Controllable module for manipulation of a qudit, quantum processor comprising said module

Abstract

The present invention relates to a controllable module for manipulation of a qudit, characterized in that it comprises: a multimodal waveguide (10) with square cross-section comprising a modulating geometric modification (24, 24a, 24b, 24c) localized on said waveguide, where the modulating geometric modification (24, 24a, 24b, 24c) is controllable to manipulate the modes of the qudit.

Description

[0001] Title : Controllable module for manipulation of a qudit , quantum processor comprising said module .

[0002] DESCRIPTION

[0003] The present invention relates to a controllable module for manipulation of a qudit and to a quantum processor comprising said module .

[0004] The invention has been developed with particular attention to the reali zation of a quantum apparatus , for example a quantum computer, however other applications are not excluded, such as for example the reali zation of a classical computer, where it nevertheless allows reduced consumption and higher calculation speed than current computers based on bit calculation .

[0005] DEFINITIONS

[0006] A "quantum apparatus" comprises at least one "quantum circuit" , for example part of a quantum processor , configured to perform a quantum calculation so as to generate output data .

[0007] The output data may be of quantum type ( qubit ) , classical type (bit ) , or their extensions , such as qudits or their combinations, generally in string form.

[0008] The quantum circuit also has input data which preferably comprise classical data, such as bits, objects, events, symbols or signals also in quantum regime, generally in string form.

[0009] The quantum calculation is used to construct the output data based on input data.

[0010] Quantum apparatuses may comprise a quantum computer, a network thereof, a quantum data transmission device, sensors, classical and combinations thereof, or a network thereof .

[0011] The definition of quantum apparatus also includes quantum cryptographic systems, possibly coupled with other "classical" devices, suitable for generating cryptographic keys or sequences of objects, events, or symbols .

[0012] The concept of "event" is understood as a generic physical manifestation that occurs within the Universe or possible Multiverses or even more abstractly in Metaverses .

[0013] It is therefore understandable how, for example, the apparatus can be a quantum sensor, and the quantum calculation is in this case a measurement.

[0014] Each one of these quantum apparatuses is realized on relative hardware parts, herein defined as supporting hardware apparatuses.

[0015] A quantum apparatus may contain a single quantum circuit or a set of them. A quantum processor is a processor dominated or regulated by the laws that we associate with quantum mechanics, meaning any processor capable of performing at least one "quantum calculation". The quantum processor may comprise one or more quantum circuits.

[0016] By quantum calculation we mean "any process performed by a quantum circuit" such as, for example, any of the following operations based on the laws of quantum mechanics: measuring, generating, manipulating quantum states, sequences of symbols derived from them, et similia, without further restrictions.

[0017] Quantum calculation is traditionally based on a basic unit called qubit, i.e., the quantum information unit described by a superposition of two states.

[0018] Quantum calculation can also be based on extensions of qubits. For example we know the qudit, i.e., the quantum information unit described by a superposition of a plurality of states, where the number of states is an integer greater than two (Wikipedia) .

[0019] We also know the qutrit, i.e., the quantum information unit described by a superposition of three states, which is therefore a three-state qudit.

[0020] Qubits are for example states of subatomic particles such as photons or electrons, where since every particle, for the superposition principle, can be simultaneously, and with different probabilities, in multiple different states, it is possible to "overcome" the dualism of classical binary codes 0 / 1 and to convey much more information, thus being able to perform multiple operations simultaneously.

[0021] TE : We shall define as TE waves the electromagnetic waves that have only electric field components perpendicular to the direction of propagation of the electromagnetic wave (i.e., components in an x and y plane) . TE modes are often indicated as TEmn, where m and n are mode indices representing the number of nodes along the x and y directions respectively.

[0022] A=TE10 = fundamental electric mode

[0023] B=TE01 = second-order electric mode

[0024] 0= (0AM L=+l) = positive orbital angular momentum of value +1

[0025] D= (0AM L=-l) = negative orbital angular momentum of value -1

[0026] And subsequent modes of orbital angular momentum.

[0027] More generally:

[0028] 0AM = Orbital angular momentum

[0029] SAM = Spin angular momentum

[0030] STATES = quantum states associated with the photon

[0031] 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.

[0032] VORTEX = mode with non-zero orbital angular momentum

[0033] OAM, i.e., with L different from zero.

[0034] L(+l) and L (— 1) identify the OAM modes that in the literature have orbital angular momentum L=+l and L=-l. In extended form we therefore indicate with OAM L(+l) the OAM mode with L=+l, and with OAM L ( — 1) the OAM mode with L=-l. Said modes are alternatively also indicated as OAM (L=+l) and OAM (L=-l) or as OAM+1 and OAM-1.

[0035] BASE = corresponds to the set of 4 photon states TE01, TE10, L(+l) and L (— 1) (or with TM modes in alternative to one or more mentioned TEs and their equivalents, and called for simplicity TM modes alternative to TEs) that constitute directions in the 4- dimensional Hilbert space. The base is a mathematical term that indicates the fundamental vectors that constitute 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 axes. 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 base vectors. In our case a vector in the at least 4-dimensional Hilbert space represents the quantum state of the photon at the output of a calculation module, which can be either one of the at least 4 states or an appropriate combination of them. STATE OF THE ART

[0036] This invention substantially intends to improve the invention presented in our previous patent application W02024095083 .

[0037] Our previous patent application W02024095083 describes a quantum calculation module by means of a multimode waveguide with rectangular cross-section with a modulating geometric modi fication in the form of a trench carved in the structure . This architecture allows to construct qudits and to manipulate them by means of chosen paths , each comprising a trench with chosen fixed geometry .

[0038] This system has proven very ef fective , as it drastically reduces losses since the photon encounters the modulating part directly along the waveguide without having to " j ump" into modules interposed between multiple guides . Furthermore , with this system the manipulation is directly on the states of individual photons and does not require photon couplers .

[0039] The inventor has now succeeded in further improving the system of the aforementioned previous application .

[0040] The inventor, in fact , has set the goal of the present invention to satis fy at least in part , preferably totally, the following requirements : to increase the dimension of the qudit of the previous application; to control the modulation of a plurality of qudit modes , preferably all , in a single path instead of respective paths , further reducing losses ; to achieve this obj ective through a processor that can be easily built , especially on chip ; to improve the state manipulation module to make it capable of generating on command a superposition of d- states of the qudit and make a "mixed" superposition; to obtain the output of various gates in a single path, drastically reducing losses ; to maintain the possibility of path entanglement ; to ef fectively correct errors during calculation that would alter the expected superposition of qudit states .

[0041] GENERAL INTRODUCTION

[0042] In general , the present invention uses at least one qudit obtained from at least 6 states derived from said four states of the base . The waveguide modes used in our previous patent application W02024095083 are 4 , namely TE01 , TE10 , L=+ l , L=-l . They do not take into account the polari zations .

[0043] According to the present invention, on the contrary, we distinguish the OAMs based on at least two polari zations ; in this way we have that L=+ l and L=- l are multiplied by the at least two polari zation states ( for example vertical and hori zontal ) . We thus have at least 4 OAM modes available to derive the qubit .

[0044] Using said four OAM modes and the two TE01 and TE10 modes , which correspond to the at least two polari zation states of TE ( for example hori zontal and vertical ) , we have at least 6 states available to derive the qudit and a register that comprises at least said qudit with at least 6 modes .

[0045] At the construction level the present invention concerns "A CONTROLLABLE MODULE FOR MANIPULATION OF A QUDIT" , comprising a single multimode waveguide with square cross-section comprising a modulating geometric modi fication locali zed on said waveguide , where the modi fication is controllable to manipulate the modes .

[0046] Said module is an embodiment , easily buildable on chip, of a processor configured to manipulate said qudit with at least 6 states when it travels along said waveguide .

[0047] Said controllable modules are also called quantum circuit , or may be part of a more complex quantum circuit , comprising for example a plurality of said modules .

[0048] Preferably said manipulation comprises a multimodal conversion simultaneously of "d" modes of a single photon supported by said guide . Said multimodal conversion is defined as the passage from one mode to another of the "d" modes. The multimodal conversion is preferably actuated by means of phase variations of the modes.

[0049] In preferred embodiments said module may comprise thermo-optic control means configured to locally heat said multimodal waveguide (4) and to generate or modify in this way said modulating geometric modification. The control means may also be waveguide inserts controllable piezoelectrically or in other ways.

[0050] The modulating geometric modification can for example be a trench, i.e., a recess, carved in the waveguide, in which case we speak for simplicity of "active trench", where the term "active" indicates the fact that its formation or modification is controllable.

[0051] Thanks to the square cross-section of the guide the "d" modes supported by the guide can be at least 6, therefore it is possible to define a qudit (or a register of qubits) in input and output from said module comprising at least the following 6 states: A, B, C(1 and 2) and D(1 and 2) corresponding to the following 6 propagation modes of a quantum:

[0052] A= TE10 associated with a polarization, for example vertical

[0053] B= TE01 associated with a polarization different from the polarization of A, for example horizontal

[0054] Cl= (0AM L=+l) associated with a polarization C2= (OAM L=+l) associated with a polarization different from the polarization of Cl

[0055] Dl= (OAM L=-l) associated with a polarization

[0056] D2= (OAM L=-l) associated with a polarization different from the polarization of DI.

[0057] The polarizations of the OAMs are also for example horizontal and vertical.

[0058] The polarizations are for example defined in general by polarization axes orthogonal to each other and to the direction of propagation of the quantum in the waveguide.

[0059] The polarization axes of the TE01, TE10, and OAM modes may coincide.

[0060] The polarizations of A and B can also be interchanged .

[0061] According to some preferred embodiments the "d" states are also in number greater than 6, and correspond to the higher propagation modes possibly supported by the waveguide (10) with OAM values greater than +1 and lower than -1.

[0062] Preferably said manipulation comprises the step of generating from at least one of said propagation modes or their superpositions, by beating on a localized modulating geometric modification (24) of the waveguide (10) , two linear polarization LP modes with different propagation constants ( p l and p2 ) , where at the output o f the geometric modi fication obtained by means of devices suitable for modi fying the local geometry of the guide in an appropriate way ( 24 ) the two linear polari zation LP modes interfere generating one of the "d" propagation modes of the quanta depending on their phases .

[0063] The invention further relates to a quantum processor comprising :

[0064] - at least one of said controllable modules ;

[0065] - at least one input register ( 5 ) of information units corresponding to said qudit with at least 6 states placed at the input of said controllable module

[0066] - at least one output register ( 15 ) placed at the output of said controllable module and configured to decode the information corresponding to the manipulated modes .

[0067] Preferably, also the output register ( 15 ) is a register of information units corresponding to said qudit with at least 6 states .

[0068] Said processor preferably comprises a plurality of said controllable modules arranged in series with one another, where the respective modulating geometric modi fications of said modules are on the same waveguide , therefore called common waveguide .

[0069] Preferably, said modulating geometric modi fication comprises a modi fication, or a reduction or an enlargement of the cross-section of said waveguide . According to some preferred embodiments said modulating geometric modi fication comprises a concavity positioned to define a recess of said cross-section, where preferably said concavity has a cross-section comprising two branches that proj ect in di f ferent directions . Said branches , for example , are such that said waveguide in correspondence with said concavity has a cross-section shaped substantially as a V or an L .

[0070] According to some preferred embodiments of the invention said waveguide is a single optical fiber and said modulating geometric modi fication is a modi fication of the cross-section of the optical fiber .

[0071] In this case, preferably said optical fiber has a substantially square cross-section or has a core with substantially square cross-section, and said geometric modi fication is a recess in correspondence with a corner of said square cross-section obtained by actively deforming the waveguide with thermal means or means controllable piezoelectrically or in other ways .

[0072] Preferably said manipulation comprises a multimodal conversion defined as the passage from one to another of at least some of the "d" modes of the at least one quantum .

[0073] According to some preferred embodiments the input register is a qudit register with "d" states or a qubit register with "d" levels , corresponding to said "d" propagation modes of said at least one quantum, and the waveguide 10 has a geometry that supports exclusively "d" propagation modes and their superpositions.

[0074] According to a particularly preferred example the modulating geometric modification (24) is configured to excite, starting from one of the input propagation modes, two linear polarization LP modes of the at least one quantum, hereinafter called LP modes, with different propagation constants (pl and p2) , where at the output of the geometric modification (24) the two LP modes interfere generating at least one of the "d" propagation modes of the quanta.

[0075] Preferably the waveguide has an active part that, starting from the square cross-section, deforms by control into a cross-section with two main development dimensions X and Y orthogonal to each other and to the quanta propagation direction Z, where said cavity comprises a dimension "a" along X and an equal dimension "a" along Y. For example said active modulating geometric modification (24) comprises a waveguide section where the deformation mechanism of the guide creates an L or V cross-section in a plane transverse to the propagation direction Z.

[0076] Preferably the modulating geometric modification extends for a length L in the propagation direction Z, where L is equal to: or its multiples where pi and p2are the propagation constants of the two LP modes .

[0077] Preferably the polari zation states are a hori zontal state | H) along x, and a vertical state | V) along y of the corresponding quantum .

[0078] In our previous patent application the polari zation was exploited di f ferently compared to the present patent application, in particular it was exploited to multiply the number of qudits or in a control register . In the present invention the calculation power is increased in a single passage by exploiting the polari zation to increase the dimensions of the qudit from 4 to at least 6 modes , associating them at least to L=1 and L=- l to distinguish them based on their polari zation and thus double them . In this way the qudit , instead of having two 0AM modes as in the previous application, has at least four derived from the same two .

[0079] Preferably the input register has at least 8 , preferably at least 16 , of said qudits with 6 or more states whose number depends on the higher modes supported by the main waveguide .

[0080] According to some preferred embodiments the processor is configured to reali ze at least one among known gates ( quantum circuits ) such as for example the CNOT , CCnot ( Tof foli ) or Hadamard gate . While our previous patent application W02024095083 contemplated fixed geometric modi fications ( trenched) placed on multiple paths , and the calculation result was obtained by "path entanglement" , i . e . , by exploiting the various paths , in the present invention the calculation result can derive totally or at least in part from one single path . Said gates , in fact , compri se at least one path in which the photon encounters the controlled modulating geometric modi fications placed in series along a waveguide with square cross-section common to multiple modules . In this way in the present invention the same calculation result is obtained in fewer steps compared to path entanglement alone . Es sentially, the path entanglement is obtained by making the photon travel through a plurality of paths , at least one of which comprises said series of modules along the common waveguide .

[0081] The fact that the controllable modulating geometric modi fication ( or a circuit equivalent to it such as a higher mode waveguide modulator ) can make intermediate steps of phase shi ft or mode change allows us to have superpositions that would not exist with a finite set of fixed modulating geometric modi fications ( trench) . Of course each gate may comprise a plurality of said processors placed in series and parallel to define a plurality of said paths , where each path comprises a plurality of modulating geometric modi fications placed in series on a waveguide with square cross-section common to multiple processors .

[0082] According to some preferred embodiments said input register is placed at the input of at least one waveguide , comprising at least one of said modulating geometric modi fications ( 24 ) , and preferably a plurality of them .

[0083] It is not excluded that the input register is common to a plurality of said guides .

[0084] According to another aspect the invention relates to an input register of a quantum processor comprising at least one qudit with 6 states of the type indicated above .

[0085] According to another aspect , the invention relates to a method of qudit modulation in a quantum processor characteri zed by the fact of providing a quantum processor ( 1 ) of the type indicated above , of feeding at the input of a waveguide with square cross-section ( 10 ) , common to multiple controllable modules , at least one quantum characteri zed by at least six states corresponding to respective propagation modes supported by said guide ( so as to define a qudit with at least 6 modes ) , and of manipulating said propagation modes by controlling said modules .

[0086] The invention also relates to a quantum processor comprising a calculation circuit and a calculation correction circuit at the output of the calculation circuit , where at least the correction circuit , and preferably both, comprise said module .

[0087] DETAILED DESCRIPTION

[0088] Further features and advantages of the present invention will result better from the following detailed description of its preferred embodiments , made with reference to the attached drawings and given by way o f indication and not of limitation . In such drawings :

[0089] - figure 1 schematically shows a quantum processor where a quantum circuit is represented, comprising a controllable module comprising a waveguide having structural continuity; said guide is for example an optical fiber ;

[0090] - figure 2 schematically shows a selection section of "d" modes of the waveguide of f igure 1 having a square cross-section; figure 3 schematically shows a mode modulation section of the waveguide of figure 1 , with a modulating geometric modi fication with respect to the selection section and structurally and optically continuous with respect to it .

[0091] - figure 4 shows the fiber states that are formed by coupling the linear polari zation LP modes ( also called LP-like modes ) of the modulation section of figure 1 based on the phase shi ft they have between each other at the exit of this section .

[0092] - figure 5 shows the electric field and the magnetic field in the waveguide of figure 1 , in a section with square cross-section cavity preceding the modulating geometric modification;

[0093] - figure 6 shows the first 12 modes of a waveguide with known generic rectangular cavity; figures 7 and 8 indicate the equations that demonstrate the selection ef fect , generated by the transverse dimensions a and b, of the four waveguide modes TE10 , TE01 , ( OAM) L=+ l , ( 0AM) L=- l , called A, B, C , D;

[0094] - figure 9 shows the modi fication from a TE10 state to an 0AM state due to the pas sage in the modulating geometric modification of figure 1 ;

[0095] - figure 10 shows a quantum processor according to the present invention comprising at least one path defined by at least one waveguide common to multiple controllable modules placed in series with one another, where said modules each comprise a modulating geometric modi fication locali zed on the same waveguide common to all said controllable modules in series ;

[0096] - figure 11 shows a quantum processor according to the present invention, comprising a plurality of paths as in figure 11 placed in parallel ;

[0097] - figure 12 shows a quantum processor according to the present invention comprising a calculation circuit and a calculation correction circuit placed at the output of the calculation circuit , where at least one of the two comprises at least one controllable module .

[0098] FIGURE CAPTIONS TRANSLATION :

[0099] • Figure 4 :

[0100] - Polari zation LP Modes = Polari zation LP Modes

[0101] - Trench waveguide = Trench waveguide

[0102] - Mode shift = mode shi ft

[0103] - Phase intensity = Phase intensity

[0104] - Polari zation = polari zation • Figure 5:

[0105] - Cross section / side view / top view = cross section / side view / top view.

[0106] • Figure 7 :

[0107] - The governing equation for TE analysis is = The governing equation for TE analysis is

[0108] - after a solution is obtained the remaining field components are calculated according to = after a solution is obtained the remaining field components are calculated according to

[0109] - low frequency cutoff = low frequency cutoff

[0110] - we just found the lower frequency cutoff = we just found the lower frequency cutoff

[0111] - High-frequency cutoff = High-frequency cutoff

[0112] - The high frequency cutoff is the frequency where the second-order TE mode is supported = The high frequency cutoff is the frequency where the second-order TE mode is supported

[0113] This could be the TE01, TE11 or TE20 mode. We must consider all = This could be the TE01, TE11 or TE20 mode. We must consider all.

[0114] TE11 will always have a higher cutoff frequency than TE01 = TE11 will always have a higher cutoff frequency than TE01.

[0115] The second order mode depends on our choice of a and b = The second order mode depends on our choice of a and b . • Figure 8 :

[0116] Field solution = Field solution

[0117] TEOO mode does not exist = TEOO mode does not exist (note: more precisely: does not propagate effectively)

[0118] TE10 is the lowest order TE mode = TE10 is the lowest order TE mode

[0119] Phase constant = phase constant cutoff frequency = cutoff frequency

[0120] Characteristic impedance = characteristic impedance.

[0121] GENERAL PRINCIPLE

[0122] The general principle underlying the present invention is to realize a quantum circuit comprising at least one waveguide (for example a single optical fiber) comprising at least one local modification of the geometry obtained actively (i.e., controllable) and reconfigurable each time according to calculation needs, called controllable modulating geometric modification, acting on the quantum state of each quantum that travels along the waveguide. A waveguide section with a controllable modulating geometric modification is also called controllable module, as we will see later, and indicated as a whole with reference number 2. The controllable modulating geometric modifications, also called for simplicity "controllable geometric modifications", have the function of manipulating the quantum state (and its associated quantum information) and said manipulation (also called modulation) is part of the quantum computation process. This reduces losses of quanta, for example photons , and consequently calculation errors , compared to the known case of inserting foreign devices in the waveguide giving rise to interruptions in the quanta path .

[0123] A quantum processor may comprise a plurality of said modulating geometric modi fications , preferably in series on the same waveguide , in thi s case called common waveguide .

[0124] In general the waveguide can be solid or tubular ; in both cases , it is often indicated in the literature as cavity, so this term is understood as a general synonym indicating the material and the relative geometry where radiation propagates .

[0125] In the following we use as an example an apparatus based on photonic quantum calculation, without excluding apparatuses based on analogous procedures that make use of the quantum mechanical wave properties of any other quantum such as atoms , ions , elementary and non- elementary particles and their sets etc . . . Hybrid circuits that use two or more quanta types are not excluded either .

[0126] Quantum calculation preferably occurs by inj ection ( input ) of one or more quanta (photons in our example ) , single or superposed between them, or bound between them in " entangled" states , or more generally in bound or correlated states , reali zed by means of a single quantum or states of multi-quantum .

[0127] Each of these quanta possesses a predetermined quantum state to which information is associated . Quantum information is expressed in terms of qubits , by means of a superposition of two mutually orthogonal states , or in terms of qudits , by means of a superposition of "d" mutually orthogonal states . A d-dimensional Hilbert space is associated with a qudit , a 2-dimensional Hilbert space with a qubit . Proj ective techniques of Hilbert space geometry can map Hilbert spaces of di fferent dimensions into subspaces or into product spaces , meaning it is possible to express a qudit by means of an appropriate set of qubits .

[0128] To perform a quantum calculation the quanta (photons in our example ) are inserted into a circuit ( optical in our example ) along which one or more local modi fications of the waveguide cavity geometry are arranged, configured to generate a path for modulation of the quantum states of the quanta (photons ) . At the end of the circuit single quantum (photon) detectors or equivalent sensors are placed, to detect the presence or absence of quanta (photons ) at a speci fic moment in time , thus obtaining the result sought by the quantum computation .

[0129] The path of each quantum that participates in the computation, whether by light quanta or other types , is obtained by confining it in a set of waveguides (which in our example is one or more cavities also simultaneously) in which the carried information, which is linked to its quantum state , is preserved, i . e . , for example the polari zation of the photon or a field propagation mode such as the orbital angular momentum ( OAM) , cavity modes such as Hermite-Gauss or more general properties that can be associated with a quantum state that forms a set of preferably orthogonal states .

[0130] A photon used as a quantum in the computation process , for example , can simultaneously be found in all the parallel paths within a quantum circuit or have all the polari zation or OAM states superposed in a quantum mixture . By advancing the calculation, new paths and therefore new quantum states superposed on, and coexisting with, the previous ones can be generated . The final quantum calculation is to tame all the superpositions ( for example for a 16A16 module ) and make them proj ect into a final string of bits ( for example 64 bits ) with the final collapse of the wave function, which is the result of the calculation . It is in all respects a real physical process , not a process simulated by using quantum logic as in a classical calculation . We use the language of nature .

[0131] In general the invention comprises a processor comprising at least one input register 5 of information units , in the form of qubits or preferably qudits , in which certain information is encoded and placed at the input of at least one waveguide 10 that defines the path of the corresponding quanta . The waveguide is configured to support a plurality "d" of quanta propagation modes , in input and preferably also in output , and comprises one or more modulating geometric modi fications , each configured to manipulate them by transforming at least one propagation mode into one of the other modes of the qubit or qudit. At the output of the waveguide the result is read by decoding the information in an output register 15.

[0132] The modulating geometric modifications break the original rotational symmetry and divide the mode degeneracy into two linear polarization LP propagation modes (also called LP-like modes and hereinafter for brevity also LP modes) . At the exit of the modulating geometric modifications the two LP modes interfere and generate one of the supported "d" modes, based on the phase shift, so the modulating geometric modifications enable the passage from one mode to another.

[0133] In this way each qubit or qudit has "d" states manipulated by waveguide geometry.

[0134] In a specific preferred example the waveguide geometry has a square cross-section and supports 6 propagation modes, so each qudit used for calculation has 6 states, preferably orthogonal to each other, preferably TE01, TE10, OAM+1 with a first polarization 1, OAM+1 with a second polarization 2, OAM-1 with said first polarization 1, OAM-1 with said second polarization 2.

[0135] Each modulating geometric modification of the waveguide is configured to transform at least one of the six propagation modes, and therefore of the six qudit states, into one of the others. The transformation occurs because the modulating geometric modifications are configured to support for each mode two orthogonal LP linear polarization modes, which have two different propagation velocities. In the case of a waveguide with rectangular cross-section transverse to the propagation direction Z and with sides parallel to the X and Y directions, for example, the two LP modes have optical axes rotated by about 45° with respect to X and Y. When the two LP modes interfere, at the output of the modulating geometric modification, depending on their phases they generate one of the modes supported by the rectangular waveguide. When the two LP modes are in phase, they form the TE10 mode.

[0136] The waveguide which favors the propagation of OAMs with polarization and which simplifies the construction of chip microprocessors has a square cross-section, where the cross-section is considered orthogonal to the propagation direction.

[0137] Preferably the modulating geometric modification is interposed between an input waveguide section and an output section which have common geometry.

[0138] Figure 4 shows the transformation table of the at least 6 modes of a qudit according to the present invention in a controllable modulating geometric modification on a square cross-section waveguide. The transformation shown is based on the phase differences (called shift or phase-shift) of the linear polarization LP modes at the output of the modulation section 24. In figure 4 "a" is a conversion parameter from one mode to another (for example a=l) which generalizes the controllable property of the modulating geometric modification .

[0139] The OAM=0 states, with PV and PH polarizations, are the TE01 and TE10 states; they represent the two states of the OAM mode 0 with V, vertical and H, horizontal polarization. They can also be chosen with COW (counterclockwise) or CW (clockwise) start.

[0140] Polarization 1 and 2 of the OAM are also indicated, corresponding to horizontal and vertical polarizations.

[0141] The example shows 2 input rows of OAM states with different polarization; then, with a translation of a*fractions of pi, all the other states are made by exploiting the control of the modulating geometric modification .

[0142] Since the six modes are mutually orthogonal and independent, they can be used both for channel multiplexing and for setting six independent modes for quantum calculation.

[0143] Based on these basic principle premises, figure 1 represents a quantum processor 1 comprising at least one CONTROLLABLE MODULE 2 FOR MANIPULATION OF A QUDIT. The controllable module 2 comprises: a waveguide 10, a quantum source 5 (for example photons) part of a register in input to waveguide 10, and a quantum detector device 15 (for example photons) part of a register in output from waveguide 10. The waveguide 10 generally defines an electromagnetic propagation path of the quanta in a propagation direction Z, coinciding with its main development direction.

[0144] The waveguide 10 in this example comprises the cavity 12 of a tubular body, which extends along its entire z development. Said cavity 12 may be empty or full, for example it is not excluded that it is filled, for example with dielectric material.

[0145] The waveguide, for example, is a single optical fiber with square cross-section for photon transport.

[0146] The waveguide 10 has at least one section 19 for the selection of propagation modes having a first crosssection 20 transverse to the propagation direction Z. In the example of figure 1, and as better visible in figure 2, the cross-section is characterized by a square cavity 12, i.e., it has two main development directions X and Y, where the dimensions of cavity 12 in said directions are equal and indicated with the dimension "a", and where preferably they are such as to define a selection of the supported propagation modes; in our example the cavity of the first cross-section 20 is configured to support the following modes:

[0147] TE01, TE10, OAM+1 with a first polarization 1, OAM+1 with a second polarization 2, OAM-1 with said first polarization 1, OAM-1 with said second polarization 2.

[0148] More precisely, in the example we use square fibers dimensioned to have transverse electric (TE) modes limited to the fundamental mode and to the second order of TE10 and TE01 respectively, and to two orbital angular momentum (OAM) modes L=+ / -l. The Z axis, as said, is the propagation axis.

[0149] These six are independent propagation modes orthogonal to one another indicated with A, B, C(1 and 2) and D(1 and 2) , and they are the six modes that define the states of the preferred qudit according to the present invention.

[0150] We note that by convention we define the propagation modes based on the wave-field approach based on the known Maxwell equations.

[0151] Based on this approach the propagation modes in a waveguide are subdivided into transverse-electric (TE) and transverse-magnetic (TM) modes, depending on whether the electric or magnetic field are purely transverse with respect to the propagation direction.

[0152] The cross-section 20 mentioned above is obtained actively when abb since the low frequency cutoff for the TE01 mode is when fc, oi=l / (2b (ps ) ) is active for ad2b.

[0153] By definition we have fci=l / (2a (ps) ) , where p and s are the dielectric and magnetic permittivity of the fiber and c=l / (ps) is the propagation velocity of light in the medium.

[0154] Figure 5 shows the electric field and magnetic field in the rectangular cross-section cavity 12 of guide 10 when abb, in particular it shows the fundamental TE10 mode .

[0155] Figure 6 generally shows the first 12 modes of a waveguide with rectangular cavity. The arrows indicating the direction and polarization of the E fields are drawn.

[0156] The three "rules" for E and H (M) fields inside the waveguide, according to Maxwell's equations, are:

[0157] • Electromagnetic waves do not pass through or cross conductors, they are always reflected by conductors .

[0158] • Electric field lines that touch a conductor must be perpendicular to it.

[0159] • Magnetic field lines near a conductor must be parallel to it.

[0160] Based on these rules it is possible to formulate the equations of figures 7 and 8 which show how the choice of a and b is able to effect the selection of the supported propagation modes mentioned above, where a=b is contemplated, i.e., a square cross-section guide as used in the present invention.

[0161] The waveguide 10 comprises at least one modulation section 24 having a second cross-section 25, downstream of the selection section 19, with respect to the propagation direction Z. The modulation section 24 defines a modulating geometric modification according to the present invention, also called local geometric modification . Considering for example the second-order mode ( TE01 ) supported by the selection section 19 , its passage in the second section 24 excites two orthogonal LP modes with di f ferent propagation constants ( p l and p2 ) . These , propagating in the modulation section 24 , have a phase shi ft between them induced by the geometry of the modi fied cavity 12a . The modulation section 24 is configured to generate phase shi fts of n / 2 or its multiples . Thus one of the six independent modes that form the qudit according to the present invention is obtained at output . Figure 9 illustrates an example of modulation to trans form an input TE10 mode into an output CAM mode .

[0162] Coming to the preferred geometric examples of section 24 , the second cross-section 25 defines a local modi fication of the geometry of cavity 12 , better visible in figure 3 , in particular the modi fied cavity is indicated with 12a and comprises two main development directions orthogonal to the propagation direction Z . In the example the two directions are the X and Y directions . To obtain this in the example the crosssection 25 comprises with respect to cross-section 20 a recess 26 , preferably so as to form an L . As visible in figure 1 , assuming that the external shape of the waveguide follows the cavity, except for the wall thickness , the recess 26 forms a trench along the second section 24 that interrupts one of the corners of the rectangular cross-section of the selection section 19 .

[0163] In general the geometry of the modulation section 24 has the task of generating LP ( linear polari zation) modes and maintaining them distinct.

[0164] At the exit of the modulation section 24 there is an interference section 30 of the LP modes where they rejoin and form one of the six modes A, B, Cl, C2, DI, D2 depending on their phase. The interference section 30 in fact has a geometry that supports said four modes, and preferably has the same geometry as the selection section 19.

[0165] The phase shifts between the LP modes in output depend on the length of the modulating geometric modification in the propagation direction Z obtained by control means comprising thermal or piezoelectric activators or other known technique.

[0166] Said length is indicated with L in figure 1 and to obtain phase shifts of n / 2 (as in the case of generation of 0AM mode = L=+l or L+l starting from TE10) is given by : while to obtain phase shifts of 3n / 2 (as in the case of generation of 0AM mode L=-l or L-l starting from TE10) : where pi and p2are the propagation constants of the two

[0167] LP modes (Linear Polarization / LP-like modes) .

[0168] In general therefore L is equal to: or its multiples.

[0169] Regarding the dimensions w and h of trench 26 that forms the L shape, generally they are not the result of a calculation through a formula, but are more conveniently optimized based on backward calculation techniques starting from an expected result, in particular they are optimized backward to adjust, depending on the chosen materials, the desired effect of modifying electromagnetic fields and minimizing losses. Likewise, we have a similar behavior for higher modes associated with greater values of orbital angular momentum, obtaining a qudit with d>6.

[0170] This effect is described as perturbations of the refractive index on a multimodal waveguide (as the one in the present invention) ; the energy can be coupled from one waveguide mode to other modes (which are A B Cl C2 DI D2 in our example) , and the amplitude of each mode along the propagation direction Z can be determined by a set of differential equations of this type, for each mode p of the cavities we are interested in (in our example there are 2 differential equations for modes TE01 and TE10 and two others to describe the phase shift of + / - n / 2 of the two superposed modes TE01 and TE10, which are modes OAM+1 and OAM- 1) : where Apand Aqare the amplitudes of waveguide modes p and q, and ppand pqare respectively their propagation constants. The index m indicates the order of the highest order mode in the multimodal waveguide. Kpqrepresents the modal coupling coefficient between waveguide modes p and q, which can be defined as: where the integration region S is the cross-section of the waveguide material (which can be for example silicon) , Ep(x,y) and Eq(x,y) are the electric field profiles of waveguide modes p and q in the cross-section respectively, and As (x,y,z) represents the refractive index perturbation on the waveguide given by the shape of trench 26. According to equation 2 above, Kpqis proportional to the spatial integral of perturbation As (x,y,z) with Ep(x,y) and Eq(x,y) , which we call electric field overlap.

[0171] There are two necessary requirements for multimodal conversion (i.e., passing from one to another of modes A, B, C(1 and 2) , D(1 and 2) ) based on Equation (1) . The first is to obtain large values of modal coupling coefficients between the incident modes (the starting one, for example mode A) and the target modes (where the mode transforms, for example to mode B or subsequent) . This concept also applies to mode superpositions and therefore to a generic qudit made by modes A, B, C(1 and 2) , D (1 and 2) .

[0172] The second requirement is to satisfy the phase matching condition along the propagation direction, which compensates for the discontinuity of the propagation constant Ap (i.e., pp- pq) of the oscillating exponential term present in Equation 1. The phase matching condition for modal coupling between modes p and q can be deduced from the following relation: where 5pqrepresents the cyclic period of refractive index perturbation. The discontinuity given by Ap which is also found in Equation (3) between different pairs of cavity modes (of modes A, B, C, D) presents different values in the periods where this perturbation, which transforms one mode into another, occurs, and therefore also leads to solutions with di f ferent coupling lengths .

[0173] For this reason, using LP modes to pass from one state to another or to trans form one qudit into another we need di f ferent lengths L of the cavity with trench 26 , to trans form with high precision and univocally one cavity mode into another .

[0174] The square waveguides according to the present invention are easily constructed for example using SiO2or other materials such as polyethylene or silicon nitride , which can be printable , for example in a silicon-on-insulator ( SOI ) chip as support . Trench 26 can be reali zed by the control means 27 comprising for example means of local thermal deformation of the optical fiber or inserts of active material such as lithium niobate , controllable also piezoelectrically, by growing the deformation, for example , in a manner equivalent to the cavity of a fixed trench 12a .

[0175] The preferred example of circuit according to the present invention is the one presented in figure 10 , comprising a path of at least one photon defined by a plurality of controllable modulating geometric modi fications 10 reali zed in series along the same waveguide , thus reali zing a series of controllable modules 24a, 24b, 24c having said waveguide in common .

[0176] Figure 11 schematically shows by way of general example a quantum processor according to the present invention comprising a plurality of paths as in figure 11 , placed in parallel .

[0177] By using controlled single module or multimodule paths , and appropriate controlled switches 88 placed between them, it is possible to al so obtain the ef fect o f path entanglement and therefore any type of gate , including known gates . It is even possible to obtain a gate only with controlled modules in series on a single waveguide . The advantage is that this can be obtained with a low number of paths .

[0178] In our previous patent application W02024095083 it was necessary to control a plurality of switches to direct the photon towards the desired fixed trenches ; now said deviations can be simpli fied since it is possible to increase the calculation power on a single path by directly controlling the modulating geometric modi fications and by exploiting the distinction between the at least 6 qudit states based on the square crosssection of the waveguide that defines a single path .

[0179] The first advantage of selecting these TE modes i s that they are stable with respect to propagation in rectangular fiber circuits , and are not suppressed . By selecting the transverse dimensions a and b of the fibers , all other higher order modes are suppressed, avoiding mixing in spurious modes .

[0180] The second key advantage is that with the controllable modulating geometric modi fication it i s possible to trans form ( or better, modulate ) one of the states into another . For example through the controllable modulating geometric modi fication 24 it is possible to trans form one of the six states of the square waveguide 12 mentioned above into another ( quantum state shi ft ) . In this way it is possible to operate on the six base states of each qudit by crossing a single one of the waveguide sections with controllable modulating geometric modi fication, also obtaining superpositions of qudit states in a single passage , reducing losses due to reflection and discontinuity that will in any case be present in smaller number in the switches introduced in the processor to build a computation path for the photon within the processor . By thus manipulating the quantum states of the photon we obtain part or all of the quantum calculation result .

[0181] The other advantage is that in this way the circuit , based on the geometry of square waveguides , supports six natural fiber modes , i . e . , two transverse electric states ( TE10 , TE01 ) and four orbital angular momentum 0AM states where the latter are states L=- l and L=+ l with a first polari zation and states L=- l and L=+ l with a second polari zation) . Waveguides of larger si ze or with other appropriate geometries can easily support higher waveguide and orbital angular momentum modes , where each orbital angular momentum can be distinguished into two respective states that di f fer by polari zation, ideally obtaining a qudit with "d" as large as desired .

[0182] Formally, to each of these orthogonal modes we associate an eigenvector with which to construct a qudit with d=6 . The direct advantage is that with the use of a qudit of order d we need a smaller number of qudits , compared with qubits , to cover the state space of a given problem, like a quantum register of cardinal order N, since ni= log2N qubits can represent an N-dimensional system, while only n2= logd N qudits are required . In our case n2= log4N .

[0183] The input to the waveguide can be reali zed for convenience through a fixed phase device , comprising for example phase masks or OAM sources , so as to directly impose a state among those supported by cavity 12 of waveguide 10 , for example the input generates photons with orbital angular momentum ( OAM) L=- l .

[0184] In this way we simpli fy the input circuitry, which would require a complicated device in the case , for example , of adoption of multiple inputs , as desirable in the present invention, for example 16 qubits .

[0185] At the output register 15 a separation of qudits into bits and a reading of N events occurs by means of a demultiplexer that can have various forms and configurations . Preferably, photon detectors are integrated in the circuit at the end of the processor , thus reducing losses . Preferably they are SPAD, single photon avalanche diodes .

[0186] Optionally it is possible to provide a read waiting state : to possibly reduce the number of SPADs for the reading, we can consider dividing the reading of quantum states at the output, not into 64 simultaneous states but into 16 or 32 states divided by time slots, and sending them not to 64 different SPADs but to 16 or 32 SPADs, to reduce costs.

[0187] The module 2 described up to here is a basic circuit, which can be used to build any type of complex quantum-logic circuit within a quantum processor 1, in particular logic gates, also called gates.

[0188] One of the fundamental logic gates that we can construct through the basic circuit 2 can be for example a controlled NOT, called C-NOT gate, a Toffoli gate or a Hadamard gate, which also realize the entanglement of quantum states, including path entanglement obtained by means of different paths guided by various switches present in the quantum calculation circuit.

[0189] A quantum calculation processor may comprise a series of C-NOT gates connected to one another or realized in a single gate by means of a superposition of states. Furthermore, to have a connection with classical calculation and algorithms, following the correspondence principle of quantum mechanics, we can construct a Toffoli circuit or gate by means of the equivalent of a series of C-NOTs, thus obtaining a controlled-controlled NOT (CCNOT) by modulating the deformation of the modulating geometric modification. To conclude we observe that , with reference to figure 12 , a quantum apparatus 1 according to the present invention can comprise at least one quantum calculation circuit 50 and one quantum correction circuit 52 at the output of the calculation circuit . At least the correction circuit 52 , and preferably both, comprise at least one controllable module 2 . The quantum apparatus 1 also comprises diagnostic means 55 configured to control the correctness of the calculation performed by calculation circuit 50 and to send the output of this calculation circuit 50 to the correction circuit 52 i f it detects at least one error with respect to an expected result .

[0190] The diagnostic means 55 for example comprise means for commanding the reiteration of at least one quantum calculation by the calculation circuit 50 , and for comparing them with an expected result . For example , the diagnostic means 55 are configured to send white noise as input to the calculation circuit 50 , to detect the calculation output and to compare it with a comparison output previously stored and obtained from the same calculation circuit 50 using white noise as input . This iteration of the diagnostic means is for example periodic, for example it is executed at every bootstrap or at every calculation .

[0191] The diagnostic means are configured to establish a calculation correction based on the deviation from the expected result obtained from said comparison and to command the correction means 52 to apply the correction to subsequent calculations.

[0192] In this way a calculation procedure is envisaged by means of the use of apparatus 1 of figure 12 in which a calculation is repeated by the calculation circuit 50 a plurality of times, and if there are deviations from the expected result established by the diagnostic means 55, the calculations are compensated by the correction circuit 52.

[0193] In general we observe that the presented examples use as modes of the qudit with 6 or more states the TE and 0AM modes seen above. However, it is possible to hypothesize the use of other combinations of modes, selected in structured light terms, where preferably at least 4 modes are distinguished two by two at least based on two polarizations.

[0194] GENERAL INTERPRETATION OF TERMS

[0195] In understanding the scope of the present invention, the term "comprising" and its derivatives, as used herein, are intended as open-ended terms that specify the presence of the stated features, elements, components, groups, integers and / or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and / or steps. The foregoing also applies to words having similar meanings such as the terms "including", "having" and their derivatives. Furthermore, the terms "part", "section", "portion", "member" or "element" when used in the singular can have the dual meaning of a single part or a plurality of parts. As used herein to describe the embodiment ( s ) above the following directional terms " forward"

[0196] "backward" , " above" , "below" , "vertical" , "hori zontal" , "under" and " transverse" , as well as any other similar directional term refer to the embodiment described in operating position . Finally, terms of degree such as " substantially" , " about" and " approximately" as used herein mean a reasonable amount of deviation of the modi fied term such that the end result is not signi ficantly changed .

[0197] While only selected embodiments have been chosen to illustrate the present invention, it will be apparent to those skilled in the art from this disclosure that various changes and variations can be made therein without departing from the scope of the invention as defined in the appended claims , including active deformation of the waveguide at multiple points of the circuit . For example , the si ze , shape , location or orientation of the various components can be changed as needed and / or desired . Components shown directly connected or in contact with each other can have intermediate structures disposed between them . The functions of one element can be performed by two , and vice versa . The structures and functions of one embodiment can be adopted in another embodiment . It is not necessary that all advantages be present in a particular embodiment at the same time . Every feature which is unique compared to the prior art , 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 embodied by such features . Therefore , the foregoing descriptions of the embodiments according to the present invention are provided for illustrative purposes only, and not for the purpose of limiting the invention as defined by the appended claims and their equivalents .

Claims

CLAIMS1. Controllable module for manipulation of a qudit, characterized in that it comprises:- a multimodal waveguide (10) with square crosssection comprising a modulating geometric modification (24, 24a, 24b, 24c) localized on said waveguide, where the modulating geometric modification (24, 24a, 24b, 24c) is controllable to manipulate the qudit modes.

2. Controllable module according to claim 1, characterized in that said manipulation comprises at least one phase variation.

3. Controllable module according to claim 1 or 2, characterized in that said modulating geometric modification can be controlled to generate or vary said manipulation on command.

4. Controllable module according to any of claims 1 to 3, characterized in that said manipulation comprises a multimodal conversion simultaneously of "d" modes of a single quantum supported by said waveguide.

5. Controllable module according to any of claims 1 to 4, characterized in that said module (2) comprises control means (27) comprising means for local thermal deformation of the waveguide (10) or inserts placed locally in the waveguide where the inserts are of activematerial controllable piezoelectrically, said control means being configured to generate or modify on command said modulating geometric modification (24, 24a, 24b, 24c) .

6. Controllable module according to any of the preceding claims, characterized in that said waveguide with square cross-section is configured to support at least 6 propagation modes of a quantum, where at least 4 modes are distinguished two by two at least based on two polarizations .

7. Module according to claim 6, characterized in that the at least 6 modes supported by the waveguide are the following:A= TE10, or a TM mode alternative to TE10, associated with a polarizationB= TE01, or a TM mode alternative to TE01, associated with a polarization different from the polarization of ACl= (CAM L=+l) associated with a polarizationC2= (0AM L=+l) associated with a polarization different from the polarization of 01Dl= (0AM L=-l) associated with a polarizationD2= (OAM L=-l) associated with a polarization different from the polarization of DI8. Controllable module according to any of the preceding claims, characterized in that the modes supported by the waveguide and manipulable by said modulating geometric modification (24, 24a, 24b, 24c) are more than 6 comprising higher propagation modes with OAM values greater than 1 and lower than -1.

9. Qudit comprising at least the following propagation modes of a quantum:A= TE10, or a TM mode alternative to TE10, associated with a polarizationB= TE01, or a TM mode alternative to TE01, associated with a polarization different from the polarization of ACl= (OAM L=+l) associated with a polarizationC2= (OAM L=+l) associated with a polarization different from the polarization of 01Dl= (OAM L=-l) associated with a polarizationD2= (OAM L=-l) associated with a polarizationdifferent from the polarization of DI10. Qudit according to claim 9, characterized in that the propagation modes are in number greater than 6 comprising higher propagation modes with 0AM values greater than 1 and lower than -1 where for each of said 0AM values there are two modes with polarizations different from each other.

11. Input register of a quantum processor characterized in that it comprises one or more information units in the form of qudit according to claim9 or 10.

12. Quantum processor comprising:- at least one of said controllable modules (2) according to any of claims 1 to 8;- at least one input register (5) of information units corresponding to said qudit of claim 9 or 10 with at least 6 states placed at the input of said controllable module- at least one output register (15) placed at the output of said controllable module and configured to decode the information corresponding to the manipulated modes .

13. Processor according to claim 12, characterized in that it comprises a plurality of said controllable modules (2) where the respective modulatinggeometric modifications (24a, 24b, 24c) of said modules are localized on the same waveguide, therefore called common waveguide (10) .

14. Processor according to claim 12 or 13, characterized in that it is configured to generate, or to form at least part of, at least one among:- a C-NOT gate- a CC-NOT gate- a Hadamard gate15. Processor according to any of claims 12 to 14, characterized in that it comprises a plurality of paths in series or parallel, each comprising at least one of said controllable modules (2) , and connected to one another by respective controllable switches (88) .

16. Quantum calculation procedure, characterized in that it comprises the following phases:- providing at least one processor according to any of claims 12 to 15;- making at least one photon travel through said controllable module (2) and modifying its states by controlling the modulating geometric modification (24a, 24b, 24c) of said controllable module.

17. Quantum calculation procedure according to claim 16, characterized in that the processor is according to claim 13 and the modification of the photonstates is performed by controlling the plurality of modulating geometric modifications placed on the common waveguide .

18. Quantum calculation procedure according to claim 17, characterized in that said common waveguide defines a path among a plurality of paths in series and in parallel of said processor, connected by controlled switches (88) , where the procedure comprises a phase of path entanglement obtained by controlling said controllable switches (88) .

19. Quantum apparatus comprising at least one quantum calculation circuit (50) and one quantum correction circuit (52) at the output of the quantum calculation circuit (50) , where at least the correction circuit (52) comprises at least one controllable module (2) according to any of claims 1 to 8; the apparatus also comprising diagnostic means (55) configured to establish whether at least one calculation performed by the calculation circuit (50) has a discrepancy with respect to an expected result, and to command the correction circuit to compensate said discrepancy by controlling said module.

20. Quantum calculation correction procedure characterized by the following phases:- providing a quantum apparatus (1) according to claim 19;- performing at least one quantum calculation bymeans of the calculation circuit (50) ,- detecting any calculation discrepancies of the quantum circuit with respect to an expected result; performing a correction of the calculation results of the calculation circuit (50) through said correction circuit (52) based on said discrepancy.

Images