Related papers: An Error Correctable Implication Algebra for a Sys…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for…
An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated…
A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a…
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…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Corrected trapezoidal rules are proved for $\int_a^b f(x)\,dx$ under the assumption that $f"\in L^p([a,b])$ for some $1\leq p\leq\infty$. Such quadrature rules involve the trapezoidal rule modified by the addition of a term…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch…
In this work, we explore the impact of logical stochastic Pauli and coherent Z-rotation errors on quantum algorithms. We evaluate six canonical quantum algorithms' intrinsic resilience to the logical qubit and gate errors by performing the…
In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a $\mathbb{Z}_N$ gauge theory with prime dimension $N$ coupled to dynamical matter can be expressed as a qudit…
Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC)…
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the…
We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a…