Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
arXiv:1504.00992 · doi:10.1103/PhysRevE.91.063306
Abstract
When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in the system size. A class of algorithms, exemplified by the Time-Evolving Block-Decimation (TEBD) algorithm, make use of this observation by selecting the relevant subspace through a decimation technique relying on the Singular Value Decomposition (SVD). In these algorithms, the complexity of each time-evolution step is dominated by the SVD. Here we show that, by applying a randomized version of the SVD routine (RRSVD), the power law governing the computational complexity of TEBD is lowered by one degree, resulting in a considerable speed-up. We exemplify the potential gains in efficiency at the hand of some real world examples to which TEBD can be successfully applied to and demonstrate that for those system RRSVD delivers results as accurate as state-of-the-art deterministic SVD routines.
14 pages, 5 figures
References in corpus (25)
- The density-matrix renormalization group in the age of matrix product states
- Area laws for the entanglement entropy - a review
- Efficient classical simulation of slightly entangled quantum computations
- Efficient simulation of one-dimensional quantum many-body systems
- Real time evolution using the density matrix renormalization group
- Entanglement renormalization
- On the role of entanglement in quantum computational speed-up
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Tensor renormalization group approach to 2D classical lattice models
- Efficient simulation of strong system-environment interactions
- Corner Transfer Matrix Renormalization Group Method
- A class of ansatz wave functions for 1D spin systems and their relation to DMRG
- Entropy scaling and simulability by Matrix Product States
- Entanglement spectrum in one-dimensional systems
- Entanglement Properties of the Harmonic Chain
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
- Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
- Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
- Exponential Decay of Correlations Implies Area Law
- Time evolution algorithms for Matrix Product States and DMRG
- An area law for entanglement from exponential decay of correlations
- Mappings of open quantum systems onto chain representations and Markovian embeddings
- Higher Order Methods for Simulations on Quantum Computers
- Graphics processing units accelerated semiclassical initial value representation molecular dynamics
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- Optimized auxiliary oscillators for the simulation of general open quantum systems
- When is a non-Markovian quantum process classical?
- Dissipation-assisted matrix product factorization
- Superdiffusive Energy Transport in Kinetically Constrained Models
- Quantum probing beyond pure dephasing
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- Fingerprint and universal Markovian closure of structured bosonic environments
- Entanglement and precession in two-dimensional dynamical quantum phase transitions
- Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
- Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
- Accelerated 2D magnetic resonance spectroscopy of single spins using matrix completion
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