Abstract:
A Periodic Cluster State Generator (PCSG) consisting of a monolithic integrated waveguide device that employs four wave mixing, an array of probabilistic Photon Guns, single mode Sequential Entanglers and an array of controllable entangling gates between modes to create arbitrary size and shape cluster states with several constraints. The cluster state is assumed linear or square lattice. Only nearest neighbor qubits are entangled. Such a cluster state resource has been proven to be able to perform universal quantum computing if the initial state is large enough.

Description:
PRIORITY CLAIM UNDER 35 U.S.C. §119(e) 
       [0001]    This patent application claims the priority benefit of the filing date of provisional application Ser. No. 61/860,427, having been filed in the United States Patent and Trademark Office on Jul. 13, 2013 and now incorporated by reference herein. 
     
    
     STATEMENT OF GOVERNMENT INTEREST 
       [0002]    The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    A cluster state can be loosely defined as an entangled set of qubits arranged in a lattice. Breigel and Raussendorf strictly define a cluster state as “Let each lattice sight be specified by a d-tuple of (positive or negative) integers aεZ d . Each sight has 2d neighboring sights. If occupied they interact with the qubit a”. This implies a cluster state has interaction between all nearest neighbor qubits. In two dimensions (d=2) this can result in a square grid of qubits, of arbitrary size and shape with each qubit connected to up to 4 of its nearest neighbors. All of the internal qubits will have 4 interactions while the edge qubits will have 1, 2, or 3 interactions. Such a two dimensional nearest neighbor (or square) cluster state has been shown to be universal for computation presuming the cluster state is “large enough”. It is however possible to create custom cluster states designed to implement a single type of algorithm with less qubits. 
         [0004]    Traditional generation of a cluster state consists of an optical table several meters on a side. On this table is a high power laser system such as a pulsed Ti:Sapphire laser. The pump beam is incident on a nonlinear material such as BBO, BiBO or PPKTP etc. The photons from the pump then have a small change to undergo Spontaneous nonlinear Parametric Down Conversion (SPDC) to create an entangle pair of photons, called signal and idler photons. Alternative means of photon generation are equally valid such as Four Wave Mixing (FWM). To create larger clusters the pump passes through multiple nonlinear materials (a cascade) or is reflected back onto it (a multi-pass pass). These methods can create multiple independent pair of qubits. To create one large cluster state the pairs are sent through (i.e. acted on by) a maximally entangling gate. Normally the Controlled Z Gate or “CZ” gate is used. The simplest and most efficient means of implementing the CZ gate requires 3 bulk optical asymmetric beamspliters in a specific alignment. Once all the entangling operations are successfully complete the cluster state is fully constructed and an algorithm can be implemented as a sequence of measurements each on a predetermined qubit. 
         [0005]    Generating cluster states beyond four qubits and one CZ gate represent significant experimental difficulties. The SPDC action is relatively inefficient, especially for generating large numbers of photon pairs. The probability of generating n+1 pairs compared to n pairs is approximately 1/1000. This number varies with setup and nonlinear material but is a useful rule of thumb. Thus it rapidly becomes unlikely that a sufficient number of photons are generated in any one time window. Also the CZ gate itself is probabilistic, with a success rate of 1/9. Thus each entangling operation decreases the rate of successful cluster state construction by nearly an order of magnitude. To generate statistics for large cluster state operations, experimentalists are routinely required to wait minutes even hours between successful cluster state generation events. 
         [0006]    A significant improvement on cluster state generation is possible with on demand photon sources. Such a source emits a single photon or pair of photons at a specified time, eliminating the need for probabilistic photon generation. No such device currently exists. As an approximation to an on demand source, the “photon gun” was recently proposed by Mower Englund (WO2013009946 A1). This device remains probabilistic but has a relatively high probability of producing a single photon at a predetermined time and is in fact intended to be periodic. In other words it will with relatively high probability emit a single photon after time T. The photon gun creates pairs of photons via probabilistic means from time 0 to T−1 and then detects (and thus destroys) the presence of one of those photons to herald the presence of the remaining photon. This heralded photon is then delayed in a variable circuit until time T. The device is nearly periodic because the probability of at least one pair being generated before time T−1 is close to 1. Thus the photon gun sacrifices repetition rate in order to maximize the photon production probability. 
       OBJECTS AND SUMMARY OF THE INVENTION 
       [0007]    Briefly stated, the present invention proposes to combine multiple “photon guns” with integrated tunable circuitry and entangling operations to create a periodic probabilistic 2D photonic cluster state with the additional feature of being having independent control (on/off) of each the entangling operations (i.e. internal interconnections). Given that the number of modes is large enough, the cluster states created by the present invention will be able to perform universal computations. In addition, the control of the internal interconnections allows for the construction of arbitrarily shaped and interconnected cluster states as well as multiple (smaller) cluster states from a single device. These controls will be simple electrical inputs and can be switched at high speed. The resulting device attempts to produce a desired cluster state after every time T CS . We call the present invention a Periodic Cluster State Generator (PCSG). 
         [0008]    A preferred embodiment of the present invention (PCSG) consists of a monolithic Integrated Waveguide (IW) chip consisting of two fundamental operations, photon generation and controllable entanglement. To produce the cluster state at high speeds while minimizing the waveguide length, the waveguide chip must be capable of rapid switching. Electro-optical materials such as Lithium Niobate (LiNbO 3 ), as opposed to slower thermal switching materials, are preferred. Note the present invention will work in materials with slow switching but will have longer delay lines and may need to be larger itself to compensate. The waveguides fabricated within the LiNbO 3  must be polarization maintaining (PM) waveguides as the invention encodes the qubits in the photons polarization. 
         [0009]    The preferred embodiment of the present invention generates photons on the principle of FWM as has been demonstrated in waveguides previously. The invention consists of two input modes. One for each of the two “waves” needed to pump the device. These modes are incident on an integrated two by N splitter based on evanescent coupling, where N is the number of guns in the device. This number, N, has no theoretical upper bound. This element separates the pumps evenly into the N modes in which the four wave mixing takes place. Such a device simplifies the problem of maintaining synchronization between modes that is otherwise difficult if each mode is individually pumped. The photons created will have orthogonal polarizations which can be set to horizontal and vertical. In order to increase the count rate for this probabilistic process the invention has large equal length meanders in each wave guide that increase the interaction time. Note that any device or method that creates photon pairs could be used with trivial modifications to the circuit design. 
         [0010]    In the preferred embodiment the photons in the waveguides are incident on hyper-spectral filters which block the propagation of both pumps. The position of the spectral filtering is not critical to the design and can be performed anywhere in the circuit after the FWM has occurred including at the end of the circuit. To use non-degenerate FWM, this filter would be replaced with a standard wave division multiplexer (WDM) which dumps the pump wavelengths into a mode that exits the IW chip while allowing the signal and idler photons to propagate. Any such device that separates the pump photons from the desired photons is usable in this invention. 
         [0011]    In the preferred embodiment the signal and idler photons travel along another section of waveguide of arbitrary size and shape and are incident on MMI. This MMI acts as a polarization beam splitter and separates the horizontal and vertical photons into two separate modes (any device that accomplishes this goal is equally valid in present invention). One photon (which polarization is used is not relevant) is detected and therefore destroyed. This is done in order to herald the existence of the second photon in the propagating mode. The type of device used to detect the present of this photon is not relevant to the present invention and can be either on the IW or off chip. The preferred embodiment of the present invention will use off chip single photon detectors such as superconducting nanowire single photon detectors or transition edge sensors. Such detectors can be fabricated directly into the IW itself but require &lt;10K (kelvin) temperatures to operate. Thus integrating the detector requires super cooling the entire chip. The preferred embodiment of the present invention operates at room temperature by channeling the heralding photon into an optical fiber which can be routed to any type of single photon detector. As the efficiency of this detector is critical to the devices operation the most efficient available detector is desired. Note that the present invention can be designed to operate with low efficiency detectors and a given pump rate by increasing the number of delay segments (defined below) at the cost of reducing the repetition rate. As the previous section of the present invention creates photons with known orthogonal polarizations and, as all waveguides are polarization maintaining, it is a trivial process to rotate the photons to the H+V, or the “+” state (ignoring normalization) by industry standard devices. This can be done at any point prior to the entangling operations. 
         [0012]    The photon pair generation method and heralding detection method of the present invention is relatively arbitrary in that the invention can be modified to accommodate different designs. Regardless of the photon generation and detection method, the next step of the “photon gun” is critical. See Mower and Englund (WO2013009946 A1). Each pump pulse has a non-unitary (i.e. less the perfect) chance to create a photon pair and the detectors have less than perfect chance of detecting one of these photons. Thus each pulse will not create a photon, in even the most ideal case. Different techniques can be used to improve these probabilities but cannot be made perfect with the current state of the art technology. Thus the “photon gun” is not periodic but probabilistic. The present invention is also probabilistic as it generates photons with period T and success probability approaching one. The critical time bucket T consists of N time bins t such that each bin is synchronized with one and only one pulse form the pump (T=Nt). The number of time bins required is determined such that with very high probability at least one photon pair is produced and heralded in each time bucket T. This is dependent on a large number of factors but can be determined by standard methods. 
         [0013]    The heralded but undetected photon, now in the “+” state, is then delayed in delay lines until it is emitted at time T or T+1. This is achieved through a series of identical delay lines which the heralded photon can be diverted into by rapidly tunable MMIs. The switches that control the photon path and therefor the delay time are controlled by off chip electronics. This device records the detection time of the heralded photon and compares it to the clock time. Thus the off chip electronics can determine in which time bin t p  the photon pair was generated and the needed delay time (T−t p ). Next, the electronic device sets the output ports for the tunable MMIs (i.e. switch directions) to implement the required delay. In the preferred embodiment this is done with industry standard electro optical control. While this calculation and reconfiguring is taking place the photon is stored in a simple waveguide meander consisting of a long spiral in the wave guide. The length of this first delay, Delay A, is determined by the maximum time required to herald and successfully reconfigure the device and, in general, will not be the same (most likely longer) as the time bin delay lines. These steps happen simultaneously in each parallel mode. The result of the first section of the present invention is a periodic (in time) sequence of synchronized arrays of N photons. In other words this first section of present invention creates an un-entangled flowing grid of photons of size N and arbitrary length. The probabilistic nature of the present invention means there will be some holes in the grid where no photon was successfully produced or a photon was lost. 
         [0014]    The photons are then guided to the next section part of the present invention that performs the controllable entanglement on the photon grid. In the preferred embodiment these two sections are both on the same monolithic IW chip. But fabrication may be simpler if the device is fabricated on two (or more) chips. The monolithic WG chip has the advantage of compactness, stability and no losses due to coupling chips into and out of fibers. 
         [0015]    The second section of the Monolithic IW chip in the preferred implementation creates the horizontal entanglement between sequential qubits. This is an application of the sequential entangler of Smith et al. and in fact requires an array of sequential entanglers. In the preferred embodiment the tunable MMI at the end of the “photon gun” serves a dual purpose. In addition to controlling the delay time it also transfers the output photons to one of two modes. In the preferred embodiment the MMI begins by putting the first photon in the “upper” mode. This means that the incident photon exits the MMI in the “upper” mode. Any device that is capable of deterministically switching the output mode of a photon is a viable alternative which doesn&#39;t affect the function of the device. The first photon, arriving in each parallel mode after time T, is then delayed in a waveguide delay line, Delay G, for exactly one period of time T. The MMI is then switched to the “lower” mode before the arrival of the second photon at time 2T by an off chip electric circuit. The maximum repetition rate of the present invention is thus limited by the minimum switching time of the MMIs or any device that replaces it 
         [0016]    The two separate “+” state photons, one in the upper mode and one in the lower mode, are then each incident on another MMI. One output mode of each of these MMIs feeds into the entangling operation. The other leg of each MMI is routed around the entangling operation in a “by pass” mode. This routing operation is implemented in the same manner as previous MMIs and is controlled buy off chip electronics. In the preferred embodiment the entangling operation is performed in the waveguide integrated CZ gate of Crespi et. al (W02012150568A1). This gate is well-known and has been implemented in waveguides. The gate consists of several static evanescent couplers. The current state of the art of entangling operations provides many implementations of this gate and numerous other gates. Any of these gates may be used to create variations of the present invention for custom purposes. The CZ gate has a success probability of 1/9 per instance. Therefore, long chains are increasing unlikely to be successfully created. Thus a high repetition rate is desirable, such that many attempts can be made in a short time. Also any improvement in the success rate of the entangling gate is desirable. The length of the bypass mode is designed such that it is the same as that in the entangling operation. 
         [0017]    The modes from the entangling operation are then merged with the “by pass” modes by additional MMIs. One photon is allowed to propagate while the other is “looped back” into the device to such that it can be entangled with the next photon in the sequence. Thus two photons in sequence in each parallel sequential entangler are entangled or not entangled based on the paired MMIs prior to the CZ operation. Rapid switching gives the capability to “add” or “remove” horizontal entanglement in between any sequential qubits in a cluster state. 
         [0018]    The third photon produced in each mode reaches the sequential entangler while one photon from the first pair is stored in a delay line, Delay H. The length of this delay line is such that these two photons will be synchronized upon reaching the paired MMIs before the CZ gate. The third and all subsequent photons are routed onto the “down” path. Which photon is “looped back” cannot be determined due to the nature of entanglement. Therefore, either mode may be fabricated with the “loop back” feature. 
         [0019]    The photons then exit the parallel set of sequential entanglers in the present invention and enter the final section of the device. This section implements the vertical entangling gates between synchronized qubits in different modes. This section consists of a cascade of entangling operations. In the preferred embodiment these entangling operations are again the CZ gate of Crespi et. al (W02012150568A1). Similar to the last section any entangling operation can be used in place of any or all of the CZ gates for custom purposes. The CZ gates are placed such that each mode interacts with its neighbors, and this condition can be relaxed for specific purposes without material changing the invention. The photons are incident on MMI which, similar to above, have one output routed to the CZ gate and one output routed to a “by pass” line. The MMI are controlled by off chip electronics and rapid switching, (i.e. faster than the photon repetition rate allows for) controlling the placement of vertical entanglement between specific qubits (i.e photons). Delay lines may be used to maintain synchronization of all modes. 
         [0020]    Combining the effect of the controllable MMIs allows for any size and shape cluster state to be created, within the following limits. The square shape of the grid remains, specifically, the maximum size of the grid N is set by the fabrication of the device and in the prefer embodiment only nearest neighbor interactions are possible. Any arbitrary number and shape of connections is then possible by preforming rapid switching of the various paired MMIs which control the “by pass” lines around each individual entangling operation. If all of the CZ operations are used the resulting output (in theory) would be an arbitrarily long flowing grid of entangled qubits, N rows tall. In practice the probabilistic nature of the present invention means that attempting to make larger and larger cluster states and states with more entangling interactions becomes increasingly unlikely. This is also true of any state of the art device and implementation. The high repetition rate possible with the monolithic IW implementation of the present invention allows for many attempts to be made in comparatively short time frames (i.e. a high repetition rate) with excellent stability and limiter coupling losses. Thus, relatively large and complicated cluster states can be made with the present invention that would be impractical with other approaches. 
         [0021]    An alternate embodiment of the present invention for the purpose of MBQC exists. Here rather than outputting the cluster state from the chip, additional hardware is fabricated such that quantum enhanced computation can be performed. Such an alternate formulation can be considered a quantum computer on a single chip. The size of the computation is limited only by the number of output modes the device is fabricated with. A 2 dimensional square nearest neighbor grid has been shown to be a universal resource form MBQC, thus we can say the quantum computer is universal. Note that arbitrarily large calculations will require arbitrarily large cluster states and due to the non-deterministic generation of cluster states in the present invention such arbitrarily large state will take an arbitrarily long time to successfully generate. 
         [0022]    Note that in the preferred implementation, the off chip electronics are broken into three chips each serving its own purpose. “Off chip electronics 1” detects/heralds the presence of photons and reconfigures the delay line circuit. “Off chip electronics 2” controls the placement of the entanglement in the cluster state. “Off chip electronics 3” an alternate embodiment implements the MBQC algorithm of single qubit rotation detection events. These three chips can be combined into a single classical device without altering the details of their operation. In fact combining the off chip electronic into a single circuit will make synchronization simpler. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIG. 1  depicts the full monolithic integrated waveguide based implementation of the present invention with dashed boxes indicating the three sections of the device as described below. 
           [0024]      FIG. 2  depicts the section of the present invention which uses four wave mixing to probabilistically create periodic (in time) photons in each mode. The number of output modes is arbitrary and is depicted here with N=3 modes but not limited to this number of modes. 
           [0025]      FIG. 3  depicts the section of the present invention in which the horizontal entanglement is implemented creating probabilistic linear cluster states in each mode. This section includes the “loop back” and controllable entanglement “by pass” elements. 
           [0026]      FIG. 4  depicts an alternate embodiment of the present invention having additional functional hardware. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0027]    Referring to  FIG. 1 , the present invention (i.e., a Monolithic IW PCSG) is shown with dashed boxes,  10  and  20  indicating the two sections in which different operations are performed (periodic single photon generation  10  and entanglement  20 ). The preferred chip IW  30  is a single large (monolithic) chip of Lithium Niobate (LiNbO 3 ). This material is chosen due to the ability to perform the four wave mixing the present invention uses as a photon source as well as the high switching speed of the electro-optical effect. This allows for faster repetition rates and faster probabilistic cluster state creation than other materials that require carrier injection or thermal switching. 
         [0028]    Referring to  FIG. 2 , shown is the first section  10 , in  FIG. 1  of the monolith IW chip  30 . The inputs to the present invention are two modes  40  each originating from a pump laser. These two pump modes are both incident on a 2 by N splitter  50  that evenly divides the input signal among all of its output modes  60 . In these modes  60  the four wave mixing takes place. The four wave mixing modes  60  each have a large meander  70  or arbitrary shape. The purpose of this meander  70  is to increase the interaction time and therefore the generation rate of the modes. The meanders  70  relative lengths to each other are arbitrarily adjustable and should be set such that the photon pulses in every mode arrive simultaneously at the hyper-spectral filters  80 . This method of generating the spontaneous photons differs from that of Mower and Englund. The hyper-spectral filters  80  block the pump pulse while allowing the degenerate spontaneously generated four wave mixing pairs to propagate. The hyperspectral filter  80  also prevents further four wave mixing in the remainder of the circuit. The degenerate photons created by the four wave mixing are orthogonally polarized with one photon having the same polarization as the two pumps. Thus the two photons can be separated by a simple polarization beam splitter (PBS) or equivalent device  90 . Such a PBS  90  can be implemented in the present invention&#39;s waveguides with simple evanescent couplers. The PBS  90  is represented here as a simple box for simplicity as they are well known devices in the state of the art. 
         [0029]    The outputs of the PBS  90  are two modes each  100  and  110 . One mode  110  from each PBS  90  all carrying the same polarization, the preferred embodiment uses the vertical polarization (this choice is arbitrary), is channeled to an integrated single photon detector  120 . Any type of single photon detector  120  can be used including off chip detectors. Such off chip detectors require channeling the photons into fibers. Such detectors are standard in the industry. 
         [0030]    The output of the detectors  120  is carried by wire  130  to off chip electronics  140 . The time of the detection by any photo-detector  120  event is determined by industry standard off chip electronics  140 . The off chip electronics  140  will be provided with a clock signal  150  produced by standard pump laser systems. The purpose of the off chip electronics  140  is to measure the time bin (t) at which each photon arrives and to modify the circuit such that each photon is delay until the end of the time bucket (T) as discussed above. 
         [0031]    The horizontal photon from each PBS  90  in each mode  100  is each routed to a polarization controller  160  which rotates the state to the |+&gt; state. The polarization controller  160  is shown as a static device as the input polarization is assumed to be constant. If this is not the case a variable device can be trivially substituted. Note that the polarization rotation need not occur at this exact point in the circuit but be implemented anywhere after the filter  80  and before the entangling operations begin in second section  20  of the present invention. 
         [0032]    The photon is the routed by waveguide  100  to a long waveguide meander  170  of arbitrary geometry, shown here as a spiral. Any device which implements a set delay, such as but not limited to toroidal resonators, fiber delay lines and cold atomic gas cells, may be trivially substituted for any delay meander in this device. The purpose of delay  170  is to store one photon from each pair while the second is being detected and the arrays of tunable MMIs are modified. 
         [0033]    The MMI  180  is a standard state of the art device and as such is not shown in detail. In LiNbO 3  of the monolithic IW  30  the MMI  180  is an electro-optically tuned device. An electrode induces a change in index due to an applied voltage (electro-optical effect). This is indicated with logical control lines  190  from the off chip electronics  140  each of which terminate at a unique MMI  180 . The MMIs  180  act as independent switches which depending upon the induced index change can diver a photon in any input mode to any output mode. Control over each MMI  180  individually is required for the device as the probabilistic photons in each mode will arrive at different time bins (t) and need different delay meander lengths  200  through  230 . Each MMI  180  has one output that routes directly to the next MMI  180  (zero delay) and one mode that forms a delay meander  200  though  230 . The length of each delay is a multiple of the pump period t. Each meander is twice the length of the previous with the first delay meander  200  being a delay oft. Thus one pass through any set of delays  210  retards the photon by a controllable time from 0 up to T. Thus the first section  10  of the present invention creates a periodic array of photons every time T. The delays meanders  200  through  230  are shown as 4 delays giving a maximum delay of 15t. The number of delay meanders  200  through  230  is arbitrary and only affects the periodicity of the device. 
         [0034]    The final MMI  240  in each mode has two outputs  250  and  260 . The MMIs  240  complete the first section of the device. At this point, the output of the MMI  240  are photon that are (ideally) periodically spaced and still synchronized such that one photon is emitted into the modes  250  and  260  every time T. Given the probabilistic nature of the present invention, the case in which a given mode MMI  140  does not produce one and only one photon at time T can be minimized but not avoided. This is due to effects including but not limited to photon loss and detector inefficiency. 
         [0035]      FIG. 3  shows the second section  20  of the present invention in the preferred embodiment. This section of the present invention probabilistically creates entanglement between sequential periodic photons in each mode and then creates entanglement between neighboring modes. 
         [0036]    MMI  240  acts as a switch between its output modes  250  and  260 . It is the same type of device as in the previous section of the present invention described in the description of  FIG. 1 . 
         [0037]    When the first set of photons enters this section  20  of the present invention, the MMIs  240  are set to divert the photon into the “upper” mode  250  and the array of photons are each sent into respective delay lines  270 . After this the MMI  240  is switched to the “lower” output mode  260 . The length of the delays  270  is set such that they are all exactly (i.e. well within one time bin t of the detector) the period T of the photon generator in the previous section  10  of the present invention. Thus when the first photon exits the delay line  270  it is synchronized (i.e. in parallel) with the second photon which has arrived from section  10  and passed through MMI  240 . The upper photon then passes through MMI  280  such that it exits the only utilized port, the path length of the lower mode  260  should be adjusted during fabrication to compensate for any difference in transit times due to the MMI  280 . MMI  280  is controlled by logical control lines  290 . 
         [0038]    The two photons are then simultaneously incident on pairs of MMIs  300 . These pairs of MMIs work together to either direct both photons into the entangling operation  310  or to direct both photons into the “by pass lines”  320 . This ability to choice the route of the photons (in advance or dynamically) allows for the probabilistic construction of arbitrary interconnected cluster states (i.e. cluster states up to a set size and shape) and is controlled by the off chip electronics  330  via control lines  340  and synchronized by the same clock signal  150  as in section  10 . Note that the length of the “by pass” lines  320  should be set such that the travel time of both paths (“by pass”  320  and entangling  310 ) are the same. The entangling operation in our preferred embodiment is the CZ gate of Crespi et. al. This gate is implemented in waveguides as several fixed evanescent couplers. The gate is probabilistic with a success rate of 1/9 and requires 4 modes 2 of which enter as vacuum. See Crespi et. al (W02012150568A1) for details. 
         [0039]    In the preferred embodiment, after passing through either the entangling operation  310  or the “by pass” lines  320  the synchronized photons enter the second paired MMIs. MMI  350  is in the upper path. MMI  360  is in the lower path. These MMIs are also controlled by the logical control lines  340 . MMI  360  acts to feed the input photons to MMI  370 . MMI  350  is more important as it takes input photons and feeds them into the “loop back” feature  380  or to the MMI  370 . 
         [0040]    A successful application of the CZ gate will produce one photon in each output and thus one photon in both MMIs  350  and  360  (equivalently use of the “bypass” lines”  320  will do the same). MMI  350  then feeds one photon into the loopback line  380 . The other photon is channeled into MMI  370 . 
         [0041]    The loop back  380  is in essence a delay line and may require a meander  390 . The photon in this mode then enters MMI  280  which has been “switched” by the electronics  290  and  330  such that it exits the only viable port. The length of  380 ,  390  and  280  are adjusted during fabrication such the a photon that enters  380  will exit MMI  280  and be incident on MMI  300  at the same time that the next photon in the sequence produce in section  10  reaches MMI  300 . In other words the delayed photon is held for one period until it is synchronized with the next photon in the sequence. Thus the CZ gate  310  which acts on simultaneously incident qubits is made to act on sequential qubits in each “single” mode. 
         [0042]    This process then repeats to create a chain of arbitrary length (assuming the CZ gate succeeds each time). When the entangled chain reaches the desired length, several things happen to terminate the chain. The last photon in the chain is sent into the loop back line  380  one last time. The MMIs  300  are set to the “by pass” path and MMI  350  is switched to the “down” path to MMI  370 . At the same time MMI  240  is set to “up” sending the next incident photon to delay line  270 . This allows the last photon in an arbitrary chain to leave this section of the device, creates a guaranteed break in the cluster state and it also effectively resets the device. Recall that the first step in creating the chain was to send photons to delay line  270  via MMI  240 . 
         [0043]    MMI  370 , which is controlled by logical control line  400  and clock signal  150 , acts as a switch similar to MMIs  300 . MMI  380  switches the photons either into the entangling operation  410  or to the “by pass” lines  420 . The order of the entangling operations  410  between neighboring modes is completely arbitrary if CZ gates are used, as in the preferred embodiment. The number of modes will determine the number of entangling operations  410  and the number of “internal” MMIs such as MMI  430 . Each entangling operations  410  has a pair MMIs preceding and following it such that each entangling operation can be independently “by passed”. The photons then exit the final MMIs  440  in each mode and exit the chip  30  via output mode  450 . 
         [0044]    The ability to rapidly switch the MMIs  370 ,  430  and  440  gives the PCSG the ability to turn the entangling operation between modes on or off arbitrarily. Combined with the ability to control the entanglement in the chains themselves (via  300  and  340  and  350 ) the PCSG can create and arbitrary size cluster state (up to the fabricated number of modes, which itself is arbitrary) with arbitrary and controlled interconnections. Thus it is a device with versatile output that can be used in a large array of applications, Including but not limited to Measurement Based Quantum Computing (MBQC), Quantum Key Distribution (QKD) and various communication protocols. 
         [0045]      FIG. 4  gives an alternate formulation of this device for the purpose of MBQC. This formulation includes all aspects of the PCSG however rather than releasing the photons after via mode  450  in section  20 , shown in  FIG. 3 , additional hardware is implemented. All of the elements in  FIG. 3  are repeated in  FIG. 4  except that mode  450  no longer exits the chip. To perform computations in the style of MBQC, each qubit in the cluster state generated by the PCSG is measured in a prescribed basis. This is accomplished by rotating each qubit individually in the Z basis and then detecting photons in either the |+&gt; or |−&gt; state. Different arrangements of the entanglement and different measurement angles will produce different computations. 
         [0046]    In  FIG. 4  mode  450  channels the photons to arbitrary polarization controllers  460 . The polarization controllers are themselves set by off chip electronics  470  and logical control lines  480 . After being rotated by polarization controllers  460  the photons are incident on polarization beam splitters  490  set for the +/− basis. The photons are then separated into + and − in two modes which can be detected with standard integrated single photon detectors  500 , similar to  120  in  FIG. 2 . One photon will activate one of each pair of detectors  500 . This can be used as a post selection condition to be certain that the generation, entanglement and measurement of the photons occurred successfully. The output  510  of the detectors  500  is recorded for each qubit by the off chip electronics. This set of information (i.e. the result of the rotated +/− measurement) is required for applying post process correction require by the MBQC formulism. Such corrections consist of single qubit rotations and could be physically implemented to the output qubits of the cluster state. In the preferred embodiment these corrections will be applied by software after the measurement of the output state. This simplifies the device and reduces the number of rotations that need to be implemented on the output qubits. 
         [0047]    Having described preferred embodiments of the invention with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention as defined in the appended claims.