WO2001010027A1 - Quantic computer based on magnetic qubits - Google Patents

Abstract

Quantic computer based on magnetic cubits which consist of monodomain, nanometric, dielectric magnetic units (1), with a high ferromagnetic resonance quality factor, in a quantic superposition of the levels of the fundamental spin state and of the first excited spin state, operating in a milikelvins temperature range, each of the magnetic units (1) being deposited on a dielectric non magnetic substrate (6), inside an elementary quantic device (2) which incorporates a superconductor inductive element and a micro-SQUID sensor, and to which are associated superconductor lines (5). The quantic states of each qubit are manipulated and measured by sending and receiving electromagnetic signals to and from the corresponding quantic elementary device so that the quantic states of the various magnetic units are mixed/superposed by connecting said quantic element devices through superconductor lines (3) with switches of the Josephson union type (4).

Description

 QUANTIC COMPUTER BASED ON MAGNETIC QUBITS

FIELD OF THE INVENTION

The present invention concerns logical and data storage elements based on nanometric size structures (particles and molecular aggregate systems, or "clusters") for the processing and storage of quantum information.

The invention is based on a new class of quantum bit or qubit, a magnetic qubit, that is a mesoscopic spin system. The qubit according to the invention consists of a monodomain magnetic unit, of nanometric dimension, generally dielectric, with a high quality factor (QF) of ferromagnetic resonance, in a quantum superposition of the level corresponding to the fundamental state of spin and the level of the first excited state of spin. This magnetic unit is able to improve the magnetic recording density when the operation is performed in a temperature range of the order of the milikelvin. The invention also relates to a logic gate using a series of magnetic qubits deposited on a suitable substrate and a quantum computer based on magnetic qubits organized according to a suitable architecture.

The invention also relates to dielectric materials, such as monodomain magnetic particles of nanometric size or magnetic molecular aggregates with a total spin of less than 1,000, suitable for the preparation of said qubits.

In addition, the invention also relates to a method for operating a quantum computer built on magnetic qubits.

BACKGROUND OF THE INVENTION In conventional computers, the electric charge or its absence represents the "O" or the "1" used in the binary data storage language. In a quantum computer, the energy levels of the individual particles or aggregates of particles will represent the information. According to quantum mechanisms such energy levels are discrete states. So the state fundamental of spin or low state, will represent an "O" and the excited state of spin or high state will represent a "1".

Quantum computing has been one of the fields that in recent years has undergone a faster development partly due to its implications in theoretical physics. Today it is one of the important objectives of experimentation in physics and engineering. An element of a quantum computer is a qubit - an object that exists in a quantum superposition of two states cos (x) ¡0> + sin (x) ¡1> (Feynman).

That is, in mathematical terms, the state of a quantum system (usually denoted by | 0) is a vector in a Hilbert space of possible states for the system. The space of a single qubit covers a base consisting of the two possible classic states denoted by | 0) and 1 1). This means that any state of a qubit can be decomposed in the overlay.

| *) = a | 0> + b | l) [1] with an adequate choice of complex coefficients a and b.

Unlike a binary element of a conventional computer, which can be in a ¡0> or ¡1> state, each qubit has an infinite number of pure quantum states, characterized by the continuous variable x. The measure of x destroys the qubit while projecting its state on ¡0> or ¡1>. The interaction with the environment, which should be avoided, regardless of how weak it may be, eventually results in the same projection effect or what is the same, randomization of decoherence (loss of quantum coherence, that is to say the superposition of two states) of phase x. To perform a computation, the qubits must be coupled together in a controlled, predetermined manner. Computing involves the preparation of all qubits according to a given list, followed by the evolution by the quantum mechanics of the system towards a final state, followed by the measurement of that state. A scale computing requires a large number of interconnected qubits, which will increase decoherence. Fortunately, with a low decoherence, this problem can be solved using quantum correction algorithms (Shor, Steane). These algorithms are based on a theoretical concept of expanding the Hilbert space of the qubits beyond two dimensions (¡0> and ¡1>), creating a redundancy that protects against errors and increasing the decoherence time. The potential of the quantum computer derives from its equivalence with a conventional computer with an infinite number of parallel processors. Quantum computers, if they develop, will be used in different scientific, technological and business disciplines. In physics, for example, applications such as powerful simulations in atomic and nuclear physics, of the electrical, optical and magnetic properties of materials can be anticipated. Indeed, quantum computers, with their quantum dynamics, will be the most suitable machines for such computations, producing fast and reliable responses. A conventional computer, looking for an element among a list of N elements, has to examine N / 2 elements so that it has a 50% chance of success. A quantum computer that performed the same task would require only the square root of N stages, since it can examine multiple elements simultaneously (Grover). By

An example for 10,000 elements would be the difference between 5,000 and 100 stages, which suggests an immediate commercial application of quantum computers. Consequently, as a qubit is based on two states, a complete system of m qubits will involve 2 ^m states. A classic computer with an m-bit input register can only be prepared in one of these possible states, and therefore calculations with different input values must be performed as separate calculations. However, by extrapolating the principle of superposition of equation {11 to a machine with an input register of m qubits, a quantum computer allows an overlapping of all its possible classical binary states.

This means that you could perform a single calculation with your inputs set to an overlay of all classic input values! This phenomenon called quantum parallelism is the basis for solving some problems much more quickly with a quantum processor.

Some devices for quantum computing that have been proposed and that appear in the technical literature are:

1. Ions in an electromagnetic trap, interacting through their vibration modes, with quantum states prepared and read by an external laser (JI Cirac and P. Zoller). Although it is possible to implement it with a few ions, this system is difficult to build on a larger scale, with a size necessary for useful computing. US patent 5,793,091 by Ralph Godwin Devoe refers to a parallel architecture for a quantum computer using ion traps.

2. Atoms in rays, interacting electromagnetically with each other and with external photons (Kimble et al., Aspect). This system presents the same problem as the previous one: it can be relatively easy to operate with a small number of atoms but very difficult to build on a large scale. US patent 4,984,959 to Houk et al. refers to an optical computer including a mediated conversion of numbers into a residual representation.

3. Electrons at quantum points interacting electrostatically (Ekkert and Jozsa). The qubits are formed by quantum levels of confined electrons. This system needs to operate at the level of electrons, individually, which in fact is more a theoretical issue than a practical possibility. US patent Di Vicenzo 5,530,263 refers to three quantum dot computing elements of an atomic or near scale.

4. Electrically coupled nanometric superconductors (Shnirman et al.). The qubits are formed by discrete levels due to the flow rate.

5. Nuclear spins coupled through interaction of magnetic dipoles (Kane, Gerchenfeld and Chuang, Cory et al.). Magnetic fields can be used to manipulate this system at low temperature. Nuclear spins have a great decoherence time. The problem with this proposal is that it is not clear that individual nuclear spins can be handled efficiently in a system that has reasonable dimensions. WO 99/14858 refers to a quantum computer comprising a semiconductor substrate in which donor atoms are introduced to produce a series of donor nuclear spin electron systems with non-zero electronic wave functions inside the core of the core. donor atom Other references in the specialized literature known to applicants, of possible interest in this field for a better understanding of the principles of the invention are detailed below:

1.- R.P. Feynman, Opt. News 11, 11 (February 1985).

2.- PW Shor, "Fault-tolerant quantum computation" in Proc. 37 * Symp. On Foundations of Computer Science (IEEE Computer Society Press).

3:00 A.M. Steane, Phys. Rev. Lett. 78, 2252 (1997).

4.- LKGrover, "A fast quantum mechanical algorithm for datábase search" in Proc. 28 ^Λ Annual ACM Symposium on the Theory of Computing "(1996); Phys. Rev. Lett. 79, 325 (1997).

5.- J.I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).

6.- H.J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691

(1997).

7.- A. Aspect et al. , Phys. Rev. Lett. 45, 617 (1980). 8.- A. Ekkert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).

9.- A. Shnirman, G. Schón and Z. Hermon, Phys. Rev. Lett. 79, 2371 (1997).

10.- B.E. Kane, Nature 393, 133 (1998).

11.- N.A. Gershenfeld and I. L. Chuang, Science 275, 350 (1997).

12.- D. Cory, A. Fahmy and T. Havel, Proc. Nat. Acad. Sci. 94 (5), 1634 (1997).

13.- C.P. Collier, E.W. Wong, M.Belohradsky, F.M. Raymo, J.F. Stoddart,

P.J. Juekes, R.S. Williams, and J.R. Heath "Electronically Configurable

Molecular-Based Logic Gates "Science Jul 16, 1999: 391-394.

14.- E. Del Barco, N. Vernier, JM Hernández, J. Tejada, EMSchudnovsky, E. Molins and G. Bellessa "Quantum Coherence in Fe ₈

Molecular Nanomagnets "pending publication in Europhysics Letters,

1999.

EXHIBITION OF THE INVENTION

The objective of the invention is the exploitation of magnetic systems, operating in a range of milikelvins temperatures and duly shielded with respect to external magnetic fields, for quantum computing.

This invention describes a quantum computer based on magnetic qubits, that is, monodomain magnetic particles of nanometric size or molecular aggregates as previously defined. While all molecular aggregates are identical, monodomain magnetic particles may differ in size and shape.

The term "domain" is described for example in CP Bean and J. D. Livingston J. Appl. Physics, 30, 120 (1959); and BD Cullity. Introduction to Magnetic Materials, Addison-Wesley Publishing Co., Massachusets, (1972), see also The Magnetic Properties of Materials by JE Thomson, Newnes International Monographs on Materials Science an Technology, CRC Press, Cleveland, Ohio 1968. Each magnetic particle of nanometric size, monodomain or molecular aggregate is deposited, first, in a well-controlled area on a dielectric substrate, for example embedded within a solid matrix, and is located inside a quantum elementary device consisting of a superconductive inductive element and a micro-SQUID (microscopic device, superconductor, quantum interference) in sensor functions. The quantum states of each qubit are manipulated and measured by sending and receiving electromagnetic signals to and from the corresponding set of superconductive inductive element and micro-SQUID. The quantum states of the different particles of nanometric size are mixed / superimposed by the connection of said quantum elementary devices by superconducting lines with Josephson switches.

Two sets of quantum states can be used in a magnetic qubit. The first one, detailed in Fig. 1 of the attached drawings, refers to the situation in which the passage, by tunnel effect, of the spin of the nanometric particles, monodomain, is suppressed. In this case, the first excited state of the spin corresponds, in classical terms, to the uniform precession of the magnetic moment of the particle around its axis of anisotropy. This excited state is separated from the fundamental spin state by the energetic distance that is equal to the product of the Planck constant by the ferromagnetic resonance frequency (FMR). The quality factor (QF) in dielectric ferromagnetic materials can be as high as 10 ⁶ , which suggests a very low decoherence rate.

This kind of qubit and its manipulation are very similar in concept to qubit based on NMR (nuclear magnetic resonance), see for example Chuang, in the work "Introduction to Quantum Computation and Information", World Scientific, 1998). This last qubit must be manipulated by applying radio frequency fields at the level of an individual nuclear spin in the range of NMR frequencies, which is extremely difficult to implement (although possible, in principle). On the contrary, the FMR qubit can be easily manipulated inside a set of superconductive and micro-SQUID inductive element, due to the fact that the Typical FMR frequencies and typical micro-SQUID frequencies are in the same microwave range.

The QF of the FMR of pure dielectric ferromagnetic crystals can be as high as one million, well above the QF of one thousand, widely cited as necessary to perform computation at an adequate scale. Although FMR and its QF have not been measured in individual nanometric particles, there is no reason to believe that it should be smaller than in large crystals.

The second situation of quantum states corresponds to small magnetic particles or molecular aggregates where the spin passes through the tunnel through the anisotropic barrier. The phenomenon has been considered both theoretically and experimentally by two of the present inventors Chudnowsky E..M. and Tejada J. in the work "Macroscopic Quantum Tunneling of the Magnetic Moment", (Cambridge University Press 1998). In this case, which is illustrated in Fig. 2, the fundamental state of the particle is divided into two states that can be used as states 10) and 1 1).

In both situations the operating temperature must be low compared to the energy distance Δ between the states | 0) and 1 1). The energy distance of the first situation is of the order of 0.1 K, while in the second situation said energy distance can be controlled by applying the external magnetic field perpendicular to the anisotropic axis of the particle or molecular aggregate. In any case the temperature of the operation must be in the range of the milikelvin.

The deposition and characterization of the sets of particles or molecular aggregates on a dielectric substrate will be achieved using techniques such as lithography based on very high scale integration (VLSI), atomic force microscopy (AFM), scanning effect microscopy tunnel (STM) and magnetic force microscopy (MFM), see Proceeding of the IEEE, Special Edition "Quantum Devices and Application" April 1999, pages 652-657, The Institute of Electrical and Electronics Engineers Inc. Edited by Alan C. Seabangh and P. NarKi Mazunder, USA. Examples of substrates for organizing these magnetic units, whether nanoparticles or molecular aggregates in sets of 1, 2 and 3 dimensions can be matrices such as molecular clathrates, porous zeolites, Langmuir-Blodgett epitaxial film films, plastics and nanotubes. Each nanoparticle or molecular aggregate will act as an individual and identifiable qubit.

The mixing or superposition between different qubits is achieved in this invention by placing the magnetic units inside a superconductive and micro-SQUID inductive element assembly, and connecting these quantum elementary assemblies or devices to each other by means of superconducting lines such as shown in Fig. 3 of the attached drawings. The change in the magnetic states of any particle will result from the electromagnetic induction of a superconducting current in the set of superconductive and micro-SQUID inductive element that surrounds said magnetic unit. This current will flow to the neighboring assemblies changing the quantum states of the nearby magnetic units. For this purpose, Josephson type connections (schematized as switches) acting as switches will be used. Josephson type joints allow switching between different states in extremely short times. It is feasible to control the interaction between qubits simply by connecting or disconnecting the corresponding superconducting lines that relate them.

Logic gates based on magnetic nanometric structures need to maintain consistency during computing time. In the magnetic qubit described in this invention the effect of decoherence can be diminished by purifying the particles both chemically and isotopically.

In addition, the particles must be dielectric in order to avoid the decoherence phenomena associated with the conducting electrons.

Examples of materials suitable for the situation shown in fig. 1 are ferro and ferri nanometric particles with an anisotropic field greater than 0.05 T, such as CoFe ^ O ,,, -Fe ^ and BaFe ₁₂ O ₁₉

In the situation of Fig. 2, anti-ferromagnetic particles or nanometric molecular aggregates can be used. Examples are ferritin and molecular aggregates of Fe ₈ synthesized according to Wiedghardt K., Pohl K, Jibril I and Huttner G. "Angew. Chem. Int. Ed. Engl. (1984) 77 and with a nominal composition [( C ₆ H ₁₅ N ₃ ) ₆ Fe ₈ (μ ₃ -O) ₂ (μ ₂ -OH) ₁₂ (Br ₇ (H ₂ O)) Br ₈ H ₂ θ] checked by chemical and infrared analysis. ₈ the distance between the levels corresponding to the two lowest levels within the magnetic anisotropic wells is around 5K. As soon as the temperature drops significantly below that value, the number of excited spin levels is reduced exponentially and only transitions between the levels corresponding to the fundamental spin state are of practical interest. By applying a static external magnetic field perpendicular to the axis of easy magnetization, the energy of these transitions can be adjusted to the frequency of the radiation field and observe coherent quantum oscillations of the spin, similar to the example of ammonia molecules described in the literature.

The quantum states of the particles can be manipulated by combining two techniques:

- firstly by applying external magnetic fields of the order of the anisotropic magnetic field of the particles;

- secondly, by sending electromagnetic signals to the superconductive and micro-SQUID inductive element assemblies with a frequency that equals the energy distance between 10) and 1 1) divided by the Planck constant; said frequency shall be equal to the FMR frequency for the first situation described in Fig. 1 and equal to the "quantum splitting" or energy distance that separates the levels | O) and 1 1) described in Fig. 2. In the second case (Fig. 2) the frequency can be adjusted by the transverse magnetic field.

The advantage of this method of manipulating qubits over all other existing proposals derives from the fact that electrical circuits will be used in a manner similar to that of conventional computers and that external radiation is not required.

To this end, the coupling of magnetic particles to the superconductive and micro-SQUID inductive element assemblies is an ideal arrangement since both the magnetic units (particles or molecular aggregates) and the said assemblies can operate in the same frequency range.

In the same way, the final state of the qubits can be easily read through the micro-SQUIDs in the conventional manner.

The quality factor (QF) of 10 ³ -10 ⁶ will make it possible for the proposed computer to perform 10 ³ -10 ⁶ operations without applying error correction. By applying the error correction algorithm the number of operations can be drastically increased. DESCRIPTION OF THE DRAWINGS

Other features and advantages of the present invention will be apparent. from the following description, considered in conjunction with the accompanying drawings, in which: Fig. 1 is a schematic drawing showing the structure of spin levels in the two potential wells associated with the magnetic anisotropy of the nanometric particles; Fig. 2 is a schematic drawing showing the structure of spin levels in two potential wells. The breakage of the degeneration of the fundamental state Δ due to the tunnel effect is also indicated; and Fig. 3 is a schematic drawing indicative, in a simplified, convenient form, of a portion of a possible arrangement of magnetic units (nanometric particles or molecular aggregates), as proposed by the invention deposited on a substrate and whose quantum states are properly mixed / superimposed so that they constitute a logical element suitable for a quantum computer; The figure also includes the symbol of the two quantum states of the spin.

In Fig. 3 a plurality (the drawing only represents a minimum part of the arrangement) of magnetic units (1), are surrounded by a set (2) or quantum elementary device that includes a superconductive inductive element and a micro-SQUID, which will generally surround both the magnetic unit, although the micro-SQUID could adopt another alternative arrangement. Said assemblies (2) are interrelated through superconductive inductive lines (3) each of which contains a control switch (4) that can be a Josephson type junction. Each set (2) is connected to lines (5), preferably also superconductors, to measure and manipulate the qubits. The magnetic units (particles or molecular aggregates) are deposited on a non-magnetic dielectric substrate (6) by the techniques already defined that enable a quality factor (QF) that must exceed the QF of the NMR qubit in the milikelvin range .

A set of superconductive and micro-SQUID inductive element can, in principle, manipulate the magnetic state of the magnetic unit (1) with a precision of a quantum of magnetic flux. Connecting said assemblies (2) as shown in Fig. 3 will imply mixing or superimposing the states of the different particles (1). The change in the quantum magnetic state of any magnetic unit will result in the generation of an electromagnetic induction in the assembly (2) surrounding said particle (1). This current will flow to the neighboring assemblies (2) changing the quantum states of the corresponding magnetic units (1) that they enclose. Josephson type connections (5) have already been applied as building blocks for classic digital circuits. The advantage of magnetic systems for quantum computing over all the above mentioned proposals is twofold. In the first place, all the elements necessary to build the said quantum computer already exist and have been experimentally tested. The materials, both the monodomain magnetic particles of nanometric size and the molecular aggregates, have been studied intensively and characterized by the present inventors and other groups during the last years (see the published documents that have been cited). Regarding the measurement of the magnetic moment of the particles, it is currently possible to measure particles with a total spin below 1000 inside a micro-SQUID arrangement (eg Wensdorfer and others in the CNRS - Grenoble). Secondly, no external radiation is required to manipulate the magnetic qubits. All operations can be performed electronically, as in conventional computers, so that all existing experience can be used.

Claims

CLAIMS 1. A logical element comprising: a first magnetic unit consisting of a particle or molecular aggregate prepared in a first superposition of two different quantum states of the spin; a second magnetic unit consisting of a particle or molecular aggregate prepared in a second superposition of two different quantum states of the spin; said first and second magnetic units being firmly coupled or fixed to a dielectric substrate and interacting through a superconducting circuit provided with control switches to be able to mix / superimpose the quantum states of the magnetic units; in which logical element the magnetic units are able to provide a high density of magnetic storage when the operation is performed in a range of temperatures in the range of millikelvin so that each particle acts as an individual and identifiable qubit, and the system is shielded with respect to external magnetic fields. 2. A logical element according to claim 1, wherein said preparation of said first and second magnetic units involves sending electromagnetic signals through a superconducting ring that surrounds each of said magnetic units. 3. A logical element according to claim 1, wherein said first and second magnetic particles are monodomain magnetic particles or molecular aggregates with a total spin of less than 1,000. 4. A logical element according to claim 3, wherein said magnetic particles or molecular aggregates are dielectric in nature. 5. A logical element according to claim 3, in which the materials of said first and second magnetic particles are subjected to chemical and isotopic purifications to acquire a low decoherence. 6. A logical element according to claim 3, wherein said superconducting ring consists of a quantum elementary device comprising a superconductive inductive element and a micro-SQUID, with a device associated with each magnetic unit and surrounding at least said element inductive superconductor to each of said magnetic units. 7. A logical element according to claim 1, wherein said control switches are high frequency switches of the Josephson junction type for controlling the interaction between said first and second magnetic units. 8. A logical element according to claim 56 and further comprising data acquisition means for measuring said two different quantum states of the spin, of said first and second magnetic units. 9. A logical element according to claim 8, wherein said data acquisition means are constituted by said micro-SQUIDs that have conductive wires connected to measure and manipulate said qubits. 10. A logical element according to claim 9, wherein said conductive wires are superconducting lines. 11. A logical element according to claim 2, wherein said two different quantum states of the spin, are either the quantum states of the operator S _z , or the different quantum states that derive by tunnel effect from the breakage of the degeneration. of the fundamental state of said magnetic units. 12. A logical element according to claim 11, in which to acquire said two different quantum states of the spin, an external magnetic field is applied through said superconducting ring. 13. A logical element according to claim 12, in which to acquire said two different quantum states of the spin that derive by tunnel effect of the breakage of the degeneration of the fundamental state of said magnetic units, said external magnetic field must be perpendicular to the easy magnetization axis of magnetic anisotropy. 14. A logical element according to claim 12, in which to acquire said two different quantum states of the spin, of the operator S _z , of each of said magnetic units, said external magnetic field must be parallel to the axis of easy magnetization of magnetic anisotropy. 15. A logical element according to claim 11, wherein said superconducting ring receives electrical signals of FMR frequencies for the manipulation of said first and second magnetic units, which in this case are monodomain magnetic particles of nanometric size. 16. A logical element according to claim 11, wherein said superconducting ring receives electrical signals of frequencies corresponding to said breakage of the degeneration of the fundamental state or tunnel effect of the magnetic units, which are in this case molecular aggregates. 17. A logical element according to claim 16, wherein said frequencies can be adjusted by means of the transverse magnetic field. 18. A logical element according to claim 3, wherein said two different quantum states of the spin, are the fundamental states of the S _z operator and said monodomain, nanometric magnetic particles are ferro and ferri nanometric size particles with higher anisotropic fields at 0.05 T, such as CoFe ^ _t , -Fe ₂ θ ₃ and BaFeι ₂ O ₁₉ 19. A logical element according to claim 3, wherein said two different quantum states of the spin are the states that derive from the breakage of the degeneration of the fundamental state by tunnel effect of each of said magnetic units, which consist in anti-ferromagnetic particles and molecular aggregates such as ferritin and Fe ₈ . 20.- A logical gate based on a qubit consisting of a monodomain magnetic particle, of nanometric size or molecular aggregate, with a high quality factor of the ferromagnetic resonance, in a quantum superposition of its fundamental state and the first excited state of spin , firmly coupled to a dielectric substrate and surrounded by a quantum elementary device comprising a superconductive inductive element and a micro-SQUID. 21. A logic gate comprising two magnetic qubits according to claim 20, with their quantum states mixed / superimposed by means of a superconducting line that includes a control switch. 22.- A logical door comprising: a first magnetic unit consisting of a particle or molecular aggregate prepared in a first superposition of two different quantum states of the spin; at least a second magnetic unit consisting of a particle or molecular aggregate prepared in a second superposition of two different quantum states of the spin; a superconducting circuit equipped with control switches that allow interact with said magnetic units; a quantum elementary device comprising a superconductive inductive element and a micro-SQUID, associated to each magnetic unit and surrounding at least said inductive element to said magnetic unit, whose elementary device is linked to conductive lines, and means for measuring and manipulating said quantum elementary device, through said conductive lines. 23. A quantum computer comprising a series of magnetic units according to any one of claims 1 to 19, surrounded by a quantum elementary device comprising a superconductive inductive element and a micro-SQUID, connected to superconducting lines and interrelated by a circuit Superconductor with communication control switches between magnetic units. 24.- A method for a general purpose quantum computation comprising a plurality of interconnected logical elements, each of which includes: a first magnetic unit consisting of a particle or molecular aggregate prepared in a first superposition of two different quantum states of the spin ; at least a second magnetic unit consisting of a particle or molecular aggregate prepared in a second superposition of two different quantum states of the spin; said first and second magnetic units interacting through a superconducting circuit provided with control switches, so that the quantum states of the units can be mixed / superimposed; a superconducting ring that surrounds each of said magnetic units, wherein the method comprises the following steps: a) introducing a data carrier signal through said superconducting ring, so that one of said two different quantum states of the spin b) close the switches in a chosen order to interconnect a certain number of magnetic units with each other; c) read the final states of the connected logic elements.