Abstract:
An apparatus providing an integrated waveguide device that creates entanglement between a symmetrical sequence of periodically spaced (in time) photons in a single input and output mode. The invention comprises a polarization maintaining integrated waveguide chip containing a number of delay lines, integrated multimode interferometers with the potential for rapid switching, a polarization controller and off chip computer logic and timing.

Description:
PRIORITY CLAIM UNDER 35 U.S.C. §119(e) 
     This patent application claims the priority benefit of the filing date of provisional application Ser. No. 61/857,710, having been filed in the United States Patent and Trademark Office on Jul. 24, 2013 and now incorporated by reference herein. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     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 
     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 site be specified by a d-tuple of (positive or negative) integers a εZ d . Each sight has 2 d neighboring sites. If occupied, they interact with the qubit a”. This implies a cluster state has interaction between all nearest neighbor qubits. In one dimension (d=1) this results in a linear chain of qubits, of arbitrary length with each qubit entangled with both of its nearest neighbors. All of the internal qubits will have two interactions while the edge qubits will have one. Such a one dimensional nearest neighbor cluster state has been shown to be amenable to several applications for computation presuming the cluster state is “long enough”. 
     Traditional generation of a cluster state consists of an optical table several meters on each 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 chance to undergo industry standard Spontaneous Nonlinear Parametric Down Conversion (SPDC) to create an entangled pair of photons, called signal and idler photons. Alternative means of photon generation are equally valid such as but not limited to four wave mixing (FWM). To create larger cluster states the pump passes through multiple nonlinear materials (a cascade configuration) or is reflected back onto the original material (a multi-pass configuration). These methods can create multiple simultaneous independent pairs of qubits. To create one large cluster state the pairs are sent through (i.e. acted on by) an entangling operation. Normally the industry standard two qubit entangling gate controlled phase gate (CPhase) or controlled Z gate (CZ) is used. The simplest and most efficient means of implementing the general CZ gate requires 3 bulk optical asymmetric beam splitters in a specific alignment. These operations are effectively performed in parallel with each qubit entering and exiting in its own mode. Once all the entangling operations are successfully completed the cluster state is fully constructed and an algorithm can be implemented as a sequence of single qubit rotations and measurements on each qubit in a predetermined sequence. Thus in the state of the art, linear cluster states are created from simultaneously generated qubits in parallel modes rather than from sequential qubits in a single mode. This is mainly due to the spontaneous nature of single photon sources. It is impossible to predict the time between two subsequent spontaneous events. 
     The present invention builds upon the periodic photons source of Mower and Englund (WO2013009946 A1) to create entanglement between sequential separable qubits delivered in a single mode and create a linear cluster state of sequential qubits which is output in a single mode. Such a device is of interest in and of itself for quantum computing. Applications include but are not limited to Measurement Based Quantum Computing (MBQC) implementation of the Deutsch-Jozsa algorithm on a four qubit chain, arbitrary single qubit rotations on a four qubit chain, quantum key distribution, quantum information, quantum metrology and quantum lithography. 
     OBJECTS AND SUMMARY OF THE INVENTION 
     Briefly stated, the present invention (the Sequential Entangler or S.E.) combines reconfigurable optical Integrated Waveguides (IW) with a periodic photon input to create linear cluster states in a single mode. 
     The present invention creates the entanglement of sequential qubits by using a unique “loop back” architecture that delays one photon for one period T of the sequence thus allowing for two photons to be acted on by a standard entangling element; which, in the present invention uses the simple polarization encoded CZ gate of Crespi et. al (WO2012150568A1). After the CZ gate one photon (now entangled so which cannot be distinguished) is then released and the second is looped back to coincide with the arrival of the next photon and so on. This will probabilistically produce a linear cluster state. The term probabilistically as the state of the art CZ gate has a one in nine ( 1/9) success rate. Thus the longer a desired cluster state is the less likely it is to be created in any one attempt. This is a result of the entangling operation and not the S.E. per say as no photonic entangling operation can be performed with unit success. The present invention will create a cluster state numerically identical to the industry standard parallel method but arranges the qubits as a periodic sequence (with a constant period T) in a single optical mode. Any two qubit entangling operation can be used in place of the CZ however such gates may produce different cluster states. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       It is noted that all figures are schematic and are said to be “not to scale”. 
         FIG. 1  depicts the preferred embodiment of the present invention, i.e., full reconfigurable monolithic integrated waveguide based Symmetrical Sequential Entangler (S.E.) with one input mode and one output mode with labeled features. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A sequence of periodic photons created by any means enter the integrated waveguide chip  10  in  FIG. 1  via the input port  20 , The integrated waveguide may be made from any of a number of materials. In our preferred embodiment we will use Lithium Niobate (LiNbO 3 ) as the waveguide material. The input port  20  is a polarization maintaining optical waveguide fabricated in the LiNbO 3  chip  10 . Polarization maintaining waveguides are required as we chose to encode our qubits in the polarization modes of each photon. Thus the resource of periodic photons must also be in a known polarization state. It is then trivial to rotate the input state polarization state to any desired state via a polarization controller  30 . The preferred embodiment of the present invention uses integrated waveguide based polarization controllers  30  which function via the electro-optical effect. The preferred embodiment of the present invention utilizes the Pockels effect which is innate to lithium niobate. Such rotations could take place prior to the photons entering the chip but for generality and controllability we rotate the polarizations on chip. In the preferred embodiment the invention rotates the incoming photons at  30  to the plus state (equal superposition of horizontal and vertical polarization, H+V up to normalizations). The photons then enter the first of several multimode interferometers (MMI)  40 . All such interferometers are integrated on chip  10  and consist of a multimode slab of the waveguide material similar to that described by Soldano and Pennings (J. of Lightwave Tech. Vol. 13 No. 4, 1995). The switching and coupling effect of such MMI&#39;s  40  is depended on their geometry and the index change induced via the electro-optic effect. The fabrication and operation of MMIs is well known in the state of the art. In the preferred embodiment the MMIs act as high speed spatial mode switches that route photons from a specific input mode to a specific output mode. In the preferred embodiment there are several species of MMIs (such as 1 by 2, 2 by 2 and 2 by 1 MMIs in terms of the number of input and output modes) however it is noted that the device could be trivially redesigned with a single species of 2×2 MMI in which unused ports are bulk terminated. MMI  40  switches input photons from mode  20  to modes  60  or  70 . In other words the MMI  40  will be controllable such that a photon entering in input mode  20  can be deterministically routed to either waveguide  60  or  70 . Such MMI switches are well known in the state of the art. The control element is therefore shown as a logical connection  80  and its setting is determined by off chip electronics  90 . To achieve proper synchronization with the periodic input source a clock signal  100  must be sent to the device. In the preferred embodiment the high speed electro-optical effect (&gt;40 GHz) is used to modify the index within each of the MMI. 
     Now two photons which were sequential in time are now synchronized in time on the chip  10 . This allows for industry standard two qubit entangling operations to be implemented. 
     The photons now propagate along two parallel waveguides, the “upper”  60  waveguide and the “lower” waveguide  70 . Here and below “upper” and “lower” are used only in reference to the appearance of the schematic  FIG. 1  and not to a design element. The photons in these waveguides  60  and  70  then enter two parallel MMIs  120 . These MMIs  120  effectively control whether or not the entangling operation  130  (contained in the dashed box) is implemented. In the preferred embodiment of the present invention the MMIs  120  can be set to either pass the photons to the entangling operation  130  or to divert them around the entangling operation  130  via bypass lines  140 . The preferred embodiment uses bypass lines  140  because the entangling gate  130  chosen for our preferred embodiment is the CZ gate as described by A. Crespi (WO2012150568 A1). This is a static operation thus to “turn off” the interaction the photons must be routed around it. The length of the bypass  140  lines is such that they are the same length as the paths in the CZ gate  130  and as such synchronization is maintained. The MMIs  120  are controlled by the off chip electronics  90  via control lines  150 . In the preferred embodiment this control is implemented similarly to that of 40. If the MMIs  120  are “on” then both photons enter the CZ gate  130  at the same time and may become entangled. If the switches are “oft” the photons remain separable after passing through the “bypass” lines  140 . This operation is performed in tandem thus we refer to them as paired. Note that the CZ gate has a success rate of one in nine ( 1/9) and requires two vacuum modes. Should the CZ gate  130  succeed or the photons be diverted to the bypass lines  140  they will then each enter another MMI. The “upper” MMI  160  will divert the photon into the loop back mode  170 . The “lower” MMI  180  will divert its photon into the loop back mode  240 . The MMI  160  and  180  are controlled by 90 via logical control line  210 . MMI  190  is controlled by 90 via logical control line  220 . 
     The photon in the loopback mode  170  will be delayed in delay line  230 . The photon in loopback mode  240  will be delayed in delay line  250 . The third (and all subsequent) photons that enter the chip  10  in mode  20  are rotated to the correct input polarization by 30. Delay lines  230  and  250  are carefully fabricated such that the photons they each hold are released at the appropriate time such that the two photons are synchronized similar to the way the first two photons were synchronized. In other words, the two “looped back” photons again reach the pair of MMI&#39;s  120  at the same time. 
     As already described, the present invention features loop backs on both the “upper” and “lower” modes. This allows for shorter meander delay lines which may ease fabrication. Both MMIs  120  as well as MMI  160  and  180  are preferably 2×2 MMIs. The significant additions in the present invention are the first and second loop back modes  170 ,  240  and corresponding delays  230 ,  250 . The invention operates in the following manner. The first photon in the chain is routed up by MMI  40 , then around the CZ gate  130  by MMI  120  and then into the upper loop back mode  170  by MMI  160 . The length of this path, particularly the delay  230 , is fabricated such that it is a delay of exactly 1 period T of the input. The second (and all subsequent) photon is diverted to the “lower” mode. Due to delay of the first photon both photons are simultaneously incident on the paired MMIs  120 . The device proceeds as above. 
     The procedure to terminate a linear cluster state at a given length is different in this instance. Given that a cluster state has been completed (i.e. every CZ  130  is successful) and there are now two photons on each in MMIs  160  and  180 . To extract the last two photons the following steps occur. One photon is “looped” back via one of the loop back modes  170  or  240 . The other is channeled to MMI  190  and out of the chip  10  via mode  200 . If there are no additional photons sent to the device then MMIs  120 ,  160  or  180  and  190  can channel the last photon out of the device after delay T. However if the input is an arbitrarily long sequence of photons then when the nth photon reaches MMI  120  the n+1th photon in the sequence will also reach MMI  120  in the other mode. After the bypass mode the two photons will be in MMI  160  and  180 . The n th  and final photon in the cluster state is diverted to MMI  190  and out of the chip  10  via  200 . The other is looped back in the other (currently unused) “loop” back mode  170  or  240 . This allows the first chain to exit the device unperturbed and effectively resets the device as the N+1th photon will be synchronized at MMI  120  with the arrival of the n+2nd photon. The n+2nd photon will be diverted into the other mode and the device operation repeats. Thus a second chain can be started without losing any of the input photons. 
     Having described preferred embodiments of the invention with reference to the accompanying drawing, 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.