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Qubit

About: Qubit is a research topic. Over the lifetime, 29978 publications have been published within this topic receiving 723084 citations. The topic is also known as: quantum bit & qbit.


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Journal ArticleDOI
TL;DR: In this article, the authors studied the decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain, where the dynamics of the chain is determined by the Ising, $XY, or Heisenberg exchange Hamiltonian.
Abstract: We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

165 citations

Journal ArticleDOI
TL;DR: By studying the Coffman-Kundu-Wootters inequality, it is found that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.
Abstract: We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a $W$ state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this ``monogamy'' can be lifted for mixed states by virtue of vanishing tangle measures.

165 citations

Journal ArticleDOI
23 Feb 2012-Nature
TL;DR: This work demonstrates the viability of topological error correction for fault-tolerant quantum information processing and shows that a correlation can be protected against a single error on any quantum bit.
Abstract: Scalable quantum computing can be achieved only if quantum bits are manipulated in a fault-tolerant fashion Topological error correction--a method that combines topological quantum computation with quantum error correction--has the highest known tolerable error rate for a local architecture The technique makes use of cluster states with topological properties and requires only nearest-neighbour interactions Here we report the experimental demonstration of topological error correction with an eight-photon cluster state We show that a correlation can be protected against a single error on any quantum bit Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing

164 citations

Journal ArticleDOI
TL;DR: It is shown that for D=1,2 the height of the energy barrier separating different logical states is upper bounded by a constant independent of the lattice size L, and it is demonstrated that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D= 1,2.
Abstract: We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of constant size. Our first result concerns the optimal scaling of the distance $d$ with the linear size of the lattice $L$. We prove an upper bound $d=O(L^{D-1})$ which is tight for D=1,2. This bound applies to both subspace and subsystem stabilizer codes. Secondly, we analyze the suitability of stabilizer codes for building a self-correcting quantum memory. Any stabilizer code with geometrically local generators can be naturally transformed to a local Hamiltonian penalizing states that violate the stabilizer condition. A degenerate ground-state of this Hamiltonian corresponds to the logical subspace of the code. We prove that for D=1,2 the height of the energy barrier separating different logical states is upper bounded by a constant independent of the lattice size L. The same result holds if there are unused logical qubits that are treated as "gauge qubits". It demonstrates that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1,2. This result is in sharp contrast with the existence of a classical self-correcting memory in the form of a two-dimensional ferromagnet. Our results leave open the possibility for a self-correcting quantum memory based on 2D subsystem codes or on 3D subspace or subsystem codes.

164 citations

Journal ArticleDOI
TL;DR: In this article, a quantum bit is encoded in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs, and the process pins down two computational states to separate locations in phase space.
Abstract: A quantum system interacts with its environment—if ever so slightly—no matter how much care is put into isolating it1. Therefore, quantum bits undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation2. New strategies are emerging to circumvent this problem by encoding a quantum bit non-locally across the phase space of a physical system. Because most sources of decoherence result from local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality3,4. Prominent examples are topological quantum bits, which delocalize information over real space and where spatial extent measures non-locality. Here, we encode a quantum bit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs5,6. This process pins down two computational states to separate locations in phase space. By increasing this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate7. Because bit-flips are autonomously corrected, only phase-flips remain to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with nonlinear dissipation are promising building blocks for quantum computation with drastically reduced hardware overhead8. The choice of the physical system that represents a qubit can help reduce errors. Encoding them in the quadrature space of a superconducting resonator leads to exponentially reduced bit-flip rates, while phase-flip errors increase only linearly.

164 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231,977
20224,380
20213,014
20203,119
20192,594
20182,228