Built on

X. Peng, Z. Liao, N. Xu, G. Qin, X. Zhou, D. Suter, and J. Du, Physical Review Letters 101
Original
1935
Earlier work this paper cites.
A. Y. Kitaev, (1995) , arXiv:9511026 [quant-ph]
1995
Earlier work this paper cites.
P. W. Shor, SIAM Review 41
1999
Earlier work this paper cites.
R. Fletcher, Practical Methods of Optimization , 2nd ed. (Wiley, New York, 2000)
2000
Earlier work this paper cites.
C. J. C. Burges, Factoring as Optimization , Tech. Rep. (2002)
2002
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S. Beauregard, Quantum Information & Computation 3
2003
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A. G. Fowler, S. J. Devitt, and L. C. L. Hollenberg, Quantum Information & Computation 4
2004
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A. G. Fowler and L. C. L. Hollenberg, Physical Review A 70
2004
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M. Agrawal, N. Kayal, and N. Saxena, Annals of Mathematics 160
2004
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Y. Takahashi and N. Kunihiro, Quantum Information & Computation 6
2006
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C. Zalka, (2006) , arXiv:0601097 [quant-ph]
2006
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D. D. Thaker, T. S. Metodi, A. W. Cross, I. L. Chuang, and F. T. Chong, in 33rd International Symposium on Computer Architecture (ISCA’06) , Vol. 2006 (2006) pp. 378–389, arXiv:0604070 [quant-ph]
2006
Earlier work this paper cites.
C. Y. Lu, D. E. Browne, T. Yang, and J. W. Pan, Physical Review Letters 99
Original
2007
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B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist, and A. G. White, Physical Review Letters 99
Original
2007
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A. Politi, J. C. F. Matthews, and J. L. O’Brien, Science 325
Original
2009
Earlier work this paper cites.

Similar

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information , 10th Anniversary ed. (Cambridge University Press, Cambridge, 2010)
2010
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R. V. Meter, T. D. Ladd, A. G. Fowler, and Y. Yamamoto, International Journal of Quantum Information 8
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2010
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G. Schaller and R. Schützhold, Quantum Information & Computation 10
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2010
Cited alongside, same era.
J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Molecular Physics 109
Original
2011
Cited alongside, same era.
E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X. Q. Zhou, and J. L. O’brien, Nature Photonics 6
Original

Then

E. Farhi and A. W. Harrow, (2016), arXiv:1602.07674 [quant-ph]
Original
2016
Later among the works it cites.
J. Romero, J. Olson, and A. Aspuru-Guzik, Quantum Science and Technology 2
Original
2016
Later among the works it cites.
C. Y.-Y. Lin and Y. Zhu, (2016), arXiv:1601.01744 [quant-ph]
Original
2016
Later among the works it cites.
M. Ekerå and J. Håstad, in Post-Quantum Cryptography , edited by T. Lange and T. Takagi (Springer International Publishing, Cham, 2017) pp. 347–363, arXiv:9508027 [cs.CR]
2017
Later among the works it cites.
T. Häner, M. Roetteler, and K. M. Svore, Quantum Information & Computation 17
Original

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2018

Variational Quantum Factoring

Anschuetz, Eric R., Olson, Jonathan P., Aspuru-Guzik, Alán et al.

Understand

Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor.

Unfortunately, factoring via Shor's algorithm is well beyond the capabilities of today's noisy intermediate-scale quantum (NISQ) devices.
In this work, we revisit the problem of factoring, developing an alternative to Shor's algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian.
The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian.

Built on

X. Peng, Z. Liao, N. Xu, G. Qin, X. Zhou, D. Suter, and J. Du, Physical Review Letters 101
Original
1935
Earlier work this paper cites.
A. Y. Kitaev, (1995) , arXiv:9511026 [quant-ph]
1995
Earlier work this paper cites.
P. W. Shor, SIAM Review 41
1999
Earlier work this paper cites.
R. Fletcher, Practical Methods of Optimization , 2nd ed. (Wiley, New York, 2000)
2000
Earlier work this paper cites.
C. J. C. Burges, Factoring as Optimization , Tech. Rep. (2002)
2002
Earlier work this paper cites.
S. Beauregard, Quantum Information & Computation 3
2003
Earlier work this paper cites.
A. G. Fowler, S. J. Devitt, and L. C. L. Hollenberg, Quantum Information & Computation 4
2004
Earlier work this paper cites.
A. G. Fowler and L. C. L. Hollenberg, Physical Review A 70
2004
Earlier work this paper cites.
M. Agrawal, N. Kayal, and N. Saxena, Annals of Mathematics 160
2004
Earlier work this paper cites.
Y. Takahashi and N. Kunihiro, Quantum Information & Computation 6
2006
Earlier work this paper cites.
C. Zalka, (2006) , arXiv:0601097 [quant-ph]
2006
Earlier work this paper cites.
D. D. Thaker, T. S. Metodi, A. W. Cross, I. L. Chuang, and F. T. Chong, in 33rd International Symposium on Computer Architecture (ISCA’06) , Vol. 2006 (2006) pp. 378–389, arXiv:0604070 [quant-ph]
2006
Earlier work this paper cites.
C. Y. Lu, D. E. Browne, T. Yang, and J. W. Pan, Physical Review Letters 99
Original
2007
Earlier work this paper cites.
B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist, and A. G. White, Physical Review Letters 99
Original
2007
Earlier work this paper cites.
A. Politi, J. C. F. Matthews, and J. L. O’Brien, Science 325
Original
2009
Earlier work this paper cites.

Similar

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information , 10th Anniversary ed. (Cambridge University Press, Cambridge, 2010)
2010
Cited alongside, same era.
R. V. Meter, T. D. Ladd, A. G. Fowler, and Y. Yamamoto, International Journal of Quantum Information 8
Original
2010
Cited alongside, same era.
G. Schaller and R. Schützhold, Quantum Information & Computation 10
Original
2010
Cited alongside, same era.
J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Molecular Physics 109
Original
2011
Cited alongside, same era.
E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X. Q. Zhou, and J. L. O’brien, Nature Photonics 6
Original

Then

E. Farhi and A. W. Harrow, (2016), arXiv:1602.07674 [quant-ph]
Original
2016
Later among the works it cites.
J. Romero, J. Olson, and A. Aspuru-Guzik, Quantum Science and Technology 2
Original
2016
Later among the works it cites.
C. Y.-Y. Lin and Y. Zhu, (2016), arXiv:1601.01744 [quant-ph]
Original
2016
Later among the works it cites.
M. Ekerå and J. Håstad, in Post-Quantum Cryptography , edited by T. Lange and T. Takagi (Springer International Publishing, Cham, 2017) pp. 347–363, arXiv:9508027 [cs.CR]
2017
Later among the works it cites.
T. Häner, M. Roetteler, and K. M. Svore, Quantum Information & Computation 17
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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2012

Cited alongside, same era.

E. Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, Y. Yin, A. N. Cleland, and J. M. Martinis, Nature Physics 8

Original

2012

Cited alongside, same era.

N. C. Jones, R. Van Meter, A. G. Fowler, P. L. McMahon, J. Kim, T. D. Ladd, and Y. Yamamoto, Physical Review X 2

Original

2012

Cited alongside, same era.

J. Johansson, P. Nation, and F. Nori, Computer Physics Communications 183

Original

2012

Cited alongside, same era.

M. R. Geller and Z. Zhou, Scientific Reports 3

Original

2013

Cited alongside, same era.

S. J. Devitt, A. M. Stephens, W. J. Munro, and K. Nemoto, Nature Communications 4

Original

2013

Cited alongside, same era.

N. S. Dattani and N. Bryans, (2014), arXiv:1411.6758 [quant-ph]

Original

2014

Cited alongside, same era.

E. Farhi, J. Goldstone, and S. Gutmann, (2014) , arXiv:1411.4028 [quant-ph]

Original

2014

Cited alongside, same era.

2017