Quantum Photonic Interconnect

Integrated photonics has enabled much progress towards quantum technologies. Many applications, including quantum communication, sensing, and distributed and cloud quantum computing, will require coherent photonic interconnection between separate chip-based sub-systems. Large-scale quantum computing systems and architectures may ultimately require quantum interconnects to enable scaling beyond the limits of a single wafer and towards"multi-chip"systems. However, coherently interconnecting separate chips is challenging due to the fragility of these quantum states and the demanding challenges of transmitting photons in at least two media within a single coherent system. Distribution and manipulation of qubit entanglement between multiple devices is one of the most stringent requirements of the interconnected system. Here, we report a quantum photonic interconnect demonstrating high-fidelity entanglement distribution and manipulation between two separate chips, implemented using state-of-the-art silicon photonics. Path-entangled states are generated and manipulated on-chip, and distributed between the chips by interconverting between path-encoding and polarisation-encoding. We use integrated state analysers to confirm a Bell-type violation of $S$=2.638+-0.039 between two chips. With improvements in loss, this quantum interconnect will provide new levels of flexible systems and architectures for quantum technologies.

Integrated photonics has enabled much progress towards quantum technologies. Many applications, including quantum communication, sensing, and distributed and cloud quantum computing, will require coherent photonic interconnection between separate chip-based subsystems. Large-scale quantum computing systems and architectures may ultimately require quantum interconnects to enable scaling beyond the limits of a single wafer and towards "multi-chip" systems. However, coherently interconnecting separate chips is challenging due to the fragility of these quantum states and the demanding challenges of transmitting photons in at least two media within a single coherent system. Distribution and manipulation of qubit entanglement between multiple devices is one of the most stringent requirements of the interconnected system. Here, we report a quantum photonic interconnect demonstrating high-fidelity entanglement distribution and manipulation between two separate chips, implemented using state-of-the-art silicon photonics. Path-entangled states are generated and manipulated on-chip, and distributed between the chips by interconverting between pathencoding and polarisation-encoding. We use integrated state analysers to confirm a Bell-type violation of S=2.638±0.039 between two chips. With improvements in loss, this quantum interconnect will provide new levels of flexible systems and architectures for quantum technologies.
Further progress towards quantum communication 1,2 , sensing 3 and computing 4,5 will greatly benefit from a "quantum photonic interconnect": an inter-/intra-chip linke.g. in optical-fibre or free-space-capable of coherently distributing quantum information and entanglement between on-chip sub-systems within a single complete quantum system. The significance of quantum interconnect was first highlighted by Kimble 1 , and here we study a chip-based interconnect solution, which will be essential in many future applications and provide substantial architectural flexibility. Secure quantum key distribution and quantum communication [6][7][8] , and distributed ad cloud quantum computing 9-11 require interconnected on-chip subsystems for practical implementations. Precise quantum sensing will gain flexibility and versatility from on-chip generation and detection of entanglement, with the interaction with sample performed in a different media or location, e.g., chip, optical fiber and free space [12][13][14] . Quantum computing will benefit from quantum interconnects through architectural simplifications [15][16][17] ; easier integration of materials and platforms optimised for source 18,19 , circuit 20-25 , detector 26,27 and many others 28,29 performance; and the inclusion of offchip optical delays or memories. Ultimately, large-scale integrated quantum systems may even exceed the area of a single wafer or require interconnects for architectural reasons.
A quantum photonic interconnect must maintain coherent transmission of the qubit state α |0 + β |1 between subsystems; a significant difference compared to the classi-cal optical interconnect in which transmitted state are either 0 or 1, and in which the relative phase is not maintained 30 . The quantum interconnect must also be capable of coherently interconverting between the preferred encodings in the platforms and media through which it connects 1,31 . Perhaps, the most demanding requirement for an interconnect is the preservation of high-fidelity entanglement throughout any manipulation, interconversion and transmission processes within the full system. Distributing entanglement 32 between integrated chips is a key requirement and a major technical challenge due to the highly fragile nature of entanglement and the potential for decoherence of quantum states transmitted between different chips. Path-encoding 20-24 -a photon across two waveguides-is a natural choice of robust on-chip encoding for quantum information processing, however, polarisation 6-10 , spatial-mode 33,34 , or time-bin 35 encoding is typically more suitable in fibre and free space for quantum information transmission and distribution. Already there have been demonstrations of important features of quantum interconnect components, including onchip entanglement generation and manipulation [20][21][22][23][24][25]36,37 , photon detection 26,27 , interfacing of light's different degrees of freedom [38][39][40] , and multi-chip links 28,29 . However, to date there has been no demonstration of a complete quantum photonic interconnect system capable of coherently distributing and manipulating qubit entanglement across two or more integrated quantum circuits.
Here, we demonstrate a high-fidelity quantum photonic interconnect. Telecom-band entangled photons are gener-arXiv:1508.03214v2 [quant-ph] 26 Sep 2015 Figure 1: Quantum photonic interconnect and entanglement distribution between two integrated Si photonic chips. a, Chip-A comprises path-entangled states generation, arbitrary projective measurement A(θAZ , θAY ), and path/polarisation conversion (PPC). b, Chip-B includes a projective measurement B(θBZ , θBY ) and PPC. On the chip-A, signal-idler photon-pairs are created in the spiralled waveguide single-photon source. Bell states |Φ ± are produced when θSS is controlled to be π/2 or π. Idler qubit initially encoded in path are coherently coupled to polarisation-encoding and transmitted through a 10m single-mode optical fibre (SMF), and reversely converted back to path-encoding on the chip-B. Signal qubit is analysed using A(θAZ , θAY ) on chip-A and idler qubit is analysed using B(θBZ , θBY ) on chip-B. The 2D grating coupler, behaving as the path/polarisation converter (PPC), is used to coherently interconvert photonic qubit between polarisation and path-encoding. Optical microscopy images of, c, the photon-pair source, d, the arbitrary state analyser (Inset shows the MMI splitter), and e, the 2D grating coupler PPC structure. ated, manipulated and distributed between two integrated silicon photonic chips linked by an optical-fibre. These chips were fabricated using state-of-the-art technologies from silicon photonics to enable and monolithically integrate all of the capabilities required for the quantum interconnect. Path-entangled Bell states are generated and manipulated on-chip. These entangled-states are distributed across two chips, by transmitting one qubit from one chip to the other via the fibre. Coherence is preserved by interconverting between path-encoding on chips and polarisation-encoding in fibre using a two-dimensional grating coupler 38 . Each qubit is analysed in the respective chips using thermal phase shifters to form integrated state analysers. We show a highfidelity interconversion from path-encoding on one chip to polarisation-encoding within the fibre, and back to pathencoding on the second chip. We implement a rigorous test of entanglement-confirming a strong Bell-type inequality violation of 16.4σ or 15.3σ-and demonstrate the quantum interconnect. Together with further improvement in loss, this approach will provide new quantum technologies and applications that rely on or benefit from quantum photonic interconnects. Figure 1 shows the schematics of a chip-to-chip quantum photonic interconnect, generating path-entangled states on chip-A and coherently distributing one entangled qubit to chip-B, via a 10m single mode optical fibre link. Chip-A and chip-B respectively have an effective footprint of 1.2×0.5 mm 2 and 0.3×0.05 mm 2 . On chip-A, a signal (λ s ∼1550.7 nm) and idler (λ i ∼1560.3 nm) photon pair is generated via the elastic scattering of two photons from a bright continuous-wave pump field (λ p ∼1555.5 nm) inside 2cm spiralled waveguide sources (Fig.1c), by using the spon-taneous four-wave-mixing (SFWM) nonlinear effect 19 . The pump is split across two sources using a multimode interference (MMI) beam splitter with a near 50/50 splitting ratio 41 (Fig.1d). The photon pairs are produced in either the top or bottom waveguides, yielding a photon-number entangled state 22 as (|1 where θ SS is a thermally-controlled phase after the sources. These photons are probabilistically separated by two demultiplexing MMIs and post-selected by two off-chip filters, producing the maximally path-entangled Bell states with a 25% success probability, when θ SS equals to (n + 1/2)π or nπ for an integer n. Subscript s and i represent the logical states of signal and idler qubits (more details see Supplementary Information). Then, we use an on-chip path/polarisation converter (PPC) to coherently interconvert the idler qubit between its path and polarisation-encoding. On chip-A, path-encoded qubit is converted to polarisation-encoded before transmitting across the fibre. Chip-B reverses this process, converting the polarisation-encoded qubit back to on-chip pathencoded qubit, by using a PPC. This PPC enables entanglement preservation throughout the chip and fibre platforms. Signal and idler qubits are manipulated and measured independently on two chips using arbitrary single qubit measurement stages A(θ AZ , θ AY ) and B(θ BZ , θ BY ), which physically consists of an on-chip Mach-Zehnder interferometer with an additional thermal phase shifter (Fig.1d).
We first discuss the coherent interconversion of path and polarisation-encoding by using the PPC. In silicon quantum photonics, transverse-electric (TE) mode is usually in use, owing to its stronger waveguide confinement and consequently enhanced SFWM effect 36 . Thus, produced photons must be guided in TE-modes, which is easily achieved by injecting pump light in this mode using a 1D TE-grating coupler. Our PPC is implemented using a 2D grating coupler (Fig.1e), where TE-polarised light coming from two nearly orthogonal waveguides is combined into two orthogonal polarised components of light 37,38 . In this way, the polarisation states of photons received by the fibre is determined by the two-waveguide on-chip states, and vice versa. This provides a coherent interconversion between path-encoding and polarisation-encoding. Details are provided in the Methods and SI. To confirm the PPC coherent mapping, we prepared arbitrary bright-light polarisation states using bulk optical components and coupled them into the on-chip receiver (Fig.2a). The 2D grating coupler converted the polarisation states into path-encoded states, which were then analysed on-chip by implementing a full state tomography 31 . We prepared a set of six polarisation states ρ pol , and measured the corresponding on-chip path states ρ path ; these states are shown as Bloch (or Poincare) vectors in Figures  2b and 2c, respectively. The distance between the states can be described by the state fidelity, which is defined as The mean fidelity of the six measured states is 98.82±0.73%. An example of a reconstructed density matrix for the path-encoded state |+ is shown in Fig. 2d (full data are provided in Fig.S5). Then, we fully quantified the PPC process using a quantum process tomography 31 . This is mathematically described by a process matrix χ, defined by ρ path = mn (E m ρ pol E † n χ mn ), where E i are the Identity matrix I and Pauli matrices X, Y, and Z, respectively. By subjecting the ρ pol states into the PPC and measuring the ρ path states, we determined the process matrix χ of the PPC, shown in Fig.2e. We find a high process fidelity of 98.24±0.82%, defined as F process = T r[χ ideal · χ], where χ ideal is the ideal process matrix with χ ideal [I, I] = 1. X, Y, and Z amplitudes of the measured matrix χ represent the probability of a bit-flip or phase-flip error on the PPC interconversion.
A ∼50 mW CW pump was injected into on-chip sources to create photon pairs. Photons were detected using two superconducting nanowire single-photon detectors (SNSPDs) with ∼50% efficiencies and ∼800 Hz dark counts. Coincidences were recorded using a time interval analyser. After the chip-A, a mean rate of 500−800 Hz photon pairs was observed, while after the two chips we obtained 8−12 Hz mean coincidences. The pump light propagates collinearly with single photons, and this allows a closed feedback loop to track photons and monitor state stability throughout the chip-to-chip quantum interconnect system. Details are provided in the Methods and SI.
We next configured chip-A to produce entangled states. Signal and idler photons were respectively collected at ports D1 and D2 of the chip-A, and routed to SNSPDs. Continually scanning θ SS , we observed the λ-classical interference and λ/2-quantum interference fringes with a visibility (V = 1 − N min /N max ) of 99.99±0.01% and 99.36±0.17%, respectively (Fig. 3a). The high visibility of this double-frequency fringe is a signature of high-quality photon-number entanglement produced inside the chip-A 12,21 . The high visibilities arise from well-balanced MMI splitters 41 and a good spectral overlap between two photon-pair sources 22,23 . Then, the photon-number entangled state evolves into the path-entangled Bell states, |Φ + or |Φ − , by setting θ SS to Figure 2: Interconversion between polarisation-encoding and path-encoding. a, Initial arbitrary polarisation-encoded states α|H + β|V (|H and |V are two orthogonally polarisedstates) were prepared by using a set of polariser (P), half-wave plate (HWP) and quarter-wave plate (QWP). A fibre polarisation controller was used to compensate polarisation rotation in the fibre. The PPC converted polarisation states into pathencoded states α|0 + β|1 , where |0 and |1 denote path states in two waveguides. The path-encoded states were analysed using B(θBZ , θBY ) to implement state tomography. b and c, the Bloch sphere representation of ideal polarisation-encoded states {|H , |V , |D , |A , |R , |L } in bulk optics, and measured pathencoded states {|0 , |1 , |+ , |− , | + i , | − i } on chip. Indicated fidelity represents the mean over all six states. d, Reconstructed density matrix of the |+ path-encoded state corresponding to the |D polarisation-encoded state. e, Reconstructed process matrix χ of the PPC using the quantum process tomography. π/2 or π. The entangled-qubits were separated and coherently distributed across chip-A and chip-B using the PPC interconversion. We measured correlation fringes across the two chips, by collecting signal photons at port D1 on chip-A and idler photons at port D3 on chip-B, and simultaneously operating A(θ AZ , θ AY ) and B(θ BZ , θ BY ) on two chips. Figures 3b and 3c show the entanglement correlation fringes for the Bell states |Φ + and |Φ − as a rotation of θ BY on chip-B, with θ AY on chip-A set at {0, π/2, π, 3π/2}. These results are in good agreement with their theoretical predictions of cos 2 [(θ AY − θ BY )/2] and cos 2 [(θ AY + θ BY )/2] 42 . The fringes exhibit a mean visibility of 97.63±0.39% and 96.85±0.51%, respectively, which is far beyond the critical visibility required of 1/ √ 2 to violate the Bell inequality 43 . We now have shown that a very high-quality entanglement is produced on the chip-A, and distributed over the fibre to the chip-B, coherently interconnecting the two chips.
To more strictly verify the existence of entanglement across the two chips, we directly measured the Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality 44 , defined as: where A i and B i briefly denote the projectors A(0, θ AY ) and B(0, θ BY ) on the two chips. Correlation coefficients A i , B i were measured, when θ AY on chip-A was set to {0, π/2} and θ BY on chip-B was set to {π/4, 3π/4}. Full data of A i , B i is provided in Fig.S6. Using equation (1), we obtained the directly measured S CHSH parameters of 2.638±0.039 and 2.628±0.041 for the two Bell states |Φ + and |Φ − , respectively. These S CHSH violate the Bell-CHSH inequality by 16.4 and 15.3 standard deviations, strongly confirming that the two photons after distributed across chip-A and chip-B are highly entangled, and therefore verifying a high-quality quantum photonic interconnect between two chips. In addition, we estimate the maximally achievable S f ringe parameters of 2.761±0.011 and 2.739±0.015 for the |Φ + and |Φ − states, from the mean visibility of the correlation fringes (shown in Fig.3) according to S f ringe = 2 √ 2V 43 . Figure  4 illustrates a good agreement of the S CHSH and S f ringe parameters.
We demonstrate high-fidelity entanglement generation, manipulation, interconversion, distribution and measurement across two separate integrated photonic circuits, successfully demonstrating the first chip-to-chip quantum photonic interconnect. Path-polarization interconversion preserves quantum coherence across the full interconnected chip-fiber-chip system, demonstrating beyond single-chip implementation of a quantum photonic experiment. The efficiency of this interconversion process can be further improved by engineering the geometry of grating coupler or utilising other polarisation control techniques 39,45 . Other interconversion approaches, e.g., path-orbital angular momentum 46,47 or path-time bins 48 may further enrich this quantum photonic interconnectivity. The use of siliconallowing large-scale integration 49 and compatibility with microelectronics and telecommunications infrastructure 30,50 , benefiting from the classical optical interconnect technology on silicon 30,39 , and also offering ability to monolithically integrate photon source 19,22 , circuit 23,41 and detector 26,27would position this quantum photonic interconnect technology at the heart of building practical, robust and scalable silicon-based quantum hardware for future and networks. This work opens the door to multi-chip integrated quantum photonic technologies, which would be capable of processing quantum information on extremely small and stable chips and also capable of robustly distributing and transmitting quantum information between chips.

Methods
Devices design and fabrication. The devices were fabricated on the standard silicon-on-insulator wafer with a 220 nm silicon layer and a 2 μm buried silica oxide layer. MMI couplers were designed as 2.8 µm×27 µm to get a balanced splitting ratio
( Fig.1d). MMIs offer a large bandwidth and a large fabrication tolerance. Spiralled waveguide sources with a 2-cm length were used to create photon-pairs. The 1D grating couplers consist of a periodic 315 nm silicon layer with a 630 nm pitch. The 2D grating couplers include 10 µm×10 µm hole arrays with a 390 nm diameter and a 605 nm pitch. Resistive heaters with a 50 µm-length were designed and formed by a Ti/TiN metal layer. The devices were fabricated using the deep-UV (193 nm) lithography at LETI-ePIXfab. Silicon waveguides were 220 nm fully etched, while 1D and 2D grating couplers were 70 nm shallow etched. The devices were covered by a 1.6 µm silica oxide layer. Devices characterisations. Optical accesses and electric accesses were independently controlled on two chips (Fig.S1). Figure 4: Verification of chip-to-chip entanglement distribution and quantum photonic interconnect. The two Bell states were distributed across two Si chips. The S parameters were obtained using two approaches. Green dotted columns are the directly measured SCHSH using Eq. (1). Pink columns are the maximal achievable S f ringe , estimated from the mean visibility of correlation fringes in Fig.3. The SCHSH and S f ringe parameters are in good agreement. Black and blue dashed lines denote the classical and quantum boundary. These results confirm the high levels of entanglement after distributed across chips, and the high fidelity of quantum photonic interconnect. Coincidences of each measurement were accumulated for 60s and accidental coincidences are subtracted. Error bars (±1 s.d.) are given by Poissonian statistics.
Optical accesses were achieved using V-groove single modes fibre arrays with a 127 µm pitch. Fibres were titled with an angle of 10∼12 degrees to guarantee both grating couplers work at the required wavelengths. Excess loss of 1D and 2D grating couplers were about -4.8 dB and -7.6 dB at peak wavelengths, respectively (Fig.S2). Extinction ratio of 1D and 2D grating couplers were measured to be larger than 20 dB and 18 dB, respectively. We estimated losses from different contributors in the system: -6 dB from off-chip filters, -6 dB from SSNPDs, -9∼9.5 dB from 1D grating couplers, -15∼15.5 dB from 2D grating couplers, -6 dB from demultiplexing MMIs, and -8∼9 dB from MMIs excess loss and propagation loss in waveguides. Totally, signal and idler photons respectively experienced -36∼38 dB and -18∼19 dB attention. The fibre channel interconnected two chips has -15∼16 dB attention mainly from the 2D grating couplers, which can be further improved by engineering the geometry of coupler and waveguide.
All thermal-driven phase shifters were controlled using homemade electric controllers. Wire bounding technology was used to contact heaters' transmission lines. Optical power was recorded as a function of electric power added on heaters. The opticalelectric power contour was fitted and used to construct the mapping between the required states and electric power. Fig.S3 shows calibration results of chip-A's and chip-B's state analysers. To avoid the influence of temperature variation, both chips were mounted on temperature stabilised stages. Fibre alignment was automatically recoupled using piezo-electronic stacks. Fig.S4 shows the stability of the chip-to-chip system, which were maintained constant more than 30 mins. This indicates path-encoded states on the two chips are very stable and polarisation-encoded states in the fibre channel are also well-stabilised.  Figure S2 shows the measured spectrums of the 1D and 2D grating couplers. Peak wavelengths of both gating couplers are dependent on the angle between fibre array and chip, and they are both around 1555.5 nm when the relative angle is in the range of 10−12 degrees. Excess loss of 1D and 2D grating couplers is about -4.8 dB and -7.6 dB at the peak wavelengths, and their 1dB-bandwidths are around 27 nm and 30 nm, respectively. The 1D grating couplers consist of a periodic 315 nm silicon layer with a 630 nm pitch. The 2D grating couplers include 10 µm × 10 µm hole arrays with a 390 nm diameter and a 605 nm pitch (Insets of Fig.S2). Optimised angles for the two chips are slightly different, owing to the wavelength difference of signal and idler photons and also fabrication deviation of the devices. Loss of grating couplers can be further reduced by engineering the grating structure and positioning reflection mirrors under the grating [5,6]. Note that other on-chip polarisation control and diversity devices can be explored for quantum linking between chips using entanglement [7].

Tomography stages characterisation
The two chips were fixed on two copper PCBs and thermal-heaters were wired-bounded to electric pads on the PCBs. Home-made computer-interfaced heater drivers were used to independently control all heaters on the two chips ( Figure S1). The output optical power was recorded as a function of electric power added on heaters, from which the relationship between states and electric power was reconstructed. A least-squares minimisation algorithm was used to fit the O-E (optical power and electric power) contour and find responding powers for different states. Figure S3 shows the calibration results of chip-A's and chip-B's projectors, A(θAZ , θAY ) and B(θBZ , θBY ), by simultaneously scanning θAY and θAZ or θBY and θBZ phase shifters, respectively. To calibrate chip-B's B(θBZ , θBY ), the input state needs to be known in advance otherwise it is difficult to access phase offset of the θBZ phase shifter. We used the 1D TE-grating coupler as an on-chip polariser to guarantee TE-polarised state was injected. Then we kept the fibre untouched and smoothly switched the input state to the 2D grating coupler on the same chip. This state is an Figure 6: Spectrums of the 1D and 2D grating couplers. Peak wavelength with maximal transmission is determined by the titled angle of fibre. These spectrums were measured when the relative angle was optimised to be 10-12 degrees. In this case, both grating couplers work near 1555.5 nm peak wavelengths. Insets show the optical microscopy images of the grating couplers.
anti-diagonal state for the 2D grating coupler. Then we determined all phase information of chip-B's B(θBZ , θBY ). Similarly we calibrated chip-A's A(θAZ , θAY ).

Systematic stability measurement
A classical reference frame is necessary for real-life scenarios. The phase matching condition of the SFWM processing allows the generated photons propagate collinearly with the pump light. Then, we can use the pump light to close a feedback loop to track single photons on both two chips and also in the optical fibre channel, and to keep state stability in the chip-to-chip system. The demultiplexing MMIs on chip-A split the pump into two parts, chip-A's projector and the chip-B. Half was used to feed-forwardly track photons at the chip-A side; the other half was transmitted through the fibre channel together with the idler photons, and further used to track photons in the optical fibre and the chip-B side. Figure S4 shows the stability of the chipto-chip system. Fibre alignment was feed-forwardly recoupled each 1 min by using a piezo electronic stacks (PEC). It  : Stability of the chip-to-chip system. Curves represent the measured optical power and self-normalised, as a function of time. Purple one is obtained at chip-A's port D1, and pink one is measured at chip-B's port D3. A(θAZ , θAY ) and B(θBZ , θBY ) on both two chips were set as the |+ projectors. Fibre alignment was feed-forwardly recoupled each 1min.