EP4705949A1 - Quantum computing module and method of manipulation of quantum propagation modes to perform a quantum computation - Google Patents

Abstract

The present invention relates to a quantum computing module comprising: - an input (2) comprising a mode separator (15), configured to separate a transverse electric mode TE and a transverse magnetic mode TM of a quantum into two parallel paths, each path being characterized by: · a single-mode waveguide (4), · mode manipulation means (20), including at least first phase variation means (22); - an output (3) including mode combination means (25); where the two parallel paths (5, 10) are distinguished from each other at least because the first path (5) includes: - first transformation means (30) of the transverse magnetic mode TM into transverse electric mode TE located upstream of said manipulation means (20), - second transformation means (32) of the transverse electric mode TM into transverse magnetic mode TM located downstream of said manipulation means (20).

Description

Owners : ROTONIUM S . R. L . , GEMONA DEL FRIULI (UD) - PIAZZA GARIBALDI 14 , CAP 33013 - VAT code 03067540306.

Title : Quantum computing module and method of manipulation of quantum propagation modes to perform a quantum computation . ★ ★ ★ ★ ★

DESCRIPTION

The present invention concerns a quantum computing module and a method of manipulation of quantum propagation modes to perform a quantum computation .

The present module includes a photonic quantum circuit that allows to perform the main fundamental operations of quantum computing . It is a versatile programmable quantum computing module that can be placed in each node of a generic quantum circuit in order to perform computational operations ( quantum and classical with the Tof foli configuration) through the use of photons . This module can also be hybridi zed or connected to other classical or quantum devices other than photonic devices .

Quantum computing is performed by rotating the bases of the photon ' s quantum mechanical states and letting the quantum states evolve as in Heisenberg ' s modality (Heisenberg picture of quantum mechanics ) .

DEFINITIONS

QAM = Orbital Angular Momentum SAM = Spin Angular Momentum

STATES = quantum states associated with the photon

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

VORTEX = modes with non-zero angular momentum, i.e. with non-zero 1.

1 (+1) and 1 (-1) : these are the OAM modes we use, they are the modes that in the literature have orbital angular momentum 1=+1 and 1=-1. In the broadest way, we therefore denote with OAM 1 ( + 1) the OAM mode with 1=+1, and with OAM 1 (-1) the OAM mode with 1=-1. Said modes are also alternatively indicated with OAM (1=+1) and OAM (1=— 1) or with OAM+i and OAM-i.

BASIS = corresponds to the set of the 4 photon states TE, TM, 1 (+1) and 1 (-1) which form directions in a 4-dimensional Hilbert space. Basis is a mathematical term for 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 basis vectors associated with the x-axis and y-axis. If chosen of unit length, they are called unit vectors. Therefore, a vector in a space is given by the sum of the projections in the basis vectors. In our case, a vector in a Hilbert space with at least 4 dimensions represents the quantum state of the photon at the output of a computation module, which can be either one of the at least 4 states or a suitable combination of them. ACTIVE TRENCH / ACTIVE TRENCH EQUIVALENT = we sometimes use these terms as synonyms for generic active phase variation means, which are equivalent to an adjustable trench (either thermally or otherwise) . They are achieved by driving a controlled variation in a predetermined area, such as a variation in waveguide geometry .

ACTIVE PHASE VARIATION MEANS: these are means that can be piloted, the active trench mentioned above is an example; in the preferred actuation forms they may include a thermo-optical device controlled to heat a predetermined area of a waveguide (4) , preferably in single mode. These are means that perform a function if activated either by piloting or piezoelectric.

PASSIVE PHASE VARIATION MEANS: These are nonpiloted means, e.g., with fixed geometry, which therefore always perform the same function regardless of an activation .

STATE OF THE ART

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

Although this system is perfectly functioning, it is linked to a waveguide and its trench, that are expensive to make as they are not directly available on the market among standard components .

The applicant therefore deepened the research with a view of overcoming this problem .

Another purpose of the present invention is to provide a versatile circuit capable of performing the main quantum operations with as few as possible photon losses , which would generate computation errors .

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

The purposes are solved by a quantum computing module and by a method according to the attached claims .

DETAILED DESCRIPTION

Further features and advantages of the present invention will be best seen from the following detailed description of its preferred embodiments , made with reference to the attached drawings and given as an indication and not as a limitation . In these drawings :

Figure 1 schematically shows a quantum computing module according to the present invention;

- Figure 2 shows the trans formation map from one mode to the other based on the applied phase variation ( of n/2 or multiples thereof ) ; - Figures 3 and 4 show two examples of passive phase variation means;

- Figure 5 shows a diagram of the OAM, TE and TM modes with the corresponding polarization.

Figure 1 shows a quantum computing module according to the present invention denoted as a whole with reference number 1.

Module 1 includes: an input 2 comprising a mode separator 15, represented as an example and not as a limitation, by a polarized beam splitter, hereinafter also referred to as PBS, configured in such a way as to divide an incoming photon beam characterized by transverse electric and magnetic fields TE and TM into two sub beams, one characterized by the transverse magnetic field TM and one characterized by the transverse electric field TE; each of said two modes TM and TE comprising a polarization Ex, Ey;

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

• a single-mode waveguide 4, for example of silicon on an insulator (SI on Insulator, also known as SOI) preferably of standard size, e.g., 220 x 480 nanometers for a 1550 nanometer wavelength. Losses are minimal in these waveguides;

• mode manipulation means 20, represented as an example and not as a limitation, by a Mach-Zehnder interferometer, hereinafter also referred to as MZI1 and MZI2, comprising first phase variation means 22 indicated in the Figure with PSI and PS2;

• an output 3 including mode combination means 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 the first and second mode transformation means 30, 32 represented as an example and not as a limitation by respective rotation means of the polarization (and therefore of the associated mode) , also called R, one upstream and one downstream of the respective manipulation means 20.

Optionally, the two paths 5 and 10 can also be distinguished because a second path includes second phase variation means 70 interposed between said mode manipulation means 20 and said second transformation means 32. This, however, may not be necessary if the first phase variation means are sufficiently performing, e.g., allowing a variation from -180° to + 180°.

The mode manipulation means 20 of each path shall preferably comprise an active power splitter device 50 at the exit of the respective MZI1 and MZI2 interferometers; the splitter is driven preferably by the phase induced by the phase variation means 22, to perform at least the following operations: sending all the radiation directly to the output of the manipulation means 20;

- sending a first portion of the radiation to the output of the manipulation means 20 and rejecting a second portion by sending it to the respective reflection means 51 and 52 (e.g., mirrors) , from which it is reflected back, as this driving configuration corresponds to a closed port for that photon state;

- rejecting all the radiation by sending it all to said respective reflection means (51, 52) which corresponds to the total closure to any photon state.

The splitter is, for example, of the 50/50 type, that is, it divides the incoming radiation into a first and second portion of radiation, where each has 50% of the incoming radiation.

The splitter device 50 can be of known type.

In general, a coupler is a device that couples the beams while the splitter divides them; often we can use the same device for both functions by simply reversing it. In the literature they are known as coupler/splitter devices.

The output patterns achieved by driving the two splitters/couplers 50 of MZI1 and MZI2 are for example as follows :

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

2. They allow an output only from MZI2 and inhibit it from MZI1;

3. They allow an output with equal power from MZI1 and MZI2; 4. They allow an output with equalized power from MZI1 and MZI2 (e.g., as the right/left balance of a stereo music player) .

Input 2 preferably includes at least one input register comprising at least one 4-state qudit of a photonic quantum, or a 4-level qubit register, characterized by the fact that said 4 quantum states correspond to the following 4 photon propagation modes and their superpositions:

A = 0AM 1 ( - 1 )

B = TM

C = 0AM 1 ( + 1 )

D = TE

Output 3 also preferably includes at least one register comprising at least one 4-state qudit, or a 4- level qubit register, characterized by said quantum states and their superpositions, where the four states are obtained by combining the two modes manipulated by the manipulation means, where the manipulation means impose phase shifts of n/2 or multiples thereof on the modes corresponding to the states (see the phase variation map in Figure 2) , so that upon recombination in the combination means C we have the following states:

D=Ex=TE

B=Ey=TM

A=Ex+iEy=l (-1) C=Ex-iEy=l (+1) where i=square root of -1

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

We also observe that, in the single-mode waveguide, after the mode separator 15, 0AM 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 which indicates a phase shift of plus or minus 90° or half a wavelength. The TE mode is related to horizontal polarization and the TM mode to vertical polarization.

The mode separator 15 splits the TE and TM modes and then decomposes the vortices into TE and TM while preserving the half-wave phase shift. Thus, the vortex, i.e., in our case the state with 1=+1 or 1=-1, is translated into polarization modes linked together by phase shifts. This is a very special case that allows the use of single-mode waveguides made to transport TE modes with the minimum possible losses. For this reason, the TM modes are temporarily converted to TE and, once manipulated as required by the computation to be made, they are converted back to TM and recomposed in order to make either a vortex or a superposition of TE and TM modes and their vortices.

We observe that before the mode separator 15 and after the output 3 it is possible to have multimode waveguides, e.g., with 4 modes. The input 2 can correspond to the output of a previous circuit and/or the output 3 can correspond to the input of a subsequent circuit .

The output 3 essentially recombines the two subspaces TE and TM in order to construct the 4 modes we use in the computation. After the output 3 we can envisage various possibilities. For example, it is possible to insert a final module 60 with the function of modulator of modes (and their superpositions) , including for example active phase variation means 40, e.g., such as an adjustable trench (either thermally or otherwise) , hereinafter called active trench, which shifts the result present in the beam combiner module C in a desired way to obtain other state transformations such as Pauli-z and Controlled-Z (CZ) . The final module 60 is a multimodal waveguide and can comprise either a separator towards two other successive computation modules or towards a detector or another single module.

The phase variation means can be of various types, e.g., active or static.

Active examples include controlled thermo-optical devices to locally heat the single-mode waveguide 4. Among the static examples, we include a trench 40b directly etched into the single-mode waveguide 4 shown in Figure 4. This phase shifter is hereinafter globally referred to as waveguide trench 40b and it modifies each of the photon states by translating the state according to a predetermined scheme, such as that of Figure 2. Note that we can also choose another sequence with a permutation of the ABCD states depending on how we define the programming language.

Figure 4 shows a support wafer 12 made of Si02. On wafer 12 is arranged the single-mode waveguide 4, made of Si with a rectangular cross-section of dimensions HxW=220x480 nanometers for a wavelength of 1550 nanometers .

The trench is realized as a rectangular-section recess starting from an edge of the waveguide, where the trench 40b has an etch depth of ed=70nm; a width w=ff*W with a factor of ff=0.25. The waveguide width W is chosen according to the frequency, 1 or 1.1 pm.

The same effect can be achieved 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.

A second static example is trench 40a of Figure 3, comprising two slits at different depths on the same above mentioned single mode waveguide 4.

Trenches 40a and 40b essentially function as a polarization rotator of n/2, so, with reference to Figure 1, these two trenches can be adopted as examples of polarization rotation means 30 and 32. Figure 2 shows the state-to-state trans formation map of the 4-dimensional Hilbert space based on the phase variations applied in module 1 and on the shi ft imposed by the phase variation means of final module 60 .

1 ) The first advantage of this circuit is its versatility to perform the main quantum operations with the least possible loss , as it is compact and does not have j unctions that could cause photon loss and therefore generate computation errors . Contrary to what already exists in the literature and in previous patents , this compact circuit allows to do almost everything required by quantum computing techniques on site . The others instead 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 of introducing errors in the computation in progress .

2 ) The second advantage is that it uses standard manufacturing waveguides and techniques widely used in the fabrication of silicon and silicon oxide components that are part of our daily use . Therefore the costs are drastically reduced .

3 ) Preferably, the computation takes place in single-mode silicon-on-insulator ( S I on Insulator, also known as SOI ) waveguides of standard dimensions , for example , 220 x 480 nanometers for a wavelength of 1550 nanometers . Losses are minimal in these waveguides . Other materials and other wavelengths have their own configurations given by known literature . 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.

5) TM modes, which would be easily dispersed in the circuit when the waveguide is heavily bent, are transformed into TE modes by the mode rotation means R, such as suitable optical components, which rotate the polarization and thus the associated quantum state. The TE modes propagate at much lower loss, are manipulated for quantum computing, and are transformed back into TM modes to superpose them with the TE modes.

6) The manipulation of photonic quantum states takes place through MZI modulation means which are activated in a predetermined way by the programmer and which allow to perform various transformations of quantum states and thus various operations through the so-called quantum logic gates and quantum state registers. The activation involves, for example, performing phase variations using active phase variation means, 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. pilotable, and therefore variable in shape at will. To achieve said phase variations, the invention also includes other active phase variation means known in the literature, such as piezoelectric means or particular materials inserted into the waveguide, which are then modified through electromagnetic fields or other.

7) The manipulation of quantum states, especially phase variation, can also be performed by means of passive optical components .

8 ) The third advantage is that by using these standard manufacturing techniques , the error in the manufacture itsel f is reduced, ensuring not only high quality but also the low cost of the previous point .

9 ) The fourth advantage is the versatility of this computation module with 4 quantum states associated to the photon . Not only does it simpli fy computation as in the circuit of our previous patent application, but it also performs the main quantum operations without the use of other circuits .

10 ) One of these modules can be employed as a distribution node for computation (photon distributor ) to other modules or other parts of the circuit .

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

12 ) Each module can also be used as a computation module and distributor to one or more modules or generic circuit components .

13 ) A single module or a network of these modules constitutes a quantum and classical computing circuit of universal character that can be coupled with other quantum or classical computers or circuits .

14 ) The computational module here presented or, more generally, the universal computing circuit can be used by manipulating the quantum states of a single photon distributed in the circuit itsel f ( i . e . , singlephoton) or multiple photons or packets of photons ( referred to as " continuous" or " in continuous mode" ) . 15 ) Pairs or groups of entangled photons can be used to enhance the computation .

16 ) Entangled photons can also be used to reduce quantum computation error . An example is "heralded" photons , i . e . the use of one or more entangled photons to announce the arrival of one or more of them at a point in the photonic circuit that is determined during the computation phase .

17 ) A further development of the circuit can also employ a multiplication in frequency of the photon or photons , generally obtained by wave beating to achieve frequencies close to the base frequency that still propagate in the circuit . This results in multiple states that increase the si ze of the qudit , as explained in the example of the additional " colored" configuration .

18 ) The computation formally takes place through rotations of the bases in a 4-dimensional Hilbert space of the quantum states that each photon can assume . Said rotations can be arbitrary, being given by the superposition of the 4 states .

It is observed that a generic photonic quantum circuit can be reali zed by connecting computation modules such as these to each other as to make a network, i . e . , a circuit for quantum and classical universal computation, and to other optical components capable of distributing and/or manipulating the quantum states of the photon or photons used for the computation .

The main quantum and classic logical circuits made by each module by appropriately implementing the manipulation means PSI and PS2 are:

Identity all three Pauli x, y, x

Hadamard

Controlled Not (CNOT)

Controlled Z (CZ)

Tof foil

Swap

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

AND

NOT

OR and some combinations of them.

This is achieved by binding polarization (SAM) to vorticity (OAM) , which is a different method than the one proposed in our previous patent application, which uses decoupled SAM and OAM polarization.

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

TE mode - i.e. transverse electric, and

TM mode - i.e. transverse magnetic, 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 thereof according to the laws of quantum mechanics) is preserved and manipulated in order to perform all the transformations associated with quantum computing.

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

By using the waveguide of the example above, i.e., realized with SOI technology and measuring 220 x 480 nanometers for a wavelength of 1550 nanometers, we get the advantage of an easier and cheaper procedure; the waveguide however is no longer square as in the main example of our previous patent application, and the TE and TM modes cannot easily create and propagate the OAM modes. The solution proposed by the present invention is in general to operate in a Hilbert 4D space by decomposing the computational configuration space into subspaces, obtained by decomposing the initial 4D field into two superposed 2D subspaces, one representing the TE mode and the other the TM mode, respectively. This division is carried out by the polarized beam splitter (PBS) . Due to the geometry of the waveguide, the TM mode may exhibit some losses or modifications of the photon state if the photon's path in the waveguide is bent. To avoid these losses, the invention converts in the part of the circuit that corresponds to the subspace TM in TE mode (corresponding to one of the two paths 5, 10) , performs a local operation, according to the superposed subspace TE, and converts back the TE mode to TM mode and finally superimposes it on the TE mode in the "combination" zone, defined by the sub beam combination means C. Here it recreates the necessary 0AM or TE/TM modes or a superposition of them. Of course, the other TE mode (in the other path 5, 10) executes other transformations according to the computation.

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

Module 1 is made with a l-to-2 cascade structure which connects modules that already operate as CCNOT gates on their own (and by driving the final module 60 in a suitable way, we obtain 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 the TE and TM modes) , which include very high precision phase variation means 22 for TE modes and TM modes, each with variable phase ( t>l and t>2 ) and connected in parallel after the polarized beam splitter (PBS) used as input.

Optionally, the output of the two MZIs in parallel can be phase-adjusted by acting on phase variation means 70 ( t>m) on the Ex path after the MZI1 x-polarization interferometer .

In reality, if the two phase variation means 22 associated with the MZI1 and MZI2 interferometers are sufficiently precise, the phase variation means 70 are not needed, and can therefore be omitted. From field tests, it is already possible to achieve extremely precise phase shifts from -180° to + 180° only with phase variation means 22.

The output field and its computation are determined by the phase modulation ( t>l, t>2 and <I>m) .

The TM field is rotated by 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 be sent for example to an active phase shifter 40 in the final module 60.

The final module includes active phase variation means, e.g., an active trench, to make for example the Pauli-z and the CZ, and changes the phase from 0 to 360° thus obtaining the desired shift of the photon modes (A,B,C,D) .

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

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

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

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

To avoid the ef fects of the 220x480nm waveguide birefringence in the transport of the TE and TM modes , especially when the waveguides are bent or in coupling mode , it is preferable to trans form the TM mode into TE mode through mode rotation means (which rotate the polari zation) after the polari zed beam splitter ( PBS ) used as input port . After the necessary trans formation and manipulation of the photonic states , the two paths are sent to the beam combiner C and to an active mode modulator 60 .

Throughout the circuit , SAM and 0AM are coupled with the result that 0AM modes are given as superpositions of SAM modes , and the mode rotation means R trans form 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 OAM.

The OAM modes therefore depend on SAM as follows:

- 1=-1 (clockwise) given by TE+iTM, which means that they are realized with the polarization states H+iv, i.e., elliptical clockwise polarization, Ex+iEy and

1=+1 (counterclockwise) given by TE-iTM, which means that they are realized with the polarization states H-iv, i.e., counterclockwise rotating elliptical polarization, and Ex-iEy will be decomposed by the PBS.

Any OAM mode, being realized with superpositions of TE=Ex and TM=Ey, when passing through the PBS, is decomposed into the two basic components TE and TM, while maintaining the phase shift that characterizes the positive and negative OAM mode and, in the absence of a phase modulator such as the trench waveguide, it preserves the OAM modes at the combination of the two paths, if no phase shift has been added or inverted when a phase of n is added; the other two cases with n/2 and 3/2 n (=-n/2) will generate a superposition in the TM and TE mode phase, which means inducing diagonal polarizations .

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

Quantum computing is shown in the table of states and transformations.

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

As an example of notation, if an OAM mode passes through the PBS, and we decide that the TE=Ex mode passes through the respective phase variation means 22 without any change, we associate it with the | 0> status label (or in the truth table the symbol 0) . This means that means 22 is deactivated, so it preserves the initial phase shift that generates the OAM mode with the TM mode of ±n/2 (i.e. ±i) from the 1=±1 OAM mode, respectively.

Note that after passing through the PBS 15, the TE=Ex mode arrives at the input of MZI1 and at the respective phase variation means 22 unchanged (remains TE) , thus preserving the initial phase shift that generates the OAM mode with the TM mode of ±n/2 (i.e. ±i) from the 1=±1 OAM mode, while the other mode, the TM=Ey, passes through the respective polarization rotation means 30, and is transformed into TE mode for input to MZI2, because this mode in this single-mode waveguide has no difficulty propagating and can be modulated appropriately with almost zero losses and then be converted back by the polarization rotation means 32 into TM mode and recombined into mode combination means 25 to generate the output state required by the quantum computation prepared by MZI1 and MZI2, in this way keeping the losses to a minimum.

To obtain quantum computation in module 1, we use the phase variation means 22 in MZI1 and MZI2 and possibly the optional phase variation means PS-EX 70. For example, when passing through the phase variation means 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. We associate to this operation the | 0> status label (or in the truth table the symbol 0) .

If at the input 2 there is a superposed TE+TM mode corresponding to a 45° linear polarization, it will be decomposed by the PBS 15 into a TE mode going towards MZI1 and a TM mode going towards MZI2. To prepare an output state, if the phase variation means 22 in MZI2 are activated, the TM mode has a phase shift of +n/2 and becomes after the rotation means 32 a +iTM mode which, added in combiner 3 with what came out of MZI1 unchanged, will become a 1=-1 mode which is TE+iTM with clockwise rotating elliptical polarization. The 1=+1 mode is obtained from this result, by a 180° shift using the active trench 40.

In quantum computing, there are combinations of the modes transverse electric TE and transverse magnetic TM of the fields in the waveguides, such as an unchanged phase superposition in the case of an 1=-1 mode and a TM mode that results in a superposed mode TE+ iTM ± TM. This corresponds to a vortex mode with polarization rotation, a superposition of 1=-1 and TM. The same thing happens for the 1=+1 mode, which gives a superposition between 1=1 and TE .

If the input direction of the field is set to direction V for the PBS, then | 0> means that the polarizations do not match, which is the case for the V=TM mode .

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

If TE corresponds to | 1> it generates a vortex mode, with 1=-1, after passing through the phase variation means 22 and 70 in Figure 1.

The polarization is now a superposition of TE and TM i-phase shifted modes and is polarized clockwise or counterclockwise depending on the sign of TM.

1=-1 and 1=+1 generate a superposition of (TE+- TM) + i TM and (TM +- TE) + i TE, respectively. These are superpositions of linear polarization and circular polarization, it becomes elliptically polarized.

Mode change: from linear to elliptical polarization or from circular (which is a special case of elliptical) (left- or right) to elliptical polarization, i.e. we obtain a mode superposition.

The phase variation means 70 function as an adjuster or compensator module between MZI1 and MZI2.

Circuit: rectangular waveguide on silicon chip on insulator on a 220nm thick silicon layer standard SOI wafer. Frequency 1550nm. The single-mode TE waveguide is H=220nm x W=480nm.

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

The flat structure of the waveguide implies that the 0AM is given by the superposition of the Ex field and the Ey field with a phase difference of ±n/2, and due to the SAM-OAM coupling, the 0AM beams are elliptically polarized starting from the coupling of linearly polarized light.

OAM 1=+1 is given by Ex-iEy

0AM 1=-1 is given by Ex+iEy

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

Basically, according to this example, instead of using a trench waveguide to reduce losses, we adopt 220x480nm single-mode TE waveguides and we modulate the polarization with active modifications of the waveguide obtained, for example, by thermal activation and phase modification .

As regards the realization of the (polarization) rotation means made with CMOS compatible SOI technology and based on the symmetric breaking of the waveguide cross-section, they can be created using a 220nm thick waveguide and an active component that modifies the properties of the waveguide. In this case we need to obtain a controlled rotation of the polarization vector for a superposition of TE and TM modes with respective phase delay acting as a mode conversion. Module 1 is a universal computation module capable of implementing up to the 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. The Controlled-Z and Pauli-z can be obtained at the output C in the combination zone, when the active trench 40 in module 60 before the PBS adds a 180° rotation phase, in the 4D configuration space 1=+1 in 1=-1 and vice versa, and TE in TM and vice versa. Module 60 preferentially rotates the state from 0 to 360° .

Each CCNOT module 1 generates a mode that can be split into two other successive CCNOT modules 1 which can accept or reject the photonic state (if the MZIs are both in counterphase) or modulate the fields using MZI1 and MZI2 with the phase variation means 70 (PS-EX) .

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

As regards operations through the z-axis, we observe that they are operations that involve abstract rotations in a three-dimensional space and do not directly have to do with the geometry of the circuit, therefore 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 of 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 need another degree of freedom associated with a transformation in the Hilbert space which in our case corresponds to a shift of 2 positions in the Hilbert space or rather to a double rotation of the basis; they are called parity operators because it is like a mirror reflection .

At the end of the CCNOT in the combination zone C of the two output fields, another rotation of n can be added to the phase rotation of n/2 to obtain a basis inversion in the phase shift map of Figure 2 of the configuration space, whereby the OAM 1=+1 is transformed into 1=-1, a parity operation on pseudovectors (and vice versa) and TE modes are converted to TM mode according to the parity of the OAM states (and vice versa) . This is a double rotation in the Hilbert space used for our computation .

With 10 consecutive levels of bifurcations, we obtain a reading output (detection of the photon's travel state in the circuit together with its 4 states) equivalent to IM paths for 10 qubit-output. With 20 levels 1-terapath of output.

The following table represents the truth table of the Toffoli and CNOT gates obtained with the module described above:

The Hadamard gate is achieved by switching the two MZIs to the ON position and using the PS-EX phase variation means 70.

For the Pauli-z and CZ gates, the phase variation means 40 of the final module 60 must be activated to invert the last off-diagonal CNOT elements Pauli-z and Hadamard - Pauli-x. 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 , i f we have to do the CZ or Pauli- z we have to activate the phase variation means 40 .

Additional configuration, hereinafter referred to as " colored" :

0AM and MUX (multiplexing) frequency in 0AM TE guided mode .

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

In this way, we get a qu-ququad, i . e . ( 2 ^A2 ) * ( 2 ^A2 ) =16 states which means a 16-state qudit for each frequency in the circuit . By using both frequency and 0AM multiplexing on it , we can utili ze the full potential of physical systems such as optical and photon circuits with frequency diversity, multiplying by the number of frequency bands obtained by beating on either side of the base frequency and thus including the base frequency f , identi fied by the fn parameter .

In this case and with these circuits operating in TE mode , it is possible to modulate the frequency and obtain frequencies in close proximity to the central frequency with optical-acoustic or similar techniques , and increase with two side bands from the base frequency centered at 1550nm a qudit with 400 states using pairs of entangled photons , given by the additional dimensions added by the multiplication of frequency fn . In our case we have , for fn=5 and one ququad for each frequency, frequency and OAM being independent , the superposition given by ( fn* 4 ) ^A2= ( 20 ) ^A2=4 O O-state qudit .

Optical f requency-to-OAM conversion has been shown to be feasible in a controlled manner ; it can reduce the complexity of the circuitry 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 an entangled pair of 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=l 06 . 91 , which means having an advantage of more than two orders of magnitude over the increasing complexity of the circuits .

A quantum computer comprising a module according to the present invention is an optical quantum computer, which uses qudits based on photonic states that carry orbital angular momentum ( OAM) . There are two di f ferent configurations with di f ferent construction techniques at a given fixed frequency . A further extension is to set up OAM-based qudits and frequency multiplexing techniques that use base frequency beatings to obtain di f ferent photon states , number of frequency beats fn times the qudit-based OAM state . The size of the computation depends on the dimension correlation obtained through di f ferent paths and circuit configurations in which one , two or more photons are trapped during computation . This has been extensively 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 dimensions involved. In this work, we describe the properties of two photons that are 100-dimensionally entangled. The dimensions are represented by the size of the qudit states and by the diversity of the paths obtained in the computation.

The present invention uses qudits to simplify the structure of quantum circuits. As is well known from the literature (see Wang et al., 2020) the use of qudits decreases the complexity of quantum circuitry; this 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 saving, 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 larger Hilbert state space 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 data structure of the priority queue constructed from arrays of d objects. Qudits with dimension d are described by the terms of quantum states of a vector embedded in a d-dimensional Hilbert space HD. The space is defined by a set of d-dimensional orthonormal basis vectors with the normalization condition ⁼ 1

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 computation. As an example, at least tn_l=log_2 N qubits are required to represent an N-dimensional system in qubits. Using qudits, on the other hand, only n_2=log_d N qudits are required, providing an advantage in the reduction of the complexity factor given by the ratio k=nl/n2 = log2 (d) . The qudit method provides a (log2d) ^A2 scaling advantage over the qubit case. In the case of four qudit states, a ququad with d=2, the advantage is ( log2 ( 4 ) ) ^A2=2 ^A2=4. The complexity of the order n of a circuit scales as 2^A (2*n) , a factor of four with respect to the qubit case.

In the case of entangled particles, the scale dimension of the entangled Hilbert space is d=g*n, where g stands 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 2 ^A ( 4 *n) .

I f we add additional dimensions by multipl ication of frequency fn we have , for fn=5 and one ququad for each frequency, frequency and OAM being independent , the superposition given by ( fn* 4 ) ²= ( 20 ) ²=4 O O-state qudit .

The configuration of our previous patent application is achievable with a non-standard multimodal square waveguide , on silicon wafer, with dimensions of 1 micrometer, and the computation is obtained by checking the polari zation state of each photon; this means that in this configuration the polari zation is considered a quantity independent of the possible states of the orbital angular momentum of the photons .

The second configuration according to the present patent application is based on the currently most common, cheapest and standard construction process of optical circuits with a waveguide given by a SOI layer with a 220nm thickness . Although the latter configuration is much easier to build, the price to pay is that a rectangular waveguide with 220nm height and 480nm width is a standard single-mode waveguide , and the fields associated with the photon must couple OAM and polari zation together . In fact , the waveguide is birefringent and the TE and TM modes are characterized by a di f ferent propagation . The field is then reconstructed at the fusion j unctions that j oin the TE and TM modes (x and y polari zation states ) in a synchroni zed manner with the resulting elliptical polari zation LH or RH depending on the type of OAM state . The phase variation means 70 are used to synchronize the outputs of the two MZIs to finally optimize the computation 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.

The additional advantage is that in this case there are very low losses in the transport of the photonic states even when the waveguides are bent and the TE and TM modes are phase-shifted; 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 CAM states and TE-TM modes based on combinations of TE and TM modes.

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

In standard quantum computing, the four states (A, B, C, D) of a ququad, | q> I QI, Q2, Q3, Q4>, identify an orthonormal basis of the Hilbert 4-dimensional space and represent the four orthogonal modes or quantum states allowed in a single-mode rectangular guide. The electromagnetic (EM) field states propagating in the waveguide are TM, TE (vertical and horizontal polarization) , 1=+1, 1=-1. The TM mode is related to the TM mode of the TE mode. The TE and TM modes correspond with a good approximation to the Bessel or Hermite- Gaussian modes with zero OAM. 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 a homogeneous and inhomogeneous lossless anisotropic medium.

The OAM modes are now prepared as follows:

The SAM and OAM are strongly coupled along with the elliptical polarization:

1=+1 is ccw- rotating and has RH polarization.

1=-1 is cw- rotating and has LH polarization.

This situation can be used when the fields are decoupled in the waveguide circuit and the x-y symmetry is no longer preserved as in standard single-mode waveguides in Si on SOI, 220x480nm, for a 1550nm wavelength .

In this case there are 4 available states because the polarization depends on the OAM state of the beam.

From these, it follows that each of the ququads is given by the superposition with different polarization states of the four independent eigenvectors | q±) |ip> = a|Q1 > + p |Q2> + y |Q3> + 8 |Q4> (1) with the usual normali zation condition l«l² + l |² + |y|² + |<5|² = 1 (2)

More precisely,

| Q1>= | 1 , 0 , 0 , 0), | Q2>=|0, 1, 0, 0>, | Q3>=|0, 0, 1, 0> and | Q4>=|0, 0, 0, 1).

Noteworthy, these two configurations can also operate in continuous mode for continuous variable quantum computation using the strength and the compressed states of the EM field associated with each of the four states present in the configuration, whose numerical values are adapted in input to belong to continuous intervals ; the continuous variable quantum computation 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 polari zation ( relative to spin angular momentum, SAM) and photonic orbital angular momentum ( 0AM) . In the case where SAM and 0AM are strongly coupled and the polari zation identi fies 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 the other as a "herald" to reduce the disturbance in the computation 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 inj ected 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 . On the other hand, with two entangled pairs it is possible to entangle three orthogonal Stokes operators and the corresponding SAM/ OAM states between a pair of beams in two distinct modules 1 according to the present invention . As a first basic language we can map the eigenvectors | q±) and the waveguide modes (A, B, C, D) . The bit-shi ft map cyclically shi fts each eigenvector from I q±) to | qi+i), 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 manner . Any quantum state superposition will be equally rotated in the d=4 Hilbert space .

GENERAL INTERPRETATION OF TERMS

In understanding the purpose of this invention, the term " comprehending" and its derivatives , as used herein, are understood to be open-ended terms that speci fy the presence of the stated features , elements , components , groups , integers , and/or phases , but do not exclude the presence of other unstated 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 double meaning of a single part or a plurality of parts. As used here to describe the form(s) of actuation above, the following directional terms "forward," "backward," "above," "downward," "vertical, " "horizontal, " "below, " and "transverse, " as well as any other similar directional terms refer to the actuation form described in operative position. Finally, grade terms such as "substantially, " "about, " and "approximately" as used herein mean a reasonable amount of deviation of the modified term such that the final result is not significantly changed.

While only selected embodiments have been chosen to illustrate the present invention, it will be clear to experts in the field from this description that various modifications and variations can be made without straying 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 desired. Components shown that are 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 into another form of realization. It is not necessary for all the benefits to be present in a particular form of realization at the same time. Any feature that is original compared to the known technique, alone or in combination with other features , should also be considered 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 embodiments under the present invention are provided for illustrative purposes only and not for the purpose of limiting the invention as defined by the attached claims and their equivalents .

Claims

1. Quantum computing module comprising:

- an input (2) comprising a mode separator (15) , configured to separate a transverse electric mode TE and a transverse magnetic mode TM of one quantum into two parallel paths,

- a first and a second path (5, 10) , parallel to each other, respectively for said transverse magnetic mode TM and for said transverse electric mode TE, located downstream of said mode separator (15) , each path being characterized by:

• a single-mode waveguide (4) ,

• mode manipulation means (20) , including at least first phase variation means ( 22 ) ;

- an output 3 comprising mode combination means (25) , arranged to join the two parallel paths (5, 10) ; where the two parallel paths (5, 10) are distinguished from each other at least because the first path (5) includes: first transformation means (30) of the transverse magnetic mode TM into transverse electric mode TE placed upstream of said manipulation means (20) , second transformation means (32) of the transverse electric mode TE into transverse magnetic mode TM placed downstream of said manipulation means (20) .

2. Module according to claim 1, characterized in that the mode manipulation means (20) include at least one Mach-Zehnder interferometer, comprising the first phase variation means (22) .

3. Module according to any of the preceding claims, characterized in that the mode manipulation means (20) of each path comprise an active power splitter device (50) ; the splitter (50) is driven by the phase induced by the phase variation means (22) to perform at least the following operations: sending all the outgoing radiation to the manipulation means (20) , sending a first portion of the outgoing radiation to the manipulation means (20) and rejecting a second portion by sending it to the respective reflection means ( 51 , 52 ) ;

- rejecting all the radiation by sending it all to said respective reflection means (51, 52) .

4. Module according to claim 3, characterized in that the two splitters (50) are piloted to create coordinated outputs according to the following schemes: a. they allow an output only from the manipulation means of one of the paths (MZI1) and inhibit it from the other (MZI2) and viceversa; b. they allow an output with equal power from both the manipulation means of the two paths (MZI1, MZI2) ; c. they allow an output with power equalized in a desired manner by the manipulation means of the two paths (MZI1, MZI2) .

5. Module according to claim 3 or 4 when dependent from claim 2, characterized in that the active power splitter devices (50) are in output from the respective interferometers (MZI1, MZI2) .

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

7. Module according to claim 6, characterized in that the rotation means comprise at least one optical component configured to rotate the polarization by n/2 or multiples thereof.

8. Module according to any of the preceding claims, characterized in that said waveguide (4) is rectangular in cross-section with dimensions of 220x480 nanometers, preferably for a wavelength of 1550 nanometers .

9. Module according to any of the preceding claims, characterized in that the first and second phase variation means (22, 70) are active because they are driven, i.e., they are driven-effect, while the transformation means (30, 32) are passive phase variation means, i.e., fixed-effect.

10. Module according to claim 9, characterized so that : the active phase variation means include at least one of the following: waveguide thermal regulation means, or piezoelectric driving means, or electromagnetic field driving means, used to influence insertions or depositions of material on the waveguide;

- the passive phase variation means include at least one of the following: at least one trench etched in a waveguide, preferably with a rectangular cross-section, with dimensions HxW=220x480 nanometers.

11. Module according to any of the preceding claims, characterized in that the input (2) includes at least one input register comprising at least one qudit with at least 4 quantum states of a photonic quantum, or a qubit register with at least 4 levels, characterized in that said 4 quantum states correspond to the following 4 photon propagation modes and their superpositions:

A = 0AM 1 ( - 1 )

B = TM

C = 0AM 1 ( + 1 )

D = TE

12. Module according to claim 11, characterized in that said output (3) includes at least one register comprising at least one qudit with at least 4 quantum states, or a qubit register with at least 4 levels, characterized by said quantum states and their superpositions, where the four states are those obtained by combining the two modes manipulated by the manipulation means as follows:

D=Ex=TE

B=Ey=TM

A=Ex+iEy=l (-1)

C=Ex-iEy=l (+1) where i= square root of -1

13. Module according to any of the preceding claims, characterized in that the output (3) includes third phase variation means (40) , preferably active.

14. Method of manipulation of quantum propagation modes to perform a quantum computation characterized by:

- separating a transverse magnetic mode TM and a transverse electric mode TE of a photon radiation; making the two separate modes follow two parallel paths (5, 10) up to a point of combination;

- during the travel in parallel paths (5, 10) , transforming the transverse magnetic mode TM into transverse electric mode TE, manipulating said transverse electric mode TE and transforming it back to transverse magnetic mode TM after said manipulation and before said combination .

15. Method according to claim 14, characterized in that said manipulation of the TM mode transformed into TE includes at least one phase variation.

16. Method according to claim 14 or 15, characterized in that said transformation includes at least one polarization rotation associated with the related mode.

17. Method according to any of claims 12 to 14, characterized by performing a phase variation of the TE mode in the path parallel to that of the TM mode transformed into TE .

18. Method according to any of claims 14 to 17, characterized by including a manipulation for both the TE mode in one of the parallel paths and the TM mode transformed into TE in the other parallel path, where said manipulation comprises the following operations:

- a phase variation,

- a division, driven by this phase variation as follows :

• sending out all the radiation;

• sending out a first portion of the radiation and rejecting a second portion by sending it to the respective reflection means (51, 52) ;

• rejecting all the radiation by sending it all to said respective reflection means (51, 52) .

19. Method according to claim 18, characterized by the arrangement, in each of the two parallel paths, of respective mode manipulation means (20) comprising phase variation means (22) , division means (50) and reflection means ( 51 , 52 ) .

20. Method according to any of claims 14 to 19, characterized by using at least one single-mode waveguide (4) for each of the parallel paths (5, 10) .

21. Method according to claim 20, characterized by using, as a single-mode waveguide, a rectangular cross-section guide measuring 220x480 nanometers for a wavelength of 1550 nanometers.

22. Method according to any of claims 14 to 21, characterized by manipulating said mode by commanding its passage through a waveguide trench and/or by controlling the local heating of the waveguide of its path.

23. Method according to any of claims 14 to 22, characterized by injecting in the two paths a single photon, or a plurality of photons, even entangled, or a continuous signal.

24. Method according to any of claims 14 to 23, characterized by using, as input register at a point of mode separation, a qudit with at least 4 quantum states, or a qubit register with at least 4 levels.