Measurement-Induced Criticality is Tomographically Optimal
Abstract: We develop a classical shadow tomography protocol utilizing the randomized measurement scheme based on hybrid quantum circuits, which consist of layers of two-qubit random unitary gates mixed with single-qubit random projective measurements. Unlike conventional protocols that perform all measurements by the end of unitary evolutions, our protocol allows measurements to occur at any spacetime position throughout the quantum evolution. We provide a universal classical post-processing strategy to approximately reconstruct the original quantum state from intermittent measurement outcomes given the corresponding random circuit realizations over repeated experiments. We investigated the sample complexity for estimating different observables at different measurement rates of the hybrid quantum circuits. Our result shows that the sample complexity has an optimal scaling at the critical measurement rate when the hybrid circuit undergoes the measurement-induced transition.
- D. Enshan Koh and S. Grewal, Quantum 6, arXiv:2011.11580 (2022), arXiv:2011.11580 [quant-ph] .
- H.-Y. Hu and Y.-Z. You, Physical Review Research 4, 013054 (2022), arXiv:2102.10132 [quant-ph] .
- G. Hao Low, arXiv e-prints , arXiv:2208.08964 (2022), arXiv:2208.08964 [quant-ph] .
- A. C. Potter and R. Vasseur, arXiv e-prints , arXiv:2111.08018 (2021), arXiv:2111.08018 [quant-ph] .
- M. J. Gullans and D. A. Huse, Physical Review X 10, 041020 (2020), arXiv:1905.05195 [quant-ph] .
- See Appendix A for more rigorous treatment of the normalization.
- D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology (1997).
- D. Gottesman, arXiv e-prints , quant-ph/9807006 (1998), arXiv:quant-ph/9807006 [quant-ph] .
- W. W. Ho and D. A. Abanin, Phys. Rev. B 95, 094302 (2017), arXiv:1508.03784 [cond-mat.stat-mech] .
- T. Zhou and X. Chen, Phys. Rev. E 99, 052212 (2019), arXiv:1805.09307 [cond-mat.str-el] .
- T. Zhou and A. Nahum, Phys. Rev. B 99, 174205 (2019), arXiv:1804.09737 [cond-mat.stat-mech] .
- S. Xu and B. Swingle, Physical Review X 9, 031048 (2019), arXiv:1805.05376 [cond-mat.str-el] .
- X. Chen and T. Zhou, Phys. Rev. B 100, 064305 (2019), arXiv:1808.09812 [cond-mat.stat-mech] .
- A. A. Akhtar and Y.-Z. You, Phys. Rev. B 102, 134203 (2020), arXiv:2006.08797 [cond-mat.dis-nn] .
- See Appendix A for a brief review of the Markov evolution of Pauli weights.
- See Appendix B for a statistical mechanical model interpretation for the scaling behavior.
- See Appendix C for a more detailed quantitative analysis using toy models.
- M. Ippoliti and V. Khemani, arXiv e-prints , arXiv:2307.15011 (2023), arXiv:2307.15011 [quant-ph] .
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