Compression of quantum shallow-circuit states (2404.11177v3)
Abstract: Shallow quantum circuits feature not only computational advantages over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical and practical importance that remained largely unexplored. In this work, we show that $N$ copies of an unknown $n$-qubit state generated by a fixed-depth circuit can be compressed into a hybrid memory of $O(n \log_2 N)$ (qu)bits, which achieves the optimal scaling of memory cost. Our work shows that the computational complexity of resources can significantly impact the rate of quantum information processing, offering a unique and unified view of quantum Shannon theory and quantum computing.
- S. Bravyi, D. Gosset, and R. König, Science 362, 308 (2018).
- J. Preskill, Quantum 2, 79 (2018).
- N. Yu and T.-C. Wei, arXiv:2303.08938 (2023).
- V. Giovannetti, S. Lloyd, and L. Maccone, Science 306, 1330 (2004).
- V. Giovannetti, S. Lloyd, and L. Maccone, Physical Review Letters 96, 010401 (2006).
- V. Giovannetti, S. Lloyd, and L. Maccone, Nature Photonics 5, 222 (2011).
- G. D’Ariano and P. L. Presti, Physical Review Letters 86, 4195 (2001).
- G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, Advances in Imaging and Electron Physics 128, S1076 (2003).
- H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020).
- N. Gisin and S. Massar, Physical Review Letters 79, 2153 (1997).
- R. F. Werner, Physical Review A 58, 1827 (1998).
- D. Bruss, A. Ekert, and C. Macchiavello, Physical Review Letters 81, 2598 (1998).
- C. W. Helstrom, Journal of Statistical Physics 1, 231 (1969).
- H. Yuen, R. Kennedy, and M. Lax, IEEE Transactions on Information Theory 21, 125 (1975).
- C. W. Helstrom, Quantum Detection and Estimation Theory, Vol. 123 (Elsevier Science, 1976).
- A. S. Holevo, Theory of Probability & Its Applications 23, 411 (1979).
- S. Lloyd, M. Mohseni, and P. Rebentrost, Nature Physics 10, 631 (2014).
- M. Plesch and V. Bužek, Physical Review A 81, 032317 (2010).
- M. A. Nielsen and I. L. Chuang, Physical Review Letters 79, 321 (1997).
- S. Ishizaka and T. Hiroshima, Physical Review Letters 101, 240501 (2008).
- A. M. Kubicki, C. Palazuelos, and D. Pérez-García, Physical Review Letters 122, 080505 (2019).
- M. Sedlák, A. Bisio, and M. Ziman, Physical Review Letters 122, 170502 (2019).
- M. Guţă and J. Kahn, Physical Review A 73, 052108 (2006).
- M. Guţă and A. Jenčová, Communications in Mathematical Physics 276, 341 (2007).
- J. Kahn and M. Guţă, Communications in Mathematical Physics 289, 597 (2009).
- R. D. Gill and M. I. Guţă, in From Probability to Statistics and Back: High-Dimensional Models and Processes–A Festschrift in Honor of Jon A. Wellner, Vol. 9 (Institute of Mathematical Statistics, 2013) pp. 105–128.
- F. Girotti, A. Godley, and M. Guţă, arXiv:2310.06767 (2023).
- M. Suzuki, Communications in Mathematical Physics 57, 193 (1977).
- C. M. Caves, Physical Review D 26, 1817 (1982).
- A. S. Holevo, Problemy Peredachi Informatsii 9, 3 (1973).
- R. Alicki and M. Fannes, Journal of Physics A 37, L55 (2004).
- M. M. Wilde, Quantum Information Theory, 2nd ed. (Cambridge University Press, 2017).
- S. Luo and Q. Zhang, Physical Review A 69, 032106 (2004).
- A. A. W. Harrow, Applications of coherent classical communication and the Schur transform to quantum information theory, Ph.D. thesis, Massachusetts Institute of Technology (2005).
- D. Bacon, I. L. Chuang, and A. W. Harrow, Physical Review Letters 97, 170502 (2006).
- H. Krovi, Quantum 3, 122 (2019).
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