Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem.

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

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.

Entanglement from Tensor Networks on a Trapped-Ion Quantum Computer.

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource savings when simulating quantum systems with limited entanglement. We experimentally demonstrate a significant benefit of this approach to quantum simulation: the entanglement structure of an infinite system-specifically the half-chain entanglement spectrum-is conveniently encoded within a small register of "bond qubits" and can be extracted with relative ease. Using Honeywell's model H0 quantum computer equipped with selective midcircuit measurement and reset, we quantitatively determine the near-critical entanglement entropy of a correlated spin chain directly in the thermodynamic limit and show that its phase transition becomes quickly resolved upon expanding the bond-qubit register.

EBIT Observation of Ar Dielectronic Recombination Lines near the Unknown Faint X-Ray Feature Found in the Stacked Spectrum of Galaxy Clusters.

Motivated by possible atomic origins of the unidentified emission line detected at 3.55-3.57 keV in a stacked spectrum of galaxy clusters, an electron beam ion trap (EBIT) was used to investigate the resonant dielectronic recombination (DR) process in highly charged argon ions as a possible contributor to the emission feature. The He-like Ar DR-induced transition 1s22l-1s2l3l' was suggested to produce a 3.62 keV photon near the unidentified line at 3.57 keV and was the starting point of our investigation. The collisional-radiative model NOMAD was used to create synthetic spectra for comparison with both our EBIT measurements and with spectra produced with the AtomDB database/Astrophysical Plasma Emission Code (APEC) used in the Bulbul et al. work. Excellent agreement was found between the NOMAD and EBIT spectra, providing a high level of confidence in the atomic data used. Comparison of the NOMAD and APEC spectra revealed a number of missing features in the AtomDB database near the unidentified line. At an electron temperature of T e = 1.72 keV, the inclusion of the missing lines in AtomDB increases the total flux in the 3.5-3.66 keV energy band by a factor of 2. While important, this extra emission is not enough to explain the unidentified line found in the galaxy cluster spectra.