Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 99 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 36 tok/s
GPT-5 High 40 tok/s Pro
GPT-4o 99 tok/s
GPT OSS 120B 461 tok/s Pro
Kimi K2 191 tok/s Pro
2000 character limit reached

Dynamical Magic Transitions in Monitored Clifford+T Circuits (2312.00132v3)

Published 30 Nov 2023 in quant-ph, cond-mat.mes-hall, and cond-mat.stat-mech

Abstract: The classical simulation of highly-entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in classical simulability. Here, we study simulability transitions beyond entanglement: noting that some highly-entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate, thus requiring "magic"--a subtle form of quantum resource--to achieve computational hardness, we ask how the dynamics of magic competes with measurements. We study the resulting "dynamical magic transitions" focusing on random monitored Clifford circuits doped by T gates (injecting magic). We identify dynamical "stabilizer-purification"--the collapse of a superposition of stabilizer states by measurements--as the mechanism driving this transition. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase. In establishing our results, we use Pauli-based computation, a scheme distilling the quantum essence of the dynamics to a magic state register subject to mutually commuting measurements. We link stabilizer-purification to "magic fragmentation" wherein these measurements separate into disjoint, O(1)-weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (68)
  1. R. P. Feynman, Simulating physics with computers, Int J Theor Phys 21, 467 (1982).
  2. G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003).
  3. G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004).
  4. I. L. Markov and Y. Shi, Simulating quantum computation by contracting tensor networks, SIAM Journal on Computing 38, 963 (2008).
  5. A. M. Dalzell, N. Hunter-Jones, and F. G. S. L. Brandão, Random quantum circuits anticoncentrate in log depth, PRX Quantum 3, 010333 (2022).
  6. T. B. Wahl and S. Strelchuk, Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound, Phys. Rev. Lett. 131, 180601 (2023).
  7. B. M. Terhal and D. P. DiVincenzo, Adaptive quantum computation, constant depth quantum circuits and Arthur-Merlin games (2004), arXiv:quant-ph/0205133 .
  8. F. Pan, K. Chen, and P. Zhang, Solving the sampling problem of the sycamore quantum circuits, Phys. Rev. Lett. 129, 090502 (2022).
  9. F. Arute et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019).
  10. Y. Wu et al., Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett. 127, 180501 (2021).
  11. D. Hangleiter and J. Eisert, Computational advantage of quantum random sampling, Rev. Mod. Phys. 95, 035001 (2023).
  12. B. M. Terhal and D. P. DiVincenzo, Classical simulation of noninteracting-fermion quantum circuits, Phys. Rev. A 65, 032325 (2002).
  13. S. Bravyi, Lagrangian representation for fermionic linear optics (2004), arXiv:quant-ph/0404180 .
  14. D. Gottesman, The heisenberg representation of quantum computers (1998), arXiv:quant-ph/9807006 .
  15. S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A 70, 052328 (2004).
  16. D. Aharonov, Quantum to classical phase transition in noisy quantum computers, Phys. Rev. A 62, 062311 (2000).
  17. Y. Li, X. Chen, and M. P. A. Fisher, Quantum zeno effect and the many-body entanglement transition, Phys. Rev. B 98, 205136 (2018).
  18. Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
  19. B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).
  20. Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
  21. R. Trivedi and J. I. Cirac, Transitions in computational complexity of continuous-time local open quantum dynamics, Phys. Rev. Lett. 129, 260405 (2022).
  22. X. Zhou, D. W. Leung, and I. L. Chuang, Methodology for quantum logic gate construction, Phys. Rev. A 62, 052316 (2000).
  23. S. Bravyi and A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  24. E. T. Campbell and D. E. Browne, Bound states for magic state distillation in fault-tolerant quantum computation, Phys. Rev. Lett. 104, 030503 (2010).
  25. S. Bravyi, G. Smith, and J. A. Smolin, Trading classical and quantum computational resources, Phys. Rev. X 6, 021043 (2016).
  26. M. Howard and E. Campbell, Application of a resource theory for magic states to fault-tolerant quantum computing, Phys. Rev. Lett. 118, 090501 (2017).
  27. Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum 3, 020333 (2022).
  28. T. Haug and M. S. Kim, Scalable measures of magic resource for quantum computers, PRX Quantum 4, 010301 (2023).
  29. L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
  30. S. True and A. Hamma, Transitions in Entanglement Complexity in Random Circuits, Quantum 6, 818 (2022).
  31. S. F. Oliviero, L. Leone, and A. Hamma, Transitions in entanglement complexity in random quantum circuits by measurements, Physics Letters A 418, 127721 (2021).
  32. K. Bu and D. E. Koh, Efficient classical simulation of clifford circuits with nonstabilizer input states, Phys. Rev. Lett. 123, 170502 (2019).
  33. C. D. White, C. J. Cao, and B. Swingle, Conformal field theories are magical, Phys. Rev. B 103, 075145 (2021).
  34. S. F. E. Oliviero, L. Leone, and A. Hamma, Magic-state resource theory for the ground state of the transverse-field ising model, Phys. Rev. A 106, 042426 (2022).
  35. T. Haug and L. Piroli, Quantifying nonstabilizerness of matrix product states, Phys. Rev. B 107, 035148 (2023a).
  36. T. Haug and L. Piroli, Stabilizer entropies and nonstabilizerness monotones, Quantum 7, 1092 (2023b).
  37. T. J. Sewell and C. D. White, Mana and thermalization: Probing the feasibility of near-clifford hamiltonian simulation, Phys. Rev. B 106, 125130 (2022).
  38. K. Goto, T. Nosaka, and M. Nozaki, Chaos by magic (2021), arXiv:2112.14593 [hep-th] .
  39. P. S. Tarabunga, Critical behaviours of non-stabilizerness in quantum spin chains (2023), arXiv:2309.00676 .
  40. P. S. Tarabunga and C. Castelnovo, Magic in generalized rokhsar-kivelson wavefunctions (2023), arXiv:2311.08463 .
  41. X. Turkeshi, M. Schirò, and P. Sierant, Measuring nonstabilizerness via multifractal flatness, Phys. Rev. A 108, 042408 (2023).
  42. S. Bravyi and D. Gosset, Improved classical simulation of quantum circuits dominated by clifford gates, Phys. Rev. Lett. 116, 250501 (2016).
  43. H. Qassim, H. Pashayan, and D. Gosset, Improved upper bounds on the stabilizer rank of magic states, Quantum 5, 606 (2021).
  44. M. J. Gullans and D. A. Huse, Dynamical purification phase transition induced by quantum measurements, Phys. Rev. X 10, 041020 (2020).
  45. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (CUP, 2010).
  46. C. K. McLauchlan and B. Béri, Fermion-parity-based computation and its majorana-zero-mode implementation, Phys. Rev. Lett. 128, 180504 (2022).
  47. J. Cardy, Finite-Size Scaling, Volume 2 (North Holland, 1988).
  48. A. Sorge, pyfssa 0.7.6 (2015).
  49. M. E. Fisher and M. N. Barber, Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972).
  50. D. Gottesman, Stabilizer codes and quantum error correction (1997), arXiv:quant-ph/9705052 .
  51. M. B. Hastings and J. Haah, Dynamically Generated Logical Qubits, Quantum 5, 564 (2021).
  52. C. T. Chubb and S. T. Flammia, Statistical mechanical models for quantum codes with correlated noise, Ann. Henri Poincaré D 8, 269 (2021).
  53. Y. Li and M. P. A. Fisher, Statistical mechanics of quantum error correcting codes, Phys. Rev. B 103, 104306 (2021).
  54. F. Venn, J. Behrends, and B. Béri, Coherent-error threshold for surface codes from majorana delocalization, Phys. Rev. Lett. 131, 060603 (2023).
  55. D. Greenbaum and Z. Dutton, Modeling coherent errors in quantum error correction, Quantum Sci. Technol. 3, 015007 (2017).
  56. E. Huang, A. C. Doherty, and S. Flammia, Performance of quantum error correction with coherent errors, Phys. Rev. A 99, 022313 (2019).
  57. J. K. Iverson and J. Preskill, Coherence in logical quantum channels, New J. of Phys. 22, 073066 (2020).
  58. O. Lunt, M. Szyniszewski, and A. Pal, Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional clifford circuits, Phys. Rev. B 104, 155111 (2021).
  59. S. Bravyi and D. Maslov, Hadamard-free circuits expose the structure of the clifford group, IEEE Transactions on Information Theory 67, 4546 (2021).
  60. W. Dür, G. Vidal, and J. I. Cirac, Optimal conversion of nonlocal unitary operations, Phys. Rev. Lett. 89, 057901 (2002).
  61. G. Grimmett, Probability on Graphs: Random Processes on Graphs and Lattices, 2nd ed. (CUP, 2018).
  62. G. R. Grimmett and I. Manolescu, Inhomogeneous bond percolation on square, triangular and hexagonal lattices, The Annals of Probability 41, 2990 (2013a).
  63. G. Grimmett, Percolation, 2nd ed. (Springer, 1999).
  64. C. Bezuidenhout and G. Grimmett, Exponential Decay for Subcritical Contact and Percolation Processes, The Annals of Probability 19, 984 (1991).
  65. G. R. Grimmett and I. Manolescu, Universality for bond percolation in two dimensions, The Annals of Probability 41, 3261 (2013b).
  66. T. J. Yoder, A generalization of the stabilizer formalism for simulating arbitrary quantum circuits, unpublished (2012) .
  67. F. C. R. Peres and E. F. Galvão, Quantum circuit compilation and hybrid computation using Pauli-based computation, Quantum 7, 1126 (2023).
  68. Çetin Kaya Koç and S. N. Arachchige, A fast algorithm for gaussian elimination over gf(2) and its implementation on the gapp, J. Parallel Distributed Comput. 13, 118-122  (1991).
Citations (8)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets