Related papers: Homological Quantum Rotor Codes: Logical Qubits fr…
Great attention has been paid to binomial codes utilizing bosonic systems as logical qubits with error correction capabilities. However, implementing single-qubit rotation operations on binomial codes has proven challenging, requiring an…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…
We study quantum information processing using superpositions of Fock states in superconducting resonators, as quantum $d$-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators…
Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts,…
We propose two protocols to encode a logical qubit into physical qubits relying on common types of qubit-qubit interactions in as simple forms as possible. We comment on its experimental implementation in several quantum computing…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows…
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…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
With the development of quantum hardware bringing the error-corrected quantum circuits to the near future, the lack of an efficient polynomial-time decoding algorithms for logical circuits presents a critical bottleneck. While quantum…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the…
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice…