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We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
Many problems intractable on classical devices could be solved by algorithms explicitly based on quantum mechanical laws, i.e. exploiting quantum information processing. As a result, increasing efforts from different fields are nowadays…
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…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Semiconductors are the backbone of modern technology, garnering decades of investment in high quality materials and devices. Electron spin systems in semiconductors, including atomic defects and quantum dots, have been demonstrated in the…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. Such applications require protection of the spin states against quantum decoherence due to interactions with…
Stabilization of encoded logical qubits using quantum error correction is key to the realization of reliable quantum computers. While qubit codes require many physical systems to be controlled, oscillator codes offer the possibility to…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for…
Solid-state spin qubits have emerged as promising platforms for quantum information. Despite extensive efforts in controlling noise in spin qubit quantum applications, one important but less controlled noise source is near-field…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
Spins based in silicon provide one of the most promising architectures for quantum computing. A scalable design for silicon-germanium quantum dot qubits is presented. The design incorporates vertical and lateral tunneling. Simulations of a…
Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…
Spin-orbit coupling fundamentally alters spin qubits, opening pathways to improve the scalability of quantum computers via long distance coupling mediated by electric fields, photons, or phonons. It also allows for new engineered hybrid and…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantum processor. The goal is to store over long times…