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Logical operations can be performed fault-tolerantly with only a constant number of syndrome extraction rounds for a broad class of quantum error correction codes, including the surface code with magic state inputs and feedforward, to achieve ‘transversal algorithmic fault tolerance’.

Coherent noise affecting a random error correcting code is now shown to produce a transition between phases that accumulate and destroy magic.

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.

Magic state distillation is achieved with logical qubits on a neutral-atom quantum computer using a dynamically reconfigurable architecture for parallel quantum operations.

In order to be practical, schemes for characterizing quantum operations should require the simplest possible gate sequences and measurements. Here, the authors show how random gate sequences and native measurements (followed by classical post-processing) are sufficient for estimating several gate set properties.

A programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits is described, in which improvement of algorithmic performance using a variety of error-correction codes is enabled.

Pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%, a factor of three improvement over state-of-the-art silicon devices.

Large quantum computers will require error correcting codes, but most proposals have prohibitive requirements for overheads in the number of qubits, processing time or both. A way to combine smaller codes now gives a much more efficient protocol.

Quantum error correction is essential for reliable quantum computing, but no single code supports all required fault-tolerant gates. The demonstration of switching between two codes now enables universal quantum computation with reduced overhead.

In this alternative approach to quantum computation, the all-electrical operation of two qubits, each encoded in three physical solid-state spin qubits, realizes swap-based universal quantum logic in an extensible physical architecture.

Measurement-induced phase transitions are notoriously difficult to observe. Here, the authors propose a neural-network-based method to map measurement outcomes to the state of reference qubits, allowing observation of the transition and extracting its critical exponents.

A fault-tolerant, universal set of single- and two-qubit quantum gates is demonstrated between two instances of the seven-qubit colour code in a trapped-ion quantum computer.

Digital quantum simulations of Kitaev’s honeycomb model are realized for two-dimensional fermionic systems using a reconfigurable atom-array processor and used to study the Fermi–Hubbard model on a square lattice.

Initialization and operation of spin qubits in silicon above 1 K reach fidelities sufficient for fault-tolerant operations at these temperatures.

Geometric quantum gates—engineered evolution paths for qubit control—promise noise resilience but have shown limited fidelity in prior implementations in semiconductor quantum computation. Here the authors demonstrate high-fidelity single-qubit gates in a single-hole quantum dot in Ge, outperforming conventional dynamical gates.

A four-qubit processor of three phosphorus nuclear spins and an electron spin in silicon enables the implementation of a three-qubit Grover’s search algorithm with 95% fidelity. The implementation is based on an advanced multi-qubit gate with single-qubit gate fidelities above 99.9% and two-qubit gate fidelities above 99%.

The dynamics of quantum states underlies the emergence of thermodynamics and even recent theories of quantum gravity. Now it has been proven that the quantum complexity of states evolving under random operations grows linearly in time.

The leading proposals for converting noise-resilient quantum devices from memories to processors are compared, paying attention to the relative resource demands of each.

Random sequences of unitary gate operations on an exchange-only qubit encoded in three physical electron qubits are performed using only voltage pulses and exhibit an average total error of 0.35%, where half of the error originates from leakage out of the computational subspace caused by interactions with substrate nuclear spins.

Repeatedly measuring an array of qubits can create topologically distinct phases depending on which measurements are applied. Lavasani et al. show that critical behaviour can arise from the competition between different choices of measurements.

Ising anyons are a promising platform for topological quantum computation, but braiding alone is not universal. Here, authors show that extending to non-semi simple TQFTs introduces new anyon types that enable universal quantum computation with Ising anyons.

Singlet–triplet qubits implemented in a 2 × 4 germanium quantum dot array allow for a quantum circuit that generates and distributes entanglement across the array with a remote Bell state fidelity of 75(2)% between the first and last qubit.

A low-power radio-frequency multiplexing cryo-electronics system, which is based on complementary metal–oxide–semiconductor technology, can operate below 15 mK and provide the control and interfacing of superconducting qubits with minimal cross-coupling.

Blind quantum computation is a protocol that permits an algorithm, its input and output to be kept secret from the owner of the computational resource doing the calculation. Morimae and Fujii propose a strategy for topologically protected fault-tolerant blind quantum computation that is robust to environmental noise.

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.

An electric dipole spin resonance protocol making use of hyperfine interaction enacts high-fidelity initialization of a four-qubit nuclear spin register in silicon. This protocol allows for high-fidelity qubit control and a path towards a register-based quantum computer using the exceptional coherence properties of donors in silicon.

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.

The estimation of low energies of many-body systems is a cornerstone of the computational quantum sciences. This paper demonstrates on a superconducting quantum processor that the Krylov quantum diagonalization algorithm is poised to complement its classical counterparts at the foundation of computational methods for quantum systems.

Quantum computation will depend on fault-tolerant error correction, which requires the chance for errors to occur to be below a certain threshold. Here the authors use gate set tomography as a means to rigorously characterize error rates of single-qubit operations of a qubit encoded in a trapped ion.

High-performance all-electrical control is a prerequisite for scalable silicon quantum computing. The switchable interaction between spins and orbital motion of electrons in silicon quantum dots now enables the electrical control of a spin qubit with high fidelity and speed, without the need for integrating a micromagnet.

For solid-state qubits, the material environment hosts sources of errors that vary in time and space. This systematic analysis of errors affecting high-fidelity two-qubit gates in silicon can inform the design of large-scale quantum computers.

An ultra-low-loss integrated photonic chip fabricated on a customized multilayer silicon nitride 300-mm wafer platform, coupled over fibre with high-efficiency photon number resolving detectors, is used to generate Gottesman–Kitaev–Preskill qubit states.

The presence of various noises in the qubit environment is a major limitation on qubit coherence time. Here, the authors demonstrate the use a closed-loop feedback to stabilize frequency noise in a flux-tunable superconducting qubit and suggest this as a scalable approach applicable to other types of noise.

Construction of a scalable quantum computer requires error-correcting codes to overcome the errors introduced by noise. Here, the authors develop a decoding algorithm for the gauge color code, and obtain its threshold values when physical errors and measurement faults are included.

The surface code is a keystone in quantum error correction, but it does not generally perform well against structured noise and suffers from large overheads. Here, the authors demonstrate that a variant of it has better performance and requires fewer resources, without additional hardware demands.

The exchange interaction between spins poses considerable challenges for high-fidelity control of semiconductor spin qubits. Here, the authors use pulse optimization and closed-loop control to achieve a gate fidelity of 99.5% for exchange-based single-qubit gates of two-electron spin qubits in GaAs.

Asymmetrical distribution of tau pathology in Alzheimer’s disease is linked to asymmetrical amyloid-beta deposition, not reduced brain connectivity, suggesting regional vulnerability plays a key role in determining the distribution of tau pathology.

Fault-tolerant circuits for the control of a logical qubit encoded in 13 trapped ion qubits through a Bacon–Shor quantum error correction code are demonstrated.

Spin qubits based on hole states in strained germanium could offer the most scalable platform for quantum computation.