Quantum simulation in the entanglement picture

TL;DR

The paper introduces the entanglement picture (EP), a new quantum-mechanical perspective built on channel-state duality to analyze dynamics through the entanglement space. By representing evolution as a network of quantum channels acting on an entanglement (bond) space and leveraging matrix-product state structures, EP converts state evolution into observable-overlap computations, facilitating quantum simulation tasks. The authors demonstrate EP’s applicability to quantum many-body dynamics, quantum field theory, and thermal physics, and show that bulk-edge duality emerges from channel-state duality. They also discuss extensions to entropy calculations, non-unitary evolutions, and open-system dynamics, arguing that EP provides a potentially universal framework with coherence advantages and compatibility with existing quantum-information tools like Hadamard tests (DQC1). The work broadens the toolbox for quantum simulation by linking MPS-inspired methods with a channel-network paradigm that can accommodate general geometries and higher-dimensional tensor networks.

Abstract

The notion of ``picture'' is fundamental in quantum mechanics. In this work, a new picture, which we call entanglement picture, is proposed based on the novel channel-state duality, whose importance is revealed in quantum information science. We illustrate the application of entanglement picture in quantum algorithms for the simulation of many-body dynamics, quantum field theory, thermal physics, and more generic quantities.

Figures (2)

• Figure 1: Schematic to illustrate the entanglement picture. It shows a state $|\psi\rangle$ of six explicit sites and open boundary condition, and a circuit $U$ with three layers of two-local gates, each of which is expressed as a MPS with open boundary condition. The bottom dashed line indicates the conjugate of $U|\psi\rangle$. An observable, say, $O_2 O_4$, induces the projectors inserted in between the channel evolution at the bottom layer. A vertical wire that connects two channels implies a contraction, which is a projection $|\omega\rangle \langle \omega |$ on the two ancillary spaces. A vertical wire that crosses the dashed line implies the trace over it.
• Figure 2: The DQC1 algorithm (a) and its combination with the EP scheme (b). The controlled-gate $\wedge_U$ is realized by the controlled-swap scheme with a qubit controller at $|+\rangle$. The 2nd register carries the observable $A$, and the 3rd register is an eigenstate of $U$, which could be a ground state of $H$. Using EP, the controller with encoded $|+\rangle_L$ executes the controlled-swap gates on two MPSs, and the implementation of $U$ is realized by a channel network.