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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Improved scaling of time-evolving block-decimation algorithm through reduced-rank randomized singular value

D Tamascelli1,2, R Rosenbach2, M B Plenio2

  • 1Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a randomized singular value decomposition (RRSVD) to accelerate quantum system simulations. The RRSVD method significantly speeds up the time-evolving block-decimation (TEBD) algorithm while maintaining high accuracy.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Quantum information science

Background:

  • Limited entanglement in quantum systems restricts dynamics to a small state subspace.
  • Efficient system description is achieved by focusing on this relevant subspace.
  • Algorithms like TEBD utilize decimation techniques based on SVD to select relevant subspaces.

Purpose of the Study:

  • To improve the computational efficiency of quantum system simulations.
  • To reduce the computational complexity of the time-evolving block-decimation (TEBD) algorithm.
  • To demonstrate the accuracy and speed-up achieved by using randomized SVD (RRSVD).

Main Methods:

  • Application of a randomized singular value decomposition (RRSVD) routine.
  • Integration of RRSVD into the time-evolving block-decimation (TEBD) algorithm.
  • Validation using real-world quantum system examples.

Main Results:

  • The computational complexity power law of TEBD is reduced by one degree using RRSVD.
  • A considerable speed-up in simulation time is achieved.
  • RRSVD provides results with accuracy comparable to deterministic SVD methods.

Conclusions:

  • Randomized SVD offers a significant computational advantage for TEBD simulations.
  • RRSVD maintains high accuracy, making it a viable alternative to deterministic SVD.
  • This approach enhances the efficiency of simulating quantum systems with limited entanglement.