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Quantum computing is an attractive and multidisciplinary field, which became a focus for experimental and theoretical research during last decade. Among other systems, like ions in traps or superconducting circuits, solid-states based…
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and…
The control of discrete quantum states in solids and their use for quantum information processing is complicated by the lack of a detailed understanding of the mechanisms responsible for qubit decoherences. For spin qubits in semiconductor…
General purpose quantum computers can, in principle, entangle a number of noisy physical qubits to realise composite qubits protected against errors. Architectures for measurement-based quantum computing intrinsically support…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we…
The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with…
Solid-state nuclear spins surrounding individual, optically addressable qubits provide a crucial resource for quantum networks, computation and simulation. While hosts with sparse nuclear spin baths are typically chosen to mitigate qubit…
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
Quantum error correction procedures have the potential to enable faithful operation of large-scale quantum computers. They protect information from environmental decoherence by storing it in logical qubits, built from ensembles of entangled…
We demonstrate coherent control of the fine-structure qubit in neutral strontium atoms. This qubit is encoded in the metastable $^3\mathrm{P}_2$ and $^3\mathrm{P}_0$ states, coupled by a Raman transition. Using a magnetic quadrupole…
In this paper a programmable quantum state discriminator is implemented by using nuclear magnetic resonance. We use a two qubit spin-1/2 system, one for the data qubit and one for the ancilla (programme) qubit. This device does the…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least…
Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we…
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level.…
We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…