Nishimori's Cat: Stable Long-Range Entanglement from Finite-Depth Unitaries and Weak Measurements

Approximating Many-Body Quantum States with Quantum Circuits and Measurements

We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called W and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a by-product of our work, we introduce an efficient scheme to implement certain nonlocal, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.

Higher-Form Symmetries under Weak Measurement

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions, a phase transition can be driven by weak measurements, which suppresses the spontaneous breaking of the 1-form symmetry and weakens the 1-form symmetry charge fluctuation. We analyze the nature of the transitions employing the tool of duality, and we demonstrate that some of the transitions driven by weak measurement enjoy a line of fixed points with self-duality.

Non-Abelian topological order and anyons on a trapped-ion processor

Non-Abelian topological order is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged1-4. These anyonic excitations are promising building blocks of fault-tolerant quantum computers5,6. However, despite extensive efforts, non-Abelian topological order and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian topological order. Here we present the realization of non-Abelian topological order in the wavefunction prepared in a quantum processor and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground-state wavefunction of D4 topological order on a kagome lattice of 27 qubits, with fidelity per site exceeding 98.4 per cent. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunnelling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon-a peculiar feature of non-Abelian topological order. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.