above, it is possible to define an optimal operating regime for the qubit by ensuring that certain equations are satisfied by the tunable parameters.

[0071] Maximum spin-photon coupling: The regime in which the spin-photon coupling is maximal and the quantum gate time can be as short as possible can be set by tuning the bias voltage as ε=0.

[0072] This places the qubit in a perfectly symmetric regime between the two dots, maximizing the coupling between the photonic cavity, the charge behavior of the qubit, and the spin behavior of the qubit, which maximizes the spin-photon coupling.

[0073] A trade-off between low charge noise and spin-photon coupling. Once the previous steps are completed, the qubit regime can be tuned to achieve a good compromise between low charge noise and good spin-photon coupling, which can be achieved by defining the three remaining spin qubit parameters as follows:

[0074]

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[0075] This tuning can be achieved by varying the magnetic field (Bas(x), Bs(x)) and the electrostatic potential V(x).

[0076] For example, the magnetic field may be fixed for experimental reasons, and multiple values ​​of the electrostatic potential may be numerically calculated until the above equation is satisfied.

[0077] This offers a good compromise between low charge noise and good spin-photon coupling.

[0078] Low-error qubit gates: When AC electrical control is applied to the qubit (e.g., a microwave signal) to apply a one-qubit gate (e.g., an X-gate) to a spin-photon qubit, this induces errors that lead to undesired transitions.

[0079] The quantum bit can reach a third state, resulting in a loss of information and errors in calculations using one-qubit gates. Based on experimental considerations, it is possible to set a given electrical control amplitude Ωd as desired, for example by using the amplitude of a microwave signal sent to the device.

[0080] The error can then be minimized by adjusting well-defined qubit parameters so that a particular equation is satisfied.

[0081] To simplify the formula, we can introduce temporary variables,

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[0083] In order to ensure that the certain probability of reaching an undesired transition after application of the electric drive is very low, for example P=0.01%, the following quantities can be calculated:

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[0085] P is the desired probability of an undesired transition after an AC current is applied (eg, after an X gate is applied).

[0086] It is possible to tune the qubit parameters so that P=0.01%, corresponding to very good operation of single-qubit quantum gates.

[0087] A set of steps uses previously defined adjustable parameters that are directly related to the experimental parameters of magnetic field and electrostatic potential, after which the qubit finds itself in an optimal operating regime.

[0088] This occurs because these adjustable parameters satisfy the following set of equations:

[0089]

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[0090] 5 shows a qubit operating regime that satisfies the presented inequality and results in a difference between the energy levels of the second curve from the bottom of the graph and the first curve from the bottom of the graph that is a constant function of the qubit frequency, i.e., the qubit's epsilon bias voltage. Such a regime protects the qubit from charge noise, since it is the change in this function that quantifies this charge noise.

[0091] In a particular embodiment, the distribution components of the magnetic field along a carbon nanotube are shown in Figure 6. The symmetric component is referenced by 52. ​​The antisymmetric component is referenced by 50. The wave functions are referenced by 51 and 53. For example, the magnetic field 52 is symmetric with respect to the x=0 plane, the x-axis of Figure 6. For example, the magnetic field 50 is antisymmetric with respect to the x=0 plane, which is the x-axis of Figure 6.

Claims

1. 1. A method for calibrating a two-level spin quantum system or spin qubit coupled to a microwave cavity by symmetric and antisymmetric magnetic fields, the quantum system being in the form of a double quantum dot including a left dot and a right dot, and subjecting the system to a bias voltage; - setting the bias voltage (ε) to zero volts; - determining the wave function φp of each of said quantum dots; - calculating and / or setting the antisymmetric magnetic coupling constant αas and the symmetric magnetic coupling constant αs using the following formulas: [0010] where φ is the wave function of electron orbital p (p=left dot or right dot), and Bi(x) is the symmetric magnetic field Bs(x) and the antisymmetric magnetic field Bas(x), The tunnel coupling constant (γ) and / or the symmetric magnetic coupling constant αs and / or the antisymmetric magnetic coupling constant αas, 2γαs = αs ２ +αas ２ The method according to the present invention is characterized by a step of calculating and / or setting the following: and / or [0025] is the desired probability of an undesired transition after application of an AC current, Where: [0030] and [0045] That is, the method.

2. The method of claim 1 , wherein the wave function is found by solving the Schrodinger equation assuming the system is in a double-well electrostatic potential.

3. The method according to claim 1 or 2, wherein the symmetric magnetic field and / or the antisymmetric magnetic field are adjustable.

4. - calculating each wave function in the absence of a magnetic field, - calculating the tunnel coupling constant (γ), - applying a symmetric magnetic field Bs(x) and an antisymmetric magnetic field Bas(x) to the electrons, A method according to claim 1 or 2, comprising the step of calculating the asymmetric magnetic coupling constant αas and the symmetric magnetic coupling constant αs.

5. The method according to any one of claims 1 to 4, wherein the symmetric magnetic field Bs(x) and the antisymmetric magnetic field Bas(x) are realised by magnets.

6. 6. The method according to claim 1, wherein the symmetric magnetic field Bs(x) is realised by a solenoid and the antisymmetric magnetic field Bas(x) is realised by at least one magnetic polarising electrode, preferably at least one grid electrode.

7. The method of any one of claims 1 to 6, wherein the bias voltage is adjustable.

8. 1. A quantum component comprising a two-level spin quantum system or spin qubit coupled to a microwave cavity by a symmetric magnetic field and an antisymmetric magnetic field, the quantum system being in the form of a double quantum dot comprising a left dot and a right dot, the component comprising: - means for applying an electrostatic potential so as to apply a bias voltage (ε) to said double quantum dot; - means for applying a symmetrical magnetic field and an antisymmetrical magnetic field between the left dot and the right dot, respectively; The system further comprises a bias voltage (ε) maintained at zero volts, a tunnel coupling constant (γ) and / or the symmetric magnetic coupling constant αs and / or the antisymmetric magnetic coupling constant αas, such that: 2gas = as ２ +aas ２ and / or [0050] is the desired probability of an undesired transition after application of an AC current, Where: [006] and [0070] The present invention is characterized in that -αas and αs are represented by the following formulas, [0080] Quantum components, wherein φp is the electron orbital wave function p (p=left dot or right dot), and Bi(x) is the symmetric magnetic field Bs(x) and antisymmetric magnetic field Bas(x).

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