Two-Unitary Decomposition Algorithm and Open Quantum System Simulation

Two-Unitary Decomposition Algorithm and Open Quantum System Simulation

Source Node: 2098228

Nishchay Suri1,2,3, Joseph Barreto1,2,4, Stuart Hadfield1,2, Nathan Wiebe5,6, Filip Wudarski1,2, and Jeffrey Marshall1,2

1QuAIL, NASA Ames Research Center, Moffett Field, California 94035, USA
2USRA Research Institute for Advanced Computer Science, Mountain View, California 94043, USA
3Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
4QuTech, Delft University of Technology, Delft, The Netherlands
5Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3E1, Canada
6Pacific Northwest National Laboratory, Richland, Washington 99352, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Simulating general quantum processes that describe realistic interactions of quantum systems following a non-unitary evolution is challenging for conventional quantum computers that directly implement unitary gates. We analyze complexities for promising methods such as the Sz.-Nagy dilation and linear combination of unitaries that can simulate open systems by the probabilistic realization of non-unitary operators, requiring multiple calls to both the encoding and state preparation oracles. We propose a quantum two-unitary decomposition (TUD) algorithm to decompose a $d$-dimensional operator $A$ with non-zero singular values as $A=(U_1+U_2)/2$ using the quantum singular value transformation algorithm, avoiding classically expensive singular value decomposition (SVD) with an $O(d^3)$ overhead in time. The two unitaries can be deterministically implemented, thus requiring only a single call to the state preparation oracle for each. The calls to the encoding oracle can also be reduced significantly at the expense of an acceptable error in measurements. Since the TUD method can be used to implement non-unitary operators as only two unitaries, it also has potential applications in linear algebra and quantum machine learning.

► BibTeX data

► References

[1] Yuri Manin. Computable and uncomputable. Sovetskoye Radio, Moscow, 128, 1980.

[2] Richard P. Feynman. Simulating physics with computers. Int. j. Theor. phys, 21 (6/​7), 1982. 10.1007/​BF02650179. URL https:/​/​​10.1007/​BF02650179.

[3] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum information, 2002.

[4] Seth Lloyd. Universal quantum simulators. Science, pages 1073–1078, 1996. 10.1126/​science.273.5278.1073. URL https:/​/​​doi/​abs/​10.1126/​science.273.5278.1073.

[5] John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang. Grand unification of quantum algorithms. PRX Quantum, 2: 040203, Dec 2021. 10.1103/​PRXQuantum.2.040203. URL https:/​/​​10.1103/​PRXQuantum.2.040203.

[6] I. M. Georgescu, S. Ashhab, and Franco Nori. Quantum simulation. Rev. Mod. Phys., 86: 153–185, Mar 2014. 10.1103/​RevModPhys.86.153. URL https:/​/​​10.1103/​RevModPhys.86.153.

[7] Ashley Montanaro. Quantum algorithms: an overview. npj Quantum Information, 2 (1): 1–8, 2016. 10.1038/​npjqi.2015.23. URL https:/​/​​articles/​npjqi201523.

[8] John Preskill. Quantum computing 40 years later. arXiv:2106.10522, 2021. URL https:/​/​​abs/​2106.10522.

[9] Heinz-Peter Breuer, Francesco Petruccione, et al. The theory of open quantum systems. Oxford University Press on Demand, 2002.

[10] Goran Lindblad. On the generators of quantum dynamical semigroups. Communications in Mathematical Physics, 48 (2): 119–130, 1976. 10.1007/​BF01608499.

[11] Vittorio Gorini, Andrzej Kossakowski, and Ennackal Chandy George Sudarshan. Completely positive dynamical semigroups of n-level systems. Journal of Mathematical Physics, 17 (5): 821–825, 1976. 10.1063/​1.522979. URL https:/​/​​doi/​10.1063/​1.522979.

[12] Laszlo Gyongyosi, Sandor Imre, and Hung Viet Nguyen. A survey on quantum channel capacities. IEEE Communications Surveys & Tutorials, 20 (2): 1149–1205, 2018. 10.1109/​COMST.2017.2786748.

[13] Filippo Caruso, Vittorio Giovannetti, Cosmo Lupo, and Stefano Mancini. Quantum channels and memory effects. Rev. Mod. Phys., 86: 1203–1259, Dec 2014. 10.1103/​RevModPhys.86.1203. URL https:/​/​​10.1103/​RevModPhys.86.1203.

[14] Lorenza Viola, Emanuel Knill, and Seth Lloyd. Dynamical decoupling of open quantum systems. Phys. Rev. Lett., 82: 2417–2421, Mar 1999. 10.1103/​PhysRevLett.82.2417. URL https:/​/​​10.1103/​PhysRevLett.82.2417.

[15] Dieter Suter and Gonzalo A. Álvarez. Colloquium: Protecting quantum information against environmental noise. Rev. Mod. Phys., 88: 041001, Oct 2016. 10.1103/​RevModPhys.88.041001. URL https:/​/​​10.1103/​RevModPhys.88.041001.

[16] Easwar Magesan, Daniel Puzzuoli, Christopher E. Granade, and David G. Cory. Modeling quantum noise for efficient testing of fault-tolerant circuits. Phys. Rev. A, 87: 012324, Jan 2013. 10.1103/​PhysRevA.87.012324. URL https:/​/​​10.1103/​PhysRevA.87.012324.

[17] Paolo Zanardi, Jeffrey Marshall, and Lorenzo Campos Venuti. Dissipative universal lindbladian simulation. Phys. Rev. A, 93: 022312, Feb 2016. 10.1103/​PhysRevA.93.022312. URL https:/​/​​10.1103/​PhysRevA.93.022312.

[18] Marko Žnidarič, TomažProsen, Giuliano Benenti, Giulio Casati, and Davide Rossini. Thermalization and ergodicity in one-dimensional many-body open quantum systems. Phys. Rev. E, 81: 051135, May 2010. 10.1103/​PhysRevE.81.051135. URL https:/​/​​10.1103/​PhysRevE.81.051135.

[19] Michael J Kastoryano and Fernando GSL Brandao. Quantum Gibbs samplers: The commuting case. Communications in Mathematical Physics, 344 (3): 915–957, 2016. 10.1007/​s00220-016-2641-8.

[20] Iztok Pižorn. One-dimensional Bose-Hubbard model far from equilibrium. Phys. Rev. A, 88: 043635, Oct 2013. 10.1103/​PhysRevA.88.043635. URL https:/​/​​10.1103/​PhysRevA.88.043635.

[21] Tomaž Prosen and Marko Žnidarič. Matrix product simulations of non-equilibrium steady states of quantum spin chains. Journal of Statistical Mechanics: Theory and Experiment, 2009 (02): P02035, 2009. 10.1088/​1742-5468/​2009/​02/​p02035. URL https:/​/​​10.1088/​1742-5468/​2009/​02/​p02035.

[22] Tomaž Prosen. Open xxz spin chain: Nonequilibrium steady state and a strict bound on ballistic transport. Phys. Rev. Lett., 106: 217206, May 2011. 10.1103/​PhysRevLett.106.217206. URL https:/​/​​10.1103/​PhysRevLett.106.217206.

[23] Giuliano Benenti, Giulio Casati, Tomaž Prosen, Davide Rossini, and Marko Žnidarič. Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium. Phys. Rev. B, 80: 035110, Jul 2009. 10.1103/​PhysRevB.80.035110. URL https:/​/​​10.1103/​PhysRevB.80.035110.

[24] TomažProsen and Marko Žnidarič. Diffusive high-temperature transport in the one-dimensional hubbard model. Phys. Rev. B, 86: 125118, Sep 2012. 10.1103/​PhysRevB.86.125118. URL https:/​/​​10.1103/​PhysRevB.86.125118.

[25] Susana F Huelga and Martin B Plenio. Vibrations, quanta and biology. Contemporary Physics, 54 (4): 181–207, 2013. 10.1080/​00405000.2013.829687.

[26] Zixuan Hu, Kade Head-Marsden, David A. Mazziotti, Prineha Narang, and Sabre Kais. A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex. Quantum, 6: 726, May 2022. ISSN 2521-327X. 10.22331/​q-2022-05-30-726. URL https:/​/​​10.22331/​q-2022-05-30-726.

[27] Sarah Mostame, Patrick Rebentrost, Alexander Eisfeld, Andrew J Kerman, Dimitris I Tsomokos, and Alán Aspuru-Guzik. Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes. New Journal of Physics, 14 (10): 105013, 2012. 10.1088/​1367-2630/​14/​10/​105013. URL https:/​/​​10.1088/​1367-2630/​14/​10/​105013.

[28] I. Sinayskiy, A. Marais, F. Petruccione, and A. Ekert. Decoherence-assisted transport in a dimer system. Phys. Rev. Lett., 108: 020602, Jan 2012. 10.1103/​PhysRevLett.108.020602. URL https:/​/​​10.1103/​PhysRevLett.108.020602.

[29] Frank Verstraete, Michael M Wolf, and J Ignacio Cirac. Quantum computation and quantum-state engineering driven by dissipation. Nature physics, 5 (9): 633–636, 2009. 10.1038/​nphys1342. URL https:/​/​​articles/​nphys1342.

[30] Paolo Zanardi and Lorenzo Campos Venuti. Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems. Phys. Rev. Lett., 113: 240406, Dec 2014. 10.1103/​PhysRevLett.113.240406. URL https:/​/​​10.1103/​PhysRevLett.113.240406.

[31] Jan Carl Budich, Peter Zoller, and Sebastian Diehl. Dissipative preparation of chern insulators. Phys. Rev. A, 91: 042117, Apr 2015. 10.1103/​PhysRevA.91.042117. URL https:/​/​​10.1103/​PhysRevA.91.042117.

[32] Sebastian Diehl, Enrique Rico, Mikhail A Baranov, and Peter Zoller. Topology by dissipation in atomic quantum wires. Nature Physics, 7 (12): 971–977, 2011. 10.1038/​nphys2106. URL https:/​/​​articles/​nphys2106.

[33] Charles-Edouard Bardyn, Mikhail A Baranov, Christina V Kraus, Enrique Rico, A İmamoğlu, Peter Zoller, and Sebastian Diehl. Topology by dissipation. New Journal of Physics, 15 (8): 085001, 2013. 10.1088/​1367-2630/​15/​8/​085001. URL https:/​/​​10.1088/​1367-2630/​15/​8/​085001.

[34] B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller. Preparation of entangled states by quantum markov processes. Phys. Rev. A, 78: 042307, Oct 2008. 10.1103/​PhysRevA.78.042307. URL https:/​/​​10.1103/​PhysRevA.78.042307.

[35] Florentin Reiter, David Reeb, and Anders S Sørensen. Scalable dissipative preparation of many-body entanglement. Physical review letters, 117 (4): 040501, 2016. 10.1103/​PhysRevLett.117.040501. URL https:/​/​​10.1103/​PhysRevLett.117.040501.

[36] Michael James Kastoryano, Florentin Reiter, and Anders Søndberg Sørensen. Dissipative preparation of entanglement in optical cavities. Physical review letters, 106 (9): 090502, 2011. 10.1103/​PhysRevLett.106.090502. URL https:/​/​​10.1103/​PhysRevLett.106.090502.

[37] Jeffrey Marshall, Lorenzo Campos Venuti, and Paolo Zanardi. Classifying quantum data by dissipation. Phys. Rev. A, 99: 032330, Mar 2019. 10.1103/​PhysRevA.99.032330. URL https:/​/​​10.1103/​PhysRevA.99.032330.

[38] Martin Kliesch, Thomas Barthel, Christian Gogolin, Michael Kastoryano, and Jens Eisert. Dissipative quantum church-turing theorem. Physical review letters, 107 (12): 120501, 2011. 10.1103/​PhysRevLett.107.120501. URL https:/​/​​10.1103/​PhysRevLett.107.120501.

[39] Hefeng Wang, Sahel Ashhab, and Franco Nori. Quantum algorithm for simulating the dynamics of an open quantum system. Physical Review A, 83 (6): 062317, 2011. 10.1103/​PhysRevA.83.062317. URL https:/​/​​10.1103/​PhysRevA.83.062317.

[40] Thomas Barthel and Martin Kliesch. Quasilocality and efficient simulation of markovian quantum dynamics. Physical review letters, 108 (23): 230504, 2012. 10.1103/​PhysRevLett.108.230504. URL https:/​/​​10.1103/​PhysRevLett.108.230504.

[41] J. Han, W. Cai, L. Hu, X. Mu, Y. Ma, Y. Xu, W. Wang, H. Wang, Y. P. Song, C.-L. Zou, and L. Sun. Experimental simulation of open quantum system dynamics via trotterization. Phys. Rev. Lett., 127: 020504, Jul 2021. 10.1103/​PhysRevLett.127.020504. URL https:/​/​​10.1103/​PhysRevLett.127.020504.

[42] Dave Bacon, Andrew M Childs, Isaac L Chuang, Julia Kempe, Debbie W Leung, and Xinlan Zhou. Universal simulation of markovian quantum dynamics. Physical Review A, 64 (6): 062302, 2001. 10.1103/​PhysRevA.64.062302. URL https:/​/​​10.1103/​PhysRevA.64.062302.

[43] Ryan Sweke, Ilya Sinayskiy, Denis Bernard, and Francesco Petruccione. Universal simulation of markovian open quantum systems. Physical Review A, 91 (6): 062308, 2015. 10.1103/​PhysRevA.91.062308. URL https:/​/​​10.1103/​PhysRevA.91.062308.

[44] Zixuan Hu, Rongxin Xia, and Sabre Kais. A quantum algorithm for evolving open quantum dynamics on quantum computing devices. Scientific reports, 10 (1): 1–9, 2020. 10.1038/​s41598-020-60321-x. URL https:/​/​​articles/​s41598-020-60321-x.

[45] Akshay Gaikwad, Arvind, and Kavita Dorai. Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm. arXiv:2201.07687, 2022. URL https:/​/​​abs/​2201.07687 10.1103/​PhysRevA.106.022424.

[46] Kade Head-Marsden, Stefan Krastanov, David A Mazziotti, and Prineha Narang. Capturing non-Markovian dynamics on near-term quantum computers. Physical Review Research, 3 (1): 013182, 2021. 10.1103/​PhysRevResearch.3.013182. URL https:/​/​​10.1103/​PhysRevResearch.3.013182.

[47] Andrew M. Childs and Nathan Wiebe. Hamiltonian Simulation Using Linear Combinations of Unitary Operations. Quantum Info. Comput., 12 (11–12): 901–924, nov 2012. ISSN 1533-7146. 10.26421/​QIC12.11-12.

[48] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Simulating hamiltonian dynamics with a truncated taylor series. Phys. Rev. Lett., 114: 090502, Mar 2015. 10.1103/​PhysRevLett.114.090502. URL https:/​/​​10.1103/​PhysRevLett.114.090502.

[49] Richard Cleve and Chunhao Wang. Efficient Quantum Algorithms for Simulating Lindblad Evolution. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), volume 80 of Leibniz International Proceedings in Informatics (LIPIcs), pages 17:1–17:14, Dagstuhl, Germany, 2017. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. ISBN 978-3-95977-041-5. 10.4230/​LIPIcs.ICALP.2017.17. URL http:/​/​​opus/​volltexte/​2017/​7477.

[50] Anthony W. Schlimgen, Kade Head-Marsden, LeeAnn M. Sager, Prineha Narang, and David A. Mazziotti. Quantum simulation of open quantum systems using a unitary decomposition of operators. Phys. Rev. Lett., 127: 270503, Dec 2021. 10.1103/​PhysRevLett.127.270503. URL https:/​/​​10.1103/​PhysRevLett.127.270503.

[51] Anthony W Schlimgen, Kade Head-Marsden, LeeAnn M Sager-Smith, Prineha Narang, and David A Mazziotti. Quantum state preparation and non-unitary evolution with diagonal operators. arXiv preprint arXiv:2205.02826, 2022. 10.1103/​PhysRevA.106.022414.

[52] Seth Lloyd and Lorenza Viola. Engineering quantum dynamics. Phys. Rev. A, 65: 010101, Dec 2001. 10.1103/​PhysRevA.65.010101. URL https:/​/​​10.1103/​PhysRevA.65.010101.

[53] Chao Shen, Kyungjoo Noh, Victor V. Albert, Stefan Krastanov, M. H. Devoret, R. J. Schoelkopf, S. M. Girvin, and Liang Jiang. Quantum channel construction with circuit quantum electrodynamics. Phys. Rev. B, 95: 134501, Apr 2017. 10.1103/​PhysRevB.95.134501. URL https:/​/​​10.1103/​PhysRevB.95.134501.

[54] Mario Motta, Chong Sun, Adrian TK Tan, Matthew J O’Rourke, Erika Ye, Austin J Minnich, Fernando GSL Brandão, and Garnet Kin-Lic Chan. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nature Physics, 16 (2): 205–210, 2020. 10.1038/​s41567-019-0704-4. URL https:/​/​​articles/​s41567-019-0704-4.

[55] Hirofumi Nishi, Taichi Kosugi, and Yu-ichiro Matsushita. Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation. npj Quantum Information, 7 (1): 1–7, 2021. 10.1038/​s41534-021-00409-y. URL https:/​/​​articles/​s41534-021-00409-y.

[56] Shi-Ning Sun, Mario Motta, Ruslan N. Tazhigulov, Adrian T.K. Tan, Garnet Kin-Lic Chan, and Austin J. Minnich. Quantum computation of finite-temperature static and dynamical properties of spin systems using quantum imaginary time evolution. PRX Quantum, 2: 010317, Feb 2021a. 10.1103/​PRXQuantum.2.010317. URL https:/​/​​10.1103/​PRXQuantum.2.010317.

[57] Shin Sun, Li-Chai Shih, and Yuan-Chung Cheng. Efficient quantum simulation of open quantum system dynamics on noisy quantum computers. arXiv preprint arXiv:2106.12882, 2021b. URL https:/​/​​abs/​2106.12882.

[58] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 193–204, 2019. 10.1145/​3313276.3316366. URL https:/​/​​doi/​10.1145/​3313276.3316366.

[59] Guang Hao Low and Isaac L Chuang. Hamiltonian simulation by qubitization. Quantum, 3: 163, 2019. 10.22331/​q-2019-07-12-163. URL https:/​/​​papers/​q-2019-07-12-163/​.

[60] Guang Hao Low and Isaac L Chuang. Optimal hamiltonian simulation by quantum signal processing. Physical Review Letters, 118 (1): 010501, 2017a. 10.1103/​PhysRevLett.118.010501. URL https:/​/​​prl/​abstract/​10.1103/​PhysRevLett.118.010501.

[61] Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical Review Letters, 103 (15), Oct 2009. ISSN 1079-7114. 10.1103/​physrevlett.103.150502. URL http:/​/​​10.1103/​PhysRevLett.103.150502.

[62] Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione. An introduction to quantum machine learning. Contemporary Physics, 56 (2): 172–185, 2015. 10.1080/​00107514.2014.964942. URL https:/​/​​doi/​full/​10.1080/​00107514.2014.964942.

[63] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. Quantum machine learning. Nature, 549 (7671): 195–202, 2017. 10.1038/​nature23474. URL https:/​/​​articles/​nature23474.

[64] Chahan M Kropf, Clemens Gneiting, and Andreas Buchleitner. Effective dynamics of disordered quantum systems. Physical Review X, 6 (3): 031023, 2016. 10.1103/​PhysRevX.6.031023. URL https:/​/​​prx/​abstract/​10.1103/​PhysRevX.6.031023.

[65] Trevor McCourt, Charles Neill, Kenny Lee, Chris Quintana, Yu Chen, Julian Kelly, V. N. Smelyanskiy, M. I. Dykman, Alexander Korotkov, Isaac L. Chuang, and A. G. Petukhov. Learning noise via dynamical decoupling of entangled qubits. arXiv:2201.11173, 2022. 10.48550/​ARXIV.2201.11173. URL https:/​/​​abs/​2201.11173.

[66] Koenraad M. R. Audenaert and S. Scheel. On random unitary channels. New Journal of Physics, 10: 023011, 2008. 10.1088/​1367-2630/​10/​2/​023011. URL https:/​/​​article/​10.1088/​1367-2630/​10/​2/​023011.

[67] Robert Alicki and Karl Lendi. Quantum dynamical semigroups and applications, volume 717. Springer, 2007. 10.1007/​3-540-70861-8. URL https:/​/​​book/​10.1007/​3-540-70861-8.

[68] Gilles Brassard and Peter Hoyer. An exact quantum polynomial-time algorithm for simon’s problem. In Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems, pages 12–23. IEEE, 1997.

[69] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. Contemporary Mathematics, 305: 53–74, 2002.

[70] Eliahu Levy and Orr Moshe Shalit. Dilation theory in finite dimensions: the possible, the impossible and the unknown. Rocky Mountain Journal of Mathematics, 44 (1): 203–221, 2014.

[71] Béla Sz Nagy, Ciprian Foias, Hari Bercovici, and László Kérchy. Harmonic analysis of operators on Hilbert space. Springer Science & Business Media, 2010.

[72] Robin Kothari. Efficient algorithms in quantum query complexity. PhD thesis, University of Waterloo, August 2014. URL http:/​/​​10012/​8625.

[73] Jing Xin Cui, Tao Zhou, and Gui Lu Long. An optimal expression of a kraus operator as a linear combination of unitary matrices. Journal of Physics A: Mathematical and Theoretical, 45 (44): 444011, 2012. 10.1088/​1751-8113/​45/​44/​444011. URL https:/​/​​article/​10.1088/​1751-8113/​45/​44/​444011.

[74] Pei Wu. Additive combinations of special operators. Banach Center Publications, 30 (1): 337–361, 1994. URL http:/​/​​doc/​262750.

[75] Jeongwan Haah. Product decomposition of periodic functions in quantum signal processing. Quantum, 3: 190, 2019. 10.22331/​q-2019-10-07-190. URL https:/​/​​papers/​q-2019-10-07-190/​.

[76] Rui Chao, Dawei Ding, Andras Gilyen, Cupjin Huang, and Mario Szegedy. Finding angles for quantum signal processing with machine precision. arXiv preprint arXiv:2003.02831, 2020. URL https:/​/​​abs/​2003.02831.

[77] Yulong Dong, Xiang Meng, K. Birgitta Whaley, and Lin Lin. Efficient phase-factor evaluation in quantum signal processing. Phys. Rev. A, 103: 042419, Apr 2021. 10.1103/​PhysRevA.103.042419. URL https:/​/​​10.1103/​PhysRevA.103.042419.

[78] John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang. Quantum signal processing. https:/​/​​ichuang/​pyqsp.

[79] J.R. Johansson, P. D. Nation, and F. Nori. Qutip 2: A python framework for the dynamics of open quantum systems. Comp. Phys. Comm., 184 (1234), 2013. 10.1016/​j.cpc.2012.11.019.

[80] Yu Tong, Dong An, Nathan Wiebe, and Lin Lin. Fast inversion, preconditioned quantum linear system solvers, fast green’s-function computation, and fast evaluation of matrix functions. Physical Review A, 104 (3): 032422, 2021. 10.1103/​PhysRevA.104.032422. URL https:/​/​​pra/​abstract/​10.1103/​PhysRevA.104.032422.

[81] Guang Hao Low, Theodore J. Yoder, and Isaac L. Chuang. Methodology of resonant equiangular composite quantum gates. Physical Review X, 6 (4), Dec 2016. ISSN 2160-3308. 10.1103/​physrevx.6.041067. URL http:/​/​​10.1103/​PhysRevX.6.041067.

[82] Guang Hao Low and Isaac L Chuang. Hamiltonian simulation by uniform spectral amplification. arXiv preprint arXiv:1707.05391, 2017b. URL https:/​/​​abs/​1707.05391.

[83] Sathyawageeswar Subramanian, Stephen Brierley, and Richard Jozsa. Implementing smooth functions of a hermitian matrix on a quantum computer. Journal of Physics Communications, 3 (6): 065002, 2019. 10.1088/​2399-6528/​ab25a2. URL https:/​/​​article/​10.1088/​2399-6528/​ab25a2.

Cited by

[1] Chiara Leadbeater, Nathan Fitzpatrick, David Muñoz Ramo, and Alex J. W. Thom, “Non-unitary Trotter circuits for imaginary time evolution”, arXiv:2304.07917, (2023).

[2] Juha Leppäkangas, Nicolas Vogt, Keith R. Fratus, Kirsten Bark, Jesse A. Vaitkus, Pascal Stadler, Jan-Michael Reiner, Sebastian Zanker, and Michael Marthaler, “A quantum algorithm for solving open system dynamics on quantum computers using noise”, arXiv:2210.12138, (2022).

[3] Hans Hon Sang Chan, David Muñoz Ramo, and Nathan Fitzpatrick, “Simulating non-unitary dynamics using quantum signal processing with unitary block encoding”, arXiv:2303.06161, (2023).

[4] I J David, I Sinayskiy, and F Petruccione, “Digital Simulation of Single Qubit Markovian Open Quantum Systems: A Tutorial”, arXiv:2302.02953, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-05-17 23:47:57). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-05-17 23:47:56).

Time Stamp:

More from Quantum Journal