Calibration of tunable crossing networks for gmzi

Abstract

In some implementations, a generalized Mach-Zehnder Interferometer (GMZI) can include a plurality of input ports to input light, such as quantum light (e.g., single photons) or bright light. In addition, the GMZI may include a waveguide network that includes two coupler networks, each having multiple crossing networks to interfere the light. The light can be phase shifted using arrays of phase shifters coupled to each crossing network. The arrays of phase shifters may be calibrated by mapping light from inputs to outputs and calibrating each array of phase shifters in succession, from inner arrays far from the inputs and outputs of the GMZI to outer arrays close to the inputs or outputs of the GMZI.

Description

CALIBRATION OF TUNABLE CROSSING NETWORKS FOR GMZICLAIM OF PRIORITY

[0001] This application claims the benefit of priority to U.S. Patent Application Serial No. 63 / 671,670, filed on July 15, 2024, which is incorporated by reference herein in its entirety.TECHNICAL FIELD

[0002] The present disclosure relates generally to optical devices and more particularly to phase shifters for quantum photonic interferometers.BACKGROUND

[0003] Mach-Zehnder interferometers (MZIs) are optical devices that consist of two beam splitters and two mirrors that allow a light beam to be split into two paths and later recombined. MZIs exploit interference effects between the light beams traveling in each path. By modulating the relative phase shifts between the two paths, the output intensity of the recombined beam can be varied.

[0004] Generalized Mach-Zehnder interferometers (GMZIs) include additional optical components in the two paths, enabling advanced manipulation of the beam.BRIEF DESCRIPTION OF THE DRAWINGS

[0005] The following description includes discussion of figures having illustrations given by way of example of implementations of embodiments of the disclosure. The drawings should be understood by way of example, and not by way of limitation. As used herein, references to one or more "embodiments" are to be understood as describing a particular feature, structure, or characteristic included in at least one implementation of the inventive subject matter. Thus, phrases such as "in one embodiment" or "in an alternate embodiment" appearing herein describe various embodiments and implementations of the inventive subject matter, and do not necessarily all refer to the same embodiment. However, they are also not necessarily mutually exclusive. To easily identify the discussion of any particularelement or act, the most significant digit or digits in a reference number refer to the figure (“FIG.”) number in which that element or act is first introduced.

[0006] FIG. 1 shows a first example optical switch, in accordance with some example embodiments.

[0007] FIG. 2 shows a second example optical switch, in accordance with some example embodiments.

[0008] FIG. 3 shows a third example optical switch implemented as a GMZI, in accordance with some example embodiments.

[0009] FIG. 4 shows an example GMZI configured as a N-to-1 multiplexer configuration that implements a plurality of phase shifters, in accordance with some example embodiments.

[0010] FIG. 5 shows an example linear-optical quantum generalized MZI in a 16x16 configuration, in accordance with some example embodiments.

[0011] FIG. 6 shows an example GMZI architecture, in accordance with some example embodiments.

[0012] FIG. 7 shows a GMZI switch architecture, in accordance with some example embodiments.

[0013] FIG. 8 shows close-up views of example components of a photonic integrated circuit (PIC) based GMZI, in accordance with some example embodiments.

[0014] FIG. 9 shows a quantum GMZI architecture in a balanced configuration in which the optical powers across the network are equivalent, in accordance with some example embodiments.

[0015] FIG. 10 shows the first Hadamard network of FIG. 9, in accordance with some example embodiments.

[0016] FIG. 11 shows a two-array tunable coupler network having two crossing networks and an array of phase shifters coupled to each crossing network, in accordance with some example embodiments.

[0017] FIG. 12 illustrates a simplified block diagram of a GMZI architecture having three pairs of corresponding phase shifter arrays in its coupler networks, in accordance with some example embodiments.

[0018] FIG. 13 shows a flow diagram of a method for calibrating arrays of phase shifters of a GMZI, in accordance with some example embodiments.

[0019] FIG. 14 shows a flow diagram of an example implementation of operation to calibrate the inner pair of phase shifter arrays from the method of FIG. 13, in accordance with some example embodiments.

[0020] FIG. 15 illustrates the GMZI architecture of FIG. 12 during calibration of the inner pair of phase shifter arrays, in accordance with some example embodiments.

[0021] FIG. 16 shows a flow diagram of an example implementation of operation to calibrate a second pair of phase shifter arrays from the method of FIG. 13, in accordance with some example embodiments.

[0022] FIG. 17 illustrates the GMZI architecture of FIG. 12 during a first input / output mapping for calibration of the intermediate pair of phase shifter arrays, in accordance with some example embodiments.

[0023] FIG. 18 illustrates the GMZI architecture of FIG. 12 during a second input / output mapping for calibration of the intermediate pair of phase shifter arrays, in accordance with some example embodiments.

[0024] FIG. 19 shows a flow diagram of an example implementation of operation to calibrate an outer pair of phase shifter arrays from the method of FIG. 13, in accordance with some example embodiments.

[0025] FIG. 20 illustrates the GMZI architecture of FIG. 12 during calibration of the outer pair of phase shifter arrays, in accordance with some example embodiments.

[0026] FIG. 21 shows a flow diagram of a method for adjusting the phase of light in a waveguide arm of the GMZI using a phase shifter, in accordance with some example embodiments.

[0027] FIG. 22 shows a flow diagram of a method for processing light using a GMZI, in accordance with some example embodiments.

[0028] FIG. 23 shows a flow diagram of a method for processing quantum light using a GMZI, in accordance with some example embodiments.

[0029] FIG. 24 shows a flow diagram of a method for calibrating an array of phase shifters of a GMZI, in accordance with some example embodiments.

[0030] FIG. 25 shows a flow diagram of a method for calibrating an array of phase shifters of a GMZI, in accordance with some example embodiments.

[0031] Descriptions of certain details and implementations follow, including a description of the figures, which may depict some or all of the embodiments described below, as well as discussing other potential embodiments or implementations of the inventive concepts presented herein. An overview of embodiments of the disclosure is provided below, followed by a more detailed description with reference to the drawings.DETAILED DESCRIPTION

[0032] In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide an understanding of various embodiments of the inventive subject matter. It will be evident, however, to those skilled in the art, that embodiments of the inventive subject matter may be practiced without these specific details. In general, well-known instruction instances, structures, and techniques are not necessarily shown in detail.

[0033] A generalized Mach-Zehnder interferometer (GMZI) can be integrated in photonic integrated circuits (referred to herein as an integrated GMZI) for various quantum photonic and optical communication operations. A GMZI may be implemented using coupler networks and phase shifters to perform routing of light. In some cases, the light routed by the GMZI is quantum light. As used herein, the term quantum light include one or more of the following: a single photon, squeezed light, or an entangled photonic state (e.g., Bell pair, Greenberger-Horne-Zeilinger (GHZ) state). In some cases, the light routed by the GMZI is bright light (e.g., thermal light, classical light).

[0034] The coupler networks may comprise sets of couplers, bends, and crossing couplers to couple the light. In some embodiments, a first coupler network separates the light, and a second coupler network combines the lightonto one or more output ports. In some embodiments, between and / or within the coupler networks are phase-shifter elements (e.g., a first phase shifter for switching, a second phase shifter for trim and calibration) to change a phase of the light on a given waveguide arm of the GMZI such that the light is configured according to a transfer matrix and output from the GMZI in various configurations, such as an N-to-1 configuration or an N-to-M configuration, as discussed in further detail below.

[0035] In some example embodiments, a GMZI may accumulate unwanted phase changes (also referred to herein as phase error) that build up on the various components, such as the X-couplers in the GMZI's Hadamard crossing networks, which form part of the coupler networks. The phase error can occur due to various factors, such as process variations of the components or surface roughness. In some cases, the 50:50 splitters used in the coupler networks can also contribute to decreases in phase accuracy and therefore to phase error. The phase error can affect GMZI performance and cause inaccurate phase shifting.

[0036] In some examples, adjustable phase shifters are coupled to waveguide arms joining the first coupler network to the second coupler network. In theory, these centrally-placed phase shifters (also referred to as a central array of phase shifters) should be able to provide N-way power splitting for a GMZI having N inputs, N outputs, and N waveguide arms coupled to the central array of phase shifters. However, due to the manufacturing limitations described above, the actual applied phase shifts are actually a complicated spread that depends on the path chosen between the inputs and outputs of the GMZI (e.g., inputs of the first coupler network and outputs of the second coupler network).

[0037] Thus, in some cases there may be aggregate phase accumulation, such that the phase shift values applied by the central array of phase shifters cannot simply be set to the desired values (e.g., zero and 7t). Instead, the desired values must be adjusted based on the light paths being used, each light path defining a route through the first coupler network and the second coupler network from an input to an output of the GMZI. Depending on the inputs and outputs being used by the light paths, the overall phaseadjustment being applied to each light path must be tuned to adjust the desired values of the central array of phase shifters.

[0038] For phase errors between the two Hadamard networks (e.g., the first coupler network and second coupler network), the bias offset of the central array of phase shifters can be adjusted to correct for the phase errors. However, for phase errors that accumulate in the Hadamard networks themselves, the central array of phase shifters doesn't provide enough control over the phase adjustment applied to each separate light path.

[0039] Accordingly, example embodiments described herein may provide arrays of tunable phase shifters within the coupler networks themselves. In some examples, each crossing network of the coupler networks has an array of phase shifters to adjust the phase of light propagating through the crossing network. For example, the first coupler network may have a number N>1 of crossing networks, each of which has an array of phase shifters coupled to the outputs of the crossing network to apply respective phase shift values to the outputs of the crossing network. The second coupler network may also have N crossing networks, each of which has an array of phase shifters coupled to the inputs of the crossing network to apply respective phase shift values to the inputs of the crossing network.

[0040] In some example embodiments, the phase shifters may be configured to operate in two stages. During a calibration stage, the unwanted phase changes associated with a given light path from an input to an output are identified (e.g., intensity measurement of bright light coupled to the input and measured at the output), and calibration settings for tuning the arrays of phase shifters are calculated to negate the phase error for any given light path. During an operation stage, the phase shifters continue to operate, tuned to their pre-calculated calibrated values based on the light paths being used, to negate the phase error.

[0041] For example, each crossing network could have an array of phase shifters implemented as a column of thermal tuners, positioned within the coupler network. The array of phase shifters can be calibrated for each input and output of the GMZI, and the tuning settings can be stored in a look up table (LUT) and applied during the operation stage (e.g., at runtime).However, in some cases, this approach requires a large number of phase shifters that need to be calibrated, and calculating the calibration settings for a large set of phase shifters being applied to a large number of light paths can be computationally challenging: for example, a GMZI having 64 inputs and 64 outputs may use (log2 64 = 6) six crossing networks per coupler network, thereby potentially requiring twelve arrays of phase shifters, each array of phase shifter having 64 phase shifters.

[0042] This large set of phase shifters could potentially be calibrated using brute-force exhaustion of the space of calibration settings for each of the (12 x64) phase shifters across a phase shift values from 0 to 2TI, but this could be prohibitively time-consuming and computationally expensive. Instead, in some examples described herein, methods are described that may provide greater efficiency in calibrating the arrays of phase shifters via a nominal single sweep optimization per phase shifter, thereby potentially providing a practical approach to calibrating the arrays of phase shifters to mitigate or eliminate the phase error described above. These techniques can be used to calculate and store calibration settings for each of the phase shifters in each of the mid-coupler network arrays, based on the light paths between inputs and outputs. These calibration setting can then be retrieved and applied at runtime to adjust the phase shifter arrays of the coupler networks, based on the light paths between inputs and outputs being used during the operation stage.

[0043] In some cases, the calibration settings can be calculated once for a given GMZI and used repeatedly for one or more operation stages. In some cases, there may be drift over time, such that the calibration stage may need to be repeated one or more times, such as in response to phase drift being detected by the system.

[0044] Examples are now described with reference to the drawings. FIG. 1 through FIG. 10 show examples of MZI architectures, such as GMZIs having two coupler networks and a central array of phase shifters. FIG. 11 shows an example of a coupler network having tunable arrays of phase shifters for each of its crossing networks. FIG. 12 through FIG. 20 show a sequence of calibration operations performed on an example GMZI having N=3 crossingnetworks in each coupler network. These calibration operations are described with reference to a calibration method shown in the flowchart of FIG. 13 (and further detailed in the flowcharts of FIG. 14, FIG. 16, and FIG. 19). An operation method is shown in the flowchart of FIG. 21, which can be performed using the calibration settings generated by the calibration method of FIG. 13. Bright-light and quantum-light versions of GMZI operation (e.g., operation of the pre-calibrated GMZI) are shown in the flowcharts of FIG. 22 and FIG. 23, respectively.

[0045] FIG. 1 shows an example optical switch 100, in accordance with some example embodiments. The optical switch 100 (e.g., an MZI) comprises a first splitter 105 (e.g., a beam splitter, half silver mirrors, a directional coupler, a multimode interference (MMI) waveguide, a cross coupler or “star” coupler) and a second splitter 110 (e.g., a beam splitter, a crystal, half silvered mirror, a directional coupler, an MMI) that separate the light (e.g., bright light or quantum light) onto a top arm and bottom arm and then recombine the light for output on one or both output ports. In the example of FIG. 1, the top arm comprises an active phase shifter 115 and the bottom arm comprises an active phase shifter 120. Further, the bottom arm comprises a further fixed passive phase shifter 125.

[0046] In FIG. 2, an optical switch 200 comprises the first splitter 105 and the second splitter 110 that separate the light onto the top and bottom arms and then recombine the light for output on one or output ports. Further, in the example of FIG. 2, the optical switch 200 comprises a single active phase shifter 130 on the bottom arm to implement TT phase shifts.

[0047] FIG. 3 illustrates an optical switch 300 implemented as a generalized MZI (GMZI), in accordance with some embodiments. The example GMZI is an extension of an MZI with N > 2 inputs 317 and M > 1 outputs (e.g., output ports 319), as shown in FIG. 3. This configuration allows a set of permutations to be performed on the inputs 317, thereby configuring the optical switch 300 as a useful block in the design and construction of composite N-to-1 and N-to-M switch networks. In some embodiments, varying the settings of phase shifters 310 (e.g., active phase shifters) sets specific permutations of the N inputs 317 and routes them to M> 1 output ports 319. There are a number of spatial mux schemes that select one of multiple inputs 317 from distinct locations in space. For example, a GMZI can be configured as an N-to-1 mux, as it allows routing of any input 317 to a single output port 319.

[0048] As illustrated in FIG. 3, the example GMZI comprises a first coupler network, in this example a first Hadamard network 305 (e.g., an MMI, a network of directional couplers and waveguide crossings), and a second coupler network, in this example a second Hadamard network 315 (e.g., an MMI, a network of directional couplers and waveguide crossings) that split and recombine the light propagating on one or more of a plurality of arms (e.g., eight arms, in an 8x8 GMZI) such that the light is outputted on one or more of the plurality of output ports 319. Example architectures for the first Hadamard network 305 and second Hadamard network 315 are discussed in further detail below. The terms coupler network, Hadamard network, and splitter may be used interchangeably herein to refer to a coupler network that operates to implement a Hadamard matrix applied to its inputs. Unless indicated otherwise, each coupler network described herein is understood to be a Hadamard network.

[0049] In a bright light example, the optical switch 300 can operate as a power splitter that splits the beam onto the output ports 319 in a given configuration according to settings of the phase shifters 310. In quantum light operation (e.g., propagating one photon or a small number of photons), the optical switch 300 splits superpositions of the quantum light onto the output ports 319 for recombination and output according to settings of the phase shifters 310.

[0050] FIG. 4 shows an example GMZI 400 configured as a N-to-1 multiplexer configuration that implements a plurality of phase shifters 405, in accordance with some embodiments. The GMZI 400 is an example configuration that can collect light (e.g., bright light, quantum light, single photons) from a plurality of optical sources that generate the light with a probabilistically low occurrence to output a single muxed source of light (e.g., muxed quantum light) with a probabilistically higher occurrence. The configuration of the GMZI 400 is an example of an optical switch aspreviously described (e.g., optical switch 100, optical switch 200, or optical switch 300).

[0051] FIG. 5 shows an example linear-optical quantum generalized MZI 500 in a 16x16 configuration, in accordance with some embodiments. The coupler network 505 corresponds to the first Hadamard network 305, and the coupler network 515 corresponds to the second Hadamard network 315, which together function as a 16-mode Hadamard quantum optical coupler network. In some embodiments, the plurality of phase shifters 510 are implemented as phase shifters that can be set from zero to TT shifts to select one of 16 operations (e.g., G([2, 2, 2, 2]). These phase shifters 510 correspond to the central array of phase shifters described above. In some embodiments, each phase shifter on each arm comprises a plurality of phase shifters, as discussed in further detail below. Further, the linear-optical quantum generalized MZI 500 is an example optical switch that may be used to route quantum light by configuring the phase shifters 510 in different permutations.

[0052] In quantum photonic implementations, a Mach-Zehnder Interferometer can be configured to apply identity or swap operations on two inputs. For example, to switch between transfer matrices which are pairs of Pauli operations using active phase shifters:I or X = h(I or Z)h = Shc(Z or I)hcS

[0053] As such, a GMZI can be configured to function as a switch network that implements a set of unitary transfer matrices Uk„ where each unitary routes light between a subset of input and output ports. As an example, if Uk is set to route light from port t to port s, then its sthrow and tthcolumn are set to zero apart from= 1, and similarly for other pairings of input and output ports. The following elucidates example sets of routing operations ofa photonic GMZI switch-based information processing architecture, in accordance with some embodiments. In some embodiments, the photonic GMZI switch-based information processing architecture is configured as a scalable waveguide-based switching network that implements transfer matrices using interferometer gates and phase shifters. In some embodiments, the transfer matrices are of the form: uk= w Dk V1’’wherethe unitary matrices W, V describe passive interferometers, and the -^fc form a set of diagonal phase matrices (e.g., phases applied by the phase shifters). In some embodiments, the phase matrices are implemented physically using a single layer of phase shifters acting on every waveguide arm, while in some example embodiments, each arm comprises a plurality of phase shifting units. In some embodiments, the slow phase shifters are used to zero out a given photonic device.

[0054] In the following, the phase matrix -Dis implemented in terms of a phase vector d,=dsSSttforsimplicity. In some embodiments, the photonic GMZI switch-based information processing architecture is configured to function as a scalable switch network that implements different sets of permutation matrices uk= w DkV*’ according to desired routing configurations. By adding the fixed passive network (e.g., a Hadamard network) corresponding to, e.g., U-1(e.g., the inverse of an arbitrary permutation from that set), a new set of pairwise commuting permutation matrices: {U _ k U _ 1 (— 1)} = W D ’ > (k ) W t} may be generated. At a high level, and in accordance with some embodiments, the photonic GMZI switch-based information processing architecture is configured as a switch networkmatrices corresponding to commuting permutations of N waveguide arms or modes (e.g., N = 4 in FIG. 7) for a given switch network configuration. The individual phase shifter settings in Dk correspond to given roots of unity (e.g., up to an overall global phase factor e1^ which can be chosen at will). Further, the photonic GMZI switch-based information processingarchitecture implements one or more GMZI switches with a switch setting Dk to route light from input port 1 to output port k.

[0055] The embodiments below illustrate example linear-optical photonic circuit GMZI architectures to implement different routing operations G([ni, n2, • • • , nr]) on waveguide arms yy = IT , niwith settings vector k where 0 < ki < m with I = 1, • • • , r, and further where the transfer matrices p - pp-t are as follows:

[0056] In the above transfer matrices, the Wn‘ are discrete Fourier transform (DFT) matrices and the Khsetting of the fast phase shifters are set by:

[0057] In some embodiments, scalable networks of GMZI switches are implemented to a large number of modes or waveguide arms, N, with logdepth stages of interference using the following decomposition:

[0058] In the above decomposition, the matrices S / correspond to crossing networks (e.g., the crossing network crossing network 1020, shown in FIG.10) which reorder modes in waveguides in the GMZI. In some embodiments,the subexpressions of the form I(N / nl)® wnicorrespond to repeated blocks of modes interfering according to unitary Wn‘ in the above decomposition, and thus function as stages of local interference separated by crossing networks, such as the crossing network 1020 (FIG. 10). Further, FIG. 5, discussed above, illustrates an example of a Hadamard GMZI implementing the N-M decomposition (e.g., spectral decomposition into submatrices that correspond to physical components), and FIG. 4 illustrates an example of the Hadamard GMZI implementing the GMZI as a simplified N-to-1 mux.

[0059] In some embodiments, additional GMZI architectures are implemented by decomposing the unitary matrices Wn‘ that set the design of beam-splitter operations (e.g., the first Hadamard network 305 or the second Hadamard network 315) and phase-shifter operations (e.g., phase shifter 310). It is appreciated that the optical depth of networks constructed using the recursive decomposition is reliant on high-precision optical hardware and very low optical loss, as the depth of the crossing networks must be accounted for in addition to the stages of local interference (e.g., the depth in crossings of the largest crossing network scales with (N / 2)-l).

[0060] FIG. 6 shows an example GMZI architecture 600 in accordance with some embodiments. In the example of FIG. 6, a plurality of waveguide arms input light (e.g., bright light, quantum light) into a first Hadamard network 610. The output light from the first Hadamard network 610 is then phase shifted by a plurality of phase shifters 615 and input into a second Hadamard network 620. In the example configuration of a GMZI architecture 600, a single layer of the phase shifters 615 are implemented to perform phase- shift-based light mixing (e.g., bright light mixing, quantum-light probabilitydistribution adjustments). In some example embodiments, the phase shifts applied comprise 0 to -TT phase shifts and zero to 2ir phase shifts. In some embodiments, the phase shifters are operated in an “in-between” phaseshifter configuration to act an array of beam splitters. In these in-between configuration embodiments, light is input into two target input waveguide arms and can be interfered with 50% of the light transmitted to a given output port where the measurement is made (e.g., via photodetector). Insome embodiments, a set of phase shifters are implemented on each arm, as discussed in further detail below.

[0061] Continuing, with reference to FIG. 6 and in accordance with some embodiments, the light adjusted by the second Hadamard network 620 is outputted from the second Hadamard network 620 (e.g., from the right side of the second Hadamard network 620 in the perspective view of FIG. 6) to one or more detectors 625. Although the example of FIG. 6 shows eight waveguide arms (e.g., eight modes, N=8), it is appreciated that in other embodiments different numbers of waveguide arms may be implemented in a similar manner.

[0062] In some embodiments, the one or more detectors 625 are singlephoton detectors (e.g., photon-number-resolving detectors) that detect a single photon of light as the photon exits the second Hadamard network 620. In some embodiments, the photo detectors are bright-light detectors (e.g., phototransistors, photodiodes) that are implemented to detect bright light that is power split onto the plurality of outputs of the second Hadamard network 620. For example, in some embodiments, bright light is injected into one of the input ports of the second Hadamard network 620 and is detected from one of the output ports of the second Hadamard network 620, wherein the phase shifters 615 are calibrated by modifying the phase shift settings until the phase difference between the input light and the output light is minimized or zeroed out. In some embodiments, a portion of the output bright light is tapped from the output waveguides of the second Hadamard network 620 to perform the bright-light-based adjustments and once adjusted, the architecture is configured in quantum light mode whereby single photon detectors (e.g., avalanche photodiodes, photon number resolving detectors, superconducting nanowire detectors) are implemented as the detectors 625 to detect quantum light (e.g., single photons) outputted by the quantum GMZI architecture 600. In some embodiments, once the plurality of phase shifters 615 are zeroed out using bright light, the quantum GMZI architecture 600 is operated in nonclassical quantum light mode, in which single photons or entangled photon groups are propagated through the quantum GMZI architecture 600, and the plurality of phase shifters implement zero to TT phase shifters on the superposition of the single photonin the arms of the quantum GMZI architecture 600 to modify probabilities of the quantum light exiting from one or more of the output ports (e.g., right side ports) of the second Hadamard network 620.

[0063] In some embodiments, the waveguides of the plurality of arms in the quantum GMZI architecture 600 are designed and fabricated to minimize loss as the respective arms propagate classical or quantum light in the quantum GMZI architecture 600. For example, the waveguides are configured in a fan-in configuration 605 to couple light from multiple larger separate light sources into the smaller input interface of the first Hadamard network 610. Further, the waveguides may be configured in a fan-out architecture 613 to connect the waveguides to the plurality of phase shifters 615 without incurring significant optical loss which can affect quantum light processing (e.g., cause decoherence). Further, the waveguides may be configured in a fan-in architecture 617 into the second Hadamard network 620 and / or a fan-out configuration 618 to couple to additional devices, such as other switches, further waveguide routing, fiber interfaces, or light detectors (e.g., photodetectors, photodiodes, or the detectors 625).

[0064] FIG. 7 shows a GMZI switch architecture 700, in accordance with some embodiments. As illustrated, light is input into a first Hadamard network 705 (e.g., a first Hadamard gate) and phase shifted by the waveguide arm phase shifters 710. In some embodiments, each phase shifter may be implemented by active optical components built by optical waveguides, such as an electro-optical phase shifter comprising an optical waveguide that is combined with electro-optical materials and electrodes. The optical waveguide of the phase shifter may be fabricated from different materials, including silicon, silicon nitride, doped SiCh, a complex oxide (e.g., lithium niobate, barium titanate), or III-V materials.

[0065] In some embodiments, the phase shifter operates by applying an electrical signal to the electro-optical material to change its index of refraction and thereby shift the phase of the light propagating in the waveguide. In some embodiments, the application of the electrical signal to the electro-optical material causes a phase shift from plasma dispersion effects in silicon and III-V semiconductors. In some embodiments, theelectrical signaling is applied to control a Pockels effect in the shifter (e.g., as in Lithium Niobate and Barium Titanate, BTO), or cause Kerr effects. In some embodiments, the active material is resistive and thermal-optical effects cause phase shifts in the propagating light.

[0066] In some embodiments, the electrical signaling is applied via electrodes in the phase shifter, where electrodes include different conductive contacts and conductive traces (e.g., metals such as Cu, Al, and / or Au).

[0067] In some embodiments, the pitch of the phase-shifter array is increased by fanning out optical waveguides between the Hadamard network gates and the plurality of phase shifters thereby reducing undesired crosscouplings between the separate phase shifters (e.g., minimize thermal or piezo-electric couplings). In some embodiments, the phase shifters are implemented as fast phase shifters and slow phase shifters (e.g., heaters or MEMS switches configured as a phase shifter).

[0068] Continuing with reference to FIG. 7, after shifting by the waveguide arm phase shifters 710, the light is then further processed by a second Hadamard network (e.g., the second Hadamard network 725) and output from a plurality of output ports (e.g., to further switches or detectors). In some embodiments, the components of the quantum GMZI switch architecture 700 are fabricated in a single photonic integrated circuit (e.g., on a single substrate) and the components are interconnected using integrated waveguides (e.g., silicon waveguides, silicon nitride waveguides).

[0069] Switching operations may be performed by the GMZI switch architecture 700 as follows. In some embodiments, light (e.g., one or more photons) is inputted into any of the N-input ports (e.g., left side ports of the first Hadamard network 705) and are switched to any of the N-output ports (e.g., right side of the second Hadamard network 725). As discussed, the switching operations may be implemented by the waveguide arm phase shifters 710 including the fast phase shifters 715 and the slow phase shifters 720. In some embodiments, the slow phase shifters 720 are driven by a control system (e.g., CPU based system, GPU system, microcontroller, electrical logic circuits). In some embodiments, the control system comprises a plurality of control subsystems comprising a thermal controller 730, anelectrical controller 735, and an optical controller 740. In some embodiments, the optical controller 740 receives herald data 775 (e.g., data heralding the arrival of a single photon at a photon-number-resolving detector) and adjusts operation of the quantum GMZI switch architecture 700 based on the received herald data 775. Although the thermal controller 730, the electrical controller 735, and the optical controller 740 are illustrated as external to the quantum GMZI for explanation and clarity purposes, it is appreciated that components of the thermal controller 730, the electrical controller 735, and the optical controller 740 - such as sensors, waveguides and electrical traces - may be integrated throughout the GMZI to detect and control different components.

[0070] At a high level, and in accordance with some embodiments, the electrical controller 735 controls the slow phase shifters 720 (e.g., sets biases) to tune and zero out the architecture, and the electrical controller 735 controls the fast phase shifters 715 to finish switching operations (e.g., 0 to K phase shifts to implement transform matrices or dynamic updates for error correction). In some example embodiments, the electrical controller 735 receives herald data 775 from a plurality of single photon sources (e.g., pair source generators) where the signal photon is detected and the idler photon is further propagated to the quantum GMZI switch architecture 700. In some example embodiments, in response to receiving electrical herald data 775 that a photon is being input on one of the arms of quantum GMZI switch architecture 700, the electrical controller 735 retrieves phase shifter data from a memory (e.g., a look up table having phase shifter settings determined from the transfer matrices) and applies the phase shifter settings to the fast phase shifters 715 at runtime (e.g., during routing of photons for processing of quantum information tasks). As used here, the fast phase shifters 715 generally function as the switching phase shifters that can complete phase shifts more quickly than the slow phase shifters 720 (e.g., heaters). In some example embodiments, both the sets of phase shifters are fast phase shifters that have approximately same shifting speed, wherein one of the phase shifters is used for trimming (e.g., setting phase from 0 to 2K) and the other of the phase shifter on the same arm is used for high speed switching during operation (e.g., for single photon muxing).

[0071] In some embodiments, during operation, the performance of the fast phase shifters 715 and / or the slow phase shifters 720 may drift or degrade with time. The optical controller 740 may be configured to detect the optical signal (e.g., from bright light or single photon detectors, detecting a herald photon via the herald detector) and provide feedback to the electrical controller 735. The electrical controller 735 may then adjust the phase shifter driving signals in the control circuits and the drivers to configure (e.g., bias) the phase shifters to compensate for the drifts or performance degradation.

[0072] In some embodiments, the phase shifters are sensitive to local temperature gradient of the environment in which the quantum GMZI switch architecture 700 operates. In some embodiments, throughout the operation, the temperature sensors in the thermal controller 730 monitor the temperatures at different locations of the quantum GMZI switch architecture 700 (e.g., the local temperatures of each phase shifter in the waveguide arm phase shifters 710 or the local temperatures of the first Hadamard network 705 and the second Hadamard network 725). The temperature sensors provide the feedback to the control circuits in the electrical controller 735. If the local temperature needs to be adjusted, the control circuits of the electrical controller 735 comprise logic or instructions to send signals to the heaters in the thermal controller 730 to cause the heaters to heat up the GMZI locally.

[0073] In some embodiments, the electrical controller 735 is implemented by electronic integrated circuits comprising logic to implement controls. The integrated circuits may include analog circuits and digital circuits such as high-speed phase shifter drivers, biasing network circuits, monitoring and control circuits. The electronic integrated circuits may be manufactured by different platforms, such as CMOS, SiGe, or III-V. In some embodiments, large output extinction ratio are enabled via precise control over phase-shifts in each arm. In some embodiments, the precise control is implemented via programmable DACs that control voltage levels for the slow and fast phase shifters, as well as feedback control for thermal regulation. In some embodiments, schemes such as pre-emphasis and close electrical proximity of driver circuits are implemented by the electrical controller 735 to performoptimization and achieve precise voltage settings for the settings of the fast phase shifters 715.

[0074] In some embodiments, the optical controller 740 comprises optical waveguide devices, photodetectors (e.g., bright light photodetectors, monitor photodiodes, single photon detectors), and tapping components (e.g., optical taps or switches configured to activate and tap light from a given waveguide). In some embodiments, the bright-light photodetectors of the optical controller 740 are formed from materials including one or more of: doped silicon, germanium, or superconducting materials. In some embodiments, upon the optical signal being detected by one or more of the photodetectors, electrical signal is then generated from the optical signal and transmitted to the electrical controller 735 for control signal processing.

[0075] In some embodiments, the thermal controller 730 comprises a plurality of temperature sensors that detect temperature. For example, the temperature sensors (e.g., thermometers) can be implemented by sensing the electrical signals of different materials, such as DLTM (e.g., doped Si), metals (e.g., Al, Cu, W, TiN, etc.), and dielectric materials (e.g., Barium Titanate). When temperature changes, the monitoring and control circuits sense the change of the electric signal (e.g., I-V) of the temperature sensors, and obtain the (local) temperature readings. In some embodiments, the temperature sensors are implemented by the optical signals of different materials, such as Si, SiN, Complex Oxide (e.g., Lithium Niobate, Barium Titanate), or III-V. In an optical resonator implementation, the resonant wavelength is a function of the temperature due to the thermo-optical effect of the materials. In these embodiments, the heater element is formed from materials having resistance, such as doped Si, metals (e.g., Al, Cu, W, TiN, etc.), and / or doped dielectrics.

[0076] In some embodiments, each arm in the GMZI switch architecture 700 is controlled by a set of phase shifters: a slow phase shifter 720 and a fast phase shifter 715. At a high level, the slow phase shifter 720 is configured to minimize or zero out a phase difference between input and output light. For example, input light is light inputted into the left side of the first Hadamard network 705 and the output light is light outputted from theright side of the second Hadamard network 725 (e.g., the second Hadamard waveguide coupler network) and measured to perform adjustments. In some embodiments, the slow phase shifters 720 are implemented to configure the quantum GMZI switch architecture 700 for a given optical processing configuration (e.g., zero out fabrication-based loss sources, adjust global phases, or compensate for temperature variations across the optical device). For example, the slow phase shifter 720 is configured to manage local temperature issues, such as the differences between the temperature of different areas of the quantum GMZI switch architecture 700 to ensure the phase differences are zeroed out. Further, in accordance with some embodiments, the slow phase shifters 720 are implemented to zero out phase difference between different GMZIs (e.g., other instances of the quantum GMZI switch architecture 700 that are connected to the GMZI shown in FIG. 7), such that multiple GMZIs are interconnected and zeroed out across all devices to ensure the fast phase shifters operate with sufficient 0 to 7r phase shifts in operation.

[0077] In some embodiments, one or more of the fast phase shifters 715 are implemented during operation of the GMZI switch architecture 700 to provide precise 0 to 7r phase shift swings to implement quantum entanglement operations (e.g., apply a desired Hadamard transformation matrix) and to provide routing operations (e.g., routing of bright light, routing of single photons, routing of entangled state photon probability distributions). Although, in FIG. 7, the waveguides are illustrated is straight, it is appreciated that the waveguides may fan-in and fan-out as discussed below with reference to FIG. 9 and FIG. 10.

[0078] In some example embodiments, the slow phase shifters 720 are not implemented. In place of the slow phase shifters 720, the DC bias voltages of the fast phase shifters 715 may be modified to adjust the static arm phase offsets for a given fast phase shifter 715. It will be appreciated that the electro-optical material, when activated by the electrical stimulus, undergoes a change in refractive index to couple a mode of the light within the waveguide into a portion of the electro-optical material, thereby applying a phase shift to the light.

[0079] FIG. 8 shows close-up views of example components of a PIC based GMZI, in accordance with some example embodiments. The example components can be arranged in networks to implement the interference networks (e.g., Hadamard networks). The crossing coupler 800 (e.g., star coupler, low-loss MMI) comprises two waveguides that cross one another to create a 2x2 coupler arrangement. The direction coupler 805 comprises two waveguides that come near to one another to evanescently couple light between the waveguides to form a 2x2 coupler. The direction coupler 805 can be implemented as a 50:50 coupler (e.g., beam splitter), 0: 100 coupler, or 100:0 coupler, in accordance with different implementations.

[0080] FIG. 9 shows a quantum GMZI architecture 900 in a balanced configuration in which the optical powers across the network are equivalent in accordance with some embodiments. The example quantum GMZI architecture 900 comprises two instances of an 8x8 Hadamard network: a first Hadamard network 910 and a second Hadamard network 920, which are each implemented using the configuration illustrated in FIG. 10 (flipped, in the case of second Hadamard network 920).

[0081] In some embodiments, such as in FIG. 9, the GMZI is designed so that the optical paths are balanced by default (e.g., the first Hadamard network 910 is a mirror image of the second Hadamard network 920) which may improve scalability of the GMZI by creating large self-similar waveguide network (e.g., Fractal networks) that are balanced and remain in phase. In some embodiments, light is input into a plurality of couplers 905 (e.g., grating couplers) and is coupled to a plurality of couplers 925 (e.g., a plurality of grating couplers). On a high level, the quantum GMZI architecture 900 comprises the first Hadamard network 910 and the second Hadamard network 920 connected by phase shifters 915 (shown as a central array of phase shifters).

[0082] FIG. 10 shows the first Hadamard network 910 in accordance with some embodiments. In the illustrated example of FIG. 10, the light is inputted into a plurality of directional couplers 1005 configured as 50:50 power splitters. A plurality of directional couplers 1005 are coupled into a crossing network 1010 comprising a plurality of interconnected star couplers(e.g., a waveguide star crossing network). As illustrated, one or more of the star networks in the crossing network 1010 have pairs of unused ports that are terminated with waveguide absorbers (not depicted), in accordance with some embodiments. The crossing network 1010 is physically expanded via an array of bends 1013 (e.g., Euler bends of fan-out or fan-in waveguide arrangements) that are coupled via a further array of bends 1017 into splitters 1015 (e.g., a plurality of directional couplers) configured as 50:50 power splitters, which are then coupled into a larger crossing network 1020 of star couplers, wherein one or more of the star couplers along the edge have unterminated ports and the star couplers in the middle of the crossing network 1020 have all ports that are all connected to other or subcomponents (e.g., directional couplers). Further, the directional couplers 1025 are configured as 50:50 power splitters, which couple light to the phase shifters 915.

[0083] FIG. 1 through FIG. 10 have illustrated and described MZI architectures and components that use only a central array of phase shifters, without reference to tunable phase shifters incorporated into the coupler networks themselves. Examples of GMZIs having arrays of phase shifters for applying phase adjustments to the light paths within the coupler networks will now be described, with reference to FIG. 11 through FIG. 25.

[0084] FIG. 11 shows a two-array tunable coupler network 1100 having two crossing networks and an array of phase shifters coupled to each crossing network.

[0085] The two-array tunable coupler network 1100 is similar to the first Hadamard network 910 shown in FIG. 9 and FIG. 10, modified such that its first crossing network 1106 (comparable to crossing network 1010 in FIG. 10) has its outputs coupled to a first array 1102 of phase shifters, and its second crossing network 1108 (comparable to crossing network 1020 in FIG. 10) has its outputs coupled to a second array 1104 of phase shifters. Each phase shifter 1110 in the first array 1102 and second array 1104 can be a tunable phase shifter in communication (e.g., electrical or thermal communication) with a controller (not shown) for modulating the phase shiftvalue applied by the phase shifter to the light within the waveguide arm to which it is coupled.

[0086] As shown in FIG. 11, each crossing network 1106 and 1108 has a set of eight outputs shown as eight waveguide arms. Each waveguide arm has a corresponding phase shifter 1110 coupled to it to apply a respective phase shift value to the light propagating within the waveguide arm, thereby applying a set of eight independently-controllable phase shift values to the light propagating within the corresponding crossing network 1106 or 1108.

[0087] In some examples, the first coupler network could have more than two crossing networks, such as three, four, or more, with each crossing network being coupled to a corresponding array of phase shifters. For example, the first coupler network at the input end of a GMZI may include log2 N crossing networks, and thus log2 N arrays of phase shifters, wherein N is the number of inputs of the first coupler network, as described above.

[0088] It will be appreciated that a second coupler network can be used at the output end of a GMZI in conjunction with the two-array tunable coupler network 1100. The second coupler network may have a structure corresponding to a flipped or mirrored version of the structure of the two- array tunable coupler network 1100 (or a first coupler network having a different number of crossing networks with tunable arrays of phase shifters). Thus, for example, the second coupler network can include log2 M crossing networks, and thus log2 M arrays of phase shifters, wherein M is the number of outputs of the second coupler network. Whereas the examples described and illustrated herein use a symmetrical arrangement of crossing networks in the first coupler network and second coupler network such that the numbers of GMZI inputs N and outputs M are equal, it will be appreciated that some of the examples described herein may be applicable to asymmetric GMZI architectures in which N is not equal to M.

[0089] FIG. 12 shows an example GMZI architecture 1200 having N=8 inputs 1214 and M=N=8 outputs 1216. In some examples, the GMZI (e.g., GMZI architecture 1200) includes multiple pairs of corresponding or mirrored phase shifter arrays. An inner pair of phase shifter arrays, closest to (e.g., adjacent to) the central phase shifters 1218 and farthest from the inputs1214 and outputs 1216, consists of a left-hand side (LHS) inner tuner column 1206 (also referred to as the inner array of the first coupler network 1240) and a right-hand side (RHS) inner tuner column 1208 (also referred to as the inner array of second coupler network 1242). As used herein, the terms left-hand and right-hand are used with reference from the perspective of FIG. 12, FIG. 15, FIG. 17, FIG. 18, and FIG. 20 and are not intended to limit or otherwise specify that left hand components are always on the left hand, or right hand components on the right hand side. Further, components such as couplers (e.g., directional couplers, 2x2 couplers) and tuners (e.g., heaters) are referred to as columns for explanatory purposes; it is appreciated that in some example embodiments, the sets of couplers or heaters need not be aligned or arranged as columns (e.g., the heaters may be offset in a zig zag arrangement per availability of layout space on a given PIC). Further, though a specific set of tuners and columns are included in the LHS network (first coupler network 1240) and RHS side network (second coupler network 1242) (e.g., three LHS coupler columns and corresponding LHS tuners, three RHS coupler columns and corresponding RHS tuners) it is appreciated that the following approaches can work well with fewer than three sets of components or can be expanded to additional sets or columns of components (e.g., 8 columns of couplers and tuners in each crossing network, 64 columns of tuners and couplers). The terms “array” and “column” may be used interchangeably herein when referring to sets of phase shifters within the coupler networks.

[0090] As further illustrated in FIG. 12, the GMZI architecture 1200 comprises an outer pair of phase shifter arrays, closest to (e.g., adjacent to) the inputs 1214 and outputs 1216 and farthest from the central phase shifters 1218, consisting of the LHS outer tuner column 1202 of first coupler network 1240 and the RHS outer tuner column 1212 of second coupler network 1242. In between are one or more additional pairs of phase shifter arrays, e.g., a second pair of phase shifter arrays consisting of the LHS second tuner column 1204 of first coupler network 1240 and RHS second tuner column 1210 of second coupler network 1242. In some examples, such as in the example method of FIG. 13 described below, each pair of phase shifter arrays is calibrated together, from the inner pairs of phase shifterarrays to the outer pair of phase shifter arrays. In other examples, such as in the example methods of FIG. 24 and FIG. 25 described below, the arrays or columns of phase shifters of one coupler network (e.g., first coupler network 1240 or second coupler network 1242) are first calibrated, from inner to outer, and then the arrays of the other coupler network are calibrated, from inner to outer.

[0091] FIG. 12 shows an example GMZI architecture 1200 having N=8 inputs 1214 and M=N=8 outputs 1216. The GMZI architecture 1200 includes a first coupler network 1240 and a second coupler network 1242. The outputs of the first coupler network 1240 are received by an array of N=8 central phase shifters 1218. In some examples, the central phase shifters 1218 are coupled to a central array of phase shifters, as described above, for applying switching phase shifts (e.g., the desired phase shifts of 0 or 2K described above) to the light propagating through the central phase shifters 1218. The outputs of the central phase shifters 1218 are propagated to the second coupler network 1242.

[0092] The first coupler network 1240 receives light at the inputs 1214. The inputs 1214 may be inputs of the GMZI as a whole, or simply inputs of the first coupler network 1240.

[0093] The light received at the inputs 1214 passes through an LHS outer coupler column 1222 of the first coupler network 1240, which is a crossing network (such as first crossing network 1106) close or adjacent to the inputs 1214. The outputs of the LHS outer coupler column 1222 are modulated by an LHS outer tuner column 1202 of phase shifters (such as first array 1102, having N=8 phase shifters, e.g., eight heaters) controlled by a controller. This structure repeats for two more layers of crossing networks of the first coupler network 1240: an LHS second coupler column 1224 receives the light phase-modulated by the LHS outer tuner column 1202, and its outputs are in turn modulated by an LHS second tuner column 1204; the light modulated by the LHS second tuner column 1204 is received by an LHS inner coupler column 1226, and its outputs are in turn modulated by an LHS inner tuner column 1206. The light modulated by each of the tuner columns 1202, 1204, or 1206 may pass through one or more additionalcomponents not shown in the simplified diagram of FIG. 12: for example, bends and / or splitters may be used to couple the outputs of the phase shifter arrays to the next crossing network or the next components shown in the network of FIG. 12.

[0094] The light modulated by the LHS inner tuner column 1206 of the first coupler network 1240, after passing through any additional components such as bends and / or splitters (as shown, e.g., in FIG. 11), is received by the central phase shifters 1218, where it may be further modulated by a central array of phase shifters, as described above.

[0095] The light output by the central phase shifters 1218 is received by the second coupler network 1242. The second coupler network 1242 has a structure that mirrors or flips the structure of the first coupler network 1240: an RHS inner tuner column 1208 of phase shifters phase-modulates the light at the inputs to an RHS inner coupler column 1228, an RHS second tuner column 1210 of phase shifters phase-modulates the light at the inputs to an RHS second coupler column 1230, and an RHS outer tuner column 1212 of phase shifters phase-modulates the light at the inputs to an RHS outer coupler column 1232. The light output by the RHS outer coupler column 1232 (referred to as combined light, due to the coupling effects of the second coupler network 1242), after passing through any other components such as bends and / or splitters, propagates to one or more of the outputs 1216. The outputs 1216 may be outputs of the GMZI, such as outputs ports, or may simply be outputs of the second coupler network 1242.

[0096] Example methods will now be described for calibrating the phase shifters embedded in the crossing networks (e.g., tuner columns 1202 to 1212) of the GMZI architecture 1200, with reference to FIG. 15 through FIG. 20 and the calibration method of FIG. 13. The calibration methods may make use of a Hadamard phase tuning matrix 1220, which will be populated with calibrated values for the various phase shifters of the arrays of the GMZI architecture 1200 as the method progresses toward full calibration.

[0097] FIG. 13 illustrates an example method 1300 for calibrating an array of phase shifters of a GMZI. Method 1300 is described as being applied to the GMZI architecture 1200 of FIG. 12, as further illustrated in FIG. 15through FIG. 20 undergoing calibration. However, it will be appreciated that method 1300 can be applied to any suitable GMZI having tunable phase shifter arrays integrated into its coupler networks.

[0098] Although the example method 1300 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 1300. In other examples, different components of an example device or system that implements the method 1300 may perform functions at substantially the same time or in a specific sequence.

[0099] Method 1300 performs calibration of the GMZI during the calibration stage, prior to the operation stage or in between iterations of the operation stage.

[0100] According to some examples, the method 1300 includes propagating bright light through one or more light paths of the GMZI (e.g., GMZI architecture 1200) to generate bright combined light at operation 1302. The light paths of the GMZI are defined by the first coupler network 1240, the central phase shifters 1218, and the second coupler network 1242. For example, light propagating from a first input (e.g., of inputs 1214), through one or more sequentially arranged crossing couplers 800 and / or direction couplers 805 of the first coupler network 1240 (e.g., through couplers of the LHS outer coupler column 1222, LHS second coupler column 1224, and LHS inner coupler column 1226), through a single waveguide arm (e.g., of the central phase shifters 1218), and then through one or more sequentially arranged crossing couplers 800 and / or direction couplers 805 of the second coupler network 1242 (e.g., through couplers of the RHS inner coupler column 1228, RHS second coupler column 1230, and RHS outer coupler column 1232) to arrive at a given output (e.g., of outputs 1216) may be regarded as following a single light path. In some examples, the light may propagate from a single input port, through multiple light paths (e.g., through multiple waveguide arms, such as all of the central phase shifters1218), and then be partially or fully recombined before some or all of the light arrives at a given output port as combined light.

[0101] According to some examples, the method 1300 includes detecting the bright combined light at operation 1304. Detectors may be configured to receive the bright combined light output by the outputs 1216 and measure the transmitted power of the bright combined light at each output (e.g., at each output port of the GMZI).

[0102] In some examples, the pattern of bright light inputs provided to the first coupler network 1240 at a given time during the calibration stage is configured such that the bright combined light output by a given output port corresponds to a single light path, allowing the detectors to measure the transmitted power of the light at a given output port at a given time during the calibration stage in order to generate an optimal phase adjustment pattern for the corresponding light path. The at least one controller of the system controlling the GMZI may be configured to apply a time-varying pattern of bright light to the inputs of the GMZI in order to measure a transmitted power of each light path independently.

[0103] In some examples, the pattern of bright light inputs provided to the first coupler network at a given time during the calibration stage is configured such that the bright combined light output by a given output port corresponds to multiple light paths. The light paths illuminated or used at a given time may be determined based on which input(s) and output(s) are being calibrated at that time. Patterns of illumination, detection, and adjustment of the phase shifters are described below with reference to operation 1306.

[0104] According to some examples, the method includes calibrating an inner pair of phase shifter arrays at operation 1306. The details of operation 1306 are described with reference to the flowchart of FIG. 14.

[0105] FIG. 14 illustrates an example set of operations implementing operation 1306 of method 1300 to calibrate the inner pair of phase shifter arrays of the GMZI architecture 1200. This operation 1306 is illustrated in FIG. 15.

[0106] Calibrating the inner pair of phase shifter arrays (e.g., LHS inner tuner column 1206 and RHS inner tuner column 1208) involves mapping light from a first input (shown as input port 0 1502 in FIG. 15, described below) to a first output (shown as output port 0 1504). The light paths activated or illuminated to perform this mapping in FIG. 15 pass through a set of two first array phase shifters 1234 in each coupler network, a set of four second array phase shifters 1236 in each coupler network, and all eight of the third array phase shifters 1238 in each coupler network. Thus, these are the phase shifters that are used to sweep across a range of phase shift values (e.g., a range from 0 to 2K) to identify phase shift values for the inner pair of phase shifter arrays that optimize (e.g., maximize) the optical power of light propagating from input port 0 1502 to output port 0 1504.

[0107] The mathematical operations performed to identify the optimal phase shifter values are described below.

[0108] matrix for the GMZI, with phaseshift values for the central array of phase shifters, and thermal phase tuning matrix C, 7 log iV, given phase errors in thecoupler networks. The purpose of calibrating the phase shifter arrays is to identify a thermal tuning matrix C that corrects for error 7C

[0109] denotes a transfer matrix whereby the GMZI is optimizedfor (output, input) pair (i,j).

[0110] denotes the transfer matrix element at (i,j) for theGMZI.

[0111] denotes a set of optimal phase shiftvalue settings (e.g., calibrated settings for the phase shifter arrays), such that will route input port j to output port i.

[0112] simplifiedfunction that only requires specifying the thermal phase tuning correction terms in the coupler networks given optimized calibrated phase shift values effective to route input j to output i.

[0113] The goal of calibration is to minimize crosstalk extinction in the coupler networks. Crosstalk extinction is minimized when optical power is maximized. Optical power can be defined as, assuming optimized phase shiftPijvalues. Optical power can be summed over multiple light paths (j to i) as follows:

[0114] During the calibration process, two quantities are tracked: the thermal phase tuning matrix C, and the optimal phase shift values applied by the central array of phase shifters, as defined above, for each (input to output) mapping.

[0115] The thermal phase tuning matrix C is also referred to herein as a matrix of inner array phase adjustment patterns for the various arrays of phase shifters. As shown in FIG. 12, the Hadamard phase tuning matrix 1220 is the thermal phase tuning matrix, having one column for each array of phase shifters (the first column corresponds to LHS outer tuner column 1202, the second column to LHS second tuner column 1204, the third column to LHS inner tuner column 1206, the fourth column to RHS inner tuner column 1208, the fifth column to RHS second tuner column 1210, and the sixth column to RHS outer tuner column 1212), and one row for every two phase shifters in each array. As the phase shifters are calibrated, these matrix elements are set to optimal values.

[0116] The Hadamard phase tuning matrix 1220 defines the (N / 2 x 2 log2 N) matrix C, which represents coupler network phase errors spatially arranged from left to right in the GMZI architecture 1200. At the beginning of the calibration stage, C is set to all zeros, because the thermal phase shifters have not been set. The various elements of the C matrix are denoted as Cap.

[0117] Each step of the calibration process involves sweeping the phase shift value applied by a phase shifter in the arrays of the coupler networks across a range from 0 to 2K and finding the maximum total optical power for the corresponding input (of inputs 1214) summed over a specific list of outputs (of outputs 1216) corresponding to that phase shifter. The process starts sequentially from the inner arrays of phase shifters in the middle of the GMZI architecture 1200, working outward toward the arrays of phase shifters at the inputs and outputs of the GMZI architecture 1200. Thus, as shown in FIG. 13, the inner pair of phase shifter arrays is calibrated first at operation 1306, followed by the intermediate pairs of phase shifter arrays at operation 1308, followed finally by the outer pair of phase shifter arrays at operation 1310.

[0118] Thus, optical power maximization or optimization is performed at each step based on the current input port, the output ports where the combined light is being detected for the current phase shifter, and C matrix element (CaP). The optical power maximization is denoted:wherein is a matrix of the same shape as C with all zero valuesexcept a one value at element a,p.

[0119] The various phase shifters use different inputs and outputs depending on the position of their phase shifter array within the GMZI. A phase shifter in the second coupler network 1242 uses a single input (e.g., input port 0 1502), and uses a number of output ports equal to half of the total number M (in this example, M=N) of outputs. Thus, for example, a given phase shifter in the second coupler network 1242 will use light paths that pass from input port 0 1502 through each of the output ports 0 to 3.

[0120] In contrast, a phase shifter in the first coupler network 1240, at column k of the Hadamard phase tuning matrix 1220 (having six columns numbered 0 to 5), will use 2koutput ports (e.g., the first 2koutputs ports, such as the four output ports 0 to 3 for a phase shifter in the LHS inner tuner column 1206 (column 2) of the first coupler network 1240). The phase shifter in the second coupler network 1242 also uses a single input (such as input port 0 1502).

[0121] Within these constraints, the phase shifters are each, one at a time, swept through the range of phase shift values from 0 to 2K while the set of light paths passing through the phase shifter (depending on its location) is illuminated. In this way, the phase shift values of the phase shifter arrays can be adjusted to map individual inputs to individual outputs. Once this mapping has been accomplished, the arrays can be calibrated, beginning with the inner arrays and working outward toward the outer arrays. As describedabove, the method 1300 calibrates the arrays in corresponding pairs (the inner pair of arrays, working outward in pairs to the outer pair of arrays), whereas other techniques (such as the methods of FIG. 24 and FIG. 25 below) calibrate the arrays of one of the coupler networks (e.g., the first coupler network 1240 or the second coupler network 1242), working from inner to outer, followed by calibrating the other of the coupler networks, also from inner to outer arrays. What both of these approaches have in common is that phase shifters closer to the center of the GMZI ("inner" phase shifter arrays) are tuned first, before the arrays closer to the input and outputs ends of the GMZI ("outer" phase shifter arrays).

[0122] When the calibration steps are performed for a given array, a subset of the phase shifters in the first coupler network 1240 may be held constant. These phase shifters are referred to herein as “reference” phase shifters, and the set of reference phase shifters varies according to which array is being calibrated. In some examples, the number of reference phase shifters in the first coupler network 1240 for a given array calibration operation is N-l.

[0123] By performing calibration according to one of the methods described herein, iterating the calibration procedure over all non-reference phase shifters (a total of N log2 N - N + 1 steps, accounting for the N - l reference phase shifters that do not need to be tuned), calibration settings for all arrays can be calculated and stored. This results in a set of calibration settings that do not require any phase correction by the central phase shifters 1218, such that the phase shifters of the central phase shifters 1218 need to apply only targeted runtime phase shifts (e.g., phase shifts of 0 or 7t) to implement routing of the light (directing light from one or more input ports to output ports), power splitting using classical (bright) light; or to implement routing or unitary transformations for quantum photonic operations (e.g., muxing a set of input modes, qubits or modes of an entangled state, to undergo a given unitary transformation), as discussed above, with reference to ^...

[0124] The step-by-step operations of operation 1306, to calibrate the inner pair of phase shifter arrays, are now described with reference to FIG. 14.

[0125] At operation 1402, the calibration of the inner pair of phase shifter arrays includes sweeping or modulating the phase shift values of the phase shifters of the arrays of phase shifters (e.g., from the LHS outer tuner column 1202 of the first coupler network 1240 to the RHS outer tuner column 1212 of the second coupler network 1242) across multiple values across a range between 0 to 2K. During this operation, the reference phase shifters may be held constant and not modulated. In the case of operation 1306, calibrating the inner pair of phase shifter arrays, the reference phase shifters may include a first phase shifter at the top of the LHS second tuner column 1204, and the top two phase shifters of the LHS inner tuner column 1206.

[0126] At operation 1404, the calibration of the inner pair of phase shifter arrays includes mapping the light from a first input (e.g., input port 0 1502) to a first output (e.g., output port 0 1504). This mapping is performed by, during the phase sweep of operation 1402, by inputting light at input port 0 1502, measuring the optical power (or another measure of light output) of the light at output port 0 1504, and selecting the phase shift value of each phase shifter, over its sweep, that optimizes the value measured at output port 0 1504. Thus, at operation 1404, all tuners implicated in the path from input port 0 1502 to output port 0 1504 (e.g., the first array phase shifters 1234, second array phase shifters 1236, and third array phase shifters 1238 shown in FIG. 15) are tuned to optimize the phase error correction of the mapping from input port 0 1502 to output port 0 1504.

[0127] At operation 1406, the calibration of the inner pair of phase shifter arrays includes determining phase shift values for the LHS inner tuner column 1206 of the first coupler network 1240 corresponding to a maximum optical power of the combined light from the first input. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operation 1402 and operation 1404, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the LHS inner tuner column 1206 can be calculated based on this optimization procedure.

[0128] At operation 1408, the calibration of the inner pair of phase shifter arrays includes determining phase shift values for the RHS inner tuner column 1208 of the second coupler network 1242 corresponding to a maximum optical power of the combined light from one or more inputs detected at the first output. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operation 1402 and operation 1404, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the RHS inner tuner column 1208 can be calculated based on this optimization procedure.

[0129] In some examples, operation 1306 includes storing (e.g., in a memory) the calibrated settings for the LHS inner tuner column 1206 and RHS inner tuner column 1208. However, in the context of method 1300, the settings for all calibrated arrays are stored at the end of method 1300. The LHS inner tuner column 1206 and RHS inner tuner column 1208 may be maintained at their calculated optimal settings during the subsequent calibration operations shown in FIG. 13.

[0130] The calibrated settings for the inner pair of phase shifter arrays are shown in the Hadamard phase tuning matrix 1220 as solved values for the two inner columns (the third and fourth columns) corresponding to LHS inner tuner column 1206 and RHS inner tuner column 1208. The top two values of the second and fifth columns are also filled in, corresponding to solved values for the top half of the LHS second tuner column 1204 and RHS second tuner column 1210. Finally, the top element in the first and sixth columns are also filled in, corresponding to solved values for the top two phase shifters of the LHS outer tuner column 1202 and RHS outer tuner column 1212. These solved values correspond to the light paths mapped in operation 1404.

[0131] Returning to FIG. 13, after the inner pair of phase shifter arrays are calibrated at operation 1306, the method 1300 proceeds to operation 1308 to calibrate any intermediate pairs of phase shifter arrays. The GMZI may include one or more pairs of intermediate arrays between the pair of inner arrays and the pair of outer arrays. In some examples, the GMZI may onlyinclude two pairs of phase shifter arrays, in which case there are no intermediate arrays.

[0132] FIG. 16 shows an example set of operations implementing operation 1308 of method 1300 to calibrate an intermediate pair of phase shifter arrays (in this example, the LHS second tuner column 1204 and RHS second tuner column 1210) of the GMZI architecture 1200. The input / output mappings of operation 1308 are illustrated in FIG. 17 and FIG. 18.

[0133] At operation 1602, as in operation 1402 of FIG. 14, the calibration of the intermediate pair of phase shifter arrays includes sweeping or modulating the phase shift values of the phase shifters of the arrays of phase shifters across multiple values across a range between 0 to 2K. During this operation, the reference phase shifters may be held constant and not modulated. In the case of operation 1308, calibrating the inner pair of phase shifter arrays, the reference phase shifters change for each of the two mapping operations, as described below.

[0134] At operation 1604, the calibration of the intermediate pair of phase shifter arrays includes first mapping the light from a second input (e.g., input port 4 1702) to the first output (e.g., output port 0 1504) used in operation 1306. This first mapping operation is performed in the same manner as operation 1404 described above.

[0135] The reference phase shifters used in mapping operation 1604 may include two phase shifters at the top of the LHS second tuner column 1204, and the same top two phase shifters of the LHS inner tuner column 1206 used as reference phase shifters in operation 1306.

[0136] The light paths activated or illuminated to perform this mapping, shown in FIG. 17, now pass through a set of two new first array phase shifters 1234 in the first coupler network 1240, and a set of four new second array phase shifters 1236 in the first coupler network 1240. Thus, these are the phase shifters that are used to sweep across a range of phase shift values (e.g., a range from 0 to 2K) to identify phase shift values for the intermediate pair of phase shifter arrays that optimize (e.g., maximize) the optical power of light propagating from input port 4 1702 to output port 0 1504.

[0137] At operation 1606, the calibration of the intermediate pair of phase shifter arrays includes a second mapping of the light from the second input (e.g., input port 4 1702) to a second output (e.g., output port 4 1802). This second mapping operation is performed in the same manner as operation 1404 described above.

[0138] The reference phase shifters used in mapping operation 1606 may include the same reference phase shifters used in operation 1604. In other words, in some examples, the optimized values calculated for elements in the Hadamard phase tuning matrix 1220 during operation 1306 can be used in subsequent operations (e.g., operation 1308 and operation 1310).

[0139] The light paths activated or illuminated to perform this second mapping, shown in FIG. 18, now pass through a set of two new first array phase shifters 1234 in the second coupler network 1242, and a set of four new second array phase shifters 1236 in the second coupler network 1242. Thus, these are the phase shifters that are used to sweep across a range of phase shift values (e.g., a range from 0 to 2K) to identify phase shift values for the intermediate pair of phase shifter arrays that optimize (e.g., maximize) the optical power of light propagating from input port 4 1702 to output port 4 1802.

[0140] At operation 1608, the calibration of the intermediate pair of phase shifter arrays includes determining phase shift values for the LHS second tuner column 1204 of the first coupler network 1240 corresponding to a maximum optical power of the combined light from the first input. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operation 1602, operation 1604, and operation 1606, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the LHS second tuner column 1204 can be calculated based on this optimization procedure.

[0141] The calibrated settings for the LHS second tuner column 1204 are shown in the Hadamard phase tuning matrix 1220 in FIG. 17 as solved values for the second column corresponding to LHS second tuner column 1204. The third value of the first column is also filled in. These matrix cellscorresponding to solved values for the additional light paths mapped in operation 1604.

[0142] The calibrated settings for the RHS second tuner column 1210 are shown in the Hadamard phase tuning matrix 1220 in FIG. 18 as solved values for the fifth column corresponding to RHS second tuner column 1210. The third value of the sixth column is also filled in. These matrix cells corresponding to solved values for the additional light paths mapped in operation 1606.

[0143] At operation 1610, the calibration of the inner pair of phase shifter arrays includes determining phase shift values for the RHS second tuner column 1210 of the second coupler network 1242 corresponding to a maximum optical power of the combined light from one or more inputs detected at the first output. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operation 1602, operation 1604, and operation 1606, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the RHS second tuner column 1210 can be calculated based on this optimization procedure.

[0144] In some examples, as with operation 1306, operation 1308 includes storing the calibrated settings for the LHS second tuner column 1204 and RHS second tuner column 1210, instead of all setting being stored as part of method 1300. The LHS second tuner column 1204 and RHS second tuner column 1210 may be maintained at their calculated optimal settings during the subsequent calibration operations shown in FIG. 13.

[0145] In some examples of method 1300, a version of operation 1308 is performed for one or more additional intermediate pairs of phase shifter arrays. The general pattern of re-mapping inputs and outputs continues with each step outward in calibrating pairs of arrays.

[0146] Returning to FIG. 13, after the intermediate pair(s) of phase shifter arrays are calibrated at operation 1308, the method 1300 proceeds to operation 1310 to calibrate the outer pair of phase shifter arrays.

[0147] FIG. 19 shows an example set of operations implementing operation 1310 of method 1300 to calibrate an intermediate pair of phase shifter arrays(in this example, the LHS outer tuner column 1202 and RHS outer tuner column 1212) of the GMZI architecture 1200. The input / output mappings of operation 1310 are illustrated in FIG. 20.

[0148] At operation 1902, as in operation 1402 of FIG. 14, the calibration of the intermediate pair of phase shifter arrays includes sweeping or modulating the phase shift values of the phase shifters of the arrays of phase shifters across multiple values across a range between 0 to 2K. During this operation, the reference phase shifters may be held constant and not modulated. In some examples, there are no reference phase shifters for operation 1310.

[0149] At operation 1904, the calibration of the intermediate pair of phase shifter arrays includes a first mapping of the light from a third input (e.g., input port 2 2002) to the second output (e.g., output port 4 1802). This first mapping operation is performed in the same manner as operation 1404 described above.

[0150] At operation 1906, the calibration of the intermediate pair of phase shifter arrays includes a second mapping of the light from the third input (e.g., input port 2 2002) to a third output (e.g., output port 2 2006). This second mapping operation is performed in the same manner as operation 1404 described above.

[0151] At operation 1908, the calibration of the intermediate pair of phase shifter arrays includes a third mapping of the light from a fourth input (e.g., input port 6 2004) to the third output (e.g., output port 2 2006). This third mapping operation is performed in the same manner as operation 1404 described above.

[0152] At operation 1910, the calibration of the intermediate pair of phase shifter arrays includes a fourth mapping of the light from the fourth input (e.g., input port 6 2004) to a fourth output (e.g., output port 6 2008). This fourth mapping operation is performed in the same manner as operation 1404 described above.

[0153] The light paths activated or illuminated to perform these mappings, shown in FIG. 20, pass through all the remaining phase shifters of the GMZI. Thus, these are the phase shifters that are used to sweep across arange of phase shift values (e.g., a range from 0 to 271) to identify phase shift values for the outer pair of phase shifter arrays that optimize (e.g., maximize) the optical power of light propagating from the various inputs to the various outputs.

[0154] At operation 1912, the calibration of the outer pair of phase shifter arrays includes determining phase shift values for the LHS outer tuner column 1202 of the first coupler network 1240 corresponding to a maximum optical power of the combined light from the various inputs. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operations 1902 to 1910, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the LHS outer tuner column 1202 can be calculated based on this optimization procedure.

[0155] At operation 1914, the calibration of the inner pair of phase shifter arrays includes determining phase shift values for the RHS outer tuner column 1212 of the second coupler network 1242 corresponding to a maximum optical power of the combined light from the various inputs. The total optical power, as described above, may be calculated and maximized based on the results of the phase sweep and input / output mapping operations of operations 1902 to 1910, according to the mathematical operations defined above. The calibrated phase shift values for the phase shifters of the RHS outer tuner column 1212 can be calculated based on this optimization procedure.

[0156] In some examples, as with operation 1306 and operation 1308, operation 1310 includes storing the calibrated settings for the LHS outer tuner column 1202 and RHS outer tuner column 1212, instead of all setting being stored as part of method 1300.

[0157] The calibrated settings for the LHS outer tuner column 1202 and RHS outer tuner column 1212 are shown in the Hadamard phase tuning matrix 1220 in FIG. 20 as solved values for the remainder of the first and sixth columns corresponding to LHS outer tuner column 1202 and RHSouter tuner column 1212. These matrix cells corresponding to solved values for the additional light paths mapped in operation 1310.

[0158] Returning to FIG. 13, after the outer pair of phase shifter arrays are calibrated at operation 1310, the method 1300 proceeds to operation 1312 to store the calibrated settings for the various arrays of phase shifters. The controller tuning and calibrating the phase shifters may store the calibrated settings (e.g., represented by the complete Hadamard phase tuning matrix 1220 in FIG. 20) in a memory of the system used to control the GMZI. These settings can then be retrieved to tune the phase shifters of the first coupler network 1240 and second coupler network 1242 during the operation stage, as described below in reference to FIG. 21.

[0159] FIG. 21 illustrates an example method 2100 for adjusting the phase of light in a waveguide arm of the GMZI using the arrays of phase shifters of the first coupler network 1240 and second coupler network 1242. Although the example method 2100 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 2100. In other examples, different components of an example device or system that implements the method 2100 may perform functions at substantially the same time or in a specific sequence.

[0160] Method 2100 processes the light during the operation stage, after the calibration stage. It may be included as a step in operating the GMZI, as described below with reference to FIG. 22.

[0161] At operation 2102, the method 2100 includes retrieving phase adjustment patterns for each of the phase shifter arrays of the first coupler network 1240 and second coupler network 1242. The phase adjustment pattern for each array corresponds to the calibrated settings for the array stored as part of method 1300.

[0162] At operation 2104, each phase shifter of the phase shifter arrays is tuned according to its retrieved phase adjustment pattern.

[0163] FIG. 22 shows a flow diagram of a method for processing light using a GMZI, in accordance with some example embodiments. Althoughthe example method 2200 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 2200. In other examples, different components of an example device or system that implements the method 2200 may perform functions at substantially the same time or in a specific sequence.

[0164] Although the method 2200 is described with reference to the components of various example GMZIs described herein, it will be appreciated that the operations of the method 2200 may be performed by any of a number of different GMZI configurations.

[0165] Method 2200 is performed at the operation stage, as described above.

[0166] According to some examples, the method 2200 includes receiving light at operation 2201. As described above, the light may be quantum light or bright light. It is received by a first coupler network (e.g., first coupler network 1240) of the GMZI.

[0167] According to some examples, the method 2200 includes distributing the light by the first coupler network at operation 2202. The first coupler network distributes the light to one or more of the plurality of waveguide arms (e.g., central phase shifters 1218).

[0168] According to some examples, the method 2200 includes adjusting a phase portion of the light at operation 2203. Operation 2203 may be implemented by method 2100, described above.

[0169] According to some examples, the method 2200 includes combining the light by a second coupler network (e.g., second coupler network 1242) of the GMZI at operation 2204. The second coupler network combines the light from one or more of the plurality of waveguide arms of the array of central phase shifters 1218, thereby generating combined light.

[0170] According to some examples, the method 2200 includes outputting the combined light from one or more output ports of the GMZI at operation 2205. The combined light is propagated from the second coupler network to the one or more outputs (e.g., output ports), and the output ports output thecombined light. In some examples, the combined light includes multiple distinct beams or portions of light, each of which is output by a distinct output port.

[0171] FIG. 23 shows a flow diagram of a method for processing quantum light using a GMZI, in accordance with some example embodiments.Although the example method 2300 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 2300. In other examples, different components of an example device or system that implements the method 2300 may perform functions at substantially the same time or in a specific sequence.

[0172] Although the method 2300 is described with reference to the components of various example GMZIs described herein, it will be appreciated that the operations of the method 2300 may be performed by any of a number of different GMZI configurations.

[0173] Method 2300 is performed at the operation stage, as described above. Method 2300 may be regarded as a special case of method 2200, in which the GMZI operates on a superposition of quantum light in a nonclassical quantum light mode, as described above.

[0174] According to some examples, the method 2300 includes receiving quantum light at operation 2301. The quantum light is received by the first coupler network of the GMZI.

[0175] According to some examples, the method 2300 includes splitting the quantum light at operation 2302. The quantum light is split by the first coupler network into one or more of the waveguide arms.

[0176] According to some examples, the method 2300 includes interfering the quantum light at operation 2303. As described above with reference to FIG. 5 and FIG. 6, in some examples, the quantum light may be split into two waveguide arms and can be interfered with 50% of the light transmitted to a given output port via the second coupler network, which combines the quantum light. For example, the central array of phase shifters mayimplement zero phase adjustments and TT phase adjustments on the superposition of the quantum light in the central phase shifters 1218 to modify probabilities of the quantum light exiting from one or more of the output ports.

[0177] According to some examples, the method 2300 includes outputting the quantum light at operation 2304. The quantum light is output by one or more outputs of the GMZI. In some examples, the quantum light output by a given output or output port may be output to a detector, such as a singlephoton detector, for measurement.

[0178] FIG. 24 illustrates a second example method 2400 for calibrating an array of phase shifters of a GMZI. Method 2400 provides an alternative order for calibrating the various arrays from inner to outer: specifically, the arrays of the first coupler network 1240 first, then the arrays of the second coupler network 1242.

[0179] According to some examples, the method 2400 includes propagating bright light through one or more light paths of the GMZI to generate bright combined light at operation 2402. Operation 2402 can be performed as operation 1302.

[0180] According to some examples, the method 2400 includes detecting the bright combined light at operation 2404. Operation 2404 can be performed as operation 1304.

[0181] According to some examples, the method 2400 includes calibrating the phase shifter arrays of the first coupler network 1240, inner to outer, at operation 2406.

[0182] According to some examples, the method 2400 includes calibrating the phase shifter arrays of the second coupler network 1242, inner to outer, at operation 2408. Operation 2408 is performed in the same way as operation 2406.

[0183] FIG. 25 illustrates as third example method 2500 for calibrating an array of phase shifters of a GMZI. Method 2500 provides a further alternative order for calibrating the various arrays from inner to outer: specifically, the arrays of the second coupler network 1242 first, then the arrays of the first coupler network 1240.

[0184] According to some examples, the method 2500 includes propagating bright light through one or more light paths of the GMZI to generate bright combined light at operation 2502. Operation 2502 can be performed as operation 1302.

[0185] According to some examples, the method 2500 includes detecting the bright combined light at operation 2504. Operation 2504 can be performed as operation 1304.

[0186] According to some examples, the method 2500 includes calibrating the phase shifter arrays of the second coupler network 1242, inner to outer, at operation 2506. The calibration of individual arrays is performed as operation 2408 described above.

[0187] According to some examples, the method 2500 includes calibrating the phase shifter arrays of the first coupler network 1240, inner to outer, at operation 2508. Operation 2508 is performed in the same way as operation 2406.

[0188] The following are example embodiments:

[0189] Example l is a method for processing light in a generalized Mach- Zehnder Interferometer (GMZI), the GMZI comprising a first coupler network and a second coupler network, the first coupler network comprising a first plurality of crossing networks, the second coupler network comprising a second plurality of crossing networks, the method comprising: receiving, by one or more inputs of the first coupler network, light comprising one or more photons; tuning a first plurality of phase shifters of the first coupler network to apply a respective first plurality of phase shift values to light propagating through the first plurality of crossing networks; tuning a second plurality of phase shifters of the second coupler network to apply a respective second plurality of phase shift values to light propagating through the second plurality of crossing networks; distributing the light via one or more light paths through the first coupler network from the one or more inputs to a plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by thesecond coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

[0190] In Example 2, the subject matter of Example 1 includes, wherein: each crossing network of the first plurality of crossing networks has a corresponding crossing network of the second plurality of crossing networks, such that the GMZI comprises a plurality of pairs of corresponding crossing networks arranged successively outward from the plurality of waveguide arms, from an inner pair of crossing networks adjacent to the plurality of waveguide arms to an outer pair of crossing networks adjacent to an input end of the first coupler network and an output end of the second coupler network.

[0191] In Example 3, the subject matter of Example 2 includes, prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating an inner pair of phase shifter arrays, comprising an inner array of phase shifters of the first plurality of phase shifters and an inner array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the inner pair of crossing networks; and successively calibrating one or more additional pairs of phase shifter arrays, ending with an outer pair of phase shifter arrays, comprising an outer array of phase shifters of the first plurality of phase shifters and an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the outer pair of crossing networks.

[0192] In Example 4, the subject matter of Example 3 includes, wherein: the calibrating of the inner pair of phase shifter arrays comprises: propagating bright light through the GMZI from one or more inputs of the first coupler network to one or more outputs of the second coupler network to generate bright combined light at the one or more outputs of the secondcoupler network; detecting the bright combined light at the one or more outputs of the second coupler network; adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output; determining an inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values; and storing the inner array phase adjustment pattern; wherein the tuning of the inner pair of phase shifter arrays comprises: retrieving the inner array phase adjustment pattern; and tuning each phase shifter of the inner pair of phase shifter arrays according to the inner array phase adjustment pattern.

[0193] In Example 5, the subject matter of Example 4 includes, wherein: the calibrating of the one or more additional pairs of arrays of phase shifters comprises calibrating a second pair of phase shifter arrays adjacent to the inner pair of phase shifter arrays, the second pair of phase shifter arrays comprising a second array of the first coupler network and a second array of the second coupler network, by: adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to: map the light from the second input to the first output based on the bright combined light detected at the first output; and map the light from the second input to a second output of the second coupler network based on the bright combined light detected at the second output; determining a second array phase adjustment pattern for the second pair of phase shifter arrays based on the adjusted phase shift values; and storing the second array phase adjustment pattern; wherein the tuning of the second pair of phase shifter arrays comprises: retrieving the second array phase adjustment pattern; and tuning each phase shifter of the second pair of phase shifter arrays according to the second array phase adjustment pattern.

[0194] In Example 6, the subject matter of Example 5 includes, wherein: the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the second pair of phase shifter arrays, calibrating a third pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and second pair ofphase shifter arrays constant while adjusting the phase shift values applied by one or more other phase shifters of the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to: map the light from a third input of the first coupler network to the second output based on the bright combined light detected at the second output; map the light from the third input to a third output of the second coupler network based on the bright combined light detected at the third output; map the light from a fourth input of the first coupler network to the third output based on the bright combined light detected at the third output; and map the light from the fourth input to a fourth output of the second coupler network based on the bright combined light detected at the fourth output; determining a third array phase adjustment pattern for the third pair of phase shifter arrays based on the adjusted phase shift values; and storing the third array phase adjustment pattern; wherein the tuning of the third pair of phase shifter arrays comprises: retrieving the third array phase adjustment pattern; and tuning each phase shifter of the third pair of phase shifter arrays according to the third array phase adjustment pattern.

[0195] In Example 7, the subject matter of Examples 4-6 includes, wherein: the one or more additional pairs of phase shifter arrays comprises N-l pairs of arrays of phase shifters, N being an integer greater than one; the first coupler network comprises 2N inputs; the second coupler network comprises 2N outputs; and the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the inner pair of phase shifter arrays and each other additional outer pair of phase shifter arrays, calibrating the outer pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and each other additional pair of arrays of phase shifters constant while adjusting the phase shift values applied by the phase shifters of the outer pair of phase shifter arrays, based on the bright combined light detected at the one or more outputs, to: sequentially map the light between each of a sequence of inputoutput pairs, the sequence of input-output pairs comprising each of the 2N inputs of the first coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays, mapped to each of the 2N outputs ofthe second coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays; determining an outer array phase adjustment pattern for the outer pair of phase shifter arrays based on the adjusted phase shift values; and storing the outer array phase adjustment pattern; wherein the tuning of the outer pair of phase shifter arrays comprises: retrieving the outer array phase adjustment pattern; and tuning each phase shifter of the outer pair of phase shifter arrays according to the outer array phase adjustment pattern.

[0196] In Example 8, the subject matter of Examples 4-7 includes, wherein: the adjusting of the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output comprises: modulating the phase shift values applied by each phase shifter of the first plurality of phase shifters and second plurality of phase shifters across a plurality of phase shift values in a range between 0 to 2K; and the determining of the inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values comprises: determining phase shift values for the phase shifters of the inner array of phase shifters of the first plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the first input detected at the one or more outputs; and determining phase shift values for the phase shifters of the inner array of phase shifters of the second plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the one or more inputs detected at the first output.

[0197] In Example 9, the subject matter of Examples 1-8 includes, wherein: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating a first set of phase shifters, followed by calibrating a second set of phase shifters, the first set of phase shifters being a first one of: the first plurality of phase shifters, or the second plurality of phase shifters; and the second set of phase shifters being an other one of: the first plurality of phase shifters; or the second plurality of phase shifters.

[0198] In Example 10, the subject matter of Example 9 includes, wherein: the calibrating of the first plurality of phase shifters comprises: calibrating an inner array of phase shifters of the first plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the first coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the first plurality of phase shifters, ending with an outer array of phase shifters of the first plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the first coupler network adjacent to an input end of the first coupler network; and the calibrating of the second plurality of phase shifters comprises: calibrating an inner array of phase shifters of the second plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the second coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the second plurality of phase shifters, ending with an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the second coupler network adjacent to an output end of the second coupler network.

[0199] Example 11 is a system comprising: a generalized Mach-Zehnder Interferometer (GMZI) comprising: a plurality of waveguide arms; a first coupler network comprising a first plurality of crossing networks and configured to perform operations comprising: receiving, by one or more inputs, light comprising one or more photons; and distributing the light to one or more of the plurality of waveguide arms; a second coupler network comprising a second plurality of crossing networks and configured to perform operations comprising: receiving the light from the plurality of waveguide arms; and combining the light to form combined light; a first plurality of phase shifters configured to apply tunable phase shift values to light propagating through the first plurality of crossing networks; and a second plurality of phase shifters configured to apply tunable phase shift values to light propagating through the second plurality of crossing networks.

[0200] In Example 12, the subject matter of Example 11 includes, wherein: each crossing network of the first plurality of crossing networks has a corresponding crossing network of the second plurality of crossing networks, such that the GMZI comprises a plurality of pairs of corresponding crossing networks arranged successively outward from the plurality of waveguide arms, from an inner pair of crossing networks adjacent to the plurality of waveguide arms to an outer pair of crossing networks adjacent to an input end of the first coupler network and an output end of the second coupler network.

[0201] In Example 13, the subject matter of Example 12 includes, at least one controller; wherein the at least one controller is further configured to perform operations comprising: tuning the first plurality of phase shifters to apply a respective first plurality of phase shift values; tuning the second plurality of phase shifters to apply a respective second plurality of phase shift values; distributing the light via one or more light paths through the first coupler network from the one or more inputs to the plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by the second coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

[0202] In Example 14, the subject matter of Example 13 includes, wherein the operations comprise: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating an inner pair of phase shifter arrays, comprising an inner array of phase shifters of the first plurality of phase shifters and an inner array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the inner pair ofcrossing networks; and successively calibrating one or more additional pairs of phase shifter arrays, ending with an outer pair of phase shifter arrays, comprising an outer array of phase shifters of the first plurality of phase shifters and an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the outer pair of crossing networks.

[0203] In Example 15, the subject matter of Example 14 includes, wherein: the calibrating of the inner pair of phase shifter arrays comprises: propagating bright light through the GMZI from one or more inputs of the first coupler network to one or more outputs of the second coupler network to generate bright combined light at the one or more outputs of the second coupler network; detecting the bright combined light at the one or more outputs of the second coupler network; adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output; determining an inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values; and storing the inner array phase adjustment pattern; wherein the tuning of the inner pair of phase shifter arrays comprises: retrieving the inner array phase adjustment pattern; and tuning each phase shifter of the inner pair of phase shifter arrays according to the inner array phase adjustment pattern.

[0204] In Example 16, the subject matter of Example 15 includes, wherein: the one or more additional pairs of phase shifter arrays comprises N-l pairs of arrays of phase shifters, N being an integer greater than one; the first coupler network comprises 2N inputs; the second coupler network comprises 2N outputs; and the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the inner pair of phase shifter arrays and each other additional outer pair of phase shifter arrays, calibrating the outer pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and each other additional pair of arrays of phase shifters constant while adjusting the phase shift values applied by the phase shifters of the outer pair of phase shifter arrays, based on the bright combined light detected at the one or moreoutputs, to: sequentially map the light between each of a sequence of inputoutput pairs, the sequence of input-output pairs comprising each of the 2N inputs of the first coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays, mapped to each of the 2N outputs of the second coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays; determining an outer array phase adjustment pattern for the outer pair of phase shifter arrays based on the adjusted phase shift values; and storing the outer array phase adjustment pattern; wherein the tuning of the outer pair of phase shifter arrays comprises: retrieving the outer array phase adjustment pattern; and tuning each phase shifter of the outer pair of phase shifter arrays according to the outer array phase adjustment pattern.

[0205] In Example 17, the subject matter of Examples 15-16 includes, wherein: the adjusting of the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output comprises: modulating the phase shift values applied by each phase shifter of the first plurality of phase shifters and second plurality of phase shifters across a plurality of phase shift values in a range between 0 to 2K; and the determining of the inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values comprises: determining phase shift values for the phase shifters of the inner array of phase shifters of the first plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the first input detected at the one or more outputs; and determining phase shift values for the phase shifters of the inner array of phase shifters of the second plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the one or more inputs detected at the first output.

[0206] In Example 18, the subject matter of Examples 15-17 includes, wherein: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating a first set of phase shifters, followed by calibrating a second setof phase shifters, the first set of phase shifters being a first one of the first plurality of phase shifters; or the second plurality of phase shifters; and the second set of phase shifters being an other one of the first plurality of phase shifters; or the second plurality of phase shifters.

[0207] In Example 19, the subject matter of Example 18 includes, wherein: the calibrating of the first plurality of phase shifters comprises: calibrating an inner array of phase shifters of the first plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the first coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the first plurality of phase shifters, ending with an outer array of phase shifters of the first plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the first coupler network adjacent to an input end of the first coupler network; and the calibrating of the second plurality of phase shifters comprises: calibrating an inner array of phase shifters of the second plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the second coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the second plurality of phase shifters, ending with an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the second coupler network adjacent to an output end of the second coupler network.

[0208] Example 20 is a non-transitory computer readable medium comprising instructions that, when executed by at least one controller of a system, cause the system to perform operations comprising: receiving, by one or more inputs of a first coupler network of a generalized Mach-Zehnder Interferometer (GMZI), light comprising one or more photons; tuning a first plurality of phase shifters of the first coupler network to apply a respective first plurality of phase shift values to light propagating through a first plurality of crossing networks of the first coupler network; tuning a second plurality of phase shifters of a second coupler network of the GMZI to apply a respective second plurality of phase shift values to light propagating through a second plurality of crossing networks of the second couplernetwork; distributing the light via one or more light paths through the first coupler network from the one or more inputs to a plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by the second coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

[0209] Example 21 is at least one machine-readable medium including instructions that, when executed by processing circuitry, cause the processing circuitry to perform operations to implement of any of Examples 1-20.

[0210] Example 22 is an apparatus comprising means to implement of any of Examples 1-20.

[0211] Example 23 is a system to implement of any of Examples 1-20.

[0212] Example 24 is a method to implement of any of Examples 1-20.

[0213] Other technical features and example embodiments may be readily apparent to one skilled in the art from the figures, descriptions, and claims herein.

[0214] As used herein, a computer-readable storage medium refers, for example, to both machine-storage media and transmission media. Thus, the terms include both storage devices / media and carrier waves / modulated data signals. The terms “machine-readable medium,” “computer-readable medium” and “device-readable medium” mean the same thing and may be used interchangeably in this disclosure.

[0215] As used herein, a machine storage medium refers, for example, to a single or multiple storage devices and media (e.g., a centralized or distributed database, and associated caches and servers) that store executableinstructions, routines and data. The term shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media, including memory internal or external to processors. Specific examples of machine-storage media, computer-storage media and devicestorage media include non-volatile memory, including by way of example semiconductor memory devices, e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), FPGA, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD- ROM and DVD-ROM disks The terms "machine-storage medium," "devicestorage medium," "computer- storage medium" mean the same thing and may be used interchangeably in this disclosure. The terms "machine-storage media," "computer- storage media," and "device-storage media" specifically exclude carrier waves, modulated data signals, and other such media.

[0216] As used herein, a non-transitory computer-readable storage medium refers, for example, to a tangible medium that is capable of storing, encoding, or carrying the instructions for execution by a machine.

[0217] It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. These terms are used only to distinguish one element from another. For example, a first tuner could be termed a second tuner, and, similarly, a second tuner could be termed a first tuner, without departing from the scope of the various described embodiments. The first tuner and the second tuner are both tuners, but they are not the same tuner.

[0218] The terminology used in the description of the various described embodiments herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used in the description of the various described embodiments and the appended claims, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and / or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and / or“comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0219] As used herein, the term “if’ is, optionally, construed to mean “when” or “upon” or “in response to determining” or “in response to detecting” or “in accordance with a determination that,” depending on the context.

[0220] The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the scope of the claims to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen in order to best explain the principles underlying the claims and their practical applications, to thereby enable others skilled in the art to best use the embodiments with various modifications as are suited to the particular uses contemplated.

Claims

1. CLAIMSWhat is claimed is:

1. A method for processing light in a generalized Mach-Zehnder Interferometer (GMZI), the GMZI comprising a first coupler network and a second coupler network, the first coupler network comprising a first plurality of crossing networks, the second coupler network comprising a second plurality of crossing networks, the method comprising: receiving, by one or more inputs of the first coupler network, light comprising one or more photons; tuning a first plurality of phase shifters of the first coupler network to apply a respective first plurality of phase shift values to light propagating through the first plurality of crossing networks; tuning a second plurality of phase shifters of the second coupler network to apply a respective second plurality of phase shift values to light propagating through the second plurality of crossing networks; distributing the light via one or more light paths through the first coupler network from the one or more inputs to a plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by the second coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

2. The method of claim 1, wherein: each crossing network of the first plurality of crossing networks has a corresponding crossing network of the second plurality of crossing networks, such that the GMZI comprises a plurality of pairs of corresponding crossing networks arranged successively outward from the plurality of waveguide arms, from an inner pair of crossing networks adjacent to the plurality of waveguide arms to an outer pair of crossing networks adjacent to an input end of the first coupler network and an output end of the second coupler network.

3. The method of claim 2, further comprising: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating an inner pair of phase shifter arrays, comprising an inner array of phase shifters of the first plurality of phase shifters and an inner array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the inner pair of crossing networks; and successively calibrating one or more additional pairs of phase shifter arrays, ending with an outer pair of phase shifter arrays, comprising an outer array of phase shifters of the first plurality of phase shifters and an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the outer pair of crossing networks.

4. The method of claim 3, wherein: the calibrating of the inner pair of phase shifter arrays comprises: propagating bright light through the GMZI from one or more inputs of the first coupler network to one or more outputs of the second coupler network to generate bright combined light at the one or more outputs of the second coupler network; detecting the bright combined light at the one or more outputs of the second coupler network;adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output; determining an inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values; and storing the inner array phase adjustment pattern; wherein the tuning of the inner pair of phase shifter arrays comprises: retrieving the inner array phase adjustment pattern; and tuning each phase shifter of the inner pair of phase shifter arrays according to the inner array phase adjustment pattern.

5. The method of claim 4, wherein: the calibrating of the one or more additional pairs of arrays of phase shifters comprises calibrating a second pair of phase shifter arrays adjacent to the inner pair of phase shifter arrays, the second pair of phase shifter arrays comprising a second array of the first coupler network and a second array of the second coupler network, by: adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to: map the light from the second input to the first output based on the bright combined light detected at the first output; and map the light from the second input to a second output of the second coupler network based on the bright combined light detected at the second output; determining a second array phase adjustment pattern for the second pair of phase shifter arrays based on the adjusted phase shift values; and storing the second array phase adjustment pattern; wherein the tuning of the second pair of phase shifter arrays comprises:retrieving the second array phase adjustment pattern; and tuning each phase shifter of the second pair of phase shifter arrays according to the second array phase adjustment pattern.

6. The method of claim 5, wherein: the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the second pair of phase shifter arrays, calibrating a third pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and second pair of phase shifter arrays constant while adjusting the phase shift values applied by one or more other phase shifters of the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to: map the light from a third input of the first coupler network to the second output based on the bright combined light detected at the second output; map the light from the third input to a third output of the second coupler network based on the bright combined light detected at the third output; map the light from a fourth input of the first coupler network to the third output based on the bright combined light detected at the third output; and map the light from the fourth input to a fourth output of the second coupler network based on the bright combined light detected at the fourth output; determining a third array phase adjustment pattern for the third pair of phase shifter arrays based on the adjusted phase shift values; and storing the third array phase adjustment pattern; wherein the tuning of the third pair of phase shifter arrays comprises: retrieving the third array phase adjustment pattern; and tuning each phase shifter of the third pair of phase shifter arrays according to the third array phase adjustment pattern.

7. The method of claim 4, wherein: the one or more additional pairs of phase shifter arrays comprises N-l pairs of arrays of phase shifters, N being an integer greater than one; the first coupler network comprises 2Ninputs; the second coupler network comprises 2Noutputs; and the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the inner pair of phase shifter arrays and each other additional outer pair of phase shifter arrays, calibrating the outer pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and each other additional pair of arrays of phase shifters constant while adjusting the phase shift values applied by the phase shifters of the outer pair of phase shifter arrays, based on the bright combined light detected at the one or more outputs, to: sequentially map the light between each of a sequence of input-output pairs, the sequence of input-output pairs comprising each of the 2Ninputs of the first coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays, mapped to each of the 2Noutputs of the second coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays; determining an outer array phase adjustment pattern for the outer pair of phase shifter arrays based on the adjusted phase shift values; and storing the outer array phase adjustment pattern; wherein the tuning of the outer pair of phase shifter arrays comprises: retrieving the outer array phase adjustment pattern; and tuning each phase shifter of the outer pair of phase shifter arrays according to the outer array phase adjustment pattern.

8. The method of claim 4, wherein: the adjusting of the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output comprises: modulating the phase shift values applied by each phase shifter of the first plurality of phase shifters and second plurality of phase shifters across a plurality of phase shift values in a range between 0 to 2K; and the determining of the inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values comprises: determining phase shift values for the phase shifters of the inner array of phase shifters of the first plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the first input detected at the one or more outputs; and determining phase shift values for the phase shifters of the inner array of phase shifters of the second plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the one or more inputs detected at the first output.

9. The method of claim 1, wherein: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating a first set of phase shifters, followed by calibrating a second set of phase shifters, the first set of phase shifters being a first one of: the first plurality of phase shifters, or the second plurality of phase shifters; and the second set of phase shifters being an other one of: the first plurality of phase shifters; or the second plurality of phase shifters.

10. The method of claim 9, wherein: the calibrating of the first plurality of phase shifters comprises: calibrating an inner array of phase shifters of the first plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the first coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the first plurality of phase shifters, ending with an outer array of phase shifters of the first plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the first coupler network adjacent to an input end of the first coupler network; and the calibrating of the second plurality of phase shifters comprises: calibrating an inner array of phase shifters of the second plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the second coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the second plurality of phase shifters, ending with an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the second coupler network adjacent to an output end of the second coupler network.

11. A system comprising: a generalized Mach-Zehnder Interferometer (GMZI) comprising: a plurality of waveguide arms; a first coupler network comprising a first plurality of crossing networks and configured to perform operations comprising: receiving, by one or more inputs, light comprising one or more photons; and distributing the light to one or more of the plurality of waveguide arms;a second coupler network comprising a second plurality of crossing networks and configured to perform operations comprising: receiving the light from the plurality of waveguide arms; and combining the light to form combined light; a first plurality of phase shifters configured to apply tunable phase shift values to light propagating through the first plurality of crossing networks; and a second plurality of phase shifters configured to apply tunable phase shift values to light propagating through the second plurality of crossing networks.

12. The system of claim 11, wherein: each crossing network of the first plurality of crossing networks has a corresponding crossing network of the second plurality of crossing networks, such that the GMZI comprises a plurality of pairs of corresponding crossing networks arranged successively outward from the plurality of waveguide arms, from an inner pair of crossing networks adjacent to the plurality of waveguide arms to an outer pair of crossing networks adjacent to an input end of the first coupler network and an output end of the second coupler network.

13. The system of claim 12, further comprising at least one controller; wherein the at least one controller is further configured to perform operations comprising: tuning the first plurality of phase shifters to apply a respective first plurality of phase shift values; tuning the second plurality of phase shifters to apply a respective second plurality of phase shift values; distributing the light via one or more light paths through the first coupler network from the one or more inputs to the plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the lighttraveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by the second coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

14. The system of claim 13, wherein the operations comprise: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating an inner pair of phase shifter arrays, comprising an inner array of phase shifters of the first plurality of phase shifters and an inner array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the inner pair of crossing networks; and successively calibrating one or more additional pairs of phase shifter arrays, ending with an outer pair of phase shifter arrays, comprising an outer array of phase shifters of the first plurality of phase shifters and an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through the outer pair of crossing networks.

15. The system of claim 14, wherein: the calibrating of the inner pair of phase shifter arrays comprises: propagating bright light through the GMZI from one or more inputs of the first coupler network to one or more outputs of the second coupler network to generate bright combined light at the one or more outputs of the second coupler network; detecting the bright combined light at the one or more outputs of the second coupler network;adjusting the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output; determining an inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values; and storing the inner array phase adjustment pattern; wherein the tuning of the inner pair of phase shifter arrays comprises: retrieving the inner array phase adjustment pattern; and tuning each phase shifter of the inner pair of phase shifter arrays according to the inner array phase adjustment pattern.

16. The system of claim 15, wherein: the one or more additional pairs of phase shifter arrays comprises N-l pairs of arrays of phase shifters, N being an integer greater than one; the first coupler network comprises 2Ninputs; the second coupler network comprises 2Noutputs; and the calibrating of the one or more additional pairs of arrays of phase shifters further comprises, after calibrating the inner pair of phase shifter arrays and each other additional outer pair of phase shifter arrays, calibrating the outer pair of phase shifter arrays by: holding the phase shift values applied by the inner pair of phase shifter arrays and each other additional pair of arrays of phase shifters constant while adjusting the phase shift values applied by the phase shifters of the outer pair of phase shifter arrays, based on the bright combined light detected at the one or more outputs, to: sequentially map the light between each of a sequence of input-output pairs, the sequence of input-output pairs comprising each of the 2Ninputs of the first coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays, mapped to each of the 2Noutputs of the second coupler network not already mapped in the calibrations of the other pairs of phase shifter arrays;determining an outer array phase adjustment pattern for the outer pair of phase shifter arrays based on the adjusted phase shift values; and storing the outer array phase adjustment pattern; wherein the tuning of the outer pair of phase shifter arrays comprises: retrieving the outer array phase adjustment pattern; and tuning each phase shifter of the outer pair of phase shifter arrays according to the outer array phase adjustment pattern.

17. The system of claim 15, wherein: the adjusting of the phase shift values applied by the first plurality of phase shifters and second plurality of phase shifters, based on the bright combined light detected at the one or more outputs, to map the light from the first input to the first output comprises: modulating the phase shift values applied by each phase shifter of the first plurality of phase shifters and second plurality of phase shifters across a plurality of phase shift values in a range between 0 to 2K; and the determining of the inner array phase adjustment pattern for the inner pair of phase shifter arrays based on the adjusted phase shift values comprises: determining phase shift values for the phase shifters of the inner array of phase shifters of the first plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the first input detected at the one or more outputs; and determining phase shift values for the phase shifters of the inner array of phase shifters of the second plurality of phase shifters corresponding to a maximum optical power, across the range of each phase shifter, of the combined light from the one or more inputs detected at the first output.

18. The system of claim 15, wherein: prior to receiving the light by the first coupler network, calibrating the first plurality of phase shifters and second plurality of phase shifters by: calibrating a first set of phase shifters, followed by calibrating a second set of phase shifters, the first set of phase shifters being a first one of: the first plurality of phase shifters; or the second plurality of phase shifters; and the second set of phase shifters being an other one of: the first plurality of phase shifters; or the second plurality of phase shifters.

19. The system of claim 18, wherein: the calibrating of the first plurality of phase shifters comprises: calibrating an inner array of phase shifters of the first plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the first coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the first plurality of phase shifters, ending with an outer array of phase shifters of the first plurality of phase shifters, to adjust the phase of light propagating through an outer crossing network of the first coupler network adjacent to an input end of the first coupler network; and the calibrating of the second plurality of phase shifters comprises: calibrating an inner array of phase shifters of the second plurality of phase shifters to adjust the phase of light propagating through an inner crossing network of the second coupler network adjacent to the plurality of waveguide arms; and successively calibrating one or more additional phase shifter arrays of the second plurality of phase shifters, ending with an outer array of phase shifters of the second plurality of phase shifters, to adjust the phase of light propagating through an outer crossingnetwork of the second coupler network adjacent to an output end of the second coupler network.

20. A non-transitory computer readable medium comprising instructions that, when executed by at least one controller of a system, cause the system to perform operations comprising: receiving, by one or more inputs of a first coupler network of a generalized Mach-Zehnder Interferometer (GMZI), light comprising one or more photons; tuning a first plurality of phase shifters of the first coupler network to apply a respective first plurality of phase shift values to light propagating through a first plurality of crossing networks of the first coupler network; tuning a second plurality of phase shifters of a second coupler network of the GMZI to apply a respective second plurality of phase shift values to light propagating through a second plurality of crossing networks of the second coupler network; distributing the light via one or more light paths through the first coupler network from the one or more inputs to a plurality of waveguide arms, each light path passing through one or more of the first plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the first plurality of phase shift values; receiving, by the second coupler network, the light from the plurality of waveguide arms; and combining the light via one or more light paths through the second coupler network to form combined light at one or more outputs of the second coupler network, each light path passing through one or more of the second plurality of phase shifters such that the phase of the light traveling via each light path is shifted in accordance with one or more phase shift values of the second plurality of phase shift values.

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