Related papers: Redheffer: Trig to Quantum Error Bounds
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an…
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information,…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis.…
Non-classical states of light find applications in enhancing the performance of optical interferometric experiments, with notable example of gravitational wave-detectors. Still, the presence of decoherence hinders significantly the…
In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
We propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor…
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…