2000 character limit reached
Augmenting Density Matrix Renormalization Group with Clifford Circuits (2405.09217v2)
Published 15 May 2024 in cond-mat.str-el and quant-ph
Abstract: Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to the study two-dimensional systems encounters challenges due to the limited entanglement encoded in the wave-function ansatz. Conversely, Clifford circuits offer a promising avenue for simulating states with substantial entanglement, albeit confined to stabilizer states. In this work, we present the seamless integration of Clifford circuits within the DMRG algorithm, leveraging the advantages of both Clifford circuits and DMRG. This integration leads to a significant enhancement in simulation accuracy with small additional computational cost. Moreover, this framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches
- E. Dagotto, Correlated electrons in high-temperature superconductors, Rev. Mod. Phys. 66, 763 (1994).
- X. G. Wen, Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons (Oxford University Press, Oxford, 2007).
- D. Cabra, A. Honecker, and P. Pujol, Modern Theories of Many-Particle Systems in Condensed Matter Physics, Vol. 843 (2012).
- E. C. Marino, Quantum Field Theory Approach to Condensed Matter Physics (Cambridge University Press, Cambridge, 2017).
- T. Senthil, Deconfined quantum critical points: a review, arXiv (2023), 2306.12638 [cond-mat.str-el] .
- S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
- U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
- S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Phys. Rev. B 49, 9214 (1994).
- F. Verstraete and J. I. Cirac, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, arXiv e-prints , cond-mat/0407066 (2004), arXiv:cond-mat/0407066 [cond-mat.str-el] .
- G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99, 220405 (2007).
- G. Evenbly and G. Vidal, Entanglement renormalization in two spatial dimensions, Phys. Rev. Lett. 102, 180406 (2009).
- R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of Physics 349, 117 (2014).
- M. C. Bañuls, Tensor network algorithms: A route map, Annual Review of Condensed Matter Physics 14, 173 (2023).
- T. Xiang, Density Matrix and Tensor Network Renormalization (Cambridge University Press, 2023).
- X. Qian and M. Qin, Augmenting density matrix renormalization group with disentanglers, Chinese Physics Letters 40, 057102 (2023).
- X. Qian and M. Qin, Absence of spin liquid phase in the J1−J2subscript𝐽1subscript𝐽2{J}_{1}-{J}_{2}italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the square lattice, Phys. Rev. B 109, L161103 (2024).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- D. Gottesman, Stabilizer codes and quantum error correction (1997), arXiv:quant-ph/9705052 [quant-ph] .
- S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A 70, 052328 (2004).
- S. Anders and H. J. Briegel, Fast simulation of stabilizer circuits using a graph-state representation, Phys. Rev. A 73, 022334 (2006).
- L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
- G. Lami and M. Collura, Learning the stabilizer group of a matrix product state (2024), arXiv:2401.16481 [quant-ph] .
- G. Lami and M. Collura, Nonstabilizerness via perfect pauli sampling of matrix product states, Phys. Rev. Lett. 131, 180401 (2023).
- C. Chamon, A. Hamma, and E. R. Mucciolo, Emergent irreversibility and entanglement spectrum statistics, Phys. Rev. Lett. 112, 240501 (2014).
- Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum 3, 020333 (2022).
- S. Bravyi and A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
- A. Ahmadi and E. Greplova, Quantifying non-stabilizerness via information scrambling, SciPost Phys. 16, 043 (2024).
- G. Lami, T. Haug, and J. D. Nardis, Quantum state designs with clifford enhanced matrix product states (2024), arXiv:2404.18751 [quant-ph] .
- A. F. Mello, A. Santini, and M. Collura, Hybrid stabilizer matrix product operator (2024), arXiv:2405.06045 [quant-ph] .
- S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
- S. Östlund and S. Rommer, Thermodynamic limit of density matrix renormalization, Phys. Rev. Lett. 75, 3537 (1995).
- R. Koenig and J. A. Smolin, How to efficiently select an arbitrary Clifford group element, Journal of Mathematical Physics 55, 122202 (2014).
- Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
- O. F. Syljuåsen and A. W. Sandvik, Quantum monte carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
- Y. Mitsuhashi and N. Yoshioka, Clifford group and unitary designs under symmetry, PRX Quantum 4, 040331 (2023).
- J. Haegeman, The SU(2) symmetry code is developed with TensorKit package at https://github.com/Jutho/TensorKit.jl.