High-dimensional one-way quantum processing implemented on d-level cluster states

Taking advantage of quantum mechanics for executing computational tasks faster than classical computers1 or performing measurements with precision exceeding the classical limit2,3 requires the generation of specific large and complex quantum states. In this context, cluster states4 are particularly interesting because they can enable the realization of universal quantum computers by means of a ‘one-way’ scheme5, where processing is performed through measurements6. The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant7, and also enables novel algorithms8. Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time9 and frequency10 domain, confirming genuine multi-partite entanglement with higher noise robustness compared to conventional two-level cluster states6,11–13. We perform proof-of-concept high-dimensional one-way quantum operations, where the cluster states are transformed into orthogonal, maximally entangled d-level two-partite states by means of projection measurements. Our scalable approach is based on integrated photonic chips9,10 and optical fibre communication components, thus achieving new and deterministic functionalities.The creation and manipulation of large quantum states is necessary for quantum information processing tasks. Three-level, four-partite cluster states have now been created in the time and frequency domain of two photons on-chip.

[1]  R. Morandotti,et al.  Micro-combs: A novel generation of optical sources , 2017 .

[2]  G. Vallone,et al.  Realization and characterization of a 2-photon 4-qubit linear cluster state , 2007, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[3]  G. Tóth,et al.  Entanglement detection in the stabilizer formalism , 2005, quant-ph/0501020.

[4]  J. Eisert,et al.  Multiparty entanglement in graph states , 2003, quant-ph/0307130.

[5]  T. Ralph,et al.  Demonstration of an all-optical quantum controlled-NOT gate , 2003, Nature.

[6]  Yoshichika Miwa,et al.  Parallel generation of quadripartite cluster entanglement in the optical frequency comb. , 2011, Physical review letters.

[7]  Franson,et al.  Bell inequality for position and time. , 1989, Physical review letters.

[8]  A. Zeilinger,et al.  Multi-photon entanglement in high dimensions , 2015, Nature Photonics.

[9]  Peter C Humphreys,et al.  Linear optical quantum computing in a single spatial mode. , 2013, Physical review letters.

[10]  T. Rudolph,et al.  Resource-efficient linear optical quantum computation. , 2004, Physical review letters.

[11]  Seth Lloyd,et al.  Quantum Computation over Continuous Variables , 1999 .

[12]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[13]  K.J.Resch,et al.  Experimental One-Way Quantum Computing , 2005, quant-ph/0503126.

[14]  Jian-Wei Pan,et al.  Experimental entanglement of six photons in graph states , 2006, quant-ph/0609130.

[15]  Adetunmise C. Dada,et al.  Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities , 2011, 1104.5087.

[16]  Pavel Lougovski,et al.  Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing. , 2017, Physical review letters.

[17]  A. Zeilinger,et al.  Experimental one-way quantum computing , 2005, Nature.

[18]  Paul G. Kwiat,et al.  Hyper-entangled states , 1997 .

[19]  Xihan Li,et al.  Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement. , 2016, Optics express.

[20]  W Dür,et al.  Measurement-based quantum computation with trapped ions. , 2013, Physical review letters.

[21]  C. Roeloffzen,et al.  Compact and reconfigurable silicon nitride time-bin entanglement circuit , 2015, 1506.02758.

[22]  Demetrios N. Christodoulides,et al.  Enhanced sensitivity at higher-order exceptional points , 2017, Nature.

[23]  Robert Raussendorf,et al.  Qudit quantum computation on matrix product states with global symmetry , 2016, 1609.07174.

[24]  Stefan Nolte,et al.  On-chip generation of high-order single-photon W-states , 2014, Nature Photonics.

[25]  Shota Yokoyama,et al.  Ultra-large-scale continuous-variable cluster states multiplexed in the time domain , 2013, Nature Photonics.

[26]  Austin G. Fowler,et al.  Experimental demonstration of topological error correction , 2009, Nature.

[27]  R. Blatt,et al.  Entangled states of trapped atomic ions , 2008, Nature.

[28]  R. Morandotti,et al.  New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics , 2013, Nature Photonics.

[29]  M. Nielsen.  Conditions for a Class of Entanglement Transformations , 1998, quant-ph/9811053.

[30]  Nathan K Langford,et al.  Generation of hyperentangled photon pairs. , 2005, Physical review letters.

[31]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[32]  N. Gisin,et al.  Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication , 1999 .

[33]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[34]  S. Chu,et al.  Generation of multiphoton entangled quantum states by means of integrated frequency combs , 2016, Science.

[35]  Jian-Wei Pan,et al.  18-Qubit Entanglement with Six Photons' Three Degrees of Freedom. , 2018, Physical review letters.

[36]  Roberto Morandotti,et al.  On-chip generation of high-dimensional entangled quantum states and their coherent control , 2017, Nature.

[37]  Philippe Emplit,et al.  Frequency Bin Entangled Photons , 2009, 0910.1325.

[38]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[39]  R. Prevedel,et al.  High-speed linear optics quantum computing using active feed-forward , 2007, Nature.

[40]  R. Morandotti,et al.  Integrated sources of photon quantum states based on nonlinear optics , 2017, Light: Science & Applications.

[41]  C. P. Sun,et al.  Quantum computation based on d-level cluster state (11 pages) , 2003, quant-ph/0304054.

[42]  Kyunghun Han,et al.  50-GHz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator. , 2018, Optics express.

[44]  Yaron Silberberg,et al.  Supersensitive polarization microscopy using NOON states of light. , 2014, Physical review letters.

[45]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

[46]  Jay Lawrence.  Mutually unbiased bases and trinary operator sets for N qutrits (10 pages) , 2004, quant-ph/0403095.

[47]  J. Gambetta,et al.  Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets , 2017, Nature.

[48]  Christian Kurtsiefer,et al.  Experimental detection of multipartite entanglement using witness operators. , 2004, Physical review letters.

[49]  G. Schinn,et al.  Single-frequency low-threshold linearly polarized DFB Raman fiber lasers. , 2017, Optics letters.

[50]  Kai Chen,et al.  Experimental realization of one-way quantum computing with two-photon four-qubit cluster states. , 2007, Physical review letters.

[51]  Nicolas Godbout,et al.  Cluster-state quantum computing in optical fibers , 2007 .

[52]  R. Morandotti,et al.  Integrated sources of photon quantum states based on nonlinear optics , 2017, Light: Science & Applications.

[53]  Jian-Wei Pan,et al.  Experimental demonstration of a hyper-entangled ten-qubit Schr\ , 2008, 0809.4277.

[54]  Jian-Wei Pan,et al.  Experimental Ten-Photon Entanglement. , 2016, Physical review letters.

[55]  H. Weinfurter,et al.  Witnessing multipartite entanglement , 2003, quant-ph/0309043.

[56]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[57]  Joseph M. Lukens,et al.  Frequency-encoded photonic qubits for scalable quantum information processing , 2016, 1612.03131.