Related papers: Noiseless Quantum Codes
The rapid development of machine learning and quantum computing has placed quantum machine learning at the forefront of research. However, existing quantum machine learning algorithms based on quantum variational algorithms face challenges…
To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real…
Realistic quantum computing is subjected to noise. A most important frontier in research of quantum computing is to implement noise-resilient quantum control over qubits. Dynamical decoupling can protect coherence of qubits. Here we…
We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8…
Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state…
We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…
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…
In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large $N$ matrix quantum mechanics models. First, we investigate the gauged $SU(N)$ matrix harmonic oscillator and different ways…
We present a technique to coarse-grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a…
When modeling the effects of noise on quantum circuits, one often makes the assumption that these effects can be accounted for by individual decoherence events following an otherwise noise-free gate. In this work, we address the validity of…
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective,…
The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…
It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any…
We introduce a novel scheme for one-way quantum computing (QC) based on the use of information encoded qubits in an effective cluster state resource. With the correct encoding structure, we show that it is possible to protect the entangled…
Quantum computers often manipulate physical qubits encoded on two-level quantum systems. Bosonic qubit codes depart from this idea by encoding information in a well-chosen subspace of an infinite-dimensional Fock space. This larger physical…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…