Entanglement between spatially distant qubits is perhaps the most counterintuitive and vital resource for distributed quantum computing. However, despite a few special cases, there is no known general procedure to maximally entangle two distant parts of an interacting many-body system. Here we present a symmetry-based approach, whereby one applies several timed pulses to drive a system to a particular symmetry sector with maximal bipartite long-range entanglement. As a concrete example, we demonstrate how a simple sequence of on-site pulses on a qubit array can efficiently produce multiple stable nonlocal Bell pairs, realizable in present-day atomic and photonic experimental platforms. More generally, our approach paves a route for exotic state preparation by harnessing symmetry. For instance, we show how it allows the creation of long-sought-after superconducting η pairs in a repulsive Hubbard model. Published by the American Physical Society 2024
Entanglement between spatially distant qubits is perhaps the most counterintuitive and vital resource for distributed quantum computing. However, despite a few special cases, there is no known general procedure to maximally entangle two distant parts of an interacting many-body system. Here we present a symmetry-based approach, whereby one applies several timed pulses to drive a system to a particular symmetry sector with maximal bipartite long-range entanglement. As a concrete example, we demonstrate how a simple sequence of on-site pulses on a qubit array can efficiently produce multiple stable nonlocal Bell pairs, realizable in present-day atomic and photonic experimental platforms. More generally, our approach paves a route for exotic state preparation by harnessing symmetry. For instance, we show how it allows the creation of long-sought-after superconducting η pairs in a repulsive Hubbard model. Published by the American Physical Society 2024
Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is “strongly symmetric,” i.e., it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qudits N . Published by the American Physical Society 2024
A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the Z 2 Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by G × H symmetry gives rise to anomalous LRE upon measuring G -charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way. Published by the American Physical Society 2024
Long-range entangled states are vital for quantum information processing and quantum metrology. Preparing such states by combining measurements with unitary gates opened new possibilities for efficient protocols with finite-depth quantum circuits. The complexity of these algorithms is crucial for the resource requirements on a large-scale noisy quantum device, while their stability to perturbations decides the fate of their implementation. In this work, we consider stochastic quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. These operations preserve a class of discrete local symmetries, which are broken due to the stochasticity arising from timing and gate imperfections. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. In the general case, by studying the time evolution under this hybrid circuit, we analyze the time to reach the target entangled state. We find two important time scales that we associate with the emergence of certain symmetry generators. The quantum trajectories embody the local symmetry with a time scaling logarithmically with system size, while global symmetries require exponentially long times. We devise error-mitigation protocols that significantly lower both time scales and investigate the stability of the algorithm to perturbations that naturally arise in experiments. We also generalize the protocol to realize toric code and Xu-Moore states in two dimensions, opening avenues for future studies of anyonic excitations. Our results unveil a fundamental relationship between symmetries and dynamics across a range of lattice geometries, which contributes to a broad understanding of the stability of preparation algorithms in terms of phase transitions. Our work paves the way for efficient error correction for quantum state preparation.
Subwavelength atomic lattices have been established as a promising platform for quantum applications, utilizing collective superradiant and subradiant behavior to enhance atom-light interactions. While previous work has demonstrated high-fidelity atom-photon entanglement in these systems, the generation of atom–atom entanglement, a crucial ingredient for full scalability, remains a conceptual challenge. Here, we propose methods for high-fidelity entanglement generation between atomic qubits by identifying specific atoms within a ring array as qubits. The entanglement generation is achieved by collective atomic excitation involving both subradiant and superradiant states and leveraging the novel symmetry properties of the ring array. Specifically, we utilize symmetry breaking within the ring by preparing atomic qubits in a superpositions of detunings for our entanglement protocols. A fidelity analysis of the protocols provides practical experimental parameters for state-of-the-art setups. Published by the American Physical Society 2024
All known resource states for measurement-based quantum teleportation in correlation space possess symmetry-protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-on-site symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry. Published by the American Physical Society 2024
Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin- 1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms. Published by the American Physical Society 2024