Unitary circuits of finite depth and infinite width from quantum channels

By S. Gopalakrishnan, Austen Lamacraft. Physical review B, 2019

146 citations recorded by the source corpus.

We introduce an approach to compute reduced density matrices for local quantum unitary circuits of finite depth and infinite width. Suppose the time-evolved state under the circuit is a matrix-product state with bond dimension $D$; then the reduced density matrix of a half-infinite system has the same spectrum as an appropriate $D\times D$ matrix acting on an ancilla space. We show that reduced density matrices at different spatial cuts are related by quantum channels acting on the ancilla space. This quantum channel approach allows for efficient numerical evaluation of the entanglement spectrum and Renyi entropies and their spatial fluctuations at finite times in an infinite system. We benchmark our numerical method on random unitary circuits, where many analytic results are available, and also show how our approach analytically recovers the behaviour of the kicked Ising model at the self-dual point. We study various properties of the spectra of the reduced density matrices and their spatial fluctuations in both the random and translation-invariant cases.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/27f5c259d486ee3e229a9c523b6fdbcf9aef5882

How researchers see this paper

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

In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. B. Bertini
6. Tomaz Prosen
7. Pavel Kos
8. Tianci Zhou

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. Tomaz Prosen
6. B. Bertini
7. Pavel Kos
8. Tianci Zhou

Citations in the corpus

• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits (2019, background): “These include spectral statistics [57], (state) entanglement spreading [58], and dynamical correlations [56] (see also [54] and [59] for other useful features of dual-unitarity).”
• Random Quantum Circuits (2022, background): “Dual-unitary circuits (209, 119, 216) are built up of certain classes of special two-site unitary gates that look unitary in both “spacelike” and “timelike” directions.”