How robust is a quantum gate in the presence of noise?

We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all unitary quantum gates, and it is found that the controlled-not is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being 0.5.Comment: 14 page

The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

Algebraic and information-theoretic conditions for operator quantum error-correction

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum error-correction, decoherence-free subspaces, and noiseless subsystems. This paper develops (a) easily applied algebraic and information-theoretic conditions which characterize when operator quantum error-correction is feasible; (b) a representation theorem for a class of noise processes which can be corrected using operator quantum error-correction; and (c) generalizations of the coherent information and quantum data processing inequality to the setting of operator quantum error-correction.Comment: 4 page

Signatures of orbital loop currents in the spatially resolved local density of states

Polarized neutron scattering measurements have suggested that intra-unit cell antiferromagnetism may be associated with the pseudogap phase. Assuming that loop current order is responsible for the observed magnetism, we calculate some signatures of such circulating currents in the local density of states around a single non-magnetic impurity in a coexistence phase with superconductivity. We find a distinct C4 symmetry breaking near the disorder which is also detectable in the resulting quasi-particle interference patterns.Comment: 5 pages, 3 figure

Exchange-controlled single-electron-spin rotations in quantum dots

We show theoretically that arbitrary coherent rotations can be performed quickly (with a gating time ~1 ns) and with high fidelity on the spin of a single confined electron using control of exchange only, without the need for spin-orbit coupling or ac fields. We expect that implementations of this scheme would achieve gate error rates on the order of \eta ~ 10^{-3} in GaAs quantum dots, within reach of several known error-correction protocolsComment: 4+ pages, 3 figures; v2: Streamlined presentation, final version published in PRB (Rapid Comm.

Probabilistic Quantum Control Via Indirect Measurement

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability on the state space become less restrictive if unitary control operations may be supplemented by projective measurement. The present work builds on this idea, introducing the additional element of indirect measurement to achieve a kind of remote control. The target system that is to be remotely controlled is first entangled with another identical system, called the control system. The control system is then subjected to unitary transformations plus projective measurement. As anticipated by Schrodinger, such control via entanglement is necessarily probabilistic in nature. On the other hand, under appropriate conditions the remote-control scenario offers the special advantages of robustness against decoherence and a greater repertoire of unitary transformations. Simulations carried out for a two-level system demonstrate that, with optimization of control parameters, a substantial gain in the population of reachable states can be realized.Comment: 9 pages, 2 figures; typos added, reference added, reference remove

A superconducting microwave multivibrator produced by coherent feedback

We investigate a coherent nonlinear feedback circuit constructed from pre-existing superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package [N. Tezak et al., arXiv:1111.3081v1] that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.Comment: 9 double-spaced pages, 5 figures and supplement. To appear in Phys. Rev. Let

Characterization of two-qubit perfect entanglers

Here we consider perfect entanglers from another perspective. It is shown that there are some {\em special} perfect entanglers which can maximally entangle a {\em full} product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as {\textsc{cnot}} and {\textsc{dcnot}}, but {\em not} {\small{\sqrt{\rm{\textsc{swap}}}}}. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value, 2/9, are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such these gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.Comment: 6 pages, 1 eps figur

Simple quantum feedback of a solid-state qubit

We propose an experiment on quantum feedback control of a solid-state qubit, which is almost within the reach of the present-day technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent (Rabi) oscillations in a qubit for an arbitrary long time; however, this is done in a significantly simpler way, which requires much smaller bandwidth of the control circuitry. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of qubit oscillations. The price for simplicity is a less-than-ideal operation: the fidelity is limited by about 95%. The feedback loop operation can be experimentally verified by appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization.Comment: 5 page

Useful entanglement can be extracted from all nonseparable states

We consider entanglement distillation from a single-copy of a multipartite state, and instead of rates we analyze the "quality" of the distilled entanglement. This "quality" is quantified by the fidelity with the GHZ-state. We show that each not fully-separable state $\sigma$ can increase the "quality" of the entanglement distilled from other states, no matter how weakly entangled is $\sigma$. We also generalize this to the case where the goal is distilling states different than the GHZ. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses).Comment: 7 page