[Paper Review] Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver

M. Meth, Viacheslav Kuzmin+8 more|arXiv (Cornell University)|Mar 24, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper demonstrates a trapped-ion quantum simulator implementing a tensor-network-based variational quantum eigensolver (TN-VQE) to prepare and characterize topological phases of quantum matter. By encoding a matrix product state ansatz into a reconfigurable ion-trap architecture using single-site optical pulses and ion shuttling, the authors prepare the ground state of the extended Su-Schrieffer-Heeger model and verify its topological order via measured invariants, achieving a proof-of-principle realization of quantum simulation with native hardware operations.

ABSTRACT

Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantum-encoded TN ansatz state using a variational quantum eigensolver on an ion-trap quantum computer by preparing the ground states of the extended Su-Schrieffer-Heeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only single-site addressing optical pulses - the native operations naturally available on the platform. We reduce nearest-neighbor crosstalk by selecting different magnetic sublevels with well-separated transition frequencies to encode even and odd qubits.

Motivation & Objective

• To develop a hybrid quantum-classical algorithm that leverages trapped-ion hardware to simulate exotic quantum phases beyond classical simulation limits.
• To encode a tensor-network ansatz directly into a quantum simulator using native trapped-ion operations, enabling exponential advantage over classical numerical methods.
• To verify topological order in many-body ground states by measuring topological invariants via quantum simulation on a NISQ device.
• To demonstrate scalable implementation of a 2D tensor network using dynamic reconfiguration of ion strings in a segmented trap architecture.

Proposed method

• Encoding a matrix product state (MPS) ansatz into a trapped-ion quantum processor using single-qubit sideband operations on individual ions.
• Utilizing a reconfigurable linear ion trap with multiple zones for loading, memory, and quantum processing to enable dynamic circuit execution.
• Implementing a variational quantum eigensolver (VQE) protocol where quantum device energy measurements guide classical optimization of variational parameters.
• Employing ion shuttling, splitting, and merging operations to dynamically reconfigure ion strings and realize non-local plaquettes in a 2D tensor network.
• Using distinct magnetic sublevels for even and odd qubits to minimize crosstalk and enable high-fidelity single-site addressing.
• Measuring topological invariants via quantum state tomography and state fidelity to verify the presence of topological order in the prepared ground state.

Experimental results

Research questions

• RQ1 Can a trapped-ion quantum simulator efficiently prepare and characterize topological phases of matter using a tensor-network-based variational approach?
• RQ2 To what extent can dynamic ion reconfiguration in segmented traps enable scalable implementation of 2D tensor networks with minimal crosstalk?
• RQ3 Can topological invariants be reliably measured on a NISQ-era quantum device to verify topological order in many-body ground states?
• RQ4 What is the resource cost and feasibility of implementing a full 2D tensor network circuit using only native trapped-ion operations?

Key findings

• The authors successfully prepared the ground state of the extended Su-Schrieffer-Heeger model using a TN-VQE protocol on a trapped-ion quantum processor.
• The simulated ground state exhibited non-trivial topological order, confirmed by the measurement of topological invariants via quantum state characterization.
• The protocol required 152 reconfiguration operations (shuttling, splitting, merging) to implement the full 2D tensor network circuit on the ion-trap platform.
• The use of distinct magnetic sublevels for even and odd qubits effectively reduced nearest-neighbor crosstalk, enabling high-fidelity single-site operations.
• The implementation demonstrated a scalable path to simulating topological phases using native trapped-ion operations and dynamic reconfiguration.
• The results validate the feasibility of using trapped-ion systems as quantum simulators for exotic quantum phases via tensor-network-based variational algorithms.