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Colour code on a superconducting qubit quantum processor is demonstrated, reporting above-breakeven performance and logical error scaling with increased code size by a factor of 1.56 moving from distance-3 to distance-5 code.

In a quantum simulation of a (2+1)D lattice gauge theory using a superconducting quantum processor, the dynamics of strings reveal the transition from deconfined to confined excitations as the effective electric field is increased.

Quantum simulation offers an unparalleled computational resource, but realizing it for fermionic systems is challenging due to their particle statistics. Here the authors report on the time evolutions of fermionic interactions implemented with digital techniques on a nine-qubit superconducting circuit.

Quantum simulators offer a test bed to emulate physical phenomena that are difficult to reproduce numerically. Using a multi-element superconducting quantum circuit, Chen et al.emulate weak localization for a mesoscopic system using a control sequence that lets them continuously tune the level of disorder.

Correlated errors coming from leakage out of the computational subspace are an obstacle to fault-tolerant superconducting circuits. Here, the authors use a multi-level reset protocol to improve the performances of a bit-flip error correcting code by reducing the magnitude of correlations.

Superconducting circuits, coupled to form a ring in which a photonic excitation can circulate between sites, are established as a versatile platform for studying the interplay of strong particle interactions and external fields.

A hybrid analogue–digital quantum simulator is used to demonstrate beyond-classical performance in benchmarking experiments and to study thermalization phenomena in an XY quantum magnet, including the breakdown of Kibble–Zurek scaling predictions and signatures of the Kosterlitz–Thouless phase transition.

By implementing random circuit sampling, experimental and theoretical results establish the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

Superconducting quantum circuits are used to directly observe and characterize topological phase transitions; this approach promises to be a powerful and general platform for characterizing topological phenomena in quantum systems.

Shor’s quantum algorithm factorizes integers, and implementing this is a benchmark test in the early development of quantum processors. Researchers now demonstrate this important test in a solid-state system: a circuit made up of four superconducting qubits factorizes the number 15.

A quantum error correction scheme is demonstrated in a system of superconducting qubits, and repeated quantum non-demolition measurements are used to track errors and reduce the failure rate; increasing the system size from five to nine qubits improves the failure rate further.

A digitized approach to adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital method, is implemented using a superconducting circuit to find the ground states of arbitrary Hamiltonians.

A universal set of logic gates in a superconducting quantum circuit is shown to have gate fidelities at the threshold for fault-tolerant quantum computing by the surface code approach, in which the quantum bits are distributed in an array of planar topology and have only nearest-neighbour couplings.

The realization of a quantum kicked top provides evidence for ergodic dynamics and thermalization in a small quantum system consisting of three superconducting qubits.

Physical realizations of qubits are often vulnerable to leakage errors, where the system ends up outside the basis used to store quantum information. A leakage removal protocol can suppress the impact of leakage on quantum error-correcting codes.

It is hoped that simulations of molecules and materials will provide a near-term application of quantum computers. A study of the performance of error mitigation highlights the obstacles to scaling up these calculations to practically useful sizes.

An experimental investigation of the dynamics of the spin ½ Floquet XXZ model finds bound states as predicted, and also robustness to noise and non-integrability when theoretical descriptions start to fail.

A study establishes a scalable approach to engineer and characterize a many-body-localized discrete time crystal phase on a superconducting quantum processor.

It is hoped that quantum computers may be faster than classical ones at solving optimization problems. Here the authors implement a quantum optimization algorithm over 23 qubits but find more limited performance when an optimization problem structure does not match the underlying hardware.

As a blueprint for high-precision quantum simulation, an 18-qubit algorithm that consists of more than 1,400 two-qubit gates is demonstrated, and reconstructs the energy eigenvalues of the simulated one-dimensional wire to a precision of 1 per cent.

Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.

Two below-threshold surface code memories on superconducting processors markedly reduce logical error rates, achieving high efficiency and real-time decoding, indicating potential for practical large-scale fault-tolerant quantum algorithms.

Measurement-induced phases of quantum information have been observed in a system of 70 superconducting qubits.

A unitary protocol for braiding projective non-Abelian Ising anyons in a generalized stabilizer code is implemented on a superconducting processor, allowing for verification of their fusion rules and realization of their exchange statistics.

A study demonstrating increasing error suppression with larger surface code logical qubits, implemented on a superconducting quantum processor.

A hybrid quantum-classical algorithm for solving many-electron problems is developed, enabling the simulation, with the aid of 16 qubits on a quantum processor, of chemical systems with up to 120 orbitals.

Repetition codes running many cycles of quantum error correction achieve exponential suppression of errors with increasing numbers of qubits.