arXiv subjects

Lorenza Viola

Publications and source records attributed to Lorenza Viola.

At least 73 records · Page 4Linked to original sources

arXiv2014

Robustness of composite pulses to time-dependent control noise

We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ~10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic $1/f$ noise spectra with a roll-off to $1/f^2$, providing independent validation of our theoretical insights.

quant-ph↗

arXiv2014

On state vs. channel quantum extension problems: exact results for UxUxU symmetry

We develop a framework which unifies seemingly different extension (or "joinability") problems for bipartite quantum states and channels. This includes well known extension problems such as optimal quantum cloning and quantum marginal problems as special instances. Central to our generalization is a variant of the Choi-Jamiolkowski isomorphism between bipartite states and dynamical maps which we term the "homocorrelation map": while the former emphasizes the preservation of the positivity constraint, the latter is designed to preserve statistical correlations, allowing direct contact with entanglement. In particular, we define and analyze state-joining, channel-joining, and local-positive joining problems in three-party settings exhibiting collective UxUxU symmetry, obtaining exact analytical characterizations in low dimension. Suggestively, we find that bipartite quantum states are limited in the degree to which their measurement outcomes may agree, while quantum channels are limited in the degree to which their measurement outcomes may disagree. Loosely speaking, quantum mechanics enforces an upper bound on the extent of positive correlation across a bipartite system at a given time, as well as on the extent of negative correlation between the state of a same system across two instants of time. We argue that these general statistical bounds inform the quantum joinability limitations, and show that they are in fact sufficient for the three-party UxUxU-invariant setting.

quant-ph↗

arXiv2014

Majorana Flat Bands in s-Wave Gapless Topological Superconductors

We demonstrate how the non-trivial interplay between spin-orbit coupling and nodeless $s$-wave superconductivity can drive a fully gapped two-band topological insulator into a time-reversal invariant gapless topological superconductor supporting symmetry-protected Majorana flat bands. We characterize topological phase diagrams by a ${\mathbb Z}_2 \times{\mathbb Z}_2$ partial Berry-phase invariant, and show that, despite the trivial crystal geometry, no unique bulk-boundary correspondence exists. We trace this behavior to the anisotropic quasiparticle bulk gap closing, linear vs. quadratic, and argue that this provides a unifying principle for gapless topological superconductivity. Experimental implications for tunneling conductance measurements are addressed, relevant for lead chalcogenide materials.

cond-mat.supr-con↗

arXiv2014

Quantum resources for purification and cooling: fundamental limits and opportunities

Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a "virtual subsystem" which has the same dimension and is in a state with the desired purity. Beside providing a unified understanding of quantum purification dynamics in terms of a "generalized swap process," our results shed light on the significance of a no-go theorem for exact ground-state cooling, as well as on the quantum resources needed for achieving an intended purification task.

quant-ph↗

arXiv2013

Hamiltonian quantum simulation with bounded-strength controls

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a suitable modification of an "Eulerian decoupling cycle," that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system, while suppressing unwanted decoherence to the leading order. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

quant-ph↗

arXiv2013

Compatible quantum correlations: on extension problems for Werner and isotropic states

We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

quant-ph↗

arXiv2013

Long-time Low-latency Quantum Memory by Dynamical Decoupling

Quantum memory is a central component for quantum information processing devices, and will be required to provide high-fidelity storage of arbitrary states, long storage times and small access latencies. Despite growing interest in applying physical-layer error-suppression strategies to boost fidelities, it has not previously been possible to meet such competing demands with a single approach. Here we use an experimentally validated theoretical framework to identify periodic repetition of a high-order dynamical decoupling sequence as a systematic strategy to meet these challenges. We provide analytic bounds-validated by numerical calculations-on the characteristics of the relevant control sequences and show that a "stroboscopic saturation" of coherence, or coherence plateau, can be engineered, even in the presence of experimental imperfection. This permits high-fidelity storage for times that can be exceptionally long, meaning that our device-independent results should prove instrumental in producing practically useful quantum technologies.

quant-ph↗

arXiv2013

Multiband s-wave topological superconductors: role of dimensionality and magnetic field response

We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced in Phys. Rev. Lett. 108, 036803 (2012). We show how, in the presence of time-reversal symmetry, Z_2 invariants that distinguish between trivial and non-trivial quantum phases can be constructed by considering only one of the Kramers' sectors in which the Hamiltonian decouples into. We find that the main features identified in our original 2D setting remain qualitatively unchanged in 1D and 3D, with non-trivial topological superconducting phases supporting an odd number of Kramers' pairs of helical Majorana modes on each boundary, as long as the required $π$ phase difference between gaps is maintained. We also analyze the consequences of time-reversal symmetry-breaking either due to the presence of an applied or impurity magnetic field or to a deviation from the intended phase matching between the superconducting gaps. We demonstrate how the relevant notion of topological invariance must be modified when time-reversal symmetry is broken, and how both the persistence of gapless Majorana modes and their robustness properties depend in general upon the way in which the original Hamiltonian is perturbed. Interestingly, a topological quantum phase transition between helical and chiral superconducting phases can be induced by suitably tuning a Zeeman field in conjunction with a phase mismatch between the gaps. Recent experiments in doped semiconducting crystals, of potential relevance to the proposed model, and possible candidate material realizations in superconductors with $s_\pm$ pairing symmetry are discussed.

cond-mat.supr-con↗

arXiv2013

Steady-State Entanglement by Engineered Quasi-Local Markovian Dissipation

We characterize and construct time-independent Markovian dynamics that drive a finite-dimensional multipartite quantum system into a target (pure) entangled steady state, subject to physical locality constraints. In situations where the desired stabilization task can not be attained solely based on local dissipative means, we allow for local Hamiltonian control or, if the latter is not an option, we suitably restrict the set of admissible initial states. In both cases, we provide algorithms for constructing a master equation that achieves the intended objective and show how this can genuinely extend the manifold of stabilizable states. In particular, we present quasi-local control protocols for dissipatively engineering multipartite GHZ "cat" states and W states on $n$ qubits. For GHZ states, we find that no scalable procedure exists for achieving stabilization from arbitrary initial states, whereas this is possible for a target W state by a suitable combination of a two-body Hamiltonian and dissipators. Interestingly, for both entanglement classes, we show that quasi-local stabilization may be scalably achieved conditional to initialization of the system in a large, appropriately chosen subspace.

quant-ph↗

arXiv2012

Automated Synthesis of Dynamically Corrected Quantum Gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.

quant-ph↗

arXiv2012

Quantum State Preparation by Controlled Dissipation in Finite Time: From Classical to Quantum Controllers

We propose a general scheme for dissipatively preparing arbitrary pure quantum states on a multipartite qubit register in a finite number of basic control blocks. Our "splitting-subspace" approach relies on control resources that are available in a number of scalable quantum technologies (complete unitary control on the target system, an ancillary resettable qubit and controlled-not gates between the target and the ancilla), and can be seen as a "quantum-controller" implementation of a sequence of classical feedback loops. We show how a large degree of flexibility exists in engineering the required conditional operations, and make explicit contact with a stabilization protocol used for dissipative quantum state preparation and entanglement generation in recent experiments with trapped ions.

quant-ph↗

arXiv2012

Majorana modes in time-reversal invariant s-wave topological superconductors

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

cond-mat.supr-con↗

arXiv2011

Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups

We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of physically relevant entangled states, our approach has the advantage of providing an explicit stabilization test solely based on the input state and constraints of the problem. Connections with the formalism of frustration-free parent Hamiltonians are discussed, as well as control implementations in terms of a switching output-feedback law.

quant-ph↗

arXiv2011

Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation

We study dynamical error suppression from the perspective of reducing sequencing complexity, in order to facilitate efficient semi-autonomous quantum-coherent systems. With this aim, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with simple digital classical control circuitry is intrinsic, using so-called em Walsh functions as a general mathematical framework. The Walsh functions are an orthonormal set of basis functions which may be associated directly with the control propagator for a digital modulation scheme, and dynamical decoupling (DD) sequences can be derived from the locations of digital transitions therein. We characterize the suite of the resulting Walsh dynamical decoupling (WDD) sequences, and identify the number of periodic square-wave (Rademacher) functions required to generate a Walsh function as the key determinant of the error-suppressing features of the relevant WDD sequence. WDD forms a unifying theoretical framework as it includes a large variety of well-known and novel DD sequences, providing significant flexibility and performance benefits relative to basic quasi-periodic design. We also show how Walsh modulation may be employed for the protection of certain nontrivial logic gates, providing an implementation of a dynamically corrected gate. Based on these insights we identify Walsh modulation as a digital-efficient approach for physical-layer error suppression.

quant-ph↗

arXiv2011

Experimental characterization of coherent magnetization transport in a one-dimensional spin system

We experimentally characterize the non-equilibrium, room-temperature magnetization dynamics of a spin chain evolving under an effective double-quantum Hamiltonian. We show that the Liouville space operators corresponding to the magnetization and the two-spin correlations evolve 90 degrees out of phase with each other, and drive the transport dynamics. For a nearest-neighbor-coupled N-spin chain, the dynamics are found to be restricted to a Liouville operator space whose dimension scales only as N^2, leading to a slow growth of multi-spin correlations. Even though long-range couplings are present in the real system, we find excellent agreement between the analytical predictions and our experimental results, confirming that leakage out of the restricted Liouville space is slow on the timescales investigated. Our results indicate that the group velocity of the magnetization is 6.04 +/- 0.38 um/s, corresponding to a coherent transport over N ~ 26 spins on the experimental timescale. As the double-quantum Hamiltonian is related to the standard one-dimensional XX Hamiltonian by a similarity transform, our results can be directly extended to XX quantum spin chains, which have been extensively studied in the context of both quantum magnetism and quantum information processing.

quant-ph↗

arXiv2011

Pointer States via Engineered Dissipation

Pointer states are long-lasting high-fidelity states in open quantum systems. We show how any pure state in a non-Markovian open quantum system can be made to behave as a pointer state by suitably engineering the coupling to the environment via open-loop periodic control. Engineered pointer states are constructed as approximate fixed points of the controlled open-system dynamics, in such a way that they are guaranteed to survive over a long time with a fidelity determined by the relative precision with which the dynamics is engineered. We provide quantitative minimum-fidelity bounds by identifying symmetry and ergodicity conditions that the decoherence-inducing perturbation must obey in the presence of control, and develop explicit pulse sequences for engineering any desired set of orthogonal states as pointer states. These general control protocols are validated through exact numerical simulations as well as semi-classical approximations in realistic single and two qubit dissipative systems. We also examine the role of control imperfections, and show that while pointer-state engineering protocols are highly robust in the presence of systematic pulse errors, the latter can also lead to unintended pointer-state generation in dynamical decoupling implementations, explaining the initial-state selectivity observed in recent experiments.

quant-ph↗

arXiv2011

Limits on Preserving Quantum Coherence using Multi-Pulse Control

We explore the physical limits of pulsed dynamical decoupling methods for decoherence control as determined by finite timing resources. By focusing on a decohering qubit controlled by arbitrary sequences of $π$-pulses, we establish a non-perturbative quantitative upper bound to the achievable coherence for specified maximum pulsing rate and noise spectral bandwidth. We introduce numerically optimized control "bandwidth-adapted" sequences that saturate the performance bound, and show how they outperform existing sequences in a realistic excitonic-qubit system where timing constraints are significant. As a byproduct, our analysis reinforces the impossibility of fault-tolerance accuracy thresholds for generic open quantum systems under purely reversible error control.

quant-ph↗

arXiv2011

Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state

We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY quantum spin chain in a transverse field, we characterize the non-equilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasi-particle excitation which ensure Kibble-Zurek scaling to persist. The emergence of effective thermal equilibrium behavior following a sudden quench towards criticality is also investigated, with focus on the long-time dynamics of the quasi-particle excitation. For a quench to a regular quantum critical point, this observable is found to behave thermally provided that the system is prepared at sufficiently high temperature, whereas thermalization fails to occur in quenches taking the system towards a multi-critical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.

cond-mat.stat-mech↗