Perfect Sampling with Unitary Tensor Networks

By A. Ferris, Guifré Vidal. 2012

143 citations recorded by the source corpus.

Tensor network states are powerful variational Ansatze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we propose perfect sampling schemes, with vanishing equilibration and autocorrelation times, for unitary tensor networks, namely, tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary versions of the matrix product state (MPS) and tree tensor network (TTN), and the multiscale entanglement renormalization Ansatz (MERA). Configurations are directly sampled according to their probabilities in the wave function, without resorting to a Markov chain process. We consider both complete sampling, involving all the relevant sites of the system, and incomplete sampling, which only involves a subset of those sites and which can result in a dramatic (basis-dependent) reduction of sampling error.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5a012bdc62df597495d48b22c1eeb07438dd239a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. E. Stoudenmire
2. Lukasz Cincio
3. Lei Wang
4. Heng Fan
5. Zhaoyu Han
6. Pan Zhang
7. Jun Wang
8. Yiqing Zhou

In Condensed Matter Physics

1. Zhaoyu Han
2. Pan Zhang
3. Heng Fan
4. Yiqing Zhou
5. Lei Wang
6. Jun Wang
7. E. Stoudenmire
8. X. Waintal

In Nuclear and High Energy Physics

1. Lukasz Cincio
2. Patrick J. Coles
3. Andrew Arrasmith
4. Piotr Czarnik

Citations in the corpus

• Error mitigation with Clifford quantum-circuit data (2020, methodology): “To perform classical, finite-shot, large Q simulations we use perfect sampling with matrix product states [22].”
• What Limits the Simulation of Quantum Computers? (2020, background): “[20] Andrew J.”
• Reconstructing quantum states with generative models (2018, unknown): “[62] Ferris, A.”
• Unsupervised Generative Modeling Using Matrix Product States (2017, methodology): “Our model enjoys a direct sampling method, which generates a sample bit by bit from one end of the MPS to the other [36].”