References
- H.-P. Breuer and F. Petruccione, (2007). The Theory of Open Quantum Systems. Oxford University Press.
- L. H. Delgado-Granados, T. J. Krogmeier, L. M. Sager-Smith, I. Avdic, Z. Hu, M. Sajjan, M. Abbasi, S. E. Smart, P. Narang, S. Kais, A. W. Schlimgen, K. Head-Marsden and D. A. Mazziotti, (2025). “Quantum algorithms and applications for open quantum systems”. Chemical Reviews, 0, 0.
- C. M. Bender and S. Boettcher, (1998). “Real spectra in non-Hermitian Hamiltonians having PT symmetry”. Physical Review Letters, 80, 5243.
- A. Mostafazadeh, (2002). “Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian”. Journal of Mathematical Physics, 43, 205.
- A. Mostafazadeh, (2010). “Pseudo-Hermitian representation of quantum mechanics”. International Journal of Geometric Methods in Modern Physics, 7, 1191.
- C.-Y. Ju, A. Miranowicz, G.-Y. Chen and F. Nori, (2019). “Non-hermitian Hamiltonians and no-go theorems in quantum information”. Physical Review A, 100, 062118.
- A. M. Childs and N. Wiebe, (2012). “Hamiltonian simulation using linear combinations of unitary operations”. Quantum Information & Computation, 12, 901–924.
- D. W. Berry, A. M. Childs and R. Kothari, (2015). “Hamiltonian simulation with nearly optimal dependence on all parameters,” in Proceedings of the 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 792–809.
- H. Krovi, (2023). “Improved quantum algorithms for linear and nonlinear differential equations”. Quantum, 7, 913.
- G.-L. Long, (2006). “General quantum interference principle and duality computer”. Communications in Theoretical Physics, 45, 825.
- G.-L. Long and L. Yang (2008). “Duality computing in quantum computers”. Communications in Theoretical Physics, 50, 1303.
- G.-L. Long, L. Yang and C. Wang (2009). “Allowable generalized quantum gates”. Communications in Theoretical Physics, 51, 65.
- G.-L. Long, (2011). “Duality quantum computing and duality quantum information processing”. International Journal of Theoretical Physics, 50, 1305–1318.
- S.-J. Wei, D. Ruan and G.-L. Long, (2016). “Duality quantum algorithm efficiently simulates open quantum systems”. Scientific Reports, 6, 30727.
- C. Zheng, (2021). “Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm”. Scientific Reports, 11, 3960. https://doi.org/10.1038/s41598-021-83521-5.
- A. W. Schlimgen, K. Head-Marsden, L. M. Sager, P. Narang and D. A. Mazziotti, (2021). “Quantum simulation of open quantum systems using a unitary decomposition of operators”. Physical Review Letters, 127, 270503. https://doi.org/10.1103/PhysRevLett.127.270503.
- N. Suri, J. Barreto, S. Hadfield, N. Wiebe, F. Wudarski and J. Marshall, (2023). “Two-unitary decomposition algorithm and open quantum system simulation”. Quantum, 7, 1002. https://doi.org/10.22331/q-2023-05-15-1002.
- R. Hu and S. Kais, (2020). “A quantum algorithm for evolving open quantum dynamics on quantum computing devices”. Scientific Reports, 10, 3301. https://doi.org/10.1038/s41598-020-60321-x.
- A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang and D. A. Mazziotti, (2022). “Quantum state preparation and nonunitary evolution with diagonal operators”. Physical Review A, 106, 022414. https://doi.org/10.1103/PhysRevA.106.022414.
- A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang and D. A. Mazziotti, Quantum simulation of open quantum systems using density-matrix purification. arXiv:2207.07112 [quant-ph]. https://doi.org/10.48550/arXiv.2207.07112.
- S. Jin, N. Liu and Y. Yu, (2023). “Quantum simulation of partial differential equations: Applications and detailed analysis”. Physical Review A, 108, 032603. https://doi.org/10.1103/PhysRevA.108.032603.
- E. Koukoutsis, K. Hizanidis, A. K. Ram and G. Vahala, (2024). “Quantum simulation of dissipation for Maxwell equations in dispersive media”. Future Generation Computer Systems, 159, 221. https://doi.org/10.1016/j.future.2024.05.028.
- O. M. Shalit, (2021). “Dilation theory: A guided tour”, in M. A. Bastos, L. Castro, A. Y. Karlovich (eds), Operator Theory, Functional Analysis and Applications; Springer International Publishing, pp. 551–623. https://doi.org/10.1007/978-3-030-51945-2_28.
- D. C. Brody, (2013). “Biorthogonal quantum mechanics”. Journal of Physics A, 47: 035305. https://doi.org/10.1088/1751-8113/47/3/035305.
- T. Curtright and L. Mezincescu, (2007). “Biorthogonal quantum systems”. Journal of Mathematical Physics, 48, 092106. https://doi.org/10.1063/1.2196243.
- K. Sim, N. Defenu, P. Molignini and R. Chitra, (2023). “Quantum metric unveils defect freezing in non-Hermitian systems”. Physical Review Letters, 131, 156501. https://doi.org/10.1103/PhysRevLett.131.156501.
- V. Meden, L. Grunwald and D. M. Kennes, (2023). “PT-symmetric, non-Hermitian quantum many-body physics–a methodological perspective”. Reports on Progress in Physics, 86, 124501. https://doi.org/10.1088/1361-6633/ad05f3.
- T.-X. Hou and W. Li, (2024). “Nonadiabatic geometric quantum computation in non-Hermitian systems”. Physical Review A, 109, 022616. https://doi.org/10.1103/PhysRevA.109.022616.
- M. Znojil, (2008). “Time-dependent version of crypto-hermitian quantum theory”. Physical Review D, 78, 085003. https://doi.org/10.1103/PhysRevD.78.085003
- A. Mostafazadeh, (2002). “Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-hermitian hamiltonians with a real spectrum”. Journal of Mathematical Physics, 43, 2814. https://doi.org/10.1063/1.1461427
- A. Mostafazadeh, (2003). “Is pseudo-Hermitian quantum mechanics an indefinite-metric quantum theory?” Czechoslovak Journal of Physics, 53, 1079–1084. https://doi.org/10.1023/B:CJOP.0000010537.23790.8c
- E. Koukoutsis, K. Hizanidis, A. K. Ram and G. Vahala, (2023). “Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media”. Physical Review A, 107, 042215. https://doi.org/10.1103/PhysRevA.107.042215
- Q. Zhang and B. Wu, (2018). “Lorentz quantum mechanics”. New Journal of Physics, 20, 013024. https://doi.org/10.1088/1367-2630/aa8496
- A. Mostafazadeh, (2004). “Pseudounitary operators and pseudounitary quantum dynamics”. Journal of Mathematical Physics, 45, 932. https://doi.org/10.1063/1.1646448
- E. Edvardsson, J. L. K. König and M. Stålhammar, (2023). “Biorthogonal renormalization”. arXiv:2212.06004 [quant-ph], 2023. https://arxiv.org/abs/2212.06004
- M. A. Nielsen and I. L. Chuang, (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511976667
- X. Zhan, (2001). “Span of the orthogonal orbit of real matrices”. Linear and Multilinear Algebra, 49, 337. https://doi.org/10.1080/03081080108818704
- W. D. Heiss, (2004). “Exceptional points of non-Hermitian operators”. Journal of Physics A: Mathematical and Theoretical, 37, 2455. https://doi.org/10.1088/0305-4470/37/6/034
- W. D. Heiss, (2012). “The physics of exceptional points”. Journal of Physics A: Mathematical and Theoretical, 45, 444016. https://doi.org/10.1088/1751-8113/45/44/444016
- A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou and D. N. Christodoulides, (2009). “Observation of PT-symmetry breaking in complex optical potentials”. Physical Review Letters, 103, 093902. https://doi.org/10.1103/PhysRevLett.103.093902
- H. Qin, R. Zhang, A. S. Glasser and J. Xiao, (2019). “Kelvin-Helmholtz instability is the result of parity-time symmetry breaking”. Physics of Plasmas, 26, 032102. https://doi.org/10.1063/1.5088498
- R. Zhang, H. Qin and J. Xiao, (2020). “PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability”. Journal of Mathematical Physics, 61, 012101. https://doi.org/10.1063/1.5117211
- C. Zheng, (2022). “Quantum simulation of pseudo-Hermitian-ϕ-symmetric two-level systems”. Entropy, 24, 867. https://doi.org/10.3390/e24070867
- O. N. Kirillov, (2021). Nonconservative Stability Problems of Modern Physics. Berlin, Boston: De Gruyter. https://doi.org/doi:10.1515/9783110655407
- P. Pechukas. (1994). “Reduced dynamics need not be completely positive”. Physical Review Letters, 73, 1060. https://doi.org/10.1103/PhysRevLett.73.1060
- P. Stelmachovič and V. Bužek, (2001). “Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation”. Physical Review A, 64, 062106. https://doi.org/10.1103/PhysRevA.64.062106
- A. Shaji and E. Sudarshan, (2005). “Who’s afraid of not completely positive maps?” Physics Letters A, 341, 48. https://doi.org/10.1016/j.physleta.2005.04.029
- H.-P. Breuer, E.-M. Laine, J. Piilo and B. Vacchini, (2016). “Colloquium: Non-Markovian dynamics in open quantum systems”. Reviews of Modern Physics, 88, 021002. https://doi.org/10.1103/RevModPhys.88.021002
- J. Rembieliński and P. Caban, (2021). “Nonlinear extension of the quantum dynamical semigroup”. Quantum, 5, 420. https://doi.org/10.22331/q-2021-03-23-420
- A. Fring and M. H. Y. Moussa, (2016). “Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians”. Physical Review A, 93, 042114. https://doi.org/10.1103/PhysRevA.93.042114
- J. Dieudonné, (1953). “On biorthogonal systems”. Michigan Mathematical Journal, 2, 7. https://doi.org/10.1307/mmj/1028989861
- Y. Saad, (1982). “The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems”. SIAM Journal on Numerical Analysis, 19, 485. https://doi.org/10.1137/0719031