Related papers: Maps for general open quantum systems and a theory…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum…
Quantum error correction plays a key role for quantum information transmission and quantum computing. In this work, we develop and apply the theory of non-commutative operator graphs to study error correction in the case of a…
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction…
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the…
We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian…
Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…