Related papers: Quantum error correction and generalized numerical…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give a…
This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…
Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…
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…
Collective rotation channels are a fundamental class of channels in quantum computing and quantum information theory. The commutant of the noise operators for such a channel is a C*-algebra which is equal to the set of fixed points for the…
We exhibit equivalent conditions for subspaces of an inner product space to be isoclinic, including a characterization based on the classical notion of canonical angles. We identify a connection with quantum error correction, showing that…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
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…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of…
The quantum bit error rate is a key quantity in quantum communications. If the quantum channel is the atmosphere, the information is usually encoded in the polarization of a photon. A link budget is required, which takes into account the…
Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the…