We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. demonstrate the possibility of filtering out effects unwanted (not necessarily known) system-environment interactions show that noise-suppression procedure can be combined with capability retaining control over effective evolution system. Implications information processing are discussed.

The dynamics of a decohering two-level system driven by suitable control Hamiltonian is studied. procedure implemented as sequence radio-frequency pulses that repetitively flip the state system, technique can be termed quantum ``bang-bang'' after its classical analog. Decoherence introduced system's interaction with environment shown to washed out completely in limit continuous flipping and greatly suppressed provided interval between made comparable correlation time environment. model...

A measure of quality an error-correcting code is the maximum number errors that it able to correct. We show a suitable notion "number errors" e makes sense for any quantum or classical system in presence arbitrary interactions. Thus, e-error-correcting codes protect information without requiring usual assumptions independence. prove existence large both and information. By viewing as subsystems, we relate irreducible representations operator algebras noiseless subsystems are infinite-distance codes.

We show that if one can perform a restricted set of fast manipulations on quantum system, implement large class dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure be used to achieve universal noise-tolerant control based purely unitary open-loop transformations the dynamics. As result, it is in principle possible noise-protected computation using no extra space resources.

We present a generalization of entanglement based on the idea that is relative to distinguished subspace observables rather than subsystem decomposition. A pure quantum state entangled such if its expectations are proper mixture those other states. Many information-theoretic aspects can be extended this observable-based setting, suggesting new ways measuring and classifying multipartite entanglement. By going beyond distinguishable-subsystem framework, generalized also provides novel tools...

We propose a general procedure for implementing dynamical decoupling of quantum systems without requiring arbitrarily strong, impulsive control actions. This is accomplished by designing continuous propagators according to Eulerian paths in the group system. Such schemes offer two important advantages over their counterparts: they are able enforce same symmetrization but with more realistic resources and, at time, intrinsically tolerant against large class systematic implementation errors.

Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open system without encoding or measurement overhead. Our results allow low-level error correction strategy solely based Hamiltonian engineering using bounded-strength controls may substantially reduce implementation requirements fault-tolerant...

We demonstrate the protection of one bit quantum information against all collective noise in three nuclear spins. Because no subspace states offers this protection, was encoded a proper noiseless subsystem. therefore realize general and efficient method for protecting information. Robustness verified full set operators that do not distinguish Verification relied on most complete exploration engineered decoherence to date. The achieved fidelities show improved storage large, noncommutative errors.

The ability to perform measurements on a quantum system, combined with the feed back measurement results via coherent control, allows one control system follow any desired or incoherent dynamics. Such universal dynamical can be achieved, in principle, through repeated application of only two operations and simple ``Yes-No'' measurement. As consequence, computer simulate an arbitrary open-system dynamics using just qubit more than required closed-system

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem interest. dynamics describes wide class open relevance information processing, encodings offering general pathway faithfully represent information. provide explicit linear-algebraic characterizations notion invariant and noiseless for master equations, under different robustness assumptions model-parameter initial-state variations. The stronger concept an attractive is introduced,...

We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems such a way decoherence is perturbatively compensated for desired (in principle arbitrarily high) level of accuracy, which depends only on the strength relevant errors and achievable rate modulation. Our constructive fully analytical solution employs concatenated dynamically corrected gates, applicable independently detailed knowledge system-environment interactions...

We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and dephasing environments. By engineering a multidimensional frequency comb via repetition suitably designed pulse sequences, desired high-order spectra may be related observable qubit probe. prove that access high time resolution is key achieving reconstruction over an extended bandwidth, overcoming limitations existing schemes. Non-Gaussian...

We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such topological superconductor. characterize phase diagram by using partial Chern number sum, and show that latter is physically related parity fermion By taking self-consistency constraint on pairing gap into account, we also establish possibility direct superconductor-to-topological insulator quantum transition.

We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the affecting multiple qubits coupled to Gaussian dephasing environments including both classical and sources. Our are capable reconstructing all auto- cross-correlation spectra entering multiqubit dynamics, providing access, in particular, asymmetric associated with nonclassical environments. result relies on (i) an exact analytic solution reduced dynamics that holds presence arbitrary environment...

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. show how identify computationally tractable set of fundamental filter functions, out which arbitrary transfer functions may be assembled up high order principle. Besides avoiding the infinite recursive hierarchy that arises control scenarios, this filter-function suffices characterize error suppression capabilities protocol both time and frequency...

Majorana bosons, that is, tight bosonic analogs of the fermionic quasiparticles condensed-matter physics, are forbidden for gapped free matter within a standard Hamiltonian scenario. We show how interplay between dynamical metastability and nontrivial bulk topology makes their emergence possible in noninteracting chains undergoing Markovian dissipation. This leads to distinctive form topological metastability, whereby conserved boson localized on one edge is paired, general, with symmetry...

Realistic multiqubit noise processes often result in error mechanisms that are not captured by the probabilistic Markovian models commonly employed circuit-level analyses of quantum fault tolerance. By working within an open-quantum system Hamiltonian formulation, we revisit validity notion a constant gate presence is both and , impact which mitigated through perfect instantaneous dynamical decoupling subject to finite timing constraints. We study minimal exactly solvable single-qubit model...

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications NMR QIP and explain their current successes, limitations potential. spectroscopy is well known its wealth diverse coherent manipulations spin dynamics. Ideas instrumentation from liquid state have been used experiment with QIP. This approach has carried field a complexity about 10...

We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is design the propagator according rather than deterministic path on group. characterize performance protocols, identify scenarios where they can significantly weaken time scale requirements as compared cyclic counterparts. Implications reliable computation are discussed.

We combine dynamical decoupling and universal control methods for open quantum systems with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of states result in obtaining over dynamically generated noise-protected subsystems limited resources. In particular, provide constructive scheme based on two-body Hamiltonians performing computation large noiseless spaces which can be engineered the presence arbitrary linear noise.

Unentangled pure states on a bipartite system are exactly the coherent with respect to group of local transformations. What aspects study entanglement applicable generalized states? Conversely, what can be learned about from well-studied theory With these questions in mind, we characterize unentangled as extremal when considered linear functionals Lie algebra. As result, relativized notion purity emerges, showing that there is close relationship between purity, coherence, and...

Quantum systems carry information. theory supports at least two distinct kinds of information (classical and quantum), a variety different ways to encode preserve in physical systems. A system's ability is constrained defined by the noise its dynamics. This paper introduces an operational framework, using information-preserving structures classify all that can be perfectly (i.e., with zero error) preserved quantum We prove every code has same structure as matrix algebra, always corrected....

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out equilibrium, with emphasis on quench dynamics which involves non-isolated points (i.e., regions) and cannot be a priori described through standard arguments nor time-dependent perturbative approaches. Comparing to case an isolated point, we find that non-equilibrium behavior large class physical observables may still explained terms equilibrium exponents. However, latter are...