dorsal/arxiv
View SchemaThe Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
| Authors | Tobias J. Osborne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508031 |
| URL | https://arxiv.org/abs/quant-ph/0508031 |
| DOI | 10.1103/PhysRevLett.97.157202 |
| Journal | Phys. Rev. Lett. 97, 157202 (2006) |
Abstract
In this Letter we show that an arbitrarily good approximation to the propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may be obtained with polynomial computational resources in n and the error \epsilon, and exponential resources in |t|. Our proof makes use of the finitely correlated state/matrix product state formalism exploited by numerical renormalisation group algorithms like the density matrix renormalisation group. There are two immediate consequences of this result. The first is that the Vidal's time-dependent density matrix renormalisation group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretisation, such circuits are of polynomial depth.
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"abstract": "In this Letter we show that an arbitrarily good approximation to the\npropagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may\nbe obtained with polynomial computational resources in n and the error\n\\epsilon, and exponential resources in |t|. Our proof makes use of the finitely\ncorrelated state/matrix product state formalism exploited by numerical\nrenormalisation group algorithms like the density matrix renormalisation group.\nThere are two immediate consequences of this result. The first is that the\nVidal\u0027s time-dependent density matrix renormalisation group will require only\npolynomial resources to simulate 1D quantum spin systems for logarithmic |t|.\nThe second consequence is that continuous-time 1D quantum circuits with\nlogarithmic |t| can be simulated efficiently on a classical computer, despite\nthe fact that, after discretisation, such circuits are of polynomial depth.",
"arxiv_id": "quant-ph/0508031",
"authors": [
"Tobias J. Osborne"
],
"categories": [
"quant-ph",
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],
"doi": "10.1103/PhysRevLett.97.157202",
"journal_ref": "Phys. Rev. Lett. 97, 157202 (2006)",
"title": "The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently",
"url": "https://arxiv.org/abs/quant-ph/0508031"
},
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