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It is often assumed that systems that can be analyzed accurately via mean-field theory would not be worth looking at using quantum algorithms, given entanglement plays no key role. Here, the authors show instead that a quantum advantage can be expected for simulating the exact time evolution of such electronic systems.

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.

Gradient-based hybrid quantum-classical algorithms are often initialised with random, unstructured guesses. Here, the authors show that this approach will fail in the long run, due to the exponentially-small probability of finding a large enough gradient along any direction.

Typical quantum error correcting codes assign fixed roles to the underlying physical qubits. Now the performance benefits of alternative, dynamic error correction schemes have been demonstrated on a superconducting quantum processor.

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.

Experimental measurements of high-order out-of-time-order correlators on a superconducting quantum processor show that these correlators remain highly sensitive to the quantum many-body dynamics in quantum computers at long timescales.

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.

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.

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.

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 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.

Ruiz and colleagues introduce AlphaTensor-Quantum, a deep reinforcement learning method for optimizing quantum circuits. It outperforms existing methods and is capable of finding the best human-designed solutions for relevant quantum computations in a fully automated way.

Fault-tolerant quantum computation is still far, but there could be ways in which quantum error correction could improve currently available devices. Here, the authors show how to exploit existing quantum codes through only post-processing and random measurements in order to mitigate errors in NISQ devices.

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

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.

The extent of problems in quantum chemistry for which quantum algorithms could provide a speedup is still unclear, as well as the kind of speedup one should expect. Here, the authors look at the problem of ground state energy estimation, and gather theoretical and numerical evidence for the fact that an exponential quantum advantage is unlikely for generic problems of interest.

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.

Expectations for quantum machine learning are high, but there is currently a lack of rigorous results on which scenarios would actually exhibit a quantum advantage. Here, the authors show how to tell, for a given dataset, whether a quantum model would give any prediction advantage over a classical one.

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.

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

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.

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.

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

The advent of commercial quantum devices has ushered in the era of near-term quantum computing. Variational quantum algorithms are promising candidates to make use of these devices for achieving a practical quantum advantage over classical computers.