Related papers: Higher Rank Matricial Ranges and Hybrid Quantum Er…
A hybrid code can simultaneously encode classical and quantum information into quantum digits such that the information is protected against errors when transmitted through a quantum channel. It is shown that a hybrid code has the…
Quantum computing hardware is affected by quantum noise that undermine the quality of results of an executed quantum program. Amongst other quantum noises, coherent error that caused by parameter drifting and miscalibration, remains…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
The maximum operational range of continuous variable quantum key distribution protocols has shown to be improved by employing high-efficiency forward error correction codes. Typically, the secret key rate model for such protocols is…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
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…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
We study noiseless subsystems on collective rotation channels of qudits, i.e., quantum channels with operators in the set ${\mathcal E}(d,n) = \{ U^{\otimes n}: U \in {\mathrm{SU}}(d)\}.$ This is done by analyzing the decomposition of the…
We report two analytical bounds for quantum error-correcting codes that do not have preexisting classical counterparts. Firstly the quantum Hamming and Singleton bounds are combined into a single tighter bound, and then the combined bound…
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already…
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found.…
Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…