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Parallel operation of two exchange-only qubits consisting of six quantum dots arranged linearly is shown to be achievable and maintains qubit control quality compared with sequential operation, with potential for use in scaled quantum computing.

Studying many-body quantum chaos on current quantum hardware is hindered by noise and limited scalability. Now it is shown that a superconducting processor, combined with error mitigation, can accurately simulate dual-unitary circuit dynamics.

Experimental realizations of discrete time crystals have mainly involved 1D models with Ising-like couplings. Here, the authors realize a 2D discrete time crystal with anisotropic Heisenberg coupling on a quantum simulator based on superconducting qubits, uncovering a rich phase diagram.

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’.

To simulate physical systems on a quantum computer, their degrees of freedom must be encoded into qubits. This Review assesses the different methods that exist to allow quantum calculation of fermionic systems.

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

Reconfigurable arrays of up to 448 neutral atoms are used to implement and combine the key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms.

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.

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.

Certifying multipartite entanglement can benchmark quantum devices. Here, authors introduce versatile tests that can certify genuine multipartite entanglement and k-inseparability using only few-body measurements, enabling noise-robust benchmarking of large photonic and superconducting graph states.

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.

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

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 vital for scalable quantum computing, but it incurs high resource overheads. This Perspective outlines recent breakthroughs and explores the opportunities to reduce the overheads by co-designing across algorithms, error-correction schemes and hardware architecture.

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.

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.

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.

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

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.

The APOE-ε4 allele is the strongest genetic risk factor for late-onset Alzheimer’s disease, but it is not deterministic. Here, the authors show that common genetic variation changes how APOE-ε4 influences cognition.

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.

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%.

In the adrenal cortex, cholesterol used for steroid production is stored in lipid droplets. The authors demonstrate here the importance of the transcription factor HHEX in maintaining glucocorticoid levels and protecting lipid droplets from androgen-induced lipid depletion.

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 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.

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.

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 materials platform using tantalum as a base layer and silicon as the substrate to construct superconducting qubits enables device performance improvements such as millisecond lifetimes and coherence times, as well as high time-averaged quality factors.

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.

The brain can flexibly perform multiple tasks by compositionally combining task-relevant neural representations.

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.

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.

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.

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.

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.

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.