Quantum computing module and method of manipulating quantum propagation modes to perform a quantum computation

Abstract

The present invention relates to a Quantum computing module including: an input (2) comprising a mode separator (15), configured to separate an electrical transverse mode TE and a magnetic transverse mode TM of an input quantum in two parallel paths, a first and a second path (5, 10 ), parallel to each other, respectively for the said magnetic transverse mode TM and for the said electric transverse mode TE, located downstream of said mode separator (15), each path being characterized by: a single-mode waveguide (4), mode handling media (20), including at least first phase change media (22); an output 3 comprising means of combining modes (25), arranged to join the two parallel paths (5, 10); where : a) the two parallel paths (5, 10) are distinguished from each other at least because the first path (5) includes : the first means of transformation (30) of the magnetic transverse mode TM in the transverse electric mode TE located upstream of these means of manipulation (20), second means of transformation (32) of the transverse electric mode TE into transverse magnetic mode TM located downstream of these means of manipulation (20); or b) the two parallel paths (5, 10) are distinguished f rom each other at least because the second path (5) includes : the first means of transformation of the electric transverse mode TM into a magnetic transverse mode TM located upstream of these means of manipulation (20), second means of transformation of the magnetic transverse mode TM into an electrical transverse mode TE located downstream of these handling means (20).

Description

[0001] Owner: ROTONIUM S.R.L., GEMONA DEL FRIULI (UD)

[0002] PIAZZA GARIBALDI 14, CAP 33013, Tax code and registration n.to the Business Register: 03067540306.

[0003] Title: Quantum computing module and method of manipulating quantum propagation modes to perform a quantum computation.

[0004] ★ ★ ★ ★ ★

[0005] DESCRIPTION

[0006] The present invention concerns a quantum computing module and a method of manipulating quantum propagation modes to perform a quantum computation.

[0007] The present module includes a photonic quantum circuit that allows you to perform the major fundamental operations of quantum computing. It is a versatile programmable quantum computing module that can be placed in any node of a generic quantum circuit in order to perform computational operations (quantum and classical with the Toffoli configuration) using photons. This module can also be hybridized or connected to other classical or quantum devices other than photonic ones.

[0008] Quantum computing is achieved by rotating the bases of the quantum mechanical states of the photon and letting the quantum states evolve as in the Heisenberg picture of quantum mechanics.

[0009] DEFINITIONS

[0010] QAM = Orbital Angular Momentum SAM = Angular Momentum of Spin

[0011] STATES = quantum states associated with quantum (e.g. photon in the case of photon radiation)

[0012] MODES = decomposition of electromagnetic fields into fundamental waveguide modes where the TE mode is the electrical transverse mode, and the TM mode is the magnetic transverse mode.

[0013] VORTEX = modes with non-zero angular momentum, i.e. with L different from zero.

[0014] OAM (L=+l) and 0AM (L=—1): these are the 0AM modes that in the literature have orbital angular momentum L=+l and L=-l. We can also use all OAM (L≥+1) and OAM (L≤ 1) modes and their overlays.

[0015] BASE = corresponds to the set of the 4 quantum states TE, TM, OAM (L=+l) and OAM (L=—1) that constitute directions in 4-dimensional Hilbert space. The basis is a mathematical term that indicates the fundamental vectors that make up a space. For example, a vector v in a plane is described by v=a*vx+b*vy, where vx and vy are the base vectors associated with the x- and y-axis. If chosen of unit length, they are called versors. Therefore, a vector in a space is given by the sum of the projections in the base vectors. In our case, a vector in 4-dimensional Hilbert space represents the quantum state of the quantum at the output of a computational module, which can be either only one of the 4 states or a suitable combination of them. We can also use broader bases to augment the data handled, such as all OAM (L≥+1) and OAM (L≤ 1) states and their overlaps.

[0016] ACTIVE TRENCH / ACTIVE TRENCH EQUIVALENT= sometimes we use these terms as synonyms for generic active phase change means, which comprises or are equivalent to an adjustable trench (either thermally or otherwise). They are obtained for example by driving a controlled variation in a predetermined area, for example a variation in the geometry of the waveguide.

[0017] ACTIVE PHASE VARIATION MEANS: these are means that can be driven, the active trench mentioned above is an example, in the preferred forms of actuation they can include a thermo-optical device controlled to heat a predetermined area of a waveguide (4). They are vehicles that perform a function when activated by piloting, for example piezoelectric.

[0018] PASSIVE PHASE VARIATION MEANS: These are unmanned vehicles, for example with fixed geometry, which therefore always perform the same function independently of an activation .

[0019] L= Value of Orbital Angular Momenta OAM

[0020] K identifies the L values of the respective angular momenta OAM (L>+1) and OAM (L<-1) of said quantum or one of their superpositions, where K is not necessarily an integer.

[0021] Qudit: also called quantum dit, in general it is the unit of quantum information described by a superposition of states, where the number of states is an integer greater than two. In the present invention the qudits are preferably at 2L+2 states of a single quantum.

[0022] STATE OF THE ART Our previous Italian patent application No. 102022000022368, claimed as a priority and incorporated here for reference, introduces the concept of operating a quantum computation in four-dimensional Hilbert space using 4-mode qudits, carried by a selective waveguide compatible with four fundamental quantum modes, 0AM (L=+l), 0AM (L=—1), TM, TE. A trench discontinuity along the guide allows modulation of the modes.

[0023] Although this system is excellently working, it is linked to a waveguide and related trench that are expensive to make, as they are not directly available on the market among the standard components.

[0024] The applicant therefore carried out further research with the aim of overcoming this problem.

[0025] Another purpose of the present invention is to provide a versatile circuit capable of performing major quantum operations with the least possible number of photon losses that would generate computational errors.

[0026] Another purpose of the present invention is to use standard fabrication waveguides and techniques widely used in the fabrication of standard circuits, such as those for the fabrication of silicon and silicon oxide components that are part of our daily use to drastically reduce costs.

[0027] Another purpose of the present invention is to make it possible to use qudits with a large number of states, preferably more than 4. This makes it possible to handle a large amount of quantum information.

[0028] The purposes are solved by a quantum computing module and a method according to the attached claims. DETAILED DESCRIPTION

[0029] Further features and advantages of the present invention will be better shown by the following detailed description of its preferred forms of realization, made with reference to the attached drawings and given as an indication and not limitation. In such drawings:

[0030] - Figure 1 schematically shows a quantum computing module according to a first form of implementation of the present invention;

[0031] - Figure 2 shows the map of transformation from one mode to another based on the applied phase variation (of n / 2 or multiples thereof);

[0032] - Figures 3 and 4 show two examples of passive phase change media;

[0033] - Figure 5 shows a diagram of the 0AM and TE and TM modes with the corresponding polarization;

[0034] - Figure 6 schematically shows a quantum computing module according to a second form of implementation of the present invention simpler than that of figure 1

[0035] - Figure 7 shows the polarization states of the states in the single-mode drive of the actuation form of Figure 6, and the transition from one to the other according to the phase change of n / 2 or multiples thereof; the figure also shows the comparison with the states in a hypothetical multimode drive and the fact that they mimic them thanks to the SPIN ORBIT COUPLING technique;

[0036] Figure 8 shows two possible options for the output of the module in Figure 6. Figure 1 shows a quantum computing module according to the present invention denoted as a whole by reference number 1.

[0037] Module 1 includes: an input 2 including a mode separator 15, represented by way of example but not limited to a polarized beam splitter, hereinafter also called PBS, configured in such a way as to divide an input photon beam characterized by the transverse electric and magnetic field TE and TM into two subbeams, one characterized by the magnetic transverse field TM and one characterized by the electric transverse field YOU; each of these two modes TM and TE including a polarization Ex, Ey;

[0038] - two parallel paths 5 and 10 downstream of the polarized beam splitter (PBS) 15, one for each subbeam; each characterized by:

[0039] • a single-mode waveguide 4, e.g. silicon on insulator (SI on Insulator, also called SOI in jargon) preferably of standard size, e.g. 220 x 480 nanometers for the wavelength of 1550 nanometers. Losses are minimal in these waveguides;

[0040] • mode 20 manipulation means, represented by way of example and not limited to a Mach-Zehnder interferometer, hereinafter also called MZI1 and MZI2, including the first phase 22 variation media indicated in the figure with PSI and PS2;

[0041] • an output 3 including means of combining modes 25, hereinafter also called C, arranged to join the two parallel paths 5 and 10; where the two parallel paths 5 and 10 are distinguished from each other at least because a first path 5 includes first and second means of transformation of mode 30, 32 represented by way of example and not limited by the respective means of rotation of the polarization (and therefore of the associated mode) hereinafter also called R, one upstream to one downstream of the respective means of manipulation 20.

[0042] Optionally, the two paths 5 and 10 can also be distinguished because a second path includes second means of phase variation 70 interposed between these mode manipulation means 20 and the said second means of transformation 32. This, however, may not be necessary if the first means of phase change are sufficiently performing, for example allowing a variation from -180° to + 180° or greater (see below the case of [-K*180°, + K*180°] where K is not necessarily an integer.

[0043] The mode 20 manipulation media of each path preferably include an active power divider device 50 at the output of the respective interferometers MZI1 andMZI2, the divider shall be driven, preferably by the phase induced by the phase variation media 22, to perform at least the following operations:

[0044] - send all radiation directly out to the means of manipulation 20,

[0045] - send a first part of the outgoing radiation to the handling media 20 and reject a second part by sending it to the respective reflection media 51 and 52 (e.g. mirrors), from which it is pushed back because this driving configuration corresponds to a closed gate for that state of the photon,

[0046] - reject all the radiation by sending it all to the respective means of reflection (51, 51) which corresponds to the total closure at each state of the photon.

[0047] The divider is, for example, of the 50 / 50 type, that is, it divides the incoming radiation into a first and second part of radiation, where each has 50% of the incoming radiation.

[0048] The divider device 50 can be of a known type.

[0049] In general a coupler is a device that couples the bundles while the divider divides them, often the same device can be used for both functions simply by inverting it, in literature they are known as coupler / divider devices .

[0050] The output diagrams made by the driving of the two dividers / couplers 50 of MZI1 and MZI2 are for example the following :

[0051] 1. They allow an output only from MZI1 and inhibit it from MZI2;

[0052] 2. They allow an exit only from MZI2 and inhibit it from MZI1;

[0053] 3. Allow output with equal power from MZI1 and MZI2;

[0054] 4. Allows output with equalized power from MZI1 and MZI2 (e.g. as the right / left balance of the stereo). Input 2 preferably includes at least one input register including at least one quantum qudit of at least 4 quantum states of a photon radiation (more generally of a quantum), or a qubit register of at least 4-levels, characterized by the fact that these 4 quantum states correspond to the following 4 modes of propagation of a photon and their superpositions:

[0055] A = 0AM (L=-l).

[0056] B = TM

[0057] C = 0AM (L=+l).

[0058] D = TE

[0059] Output 3 also preferably includes at least one register comprising at least one quantum quditch of at least 4-states, or a qubit register of at least 4-levels, characterized by these quantum states and their superpositions, where the four states are obtained by combination of the two modes manipulated by the manipulating means, where the manipulating means impose phase shifts of n on the modes corresponding to the states / 2 or multiples of it (see the phase change map in figure 2), so that at recombination in the combination media C the following states occur:

[0060] D=Ex=TE

[0061] B=Ey=TM

[0062] A=Ex+iEy= 0AM (L=-l).

[0063] C=Ex-iEy= 0AM (L=+l). where i = square root of -1

[0064] We observe that a "state" corresponds to the quantum state of the photon or equivalently of the associated electromagnetic field, the "mode" is instead relative to the waveguide. In our case the terms mean the same thing in that we use the modes of the guide to make the quantum states of the photon. In fact, the states are those of the photon where, as is well known, from Maxwell's equations and Majorana-Wigner's quantization to the semiclassical limit, the state of the photon corresponds to the mode carried by the waveguide and the overall path.

[0065] We also observe that, in the single-mode waveguide, after the 15-mode separator, OAM and polarization are coupled. There are the TE and TM modes and their superposition TE+, i TM and TE - i TM where i is the imaginary quantity that indicates a phase shift of ± 90° or half wave (±n / 2). The TE mode is related to horizontal polarization and the TM to vertical. The mode separator 15 divides the TE and TM modes and therefore decomposes the vortices into TE and TM while preserving the half-wave phase shift. So the vortex, that is, in our case that state with OAM (L=+l) and OAM (L=—1), is translated into modes of polarization linked to each other by phase shifts. This is a very special case that allows the use of single-mode waveguides made to transport the TE modes with the minimum possible losses. For this reason, the TM modes are temporarily converted into TE and, once manipulated as required by the calculation to be made, they are converted back into TM and recomposed in order to make either a vortex or a superposition of TE and TM modes and their vortices.

[0066] We observe that before the mode separator 15 and after output 3 it is possible to have multimode waveguides, for example 4 modes. Input 2 may correspond to the output of a previous circuit and / or output 3 may correspond to the input of a subsequent circuit.

[0067] Output 3 essentially recombines the two subspaces TE and TM in order to construct the 4 modes we use in the calculation. After exit 3 you can plan for various possibilities. For example, it is possible to insert a final module 60 with the function of mode-modulator (and their superimpositions), including, for example, active phase variation means 40 along a multimode wave guide, for example equivalent to an adjustable trench (either thermally or in another way), hereinafter called active trench, which makes the result present in the C-beam combiner module move in a deliberate way to obtain other state transformations such as Pauli-z and Controlled-z (Cz). The final module 60 is a multimode guide and can include either a separator to two other successive calculation modules or to a detector or another single module.

[0068] Phase variation media can be of various types, such as active or static.

[0069] Active examples include thermo-optical means controlled to locally heat the waveguide .

[0070] Among the static examples we include a trench 40b obtained directly in the single-mode waveguide 4 illustrated in figure 4. This phase changer is globally called waveguide trench 40b and modifies the state of each of the states of the photon by translating the state according to a pre-established scheme, for example that of figure 2. Note that you can also choose another sequence with a permutation of the ABCD states depending on how you define the programming language.

[0071] In figure 4 you can see a support wafer 12 made of Si02. On wafer 12 is arranged the single-mode waveguide 4, made of Si with a rectangular section of dimensions hXW = 220 x 480 nanometers for the wavelength of 1550 nanometers.

[0072] The trench is made as a rectangular section recess to suffer from an edge of the waveguide, where the trench 40b has an incision depth of ed = 70nm; a width w= ff*W with the factor ff=0.25. The waveguide width W is chosen based on frequency, either 1 or 1.1 pm.

[0073] The same effect can be obtained by deposition of material on the same single-mode waveguide 4 or by appropriate active variations of the waveguide geometry obtained, for example, by means of thermal actuators.

[0074] A second static example is trench 40a in figure 3, comprising two cracks at different depths on the same single-mode waveguide 4 mentioned above.

[0075] Trenches 40a and 40b essentially function as a polarization rotator of n / 2, therefore, with reference to figure 1, these two trenches can be adopted as examples of means of rotation of polarization 30 and 32.

[0076] Figure 2 shows the transformation map from one state to another of the four-dimensional Hilbert space based on the phase changes applied in module 1 and the displacement imposed by the means of phase variation of the final module 60.

[0077] In general, so far we have described two parallel paths (5, 10) that differ from each other at least because the first path (5) includes:

[0078] - the first means of transformation (30) of the magnetic transverse mode TM in the transverse electric mode TE located upstream of these means of manipulation (20), second means of transformation (32) of the transverse electric mode TE into transverse magnetic mode TM located downstream of these means of manipulation (20); however, the situation in which the two parallel paths (5, 10) are distinguished from each other is not excluded, at least because the second path (5) includes:

[0079] - the first means of transformation of the electric transverse mode TM into a magnetic transverse mode TM located upstream of these means of manipulation (20),

[0080] - second means of transformation of the magnetic transverse mode TM into an electrical transverse mode TE located downstream of these handling means (20).

[0081] 1) The first advantage of the circuits described is in their versatility to perform the largest quantum operations with the least possible losses as they are compact and do not have junctions that would cause photons to be lost and therefore generate calculation errors. Contrary to what already exists in the literature and in previous patents, these compact circuits allow to do on site almost everything that is required by quantum computing techniques. The others, on the other hand, have to connect many circuits and make the photon travel a much longer and more complex path with the consequence of losing photons and therefore information and therefore introducing errors in the calculation in progress.

[0082] 2) The second advantage is that they use standard fabrication waveguides and techniques widely used in the manufacture of silicon and silicon oxide components that are part of our daily use. So costs are drastically reduced.

[0083] 3) Preferably the calculation takes place in single-mode waveguides in silicon on an insulator (SI on Insulator, also called SOI in jargon) of standard size, for example of 220 x 480 nanometers for the wavelength of 1550 nanometers. Losses are minimal in these waveguides. Other materials and other wavelengths have their configurations given by known literature.

[0084] 4) Each of the four quantum states used is decomposed at the input of the module by means of a polarized beam splitter (or equivalent apparatus) into TE and TM modes including their superpositions.

[0085] 5) Preferably it is the TM modes that are transformed into TEs. Preferably, therefore, the TM modes, which would be easily dispersed in the circuit when the waveguide is very bent, are transformed into TE modes by the means of rotation of the R mode, such as suitable optical components, which rotate the polarization and therefore the associated quantum state. The TE modes propagate at much less loss, are manipulated for quantum computation and retransformed into TM modes to make them superposition with the TE modes

[0086] 6) The manipulation of photonic quantum states takes place by means of MZI modulation means that are activated in a predetermined way by the programmer and which allow various transformations of quantum states and therefore various operations to be carried out by means of the so-called quantum logic gates and quantum state registers. Activation involves phase changes by means of active phase change media, e.g. by means of local heating of the waveguide. This mode works like a waveguide trench, but in this case it is active, i.e. driven, and therefore of variable shape at will. The invention also includes other active phase variation media known in the literature to achieve such phase variations, such as piezoelectric media or particular materials inserted in the waveguide which are then modified with electromagnetic fields or other.

[0087] 7) Manipulation of quantum states, especially phase change, can also occur using passive optical components .

[0088] 8) The third advantage is that by using these standard manufacturing techniques, the error in the manufacture itself is reduced, guaranteeing not only high quality but also the low cost of the previous point.

[0089] 9) Fourth advantage is the versatility of this computing module with 4 quantum states associated with the photon. Not only does it simplify calculations as in the circuit of the previous patent application but it does major quantum operations without the use of other circuits.

[0090] 10) One of these modules can be used as a distributor node for calculation (photon distributor) to other modules or other parts of the circuit

[0091] 11) Each of these modules can be connected to another component of the circuit and act as a photon collector

[0092] 12) Each module can also be used as a calculation module and distributor towards one or more modules or generic components of the circuit.

[0093] 13) One or a network of these modules constitutes a universal quantum and classical computing circuit that can be coupled to other quantum or classical computers or circuits.

[0094] 14) The computational module in question or, more generally, the universal computational circuit, can be used by manipulating the quantum states of a single photon distributed in the circuit itself (i.e. singlephoton) or with several photons or packets of photons (called "continuously" or "continuous mode").

[0095] 15) Pairs or groups of entangled photons can be used to enhance the calculation.

[0096] 16) Entangled photons can also be used to reduce quantum calculation error. An example is "heralded" photons, i.e. they use one or more photons entangled with each other (twinned) to announce the arrival of one or more of them at a point in the photonic circuit that is decided during the computation phase.

[0097] 17) A further development of the circuit can also employ a frequency multiplication of the photon or photons generally obtained by beating waves to obtain frequencies close to the basic frequency that still propagate in the circuit. This results in multiple states that increase the size of the qudit as explained in the example of the additional "colored" configuration.

[0098] 18) The calculation formally takes place with rotations of the bases in four-dimensional Hilbert space of the quantum states that each photon can assume. These rotations can be arbitrary, being given by the superposition of the 4 states.

[0099] It is observed that a generic quantum photonic circuit can be realized by putting computing modules such as these connected to each other to make a network, i.e. a circuit, for a quantum and classical universal calculation and connected to other optical components capable of distributing and / or manipulating the quantum states of the photon or photons used for the calculation.

[0100] The quantum and classical logic circuits that each module mainly makes, implementing the PSI and PS2 manipulation means in an appropriate way are:

[0101] Identity all three Pauli x, y, x

[0102] Hadamard

[0103] Controlled Not (CNOT)

[0104] Controlled z (CZ)

[0105] Toffoil

[0106] Swap

[0107] Phase shift gates: e.g. Pi / 8 and Phase (s,p)

[0108] AND NOT

[0109] OR

[0110] And some combinations of them.

[0111] This is achieved by binding polarization (SAM) to vorticity (OAM), which is a different method from that of our previous patent application which used decoupled SAM polarization and OAM.

[0112] The new circuit, while using vortices (OAM states) and using 4 states as in the previous patent, adopts a technique whereby at the entrance of module 1 of the present quantum circuit it decomposes the electromagnetic fields in fundamental modes of the waveguide:

[0113] TE mode - i.e. electric transverse, and

[0114] TM mode - i.e. magnetic transverse, preserving them by means of appropriate time shifts within the circuit in an appropriate way. In this way, the information of the input state, i.e. one of the four states associated with the photon (and combinations of them according to the laws of quantum mechanics) is preserved and manipulated in order to make all the transformations associated with quantum computing.

[0115] The four fundamental modes in this case are TE, polarized along the x-axis, TM which is now identified with the corresponding magnetic mode TM with vertical polarization. The modes OAM are given by the phased superposition OAM (L=+l) = TE + i TM and OAM (L= -1) = TE - i TM where i is the imaginary quantity (i.e., the square root of -1) that corresponds to the phase shift of plus or minus one wavelength in the superposition of the state TE with the state TM.

[0116] Using the waveguide of the example above, i.e., made with SOI technology and measuring 220 x 480 nanometers for the wavelength of 1550 nanometers, you gain in ease and low cost of implementation, the waveguide however is no longer square as in the main example of the previous patent application, and the TE and TM modes cannot easily build and propagate the 0AM modes. The solution proposed by the present invention is in general to operate in Hilbert's 4D space by decomposing the computational configuration space into subspaces, produced by decomposing the initial 4D field into two overlapping 2D subspaces, one representing the TE mode and the other the TM mode, respectively. This division is carried out by the polarized beam splitter (PSB). Due to the geometry of the waveguide, the TM mode may have some losses or changes in the state of the photon if the path of the photon in the waveguide is bent. To avoid these losses, the invention converts in the part of the circuit that corresponds to the TM subspace into TE mode (corresponding to one of the two paths 5, 10), performs a local operation, according to the superimposed TE subspace, and re-converts the TE mode to TM mode and finally superimposes it with the TE mode in the "combination" zone, defined by the C-subbundle combination media. Here it recreates the necessary 0AM or TE / TM modes or a superposition of them. Of course, the other way YOU (in the other path 5, 10) obeys other transformations according to the calculation.

[0117] To achieve this, the polarization, hereinafter also called SAM, is no longer independent of the 0AM, but they are coupled.

[0118] Module 1 is made with a l-to-2 cascade structure that connects modules that already operate as CCNOT gates on their own (and by driving the final module 60 in an appropriate way you get the circuit configurations for the Controlled-Z and Pauli-z that rotate the eigenstates by 180°) based on two Mach-Zehnder interferometers, one for each polarization state (Ex and Ey corresponding to TE and TM modes) comprising very high precision phase 22 variation media for TE modes and TM modes, each with variable phase (cbl and Φ2) and connected in parallel after the polarized beam splitter (PSB) used as input.

[0119] Optionally, the output of the two MZIs in parallel can be phase-adjusted by acting on phase change media 70 (Φm) on the Ex path after the MZI1 interferometer of the x- polarization .

[0120] In reality, if two sufficiently precise phase variation means 22 are used, the phase variation means 70 are not needed, which can therefore be omitted. A form of implementation that omits even MZI1 and MZI2 is described later with reference to Figure 6.

[0121] The output field and its calculation are determined by phase modulation (Φl, Φ2 and Φm).

[0122] The TM field is rotated 90° and sent to its Mach- Zehnder interferometer (MZI2) for operations to reduce the loss of TM modes in transport; then, the two fields Ex and Ey are recombined. At this point the recombined fields can for example be sent to an active phase variator 40 in the final module 60. The final module includes active phase variation means, for example an active trench, to make for example the Pauli z and the CZ and varies the phase from 0 to 360° thus obtaining a desired shift of the photon modes (A, B, C, D)

[0123] Figures 3 and 4 show two well-known examples in the literature: 40a and 40b of TE-TM rotators 30 configured as fixed trenches.

[0124] The circuit can operate in continuous mode, i.e. with many photons or with laser pulses.

[0125] To avoid signal or mode losses or to have an unintended mixing of photon states that are known to be present even conspicuously in multimode square waveguides when they are bent, followed by a possible loss of coherence of the transported quantum states, instead of a multimode waveguide as in the previous patent application, as mentioned we adopt a single-mode waveguide (singlemode) of geometry and construction known in the literature, of the type commonly used in SOI wafers with Si thickness of 220nm and width 480nm for the wavelength of 1550 nanometers. The dimensions and geometry of the guide can obviously vary to obtain equivalent results as the material and wavelength used vary, the general condition therefore is that the waveguide is single-mode.

[0126] In this configuration and at this frequency of 1550 nanometers, the waveguides can be bent without high losses and the field modes, Ex and Ey, can be compressed, which in our case correspond respectively to the TE and TM modes and corresponding TM mode.

[0127] To avoid the effects of birefringence of the 220X480nm waveguide in the transport of the TE and TM modes, especially when the waveguides are bent or in mating mode, it is preferable to transform the TM mode into TE mode through mode rotation means (which rotate the polarization) after the polarized beam splitter (PSB) used as the input port. After the necessary transformation and manipulation of the photonic states, the two paths are sent to the C beam combiner and to an active mode modulator 60.

[0128] Throughout the circuit, SAM and 0AM are coupled with the result that the 0AM modes are given as superpositions of SAM modes and the R-mode rotation media transform pure SAM and mixed SAM / 0AM states into SAM or 0AM modes. This is an example of a classical correlation (known as classical entanglement) between SAM and 0AM.

[0129] The 0AM ways therefore depend on SAM as follows:

[0130] • 0AM (L=—1) (clockwise) given by TE+ i TM, which means that they are constructed with the polarization states H+iv, i.e., elliptical clockwise polarization, Ex + iY and

[0131] • 0AM (L=+l) (counterclockwise) given by TE-i TMs, which means they are made with H-iv polarization states, i.e., counterclockwise rotating elliptical polarization, and Ex-i Y will be decomposed by PBS.

[0132] Any 0AM mode, being done with superpositions of TE = Ex and TM = Ey, when it passes through the PBS it is decomposed into the two basic components TE and TM retaining the phase shift that characterizes the positive and negative 0AM mode and in the absence of a phase modulator such as the trench waveguide it retains the OAM modes to the combination of the two paths if no phase shift has been added or reversed when a n step is added; the other two cases with n / 2 and 3 / 2 n (= - n / 2) will generate an overlap in the TM and TE mode phases, which means inducing diagonal polarizations.

[0133] The PBS acts as a projector of the 4D Hilbert space in the 2D subspaces (corresponding to each of the Mach- Zehnder interferometers MZI). Routes must be synchronized.

[0134] Quantum computing is reported in the table of states and transformations.

[0135] When the OAM mode passes through the PBS, the beam splitter into polarizing beamsplitter (PBS) states as known from international literature, each OAM mode is decomposed into the two polarization states (SAM) TE and TM.

[0136] As an example of notation, if an OAM mode passes through PBS, and we decide that the mode TE = Ex passes through the respective phase change media 22 without any change, we associate it with the state label |0> (or in the truth table the symbol 0). This means that medium 22 is deactivated, therefore it retains the initial phase shift that generates the OAM mode with the TM mode of ±n / 2 (i.e. ±i) from the L=±l OAM mode, respectively.

[0137] Note that after crossing PBS 15, the mode TE = Ex arrives at the input to MZI1 and the respective means of phase variation 22 unchanged (TE remains) so it retains the initial phase shift that generates the mode OAM with the mode TM of ±n / 2 (i.e. ±i) from mode L=±l OAM, while the other mode, the TM = Ey, passes through the respective bias rotation media 30, and is transformed into TE mode for input to MZI2 because this mode in this single-mode waveguide has no difficulty in propagating and can be modulated appropriately with almost zero losses and then be converted back by the bias rotation media 32 into TM mode and recombined into the mode combination media 25 to generate the output state wanted by quantum computing prepared by MZI1 and MZI2, thus keeping the losses to a minimum.

[0138] To obtain quantum computation in module 1, the phase variation means 22 in MZI1 and MZI2 and possibly the optional phase variation means PS-EX 70 are used. For example, when passing through phase change media 22, 70 and 40, if they are deactivated, module 1 returns to output 3 the same input it received at input 2. This corresponds to the identity operator. To this operation we associate the status label |0> (or in the truth table the symbol 0).

[0139] If input to input 2 there is an overlapping mode TE+TM that corresponds to a linear polarization of 45° it will be decomposed by PBS 15 in the TE mode that will go towards MZI1 and in TM mode that will go towards MZI2. To prepare an output state, if the phase change media 22 in MZI2 are activated, the TM mode has a phase shift of +n / 2 (=90°) and becomes after the rotation media 32 a mode + i TM which, added in combiner 3 with what came out of MZI1 unchanged, will become an 0AM mode (L=-l) which is TE+ i TM with elliptical polarization rotating clockwise. The 0AM mode (L=+l) is obtained from this result by a displacement of n (=180°) using the active trench 40.

[0140] In quantum computing, there are combinations of the electric transverse TE and magnetic transverse TM modes of the fields in the waveguides, such as an unchanged phase superposition in the case of an L=-l mode and a TM mode that results in a superimposed TE+ i TM ± TM mode. This corresponds to a vortex mode with polarization rotation, a superposition of OAM (L=—1) and TM. The same thing happens for the OAM mode (L=+l), which gives an overlap between OAM (L=+l) and TE.

[0141] If you fix the direction V for PBS as the input direction of the field, then |0> means that the polarizations do not match, which occurs for mode V=TM.

[0142] If TM is invariant - we have no change and the status is |0>.

[0143] If TE corresponds to |1> generates a vortex mode, with L=-l, after passing through the phase variation media 22 and 70 in figure 1.

[0144] Polarization is now a superposition of TE and TMi- phased modes and is polarized clockwise or counterclockwise depending on the sign of the TM.

[0145] OAM (L=—1) and OAM (L=+l) generate an overlap of (TE+- TM) + TMs and (TM +- TEs) + TEs, respectively. They are superimpositions of linear polarization and circular polarization, it becomes elliptically polarized.

[0146] Change of mode: from linear to elliptical polarization or from circular polarization (which is a special case of elliptical) (left- or right) to elliptical, i.e. an overlap of modes is obtained.

[0147] The 70 phase variation media function as an adjuster or compensator module between MZI1 and MZI2.

[0148] Circuit: Standard SOI wafer with a 220 nm thick silicon layer rectangular waveguide on silicon chip on insulator. Frequency 1,550 nm. The single-mode TE waveguide is h=220nm X w=480nm.

[0149] Waveguide: Silicon (n=3.48 @ 1550 nm) with SiO2 coating (n = 1.445 @ 1550 nm) thickness of silicon 220nm as in standard SOI wafers.

[0150] The flat structure of the waveguide implies that the OAM is given by the superposition of the Ex field and the Ey field out of phase by ±n / 2 and due to the SAM-OAM coupling, the OAM beams are elliptically polarized starting from the linear polarized light coupling.

[0151] OAM (L=+l) is given by Ex - iEy

[0152] OAM (L=—1) is given by Ex + iY

[0153] According to a preferred example, mode modulation occurs through an active mode modulator of which phase variation media 22 is an example (e.g. a waveguide heater to achieve a polarization rotation - a practical example is a controlled thermo-optical device). The 70 phase variation means, as mentioned, are used to tune the two MZI in case something is out of phase or you want to reverse the mode.

[0154] Basically, according to this example, instead of using a trench waveguide, to reduce losses, we adopt 220X480nm single-mode TE waveguides and modulate the polarization with active modifications of the waveguide obtained, for example, with thermal activation and phase change. On the other hand, as regards the realization of means of rotation (of polarization) made with SOI technology and CMOS compatible based on the symmetrical breaking of the cross-section of the waveguide, they are feasible with a 220nm thick waveguide and an active component that modifies the properties of the waveguide. We need in this case to achieve a controlled rotation of the polarization vector for a superposition of TE and TM modes with respective phase delay acting as a mode conversion .

[0155] Module 1 is a universal calculation module capable of realizing up to CCNOT mode (Toffoli) and with the CNOT subunit including the Hadamard gate. Each module 1, with PSI and PS2, can be a unit of a quantum processor. Controlled-Z and Pauli-z can be obtained at exit C in the combination zone when active trench 40 in module 60 before PBS adds a 180° rotation phase, in configuration space 4D OMA (L=+l) in 0AM (L=—1) and vice versa and TE in TM and vice versa. The module 60 preferably rotates the state from 0 to 360°.

[0156] Each CCNOT 1 module generates a mode that can be split into two other successive CCNOT 1 modules that can either accept or reject the photon state (if MZI are both out of phase) or modulate the fields using MZI1 and MZI2 with the 70 phase change media (PS-EX).

[0157] When the final module 60 with the active trench 40 rotates the mode by 180° we get the operations through the z-axis as parity operators. This language is a change in the basis of Hilbert space, and the state of the photon is unchanged, as in Heisenberg's image of quantum mechanics.

[0158] As for operations through the z-axis, we observe that they are operations that involve abstract rotations in three-dimensional space and do not directly have to do with the geometry of the circuit, so z is not an axis of the circuit. In practice, Pauli matrices express the rotation of a vector in a 3D space. In our case the spatial rotations from Pauli-x and Pauli-y are obtained with a matrix that is a submatrix of the CNOT and obviously of the CCNOT, while the Pauli-z and CZ cells need another degree of freedom associated with a transformation in the Hilbert space which in our case corresponds to a displacement of 2 squares in the Hilbert space or rather to a double rotation of the base, They are called equality operators because it is like a mirror reflection.

[0159] At the end of the CCNOT in the combination zone C of the two output fields, another rotation of n (=180°) can be added to the phase rotation n / 2 (=90°) to obtain a basic inversion in the phase shift map of figure 2 of the configuration space, whereby the 0AM 0AM (L=+l) is transformed into 0AM (L=—1), a parity operation on pseudovectors (and vice versa) and TE modes are converted to TM mode according to the parity of the 0AM states (and vice versa). This is a double rotation in the Hilbert space used for our calculations.

[0160] With 10 consecutive bifurcation levels, a reading output (detection of the travel state of the photon in the circuit together with its 4 states) equivalent to IM qubitoutput is obtained. With 20 tiers 1-terabytes of output. The following table represents the truth table of the Toffoli and CNOT gates obtained with the module described above:

[0161] The Hadamard gate is obtained by switching the two

[0162] MZIs to the ON position and using the PS-EX 70 phase variable speed drive.

[0163] For the Pauli-z and CZ gates, the phase variation media 40 of the final module 60 must be activated to reverse the last off-diagonal CNOT Pauli-z and Hadamard - Pauli-x elements. By first setting up an identity operation with the MZI and setting the phase first with the phase variation means 22 and then possibly with the phase variation means 70, if CZ or Pauli-Z is to be done, the phase variation means 40 are activated.

[0164] Additional configuration, hereinafter referred to as "colored":

[0165] OAM and MUX (multiplexing) frequency in 0AM TE wizard mode

[0166] We can augment both configurations using an entangled source of photon pairs and techniques to discriminate photonic states also in frequency.

[0167] In this way, we get a qu-ququad, i.e. (22)*(22) = 16 states which means a 16-state qudit for each frequency in the circuit. Using both frequency and OAM multiplexing on it one can utilize the full potential of physical systems such as optical and photon circuits with frequency diversity, multiplying by the number of frequency bands obtained by tapping on both sides of the main frequency and thus including the main frequency f, identified by the parameter fn. In this case and with these circuits operating in TE mode, it is possible to modulate the frequency and obtain frequencies close to the central frequency and with optical-acoustic or similar techniques and increase with two sidebands from the main frequency centered at 1550nm a qudit with 400 states using pairs of entangled photons, given by the additional dimensions added by the frequency multiplication fn. In our case we have for fn=5 and a ququad for each frequency, being frequency and 0AM independent, the superposition is given by (fn*4)A2 = (20)A2 = 400-state qudit.

[0168] Optical frequency-to-OAM conversion has been shown to be feasible in a controlled manner, the complexity of the circuitry can be reduced by a factor of log2(400) = 8.65 and the advantage is (log2 (400))A2 = 75 obtained with five frequencies and four qudits states of a pair of entangled photons. For the extreme case of fn=9, four frequency beats side by side, the maximum that can be obtained is 362 = 1296 and log2(1296) = 10.34 and the advantage is (log2 (1296))A2 = 106.91, which means having more than two orders of magnitude advantage over the increasing complexity of the circuits.

[0169] A quantum computer comprising a module according to the present invention is an optical quantum computer, which uses qudits based on the photonic states that carry orbital angular momentum (0AM). There are two different configurations with different construction techniques at a given fixed frequency. A further extension is to set up qudits based on 0AM and frequency multiplexing techniques that use beats of the main frequency to obtain different states of the photon, number of frequency beats fn times the qudit-based OAM state. The size of the computation depends on the correlation of dimensions obtained through different paths and circuit configurations in which one or two or more photons are trapped during the computation. This has been widely explored in the literature, see for example (Krenn, Zeilinger et al., 2014) where it is discussed that the size of the entangled quantum state can increase with the number of particles or, as in our case, with the number of sizes involved. In this work, the properties of two photons that are 100-dimensionally entangled are described. The dimensions are represented by the size of the qudit states and the diversity of the paths obtained in the calculation

[0170] The present invention uses qudits to simplify the structure of quantum circuits. As is known from the literature (see Wang et al., 2020) the use of qudits decreases the complexity of quantum circuitry, which becomes essential in the design and construction of optical circuits, which are known to have a complexity that increases exponentially, step by step. In fact, speed, resource savings, and deployment on physical platforms are reduced with the use of multi-state qubits, also known as qudits. A qudit is characterized by having a Hilbert state space larger than a qubit. By definition, a qudit is the quantum version, the equivalent, of d-ary digits (or d-ary sequences), a generalization of the binary data sequence in which nodes have d children instead of 2 used in the priority queue data structure constructed from arrays of d objects. Qudits with dimension d are described by the terms of quantum states of a vector immersed in a d- dimensional Hilbert space HD. Space is defined by a set of d-dimensional orthonormal basic vectors {|q2)>khh .« with the normalization condition = 1

[0171] One of the main advantages of the qudit model over the qubit model, is a drastic reduction in the number of qudits needed to cover the state space we are using in the calculation. As an example, at least tn_l=log_2 N qubits are needed to represent an N-dimensional system in qubits. Using qudits, on the other hand, only n_2=log_d N qudits are needed, providing an advantage of a complexity reduction factor given by the ratio k = nl / n2= log2 (d). The qudit method provides an advantage (log2d)A2-scaling over the qubit case. In the case of four qudit states, a ququad with d=2, the advantage is (log(24))A2 = 22 = 4. The complexity of the order n of a circuit scales as 2A(2*n), a factor of four compared to the qubit case.

[0172] In the case of entangled particles, the size of the Hilbert space scale entangled with d = g*n, where g is for the entangled dimensions and N is the number of parts involved. If we consider two entangled ququads (g=4) obtained with pairs (g=2) of entangled photons, we have the tensor product of d=16. Then the complexity of the circuit scales as 24*n.

[0173] If we add additional dimensions through frequency multiplication fn we have for fn=5 and a ququad for each frequency, since frequency and OAM are independent, the superposition is given by (fn*4)2 = (20)2 = 400-state qudit.

[0174] The configuration of the previous patent application is achievable with a non-standard multi-mode square waveguide, on silicon wafers, with dimensions of 1 micrometer and the calculation is obtained through the control of the polarization state of each photon, which means that in this configuration the polarization is considered an independent quantity from the possible states of the orbital angular momentum of the photons.

[0175] The second configuration according to this patent application is based on the currently most common, cheapest and standard construction process of optical circuits with a waveguide given by a layer of SOI with a thickness of 220nm. Although the latter configuration is much easier to build, the price you pay is that a rectangular waveguide with a height of 220nm and a width of 480nm, is a standard single-mode waveguide, and the fields associated with the photon must couple OAM and polarization together. In fact, the waveguide is birefringent and the TE and TM modes are characterized by different propagation. The field is then reconstructed at the fusion junctions joining the TE and TM modes (x and y polarization states) in a synchronized manner with the resulting elliptical LH or RH polarization depending on the type of OAM state. The 70 phase variation means are used to synchronize the outputs of the two MZIs to optimize the calculation made by the CCNOT module and thus reduce any errors (local means that that module does it, then there will be others to follow and so on. A complex quantum circuit may comprise a cascade or network of these CCNOT - CZ Pauli-z modules.

[0176] The additional advantage is that in this case there are very low losses in the transport of photonic states even when the waveguides are bent and the TE and TM modes are out of phase, for this reason the propagation must be converted mainly to TE mode and TM (y-polarization) is obtained again by another polarization rotator and with a phase regulator for synchronization. This results in four independent states, including OAM states and TE-TM modes based on combinations of TE and TM modes.

[0177] These quantum computer configurations describe a modular unit of a quantum and classical optical computer that operates with four-state units of information identified here by the four labels (A, B, C, D) also known in quantum computing as four-state qudits, i.e., ququads.

[0178] In standard quantum computing, the four states (A, B, C, D) of a ququad, |q>|ql, Q2, Q3, Q4>, identify an orthonormal basis of four-dimensional Hilbert space and represent the four orthogonal modes or quantum states allowed in a single-mode rectangular guide.

[0179] The electromagnetic field (EM) states propagating in the waveguide are TM, TE (vertical and horizontal polarization), 0AM (L=+l), 0AM (L=—1). TM mode is tied to the TM mode of TE mode. The TE and TM modes correspond with a good approximation to the Bessel or Hermite-Gaussian ones with zero 0AM. The Si on SOI material of the waveguide chosen to drive photon propagation at 1550nm satisfies the sufficient condition of having independent TE and TM modes in a waveguide filled with homogeneous and inhomogeneous anisotropic lossless media.

[0180] 0AM modalities are now prepared as follows:

[0181] SAM and 0AM are strongly coupled together with elliptical polarization:

[0182] 0AM (L=+1) is ccw- rotating and has RH polarization.

[0183] 0AM (L=—1) is cw- rotating and has LH polarization.

[0184] This situation can be used when the fields are decoupled in the waveguide circuit and x-y symmetry is no longer preserved as in standard single-mode waveguides in Si over SOI, 220 x 480 nm, for 1550nm wavelength.

[0185] In this case there are 4 states available because the polarization depends on the 0AM state of the beam.

[0186] From these it follows that each of the ququads is given by the superposition with different polarization states of the four independent eigenvectors |q±)

[0187] |ip>=a|q1>+ p|Q2>+y|Q3>+8|Q4> (1) with the usual normalization condition

[0188] More precisely,

[0189] |ql>= |1, 0, 0, 0), |q2>=|0,1,0,0), |q3>=|0,0,1,0) and |q4)=10,0,0,1).

[0190] Noteworthy, these two configurations can also operate in continuous mode for variable continuous quantum computing using the force and compressed states of the EM field associated with each of the four states present in the configuration whose numerical values are input matched to belong to continuous intervals and the variable continuous quantum computing thus set up is analog with infinite-dimensional Hilbert spaces where in these configurations the Continuous intervals can be obtained through the classical entanglement mechanism between polarization (relative to spin angular momentum, SAM) and photon orbital angular momentum (CAM). In the case where SAM and 0AM are strongly coupled and the polarization identifies a given 0AM state present in the quantum computer, the input photon is appropriately operated by taking it from a pair of entangled photons and using one as a "herald" to reduce the noise in the calculation due to the noise of the detectors. Another approach is based on compressed photonic states, the chip is connected to a squeezed light source (infrared laser pulses and microscopic resonators) then injected into the first ports that encode the pulses in a superposition of the four states (A, B, C, D) to then perform CV-quantum computing. Instead, with two entangled pairs it is possible to entangle three orthogonal Stokes operators and corresponding SAM / OAM states between a pair of beams in two distinct modules 1 according to the present invention. As the first basic language we can fix a map between the eigenvectors |q±) and the waveguide modes (A, B, C, D). The bit-shift map cyclically shifts each eigenvector from |q±) to |qi+l), in a rotation of the local quantum state of the photon, corresponding for example from A to B, to C to D in a cyclic fashion. Any superposition of quantum state will also be rotated in Hilbert's space d=4.

[0191] With reference to figures 6, 7 and 8, a quantum computing module 101 will now be described according to an alternative form of implementation of the invention that simplifies the construction compared to module 1.

[0192] Elements equal to or similar to those described in the previous figures will be indicated here with the same reference numbers, or with the same numbers increased by 100 or multiples thereof.

[0193] As will be seen from Figure 6, module 101 differs from module 1 substantially because mode 20 manipulation media include phase variation media 22 placed directly along the single-mode waveguide, i.e. independently and preferably in the absence of the presence of Mach-Zehnder interferometers MZI1 and MZI2. In other words, the means of phase variation 22 may be the only means of phase variation along both the first and second paths (5, 19).

[0194] Module 101 phase 22 variation media must be sufficiently performing to ensure a variation of at least -180° to +180° or greater.

[0195] In this way, the second phase variation media 70 at the output of MZ1, the active power divider media 50 and the reflection media 51 and 52 are also superfluous and therefore can be omitted.

[0196] It should be noted that:

[0197] As in module 1, the states 0AM (L=+1), 0AM (L=—1) and TE01 and TE10 (=TM) are used

[0198] • Unlike module 1, polarization is coupled with 0AM states by means of the classic entanglement phenomenon spin-orbit coupling (SOO); For example, the module includes an input register comprising such 0AM states coupled with polarization.

[0199] • It is imposed: TE01 = Ex, horizontal polarization and TE10 = Ey vertical polarization (and is equivalent to the TM mode linked to Ex)

[0200] • With the SOO the 0AM is related to polarization: OAM(L=+1), OAM(L=-1) will be elliptically polarized counterclockwise and clockwise and given by a superposition in modes TE and TM, OAM(L=+1) = TE- i TM = Ex - i Ey, and, OAM(L=-1) = TE+ i TM = Ex + i Ey; where i is the imaginary quantity indicating a phase shift of ±90° or half wave. This can be seen in figure 7.

[0201] Basically, with polarization, 0AM and TE and TM are divided into two Hilbert subspaces Hx and Hy, one for each path 5 - 10, linked to TE and TM of dimension 2, encoded by the 1 / 2 wave phase shift term between TE and TM, ±i, and then recombined after the calculation.

[0202] Ultimately in module 101 a polarized mode separator 15 (polarizing beamsplitter = PBS) divides the input state into TE and TM modes like a TE-pass and TM- pass filter defining two Hilbert subspaces Hx and Hy, to which they are no longer associated respective Mach- Zehnder as in module 1.

[0203] • The TM mode of path 5 is converted to TE, the state is prepared in Hy, then it is converted back to TM to be recombined with the output of the other path 10.

[0204] It is noted that it is also possible to obtain 0AM with L greater than +1 or less than -1.

[0205] For example, it is contemplated to impose phase variations from -K*180° to +K*180°, where +K and -K identify the L values of the respective angular momentums 0AM (L>+1) and 0AM (L<-1) of said quantum or one of their superpositions, where K is not necessarily an integer.

[0206] The respective OAMs can be those simulated by OAM(L>+1) = TE- i*K*TM = Ex - i*K*Ey, and OAM(L<-1) = TE+ i*K*TM = Ex + i+K*Ey and where is the imaginary quantity that indicates a phase shift of ±90° or half wave, or multiples thereof. Preferably i= (square root of -1).

[0207] The CAM angular moments are encoded in the phase and path differences of the TE and TM modes

[0208] In this way it is possible to obtain Qdits at 2L + 2 states (L simulated orbital angular momentum states (or equivalent) plus the qubit for L = 0).

[0209] Ultimately, this means being able to handle more quantum information.

[0210] It is noted that this can also be done in the form of implementation with MZI1 and MZI2.

[0211] • Also in module 101 the calculation can be carried out in single-mode silicon waveguides on an insulator (SI on Insulator, also called SOI in jargon) of standard size,

[0212] • For example, 220 x 480 nanometers for the wavelength of 1550 nanometers.

[0213] Losses are minimal in these waveguides. Other materials and other wavelengths with their other dimensions are not excluded.

[0214] For the final module 60, also known as the output module, two forms of implementation are preferably contemplated, schematized in figure 8.

[0215] According to the first form of actuation, module 60 is a single-way output module to a state polarization analyzer.

[0216] According to a second form of actuation, module 60 is an output module with a 2-way switch that can be programmed independently of polarization, and the vias lead to two other compute modules.

[0217] In general, the calculation takes place with rotations of the bases in four-dimensional Hilbert space of the quantum states that the photon can assume, so it is possible, by way of example and not limitation, to realize the following modules: •Identity

[0218] • all three Pauli x, y, x

[0219] •Hadamard

[0220] • Controlled Not (CNOT)

[0221] • Controlled z (CZ)

[0222] • Toffoli (CCNOT)

[0223] • Quantum Swap

[0224] • Phase shift gates: e.g. Pi / 8 and Phase (s,p)

[0225] • AND, NOT, OR

[0226] Ultimately

[0227] • By coupling the polarization with 0AM by means of Spin-Orbit Coupling, i.e. classical entanglement of the total angular momentum J where J = SAM + 0AM = Polarization + 0AM, the 4 modes of the ququad can be decomposed into polarization and then into TE and TM. The 4 states of ququand are therefore the following:

[0228] TE, TM, TE + i TM, TE - the TMs with synchrony between the TE and TM modes.

[0229] • Standard waveguides and active trenches can be used to create the circuit.

[0230] By doing so

[0231] • The original Hilbert space is divided: H4=Hx0Hy

[0232] • You operate separately on the TE and TM modes and recombine them appropriately to obtain the final result. All operations are Toffoli submatrices in H4.

[0233] • The z-modes for Controlled-z and Pauli-z are achieved with an active trench coat final (module 60)

[0234] • The final calculation is conveyed (splitting) to at least 2 other calculation units or other (module 60). The truth table of the CCNOT module (Toffoli) is in figure 9.

[0235] The present invention is preferably applied to quanta represented by photonic radiation, however other quanta are not excluded.

[0236] GENERAL INTERPRETATION OF TERMS

[0237] In understanding the purpose of the present invention, the term "comprehending" and its derivatives, as used herein, are understood as open-ended terms specifying the presence of the stated characteristics, elements, components, groups, integers, and / or phases, but do not exclude the presence of other undeclared features, elements, components, groups, integers, and / or phases. The above also applies to words that have similar meanings such as the terms "including", "having" and their derivatives. In addition, the terms "part," "section," "portion, " "member, " or "element" when used in the singular may have the dual meaning of a single part or a plurality of parts. As used herein to describe the form(s) of actuation above, the following directional terms "forward", "backward", "above", "down", "vertical", "horizontal", "below" and "transverse", as well as any other similar directional terms refer to the form of actuation described in the operating position. Finally, grade terms such as "substantially, " "approximately, " and "approximately" as used here mean a reasonable amount of deviation from the modified term such that the end result is not significantly changed.

[0238] While only selected forms of realization have been chosen to illustrate the present invention, it will be clear to experts in the field from this description that various modifications and variants can be made without departing from the scope of the invention as defined in the attached claims. For example, the size, shape, position or orientation of the various components can be changed as needed and / or desires. The components shown directly connected or in contact with each other may have intermediate structures arranged between them. The functions of one element can be performed by two and vice versa. The structures and functions of one form of realization can be adopted in another form of realization. It is not necessary for all the advantages to be present in a particular form of implementation at the same time. Any feature that is original compared to the known technique, either alone or in combination with other features, should also be considered as a separate description of further inventions by the applicant, including the structural and / or functional concepts incorporated by those features. Therefore, the foregoing descriptions of the forms of realization under the present invention are given for illustrative purposes only and not for the purpose of limiting the invention as defined by the attached claims and their equivalents.

Claims

CLAIMS1. Quantum computing module including:- an input (2) comprising a mode separator (15), configured to separate an electrical transverse mode TE and a magnetic transverse mode TM of an input quantum in two parallel paths,- a first and a second path (5, 10), parallel to each other, respectively for the said magnetic transverse mode TM and for the said electric transverse mode TE, located downstream of said mode separator (15), each path being characterized by:• a single-mode waveguide (4),• mode handling media (20), including at least first phase change media (22);- an output 3 comprising means of combining modes (25), arranged to join the two parallel paths (5, 10); where: a) the two parallel paths (5, 10) are distinguished from each other at least because the first path (5) includes:- the first means of transformation (30) of the magnetic transverse mode TM in the transverse electric mode TE located upstream of these means of manipulation(20), second means of transformation (32) of the transverse electric mode TE into transverse magnetic mode TM located downstream of these means of manipulation (20); or b) the two parallel paths (5, 10) are distinguishedfrom each other at least because the second path (5) includes:- the first means of transformation of the electric transverse mode TM into a magnetic transverse mode TM located upstream of these means of manipulation (20),- second means of transformation of the magnetic transverse mode TM into an electrical transverse mode TE located downstream of these handling means (20).

2. Modulus according to claim 1, characterized by the fact that these first means of phase variation (22) are configured to generate phase variations at least in the range [-K*180°, +K*180°] where +K and -K identify the L values of the respective angular momentums 0AM (L≥+1) and 0AM (L≤ 1) of said quantum or one of their superpositions, where IK is not necessarily an integer.

3. Modulus according to claim 2, characterized by the fact that the L values of the respective angular momentums 0AM (L≥+1) and 0AM (L<-1) are obtained with the foilowing formula0AM (L≥+1) TE~ i*K*TM = Ex i*K*Ey; and0AM (td-1) TE+ i*K*TM = Ex + i*K*Ey; where i is the imaginary quantity that indicates a phase shift of + / -90° or half wave, or multiples thereof.

4. Modulus according to claim 3, characterized by the fact that the angular moments 0AM are encoded in the phase and path differences of the TE and TM modes.

5. Form according to any of the above claims, characterized by one of the following characteristics:- these first means of phase variation (22) are the only means of phase variation both along the first and along the second path (5, 19);- these mode manipulation media (20) include at least one Mach-Zehnder interferometer, including the first phase change media (22).

6. Module according to any of the foregoing claims, characterized by the fact that each of these modes comprises a polarization and the means of transformation (R) comprise means of rotation of the polarization of the modes.

7. Modulus according to any of the foregoing claims, characterized by the fact that said waveguide (4) is rectangular in section with dimensions of 220 x 480 nanometers, preferably for a wavelength of 1550 nanometers .

8. Module according to any of the above claims, characterized by the fact that the first means of phase variation (22) are active as they are piloted.

9. Modulus according to any of the above claims,characterized by the fact that input (2) includes at least one input register comprising at least one qudit at at least 2L+2 quantum states of a quantum, or a register of at least 2L+2 level qubits, characterized by the fact that said 2L+2 quantum states correspond to the following modes of propagation of a quantum and their superpositions:A = OAM (L≤ 1)B = TMC = OAM (L≥+1)D = TE10. Modulus according to claim 9, characterized by the fact that the OAM states are coupled to polarization.

11. Module according to claim 9 or 10, characterized by the fact that said output (3) includes at least one register comprising at least one qudit with at least 2L+2 quantum states, or a register of qubits with al leas 2L+2 levels, characterized by said quantum states and their superpositions, where the states are those obtained by combination of the two modes manipulated by the means of manipulation as follows:D=Ex=TE01B=Ey=TMA=Ex+i*K*Ey = (L≤-1)C=Ex-i*K*Ey = (L≥+1) where i is the imaginary quantity indicating aphase shift of + / - 90° or half wave, or multiples thereof, and where K is not necessarily an integer.

12. Module according to any of the preceding claims, characterized in that downstream of the output (3) it comprises phase variation means (40) along a multimode waveguide.

13. Module according to claim 12, characterized in that said phase variation means (40) downstream of the output (3) are active.

14. Module according to claim 13, characterized in that said active phase variation means (40) downstream of the output (3) comprise controlled thermo-optical means for locally heating the waveguide (4).

15. Method of manipulating quantum propagation modes to perform a quantum computation characterized by:- separate a magnetic transverse mode TM and an electrical transverse mode TE by a quantum;- make the two separate modes travel two parallel paths (5, 10), each characterized by a single-mode waveguide (4), up to a point of combination;- during the journey in the parallel paths (5, 10) transform:(a) the magnetic transverse mode TM into an electrical transverse mode TE, manipulate it at least by means of a phase change and transform it back into a magnetic transverse mode TM after said manipulation andbefore said combination.Or(b) the electric transverse mode TE into a magnetic transverse mode TM, manipulate it at least by means of a phase change and transform it back into an electric transverse mode TE after said manipulation and before said combination.

16. Method according to claim 15, characterised by the fact that it includes at least one of the following:- this manipulation of the TM mode transformed into TE includes at least one phase variation, this transformation includes at least one rotation of one polarisation associated with the respective mode,- make a phase change of the TE mode in the path parallel to that of the TM mode transformed into TE.

17. Method according to claim 15, characterized by the fact that it includes at least one of the following:- this manipulation of the TE mode transformed into TM includes at least one phase change, this transformation includes at least one rotation of one polarisation associated with the respective mode,- make a phase change of the TM mode in the path parallel to that of the TE mode transformed into TM.

18. Method according to claimcharacterized by the fact that these phase changes areincluded at least in the range [-K*180°, +K*180°J where +K and ~K identify the L values of the respective angular momentums OAM (L≥+1) and 0AM (L≤-1) of said quantum or one of their superpositions, where K is not necessarily an integer.

19. Method according to any of claims 15 to 18, characterized by the fact that it uses as the input register to a separation point of modes a qudit with at least 2L+2 quantum states, or a register of qubits with at least 2L+2 levels, characterized by the fact that said 2L+2 quantum states correspond to the following modes of propagation of a quantum and their superpositions:A = 0AM (L≤-1)B = TMC = 0AM (L≥+1)D = TE20. Method according to any of claims 15 to 19, characterized by the fact that the following states of said quantum are used:TE=TE01= electrical transverse mode TE;TE10=TM magnetic transverse mode transformed into an electrical transverse mode TE; to get 0AM (L≥+1) and 0AM (L≤—1) as follows:• imposes: TE01 = Ex, horizontal polarization and TE10 = Ey vertical polarizationWe obtain 0AM (L≥+1) and 0AM (L≤-1), polarizedclockwise and counterclockwise respectively, from the following combinations:OAM (L≥+1) = TE- i*K*TM = Ex - i*K*Ey; and0AM (L≤-1) = TE+ i*K*TM = Ex + i*K*Ey; where i is the imaginary quantity indicating a phase shift of + / - 90° or half wave, or multiples thereof, between TE01 and TE10 imposed by said manipulation; and where K is not necessarily an integer.

21. Method according to claim 20, which is characterised by the fact that• the polarization is coupled with the OAM states by means of the classical entanglement phenomenon spinorbit coupling (SOO);• With the SOO The OAM is linked to polarization in such a way that: OAM (L>+1), OAM (L<—1) are elliptically polarized clockwise and counterclockwise;• thanks to polarization, OAM and TE and TM are divided into two Hilbert subspaces Hx and Hy, one for each path (5, 10), linked to TE and TM of dimension 2, encoded by the phase shift term of 1 / 2 wave or its multiples between TE and TM, ±i, and then recombined.

22. Quantum associated with a qudit with at least 2L+2 states of said quantum, where L indicates an orbital angular momentum (OAM) of value L≤-1 or L≥+1 obtained by a method according to claim 15 or its dependent.

23. Quantum associated with a qudit as in claim 22where the states of said quantum are:TE=TE01= electrical transverse mode TE of said quantum;TE10=TM magnetic transverse mode transformed into an electrical transverse mode TE;OAM (L≥+1) = TE- i*K*TM = Ex - i*K*Ey; and0AM (L≤-1) = TE+ i*K*TM = Ex + i*K*Ey; where i is the imaginary quantity indicating a phase shift of + / - 90° or half wave, or multiples thereof, between TE01 and TE10 imposed by said manipulation, and where K is not necessarily an integer.