Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

Stable quantum-correlated many-body states through engineered dissipation

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory1: by collapsing the wavefunction, it can enable phenomena such as teleportation2 and thereby alter the 'arrow of time' that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time3-10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium11-13. For present-day noisy intermediate-scale quantum (NISQ) processors14, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping9,15-17 to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling3,4 to measurement-induced teleportation18. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors.

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics¹. For all elementary and quasiparticles observed to date-including fermions, bosons and Abelian anyons-this principle guarantees that the braiding of identical particles leaves the system unchanged^2,3. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions^4-8. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals^9-22, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons^9,10, we implement a generalized stabilizer code and unitary protocol²³ to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.

Formation of robust bound states of interacting microwave photons

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Ultrafast energy- and momentum-resolved dynamics of magnetic correlations in the photo-doped Mott insulator Sr2IrO4

Measuring how the magnetic correlations evolve in doped Mott insulators has greatly improved our understanding of the pseudogap, non-Fermi liquids and high-temperature superconductivity. Recently, photo-excitation has been used to induce similarly exotic states transiently. However, the lack of available probes of magnetic correlations in the time domain hinders our understanding of these photo-induced states and how they could be controlled. Here, we implement magnetic resonant inelastic X-ray scattering at a free-electron laser to directly determine the magnetic dynamics after photo-doping the Mott insulator Sr2IrO4. We find that the non-equilibrium state, 2 ps after the excitation, exhibits strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. These two-dimensional (2D) in-plane Néel correlations recover within a few picoseconds, whereas the three-dimensional (3D) long-range magnetic order restores on a fluence-dependent timescale of a few hundred picoseconds. The marked difference in these two timescales implies that the dimensionality of magnetic correlations is vital for our understanding of ultrafast magnetic dynamics.

Local vibrations and negative thermal expansion in ZrW2O8

We present an x-ray pair distribution function (XPDF) analysis and extended x-ray absorption fine structure (EXAFS) data for ZrW2O8 (10-500 K) with a focus on the stiffness of the Zr-O-W linkage. The XPDF is highly sensitive to W-Zr and W-W correlations, but much less so to O-O or W-O correlations. The Zr-W peak in the XPDF data has a weak temperature dependence and, hence, this linkage is relatively stiff and does not permit bending of the Zr-O-W link. We propose that the low energy vibrational modes that lead to negative thermal expansion involve correlated rotations of ZrO6 octahedra that produce large <111> translations of the WO4 tetrahedra, rather than a transverse motion of O atoms that imply a flexible Zr-O-W linkage.

PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals

PDFfit2 is a program as well as a library for real-space refinement of crystal structures. It is capable of fitting a theoretical three-dimensional (3D) structure to atomic pair distribution function data and is ideal for nanoscale investigations. The fit system accounts for lattice constants, atomic positions and anisotropic atomic displacement parameters, correlated atomic motion, and experimental factors that may affect the data. The atomic positions and thermal coefficients can be constrained to follow the symmetry requirements of an arbitrary space group. The PDFfit2 engine is written in C++ and is accessible via Python, allowing it to inter-operate with other Python programs. PDFgui is a graphical interface built on the PDFfit2 engine. PDFgui organizes fits and simplifies many data analysis tasks, such as configuring and plotting multiple fits. PDFfit2 and PDFgui are freely available via the Internet.