Enabling large-depth simulation of noisy quantum circuits with positive tensor networks

• URL: http://arxiv.org/abs/2403.00152v1
• Date: Thu, 29 Feb 2024 22:09:17 GMT
• Title: Enabling large-depth simulation of noisy quantum circuits with positive tensor networks
• Authors: Ambroise M\"uller, Thomas Ayral, Corentin Bertrand
• Abstract summary: Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices. MPDOs have interesting properties for mixed state representations: guaranteed positivity by construction, efficient conservation of the trace and computation of local observables. We present a systematic way to reduce the bond dimensions of MPDOs by disentangling the purified state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Locally purified density operators for noisy quantum circuits [17.38734393793605]
  We show that mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators (LPDOs) We present a mapping from LPDOs of $N$ qubits to projected entangled-pair states of size $2times N$ and introduce a unified method for managing virtual and Kraus bonds.
  arXiv  Detail & Related papers  (2023-12-05T16:10:30Z)
• Sampling reduced density matrix to extract fine levels of entanglement spectrum [3.5899681126850984]
  We propose a new scheme to extract the low-lying fine entanglement spectrum (ES) We trace out the environment via quantum Monte Carlo simulation and diagonalize the reduced density matrix to gain the ES. Our simulation results, with unprecedentedly large system sizes, establish the practical scheme of the entanglement spectrum with a huge freedom degree of environment.
  arXiv  Detail & Related papers  (2023-10-25T15:25:44Z)
• Splitting the local Hilbert space: MPS-based approach to large local dimensions [0.0]
  A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. We present a matrix product state (MPS)-based method for simulating one-dimensional quantum systems with a large local Hilbert space dimension.
  arXiv  Detail & Related papers  (2023-07-29T17:41:27Z)
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits [103.93329374521808]
  Inherent symmetry of a quantum system may protect its otherwise fragile states. We implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $mathbbZ$ parity symmetry. MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism.
  arXiv  Detail & Related papers  (2022-04-24T22:34:15Z)
• A Multisite Decomposition of the Tensor Network Path Integrals [0.0]
  We extend the tensor network path integral (TNPI) framework to efficiently simulate quantum systems with local dissipative environments. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.
  arXiv  Detail & Related papers  (2021-09-20T17:55:53Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics [51.15339237964982]
  "hierarchical equations of motion" (HEOM) is a powerful exact numerical approach to solve the dynamics. It has been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. We present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments.
  arXiv  Detail & Related papers  (2020-10-21T07:54:56Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Simulating Noisy Quantum Circuits with Matrix Product Density Operators [13.151348595345604]
  We show that the method based on Matrix Product States (MPS) fails to approximate the noisy output quantum states for any of the noise models considered. We propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions.
  arXiv  Detail & Related papers  (2020-04-06T03:26:59Z)
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits [62.997667081978825]
  We show that a controlled interaction with the environment may help to create a state, dubbed as em dark'', which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different states act as a computational basis. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.
  arXiv  Detail & Related papers  (2020-02-01T15:57:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.