METHOD FOR CALIBRATION AND / OR DESIGN ASSISTANCE FOR A TWO-LEVEL QUANTUM SYSTEM OR SPIN QUBIT AND QUANTUM COMPONENT

Abstract

The invention relates to a method for calibrating a two-level spin quantum system coupled to a microwave cavity by a symmetric and an antisymmetric magnetic field, in the form of a double quantum dot comprising a left-hand and a right-hand box, subjected to a bias voltage, characterized by the following steps: setting the bias voltage (ε) to zero volts, determining a wave function φp of each of the quantum dots, calculating and / or setting the antisymmetric magnetic coupling constants αas and the symmetric magnetic coupling constant αs, calculating and / or setting the tunneling coupling constant, and / or the symmetric magnetic coupling constant αs and / or the antisymmetric magnetic coupling constant αas. Figure to be published with the abstract: Fig. 1

Description

Title of the invention: METHOD FOR CALIBRATING AND / OR AID IN THE DESIGN OF A TWO-PART QUANTUM SYSTEM SPIN LEVELS OR QUBITS AND QUANTUM COMPONENTS TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to a method for assisting in the design and / or a method for calibrating a qubit in order to perform quantum calculations, by quantum components.

[0002] The quantum component is intended in particular, but not exclusively, for the manufacture of quantum computers. STATE OF THE ART

[0003] Qubits hosted in semiconductors have recently attracted great interest for the development of a large-scale quantum computer.

[0004] This stems from the fact that they have demonstrated good coherence times and good fidelity of quantum gates, made possible in particular by coupling via a microwave resonator, which is higher than purely magnetic coupling.

[0005] A quantum bit of spin, also called a spin-qubit, is represented in particular by an electron, whose spin, an eigenvector of a two-dimensional space, encodes the quantum information

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

[0007] In order to model the quantum bit, two quantum points are considered in order to correspond to the trapping of a single electron in two points / wells, and therefore, the generation of a quantum bit.

[0008] An interface between a single electron in a silicon quantum dot / box and a single photon trapped in a superconducting cavity is known from the paper by M. Benito, J.R. Petta, and G. Burkard, Physical Review B 100 081412 (2019), “Optimized cavity-mediated dispersive two-qubit gates between spin qubits.” This interface enables the implementation of photon-mediated two-qubit entanglement gates. In order to couple a spin to the electric field of the cavity, a certain type of spin-charge hybridization is required, which impacts spin control and coherence. A cavity-mediated two-qubit gate is proposed, along with the calculation of the fidelities of the cavity-mediated entanglement gate in the dispersive regime, taking into account errors due to spin-charge hybridization, as well as decays induced by photons and phonons.The plan is to optimize the degree of spin-charge hybridization, with a view to proposing two-qubit gates mediated by cavity photons capable of to achieve fidelities exceeding 90% in current device architectures. High iSWAP gate fidelities are achievable even in the presence of load noise at the 2p,eV level.

[0009] A scheme for a spin quantum bit based on a double quantum dot in contact with ferromagnetic elements is also known from the paper "A. Cottet and T. Kontos, Physical Review Letters 105: 160502, 2010, 'A spin quantum bit with ferromagnetic contacts for circuit QED'. The interface exchange effects allow all-electrical spin manipulation and strong switching coupling to a superconducting coplanar waveguide cavity, with a view to considering on-chip single-spin manipulation and readout using QED cavity techniques.

[0010] There are several problems that come with the state of the art:

[0011] 1. There are no well-defined adjustable parameters that allow the experimental physicist It is crucial to control the operating regime of the spin-photon qubit. For example, in the Cottet and Kontos disclosure, the inhomogeneous magnetic field that forms a field gradient is very specific and not linked to an adjustable parameter.

[0012] 2. Due to the previous problem, there is no systematic way to define a good operating regime, that is to say to design a qubit resistant to noise under load, the highest noise source responsible for the decoherence of the qubit.

[0013] 3. There is no way to make a good compromise between noise resistance and charge, while having good coupling to the cavity, which allows better control of the qubit and therefore a shorter gate time.

[0014] A gate is a quantum gate corresponding to a logical operation that can change the superposition state of a qubit. For example, a qubit may have a one in two chance of ending up in one or the other of the two states.

[0015] An object of the invention is to propose a method for assisting in the design and / or optimal calibration of a physical system containing a spin photon qubit exhibiting limited quantum decoherence, limited gate time and improved gate fidelity or reliability. SUBJECT OF THE INVENTION

[0016] To this end, and according to a first aspect, the invention proposes a method for calibrating, or for assisting in the design, of a two-level spin quantum system or spin qubit, coupled to a microwave cavity by a symmetric magnetic field and an antisymmetric magnetic field, this quantum system being in the form of a double box or a double quantum point comprising a left box or point and a right box or point, and being subjected to a biasing voltage, characterized by the following steps:

[0017] - set the bias voltage (e) to zero volts, - determine a wave function <pp de chacun des boites ou points quantiques, - calculer et régler constantes couplage magnétique antisymétrique aas symétrique as via la formule suivante : ai="2jqBi(x)q">p(x)*q)p(x)dx, where <pp est la fonction d'onde d'orbitale électronique p (p = boite ou point gauche ou boite ou point droit), et Bi(x) est le champ magnétique symétrique Bs(x) et antisymétrique Bas(x), - calculer et / ou régler la constante de couplage tunnel (y), et / ou la constante de couplage magnétique symétrique as et / ou la constante de couplage magnétique antisymétrique aas de telle sorte que : 2yas= as2 + aas2 et / ou Or And A?-:- ~ h- •

[0018] It is possible to couple the spin part and the photon part of a spin-photon qubit by two means: 1. the application of a symmetric magnetic field and an antisymmetric magnetic field, 2. the use of a microwave cavity.

[0019] The invention solves the problems mentioned above by proposing a design for a good operating regime of a qubit, which results in a series of steps enabling an experimental physicist to have access to a low-noise and highly controllable spin-photon qubit.

[0020] For the purposes of the above and the remainder of the description, calibration means the preparation or adjustment of the qubit to an optimal operating state.

[0021] In addition, the following expressions are used interchangeably: wave function or electronic orbital and will be represented interchangeably by the mathematical symbols phi ¢) or pshp.

[0022] Similarly, the following expressions are used interchangeably: antisymmetric magnetic coupling or asymmetric magnetic coupling.

[0023] In addition, the following expressions are used interchangeably: double quantum box and double quantum dot.

[0024] According to one embodiment, the wave functions are determined by solving a Schrödinger equation, preferably a single one, starting from the assumption that the system is a double electrostatic potential well.

[0025] Preferably, for each wave function, the method comprises the following steps:

[0026] - solving a Schrödinger equation starting from the assumption that the system is a double electrostatic potential well,

[0027] - calculate the wave functions considering the absence of a magnetic field,

[0028] - calculate the tunnel coupling constant y,

[0029] - apply the symmetric magnetic fields Bs(x) and antisymmetric magnetic fields Bas(x) to the electron,

[0030] - calculate the asymmetric magnetic coupling constants aas and symmetric as.

[0031] Preferably, the symmetrical magnetic field and / or the antisymmetrical magnetic field is / are adjustable.

[0032] For example, the symmetric magnetic fields Bs(x) and antisymmetric magnetic fields Bas(x) are produced by magnets.

[0033] For example, the symmetric magnetic field Bs(x) is made by a solenoid and the antisymmetric magnetic field Bas(x) is made by at least one electrode allowing magnetic polarization, preferably at least one grid electrode.

[0034] Preferably, the bias voltage is adjustable, for example via electrostatic potentials, preferably via gate electrodes of a quantum component.

[0035] According to a second aspect, the invention provides for 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, this quantum system being in the form of a double box or double quantum dot comprising a left box or dot and a right box or dot, the component comprising:

[0036] - means for applying an electrostatic potential so as to apply a a bias voltage (e) to said double quantum dot,

[0037] - means for applying a symmetrical magnetic field and a magnetic field antisymmetric genetics between the two boxes respectively left and right,

[0038] characterized in that it further comprises a bias voltage (e) maintained at zero volts and a tunnel coupling constant and / or the symmetric magnetic coupling constant as and / or the antisymmetric magnetic coupling constant aas such that: 2yas = as2 + aas2 and / or Or

[0039] where as and aas are respectively symmetric and asymmetric magnetic coupling constants via the following formula: ai=2 JqBi(x)q>p(x) * <pp(x)dx, Or <pp est la fonction d'onde de l’orbitale électronique p (p = boite ou point gauche ou boite ou point droit), et Bi(x) est le champ magnétique symétrique Bs(x) et antisymétrique Bas(x).

[0040] Preferably, said quantum component comprises one or more features of the first aspect.

[0041] There are several ways to construct a qubit.

[0042] The key factor that differentiates a good qubit from a bad one is its susceptibility to decoherence.

[0043] This affects not only the lifetime of the qubit and therefore the maximum depth of a quantum circuit running on the processor, but also the error rates of each quantum gate.

[0044] Thus, in order to identify whether carbon nanotubes are good hosts for the construction of a quantum information device, it is crucial to identify the processes leading to the decoherence of the qubit.

[0045] In order to have a somewhat realistic description of the qubit and the quantum operations that we are going to perform on it, we must take into account the deviations that accompany the external environment of the qubit, such as noise under load.

[0046] However, this is not the only source of decoherence from which the qubit suffers.

[0047] We separate them into two categories according to their effect on the qubit.

[0048] Relaxation refers to the processes by which the qubit relaxes towards its ground state over time, while phase shifting refers to the processes by which the two states of the qubit acquire a different phase over time. BRIEF DESCRIPTION OF THE FIGURES

[0049] Other features and advantages of the invention will become apparent from the detailed description of the invention which follows with reference to the accompanying figures, in which:

[0050] [Fig.1] Fig.1 represents a diagram of a double quantum point according to a mode of representation;

[0051] [Fig.2] Fig.2 represents a schematic diagram of a quantum component comprising a nanotube arranged above electrodes, including non-collinear magnetic electrodes;

[0052] [Fig. 3] [Fig. 3] represents a schematic of a quantum component comprising a nanotube positioned above electrodes, showing a leakage magnetic field dipolar;

[0053] [Fig.4] [Fig.4] shows two graphs one above the other, the graph of the above representing on the one hand in solid grey line the electrostatic potential in a nanotube as a function of distance in nanometers, and on the other hand via the black lines the two bonding (solid black line) and antibonding (dotted black line) states of an electron in a double quantum dot, the graph below representing the profile of two components of leakage magnetic field;

[0054] [Fig.5] Fig.5 shows a graph representing four qubit energy levels and illustrating noise reduction under load.

[0055] For clarity, identical or similar elements of the different embodiments are identified by identical reference numerals throughout the figures. DETAILED DESCRIPTION OF THE INVENTION

[0056] In relation to [Fig.1], the steps of the process for calibrating, or for assisting in the design, a two-level spin quantum system or spin qubit is developed according to one embodiment, this quantum system being in the form of a double box or a double quantum point.

[0057] Figures 1, 2, and 3 illustrate the charge-controlled spin state. In particular, [Fig. 1] illustrates an electron spin S=1 / 2 in a double quantum dot in a homogeneous magnetic field. [Fig. 2] illustrates the presence of an inhomogeneous magnetic field represented by the diagonal arrows on the suspension electrodes, referred to as the source and drain electrodes. [Fig. 3] illustrates the presence of an inhomogeneous magnetic field, represented by the arc-shaped arrows, generated by a magnetic electrode forming a magnet or magnetic dipole, and creating a leakage field outside of said magnetic electrode.

[0058] Definition of adjustable variables for simulation and design:

[0059] For a physical system that houses a spin qubit in a double box quantum (or double quantum dot, also called DQD), coupled to a magnetic field with a symmetric component and an antisymmetric component, it is possible to model the physical behavior of the system with the following Hamiltonian:

[0060] ;

[0061] where ri are the Pauli operators of the electron orbitals in the double point (left point and right point),

[0062] = [°° 63 1

[0064] ni are the Pauli operators of the electron spin in the double quantum dot. The four parameters with which it is possible to adjust the spin qubit are:

[0065] e is the bias voltage applied to the double quantum point, it is easily tunable experimentally;

[0066] y is the tunnel coupling constant between the two points;

[0067] as is the coupling parameter between the symmetrical part of the magnetic field applied and the magnetic moment of the electron;

[0068] aas is the coupling parameter between the asymmetric part of the applied magnetic field and the magnetic moment of the electron.

[0069] Calculation and tuning of the four spin qubit variables

[0070] Physically, it is possible to manipulate these four variables by controlling either:

[0071] - the magnetic field applied to the DQD: (Bs(x),Bas(x), x being the direction along the DQD.

[0072] This representation allows the applied magnetic field to couple the spin of the electron to its localization on the spin qubit.

[0073] For example, it is possible to control in real time the intensity of the magnetic field in both directions by adjusting the current flowing through a solenoid which constitutes the physical realization of the magnet.

[0074] It is possible to adjust the magnetic field.

[0075] - the applied electrostatic potential V(x), which depends on the system design physics hosting the double quantum dot (DQD), and, for example, voltages applied to the electrodes that control the qubit.

[0076] One way to arrive at V(x) would then be to use a numerical method such as the finite element method to solve Maxwell's equations.

[0077] It is possible to adjust the electrostatic potential V(x). Several embodiments are possible for performing this adjustment.

[0078] According to one embodiment, the Schrödinger equation of the electron in the DQD is solved, with a fixed electrostatic potential V(x) and a bias voltage e = 0.

[0079]

[0080] It is possible to solve this equation numerically, for example by the finite element method.

[0081] The solution to this equation is an infinite-dimensional vector space.

[0082] We only keep the vector subspace associated with the first two eigenvalues ​​of the Hamiltonian, which we call (E+,E-) with their respective associated wave functions (ip+(x), U_(x))-

[0083] It is possible to calculate numerically the tunnel coupling constant y with the following equation, where the bias voltage is zero, based on the previously calculated eigenvalue:

[0084] - - ; - o)

[0085] Next, it is possible to calculate the left and right eigenstates ipL(x) and rpR(x) on the basis of the numerical values ​​of the previously calculated wave functions rp+(x) and ip-(x):

[0086] i

[0087] U,)--'- v 2

[0088] Next, we can numerically calculate the magnetic coupling constants by calculating the following integrals, which can be done numerically:

[0089]

[0090]

[0091] Optimal working point of the qubit:

[0092] Based on the adjustable parameters defined above, it is possible to define the optimal operating regime of the qubit by ensuring that certain equations are satisfied by the adjustable parameters:

[0093] Maximum spin-photon coupling:

[0094] It is possible to adjust the regime at which the spin-photon coupling is maximal, thus allowing the quantum gate time to be as short as possible, by setting the bias voltage as e=0.

[0095] This places the qubit in a perfectly symmetrical regime between the two points and maximizes the coupling between the photonic cavity, the charge aspect of the qubit, and the spin aspect of the qubit. Thus, the spin-photon coupling is maximized.

[0096] Compromise between low charge noise and spin-photon coupling:

[0097] Once the previous step is completed, it is possible to adjust the qubit regime to obtain a good compromise between low charge noise and good spin-photon coupling. This can be achieved by defining the three remaining spin qubit parameters as follows:

[0098] 2^ ^ 4

[0099] This adjustment can be made by varying the magnetic field (Bas(x),Bs(x)) and the electrostatic potential V(x).

[0100] For example, it is possible that the magnetic field is fixed for experimental reasons and to calculate numerically several values ​​of the electrostatic potential until the previous equation is verified.

[0101] This allows a good compromise between low charge noise and good spin-photon coupling.

[0102] Low-error qubit gate:

[0103] When an electrical control of the alternating current (AC) type is applied to the qubit (for example, a microwave signal) to apply a 1-qubit gate (for example, an X gate) on the spin-photon qubit, this induces errors leading to undesirable transitions.

[0104] The qubit can reach a third state, which leads to information loss and errors in calculations using 1-qubit gates. It is possible to adjust a given electrical control amplitude Qd as desired based on experimental considerations, for example, with the amplitude of the microwave signal sent to the device.

[0105] It is then possible to minimize the errors made by adjusting the well-defined qubit parameters so that a certain equation is verified.

[0106] It is possible to first introduce temporary variables which will simplify the mathematical expressions:

[0108]

[0109] which depend only on the three adjustable parameters of the qubit as, aas and y, as well as the adjustable control amplitude applied to the qubit Qd.

[0110] In order to ensure that the probability of reaching an undesirable transition after the application of the electric drive is very low, for example, P = 0.01%, it is possible to calculate the following quantity: [YES] ,.

[0112] P is the desired probability of undesired transitions after the application of AC electric current (e.g. after the application of an X gate).

[0113] It is possible to adjust the parameters of the qubit so that P = 0.01%, corresponding to very good operation of a one-qubit quantum gate.

[0114] The set of steps uses the predefined adjustable parameters, which are directly related to the experimental parameters of the magnetic field and electrostatic potentials, after which the qubit is in the optimal operating regime.

[0115] This occurs because these adjustable parameters satisfy the following set of equations:

[0116] ■ "

[0117] Figure 5 illustrates the operating regime of the qubit which satisfies the inequality presented and results in the qubit frequency, i.e. the difference between the energy levels of the second curve, starting from the bottom of the graph, and the first curve, Starting from the bottom of the graph, this represents a constant function of the qubit's epsilon bias voltage. Since the variation of this function quantifies the noise under load, such a regime protects the qubit from this noise.< / pp>

Claims

Demands

1. A method for calibrating a two-level spin quantum system or spin qubit, coupled to a microwave cavity by a symmetric magnetic field and an antisymmetric magnetic field, this quantum system being in the form of a double box or double quantum dot comprising a left box or dot and a right box or dot, and being subjected to a bias voltage, characterized by the following steps: - setting the bias voltage (e) to zero volts, - determining a wave function <pp de chacun des boites ou points quantiques, - calculer et régler constantes couplage magnétique antisymétrique aas symétrique as via la formule suivante : ai="2jqBi(x)q">p(x)*q)p(x)dx, where <pp est la fonction d'onde d’orbitale électronique p (p = boite ou point gauche ou boite ou point droit), et Bi(x) est le champ magnétique symétrique Bs(x) et antisymétrique Bas(x), calculer et / ou régler la constante de couplage tunnel (y), et / ou la constante de couplage magnétique symétrique as et / ou la constante de couplage magnétique antisymétrique aas de telle sorte que : 2yas= as2 + aas2 et / ou p - "" 4- OÙ Ü. — | 4-1 j] et

2. A method according to claim 1, wherein the wave functions are determined by solving a Schrödinger equation starting from the assumption that the system is a double electrostatic potential well.

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

4. A method according to claim 1 or 2, comprising the following steps: - calculating each wave function considering the absence of a magnetic field, - calculate the tunnel coupling constant (y), - apply the symmetric magnetic fields Bs(x) and antisymmetric magnetic fields Bas(x) to the electron, - calculate the asymmetric magnetic coupling constants aas and symmetric magnetic coupling constants as.

5. A method according to any one of the preceding claims, wherein the symmetric magnetic fields Bs(x) and antisymmetric magnetic fields Bas(x) are produced by magnets.

6. A method according to any one of the preceding claims, wherein the symmetrical magnetic field Bs(x) is achieved by a solenoid and the antisymmetrical magnetic field Bas(x) is achieved by at least one electrode enabling magnetic polarization, preferably at least one grid electrode.

7. A method according to any one of the preceding claims, wherein the bias voltage is adjustable.

8. 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, said quantum system being in the form of a double box or double quantum dot comprising a left box or dot and a right box or dot, the component comprising: - means for applying an electrostatic potential so as to apply a bias voltage (e) to said double quantum box, - means for applying a symmetric magnetic field and an antisymmetric magnetic field between the two boxes respectively left and right,characterized in that the system further comprises a bias voltage (e) maintained at zero volts and a tunnel coupling constant (y) and / or the symmetric magnetic coupling constant as and / or the antisymmetric magnetic coupling constant aas such that: 2yas = as2 + aas2 and / or P — ____ A4 -3- Qi WHERE, And As, « -f- where as and aas are respectively symmetric and asymmetric magnetic coupling constants via the following formula: ai=2jqBi(x)q>p(x)*q) p(x)dx, where< / pp>

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