Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for mixed state representations: guaranteed positivity by construction, efficient conservation of the trace and computation of local observables. However, they have been challenging to use for noisy quantum circuit simulation, as the application of noise increases the dimension of the environment Hilbert space, leading to an exponential growth of bond dimensions. MPDOs also lack a unique canonical form, due to the freedom in the choice of basis for the environment Hilbert space, which leads to a vast variation of bond dimensions.
In this work, we present a systematic way to reduce the bond dimensions of MPDOs by disentangling the purified state. We optimize the basis for the environment Hilbert space by performing density matrix renormalization group (DMRG)-like sweeps of local 2-qubit basis optimization. Interestingly, we find that targeting only the disentanglement of the purified state leads to a reduction of the environment dimension. In other words, a compact MPDO representation requires a low-entanglement purified state.
We apply our compression method to the emulation of noisy random quantum circuits. Our technique allows us to keep bounded bond dimensions, and thus bounded memory, contrary to previous works on MPDOs, while keeping reasonable truncation fidelities.
Noise-induced suppression of MPO truncation errors in noisy random circuits and Lindbladian dynamics
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（联合量子研究所，美国国家标准与技术研究院/马里兰大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Department of Physics, University of Basel（巴塞尔大学物理系）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
Approximation Methods for Simulation and Equivalence Checking of Noisy Quantum Circuits
University of Chinese Academy of Sciences（中国科学院大学）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息研究中心）
Enhancing classical simulation with noisy quantum devices
Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）；Department of Mathematics, Tsinghua University（清华大学数学系）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京雁栖湖应用数学研究院）
Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies（量子技术中心）
Limitations of Noisy Geometrically Local Quantum Circuits
University of Maryland（马里兰大学）；Joint Center for Quantum Information & Computer Science, University of Maryland and NIST（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits
DIENS, \'Ecole Normale Sup\'erieure, PSL University, CNRS, INRIA, 45 rue d’Ulm, Paris, 75005, France；Institute of Physics, \'Ecole Polytechnique F\' e d\' e rale de Lausanne (EPFL), Lausanne, Switzerland；Centre for Quantum Science；Engineering, \'Ecole Polytechnique F\' e d\' e rale de Lausanne (EPFL), Lausanne, Switzerland
Classical simulation of a quantum circuit with noisy magic inputs
Graduate School of Quantum Science and Technology, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院量子科学与技术研究生院）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）
Sampling (noisy) quantum circuits through randomized rounding
IBM France（法国国际商业机器公司）；Univ Lyon, ENS Lyon, UCBL, Inria, LIP（里昂大学、巴黎高等师范学校里昂分校、里昂第一大学、法国国家信息与自动化研究所、计算与图像实验室）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits
Lomonosov Moscow State University（莫斯科国立大学）；University of Science and Technology of China（中国科学技术大学）；Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
