Abstract

Linear equations play an important role in nearly all fields of research in science and engineering. Recent studies have shown that quantum algorithms for solving linear systems of algebraic equations provide exponential speedups over their classical counterparts. Here, we present a simplified experimental scheme for implementing the quantum algorithm for solving linear equations with multiple degrees of freedom (DoF) of single photon. Compared with the previous studies, our scheme not only presents excellent efficiency, it requires fewer photons to solve the same problem. Our work highlights the potential applications of multiple DoFs of single photon in quantum information processes.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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2018 (1)

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

2017 (3)

L. Chen, Z. Li, X. Yao, M. Huang, W. Li, H. Lu, X. Yuan, Y. Zhang, X. Jiang, C. Peng, L. Li, N.-L. Liu, X. Ma, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of ten-photon entanglement using thin BiB3O6 crystals,” Optica 4(1), 77 (2017).
[Crossref]

Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
[Crossref] [PubMed]

C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
[Crossref] [PubMed]

2016 (3)

X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
[Crossref] [PubMed]

A. Montanaro and S. Pallister, “Quantum algorithms and the finite element method,” Phys. Rev. A (Coll. Park) 93(3), 032324 (2016).
[Crossref]

M. A. Ciampini, A. Orieux, S. Paesani, F. Sciarrino, G. Corrielli, A. Crespi, R. Ramponi, R. Osellame, and P. Mataloni, “Path-polarization hyperentangled and cluster states of photons on a chip,” Light Sci. Appl. 5(4), e16064 (2016).
[Crossref] [PubMed]

2014 (4)

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits,” Sci. Rep. 4(1), 4118 (2014).
[Crossref] [PubMed]

P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum support vector machine for big data classification,” Phys. Rev. Lett. 113(13), 130503 (2014).
[Crossref] [PubMed]

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B. Dakić, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4(1), 6115 (2014).
[Crossref] [PubMed]

J. Pan, Y. D. Cao, X. W. Yao, Z. K. Li, C. Y. Ju, H. W. Chen, X. H. Peng, S. Kais, and J. F. Du, “Experimental realization of quantum algorithm for solving linear systems of equations,” Phys. Rev. A 89(2), 022313 (2014).
[Crossref]

2013 (1)

X. D. Cai, C. Weedbrook, Z. E. Su, M. C. Chen, M. Gu, M. J. Zhu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110(23), 230501 (2013).
[Crossref] [PubMed]

2012 (1)

N. Wiebe, D. Braun, and S. Lloyd, “Quantum algorithm for data fitting,” Phys. Rev. Lett. 109(5), 050505 (2012).
[Crossref] [PubMed]

2011 (2)

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-Qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106(13), 130506 (2011).
[Crossref] [PubMed]

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
[Crossref] [PubMed]

2010 (1)

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
[Crossref]

2009 (2)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum algorithm for linear systems of equations,” Phys. Rev. Lett. 103(15), 150502 (2009).
[Crossref] [PubMed]

2005 (3)

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[Crossref] [PubMed]

C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett. 95(24), 240405 (2005).
[Crossref] [PubMed]

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett. 95(24), 240406 (2005).
[Crossref] [PubMed]

1998 (1)

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

1996 (2)

A. Luis and J. Peřina, “Optimum phase-shift estimation and the quantum description of the phase difference,” Phys. Rev. A 54(5), 4564–4570 (1996).
[Crossref] [PubMed]

R. B. Griffiths and C.-S. Niu, “Semiclassical Fourier transform for quantum computation,” Phys. Rev. Lett. 76(17), 3228–3231 (1996).
[Crossref] [PubMed]

1994 (1)

R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41(12), 2315–2323 (1994).
[Crossref]

Adami, C.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

Aspuru-Guzik, A.

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B. Dakić, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4(1), 6115 (2014).
[Crossref] [PubMed]

Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett. 95(24), 240405 (2005).
[Crossref] [PubMed]

Barreiro, J. T.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-Qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106(13), 130506 (2011).
[Crossref] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[Crossref] [PubMed]

Barz, S.

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B. Dakić, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4(1), 6115 (2014).
[Crossref] [PubMed]

Blatt, R.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-Qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106(13), 130506 (2011).
[Crossref] [PubMed]

Bongioanni, I.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
[Crossref] [PubMed]

Braun, D.

N. Wiebe, D. Braun, and S. Lloyd, “Quantum algorithm for data fitting,” Phys. Rev. Lett. 109(5), 050505 (2012).
[Crossref] [PubMed]

Cai, X. D.

X. D. Cai, C. Weedbrook, Z. E. Su, M. C. Chen, M. Gu, M. J. Zhu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110(23), 230501 (2013).
[Crossref] [PubMed]

Cao, Y. D.

J. Pan, Y. D. Cao, X. W. Yao, Z. K. Li, C. Y. Ju, H. W. Chen, X. H. Peng, S. Kais, and J. F. Du, “Experimental realization of quantum algorithm for solving linear systems of equations,” Phys. Rev. A 89(2), 022313 (2014).
[Crossref]

Cerf, N. J.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

Chen, C.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
[Crossref] [PubMed]

Chen, H. W.

J. Pan, Y. D. Cao, X. W. Yao, Z. K. Li, C. Y. Ju, H. W. Chen, X. H. Peng, S. Kais, and J. F. Du, “Experimental realization of quantum algorithm for solving linear systems of equations,” Phys. Rev. A 89(2), 022313 (2014).
[Crossref]

Chen, L.

Chen, L. K.

X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
[Crossref] [PubMed]

Chen, M. C.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
[Crossref] [PubMed]

X. D. Cai, C. Weedbrook, Z. E. Su, M. C. Chen, M. Gu, M. J. Zhu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110(23), 230501 (2013).
[Crossref] [PubMed]

Chen, Y. A.

C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
[Crossref] [PubMed]

X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
[Crossref] [PubMed]

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
[Crossref]

Chen, Y.-A.

Chen, Z. B.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
[Crossref]

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett. 95(24), 240406 (2005).
[Crossref] [PubMed]

Chwalla, M.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-Qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106(13), 130506 (2011).
[Crossref] [PubMed]

Ciampini, M. A.

M. A. Ciampini, A. Orieux, S. Paesani, F. Sciarrino, G. Corrielli, A. Crespi, R. Ramponi, R. Osellame, and P. Mataloni, “Path-polarization hyperentangled and cluster states of photons on a chip,” Light Sci. Appl. 5(4), e16064 (2016).
[Crossref] [PubMed]

Cinelli, C.

C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett. 95(24), 240405 (2005).
[Crossref] [PubMed]

Cleve, R.

R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, “Quantum algorithms revisited,” In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences1998 Jan 8 (Vol. 454, No. 1969, pp. 339–354).

Coish, W. A.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-Qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106(13), 130506 (2011).
[Crossref] [PubMed]

Corrielli, G.

M. A. Ciampini, A. Orieux, S. Paesani, F. Sciarrino, G. Corrielli, A. Crespi, R. Ramponi, R. Osellame, and P. Mataloni, “Path-polarization hyperentangled and cluster states of photons on a chip,” Light Sci. Appl. 5(4), e16064 (2016).
[Crossref] [PubMed]

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J. Pan, Y. D. Cao, X. W. Yao, Z. K. Li, C. Y. Ju, H. W. Chen, X. H. Peng, S. Kais, and J. F. Du, “Experimental realization of quantum algorithm for solving linear systems of equations,” Phys. Rev. A 89(2), 022313 (2014).
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R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits,” Sci. Rep. 4(1), 4118 (2014).
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A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
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Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
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X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
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X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
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X. D. Cai, C. Weedbrook, Z. E. Su, M. C. Chen, M. Gu, M. J. Zhu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110(23), 230501 (2013).
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White, A. G.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
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X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117(21), 210502 (2016).
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Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
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Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
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C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
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Xu, D.

C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
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Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
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Xu, K.

C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
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Xu, P.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
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Yan, Z.

Y. Zheng, C. Song, M. C. Chen, B. Xia, W. Liu, Q. Guo, L. Zhang, D. Xu, H. Deng, K. Huang, Y. Wu, Z. Yan, D. Zheng, L. Lu, J. W. Pan, H. Wang, C. Y. Lu, and X. Zhu, “Solving systems of linear equations with a superconducting quantum processor,” Phys. Rev. Lett. 118(21), 210504 (2017).
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Yang, C. P.

C. Song, K. Xu, W. Liu, C. P. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J. W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
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Yang, T.

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett. 95(24), 240406 (2005).
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Yao, X.

Yao, X. C.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
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Yao, X. W.

J. Pan, Y. D. Cao, X. W. Yao, Z. K. Li, C. Y. Ju, H. W. Chen, X. H. Peng, S. Kais, and J. F. Du, “Experimental realization of quantum algorithm for solving linear systems of equations,” Phys. Rev. A 89(2), 022313 (2014).
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Yin, J.

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett. 95(24), 240406 (2005).
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Yuan, X.

Zhang, J.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
[Crossref] [PubMed]

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett. 95(24), 240406 (2005).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 The overall outline of the HHL algorithm. The phase estimation operation between the Register and input is realized by a H n gate on the Register qubit, a C-U gate between input and register qubit, and a F T on the Register qubit. H n is the n-bit Hadamard gate on the register. U is determined by the matrix A. FTand F T represent the Fourier transformation and inverse Fourier transformation. The C-Rotation operation is used to obtain the factor of 1 λ j . Finally, the state is post-selected by |1 a |0 r n at the Ancilla and Register to obtain the expected results x at the input qubit.
Fig. 2
Fig. 2 (a). The optimized circuit for solving the linear equation A| x =|b, where A=( 1.5 0.5 0.5 1.5 ) . To describe the detailed realization of this quantum circuit in the experiment, we label all the quantum gates with A-J. (b). The experimental realization for solving linear equation. The experiment contains three parts, the Initial State Preparation part, the HHL Algorithm Evolution part, and the Measurement part. The GL is Glan Laser polarizer. HWP@θ represents a half wave plate with the optical axis oriented atθ. The BS is the beam splitter. The PBS is polarizing beam splitter. Detector is single photon detection module. The double sided arrow in the measurement module represents the phase adjustment between the two arms of the Mach-Zehnder interferometer.
Fig. 3
Fig. 3 The experimental results for solving linear equation A|x=|b. Orange and blue histograms represent the theoretically and the experimentally measured results. X1, X2 and X3 represent the input states for | b 1 , | b 2 and | b 3 , respectively. X, Y and Z represent the Pauli observables.
Fig. 4
Fig. 4 (a), (b) and (c) represent the single bit Hadamard gate based on the path, single bit Hadamard gate based on the polarization, and single bit X-gate based on the polarization, respectively. The BS is the beam splitter. HWP@θ is a half wave plate with the optical axis oriented at θ. |0/|1 represents the state encoded with the path DoF. |H/|V represents the polarization encoded with horizontal and vertical polarizations.
Fig. 5
Fig. 5 (a) shows the C-Not gate that the control and controlled bits are coded by the path and polarization DoFs, which is mainly realized by a PBS (polarizing sensing beam splitter). (b) shows the CH(θ) gate that the control and controlled bits are both coded by the path. When the control bit is on the |0 state, the path remains unchanged by being reflected to the origin path with two M(mirror). When the control bit is on the |1 state, the path bit is transformed by a H(θ) gate with a BS. (c) shows the CH(θ) gate that the control and controlled bits are coded by the polarization and path DoFs.
Fig. 6
Fig. 6 The measurement method of the path DoF. The double sided arrow in the measurement module represents the phase adjustment.

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