arXiv subjects

K. B. Whaley

Publications and source records attributed to K. B. Whaley.

At least 19 recordsLinked to original sources

arXiv2020

Continuous quantum error correction for evolution under time-dependent Hamiltonians

We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit flip code and bit flip errors as a canonical example. To detect errors in real time, we filter the output signals from continuous measurement of the error syndrome operators and use a double thresholding protocol for error diagnosis, while correction of errors is done as in the conventional operation. We optimize our continuous operation protocol for evolution under quantum memory and under quantum annealing, by maximizing the fidelity between the target and actual logical states at a specified final time. In the case of quantum memory we show that our continuous operation protocol yields a logical error rate that is slightly larger than the one obtained from using the optimal Wonham filter for error diagnosis. The advantage of our protocol is that it can be simpler to implement. For quantum annealing, we show that our continuous quantum error correction protocol can significantly reduce the final logical state infidelity when the continuous measurements are sufficiently strong relative to the strength of the time-dependent Hamiltonian, and that it can also significantly reduces the run time relative to that of a classical encoding. These results suggest that a continuous implementation is suitable for quantum error correction in the presence of encoded time-dependent Hamiltonians, opening the possibility of many applications in quantum simulation and quantum annealing.

quant-ph↗

arXiv2018

Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball

For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of $N$ two-level quantum systems will unitarily evolve to another state from which it can be distinguished with a fixed minimal error probability $δ\in [0,1/2]$. This condition is used to order the set of qubit states based on their distinguishability time, and to derive an optimal release time for driven two-level systems such as those that occur, e.g., in the Landau-Zener problem. For the case of non-unitary dynamics, we compare three lower bounds to the distinguishability time, including a new type of lower bound which is formulated in terms of the asymmetry of the uniformly time-twirled initial system-plus-environment state with respect to the generator $H_{SE}$ of the Stinespring isometry corresponding to the dynamics, specifically, in terms of $\Vert [H_{SE},ρ_{\text{av}}(τ)]\Vert_{1}$, where $ρ_{\text{av}}(τ):={1\over τ}\int_{0}^τdt\, e^{-iH_{SE}t}ρ\otimes \vert 0\rangle_{E}\langle 0\vert_{E} e^{iH_{SE}t}$.

quant-ph↗

arXiv2017

Stable quantum memories with limited measurement

We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher dimensional stabilizer codes with string-like excitations, like the toric code.

quant-ph↗

arXiv2016

Engineering autonomous error correction in stabilizer codes at finite temperature

We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the toric code. The primary tool employed is dynamic application of a local, unitary operator which exchanges defects and thereby translates localized excitations. Crucially, the protocol does not require any measurements of stabilizer operators, and therefore can be used to enhance the lifetime of a qubit in the absence of such experimental resources.

quant-ph↗

arXiv2014

Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space

We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch distinguishability measure is obtained and applied to superposition states of $N$ quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., N00N states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.

quant-ph↗

arXiv2014

Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a low-temperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.

cond-mat.stat-mech↗

arXiv2014

Collective Effects in Linear Spectroscopy of Dipole-Coupled Molecular Arrays

We present a consistent analysis of linear spectroscopy for arrays of nearest neighbor dipole-coupled two-level molecules that reveals distinct signatures of weak and strong coupling regimes separated for infinite size arrays by a quantum critical point. In the weak coupling regime, the ground state of the molecular array is disordered, but in the strong coupling regime it has (anti)ferroelectric ordering. We show that multiple molecular excitations (odd/even in weak/strong coupling regime) can be accessed directly from the ground state. We analyze the scaling of absorption and emission with system size and find that the oscillator strengths show enhanced superradiant behavior in both ordered and disordered phases. As the coupling increases, the single excitation oscillator strength rapidly exceeds the well known Heitler-London value. In the strong coupling regime we show the existence of a unique spectral transition with excitation energy that can be tuned by varying the system size and that asymptotically approaches zero for large systems. The oscillator strength for this transition scales quadratically with system size, showing an anomalous one-photon superradiance. For systems of infinite size, we find a novel, singular spectroscopic signature of the quantum phase transition between disordered and ordered ground states. We outline how arrays of ultra cold dipolar molecules trapped in an optical lattice can be used to access the strong coupling regime and observe the anomalous superradiant effects associated with this regime.

quant-ph↗

arXiv2014

Continuous Measurement of a Non-Markovian Open Quantum System

Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural or engineered complex systems. The system is monitored via a probe resonator coupled to a broadband (Markovian) reservoir. Based on this model, we derive a formalism of Stochastic Hierarchy Equations of Motion (SHEM) describing the decoherence dynamics of the system conditioned on the measurement record. Furthermore, we demonstrate a spectroscopy method based on weak quantum measurement to reveal the non-Markovian nature of the environment, which we term weak spectroscopy.

quant-ph↗

arXiv2013

Measurement- and comparison-based sizes of Schrödinger cat states of light

We extend several measurement-based definitions of effective "cat-size" to coherent state superpositions with branches composed of either single coherent states or tensor products of coherent states. These effective cat-size measures depend on determining the maximal quantum distinguishability of certain states associated with the superposition state: e.g., in one measure, the maximal distinguishability of the branches of the superposition is considered as in quantum binary decision theory; in another measure, the maximal distinguishability of the initial superposition and its image after a one-parameter evolution generated by a local Hermitian operator is of interest. The cat-size scaling with the number of modes and mode intensity (i.e., photon number) is compared to the scaling derived directly from the Wigner function of the superposition and to that estimated experimentally from decoherence. We also apply earlier comparison-based methods for determining macroscopic superposition size that require a reference GHZ state. The case of a hierarchical Schrödinger cat state with branches composed of smaller superpositions is also analyzed from a measurement-based perspective.

quant-ph↗

arXiv2013

Geometric properties of loop condensed phases on the square lattice

Loop condensed phases are scale-invariant quantum liquid phases of matter. These phases include topologically ordered liquid phases such as the toric code as well as critical liquids such as the Rokhsar-Kivelson point of the quantum dimer model on the square lattice. To investigate the extent to which nonlocal geometric observables capture a signature of the nonlocal quantum order present in these phases, we compute geometric properties of such loop condensed states using directed loop Monte Carlo calculations. In particular, we investigate the loop condensed nature of ground state of the square lattice quantum dimer model at the Rokhsar-Kivelson point and compare with other loop condensed states on the square lattice, including those of the toric code and fully packed loop model. The common features of such liquids are a scale invariant distribution of loops and a fractal dimensionality of spanning loops. We find that the fractal dimension of the loop condensate of the square lattice quantum dimer model at the Rokhsar-Kivelson point is 3/2, which provides quantitative confirmation of the effective height model that is commonly used to describe this critical dimer liquid.

cond-mat.str-el↗

arXiv2011

Loop condensation in the triangular lattice quantum dimer model

We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases with broken symmetry. In the context of systems with extended loop-like degrees of freedom, the formation of such topological order can be described in terms of loop condensation. Using Monte Carlo calculations with local and directed-loop updates, we compute geometric properties of the transition graph loop distributions of several triangular lattice quantum dimer wavefunctions that display dimer-liquid to dimer-crystal transitions and characterize these in terms of loop condensation.

cond-mat.stat-mech↗

arXiv2011

Optimizing entangling quantum gates for physical systems

Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.

quant-ph↗

arXiv2010

Stroboscopic Generation of Topological Protection

Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with $n$-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.

quant-ph↗

arXiv2010

Electronic structure of superposition states in flux qubits

Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by $\sim 10^6$ -- $10^{10}$ electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schrödinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems.

quant-ph↗

arXiv2010

The size of macroscopic superposition states in flux qubits

The question as to whether or not quantum mechanics is applicable to the macroscopic scale has motivated efforts to generate superposition states of macroscopic numbers of particles and to determine their effective size. Superpositions of circulating current states in flux qubits constitute candidate states that have been argued to be at least mesoscopic. We present a microscopic analysis that reveals the number of electrons participating in these superpositions to be surprisingly but not trivially small, even though differences in macroscopic observables are large.

quant-ph↗

arXiv2009

Distinguishing Phases with Ansatz Wavefunctions

We propose an indistinguishability measure for assessment of ansatz wavefunctions with numerically determined wavefunctions. The measure efficiently compares all correlation functions of two states and can therefore be used to distinguish phases by defining correlator classes for ansatz wavefunctions. It also allows identification of quantum critical points. We demonstrate the approach for the transverse Ising model, using the matrix product state formalism with the time evolving block decimation algorithm.

cond-mat.str-el↗

arXiv2009

Thermal Canting of Spin-Bond Order

Magnetism arising from coupled spin and spatial degrees of freedom underlies the properties of a broad array of physical systems. We study here the interplay between correlations in spin and space for the quantum compass model in a finite external field, using quantum Monte Carlo methods. We find that finite temperatures cant the spin and space (bond) correlations, with increasing temperature even reorienting spin correlations between orthogonal spatial directions. We develop a coupled mean field theory to understand this effect in terms of the underlying quantum critical properties of crossed Ising chains in transverse fields and an effective field that weakens upon increasing temperature. Thermal canting offers an experimental signature of spin-bond anisotropy.

cond-mat.str-el↗

arXiv2005

Electrical activation and electron spin coherence of ultra low dose antimony implants in silicon

We implanted ultra low doses (2x10^11 cm-2) of 121Sb ions into isotopically enriched 28Si and find high degrees of electrical activation and low levels of dopant diffusion after rapid thermal annealing. Pulsed Electron Spin Resonance shows that spin echo decay is sensitive to the dopant depths, and the interface quality. At 5.2 K, a spin decoherence time, T2, of 0.3 ms is found for profiles peaking 50 nm below a Si/SiO2 interface, increasing to 0.75 ms when the surface is passivated with hydrogen. These measurements provide benchmark data for the development of devices in which quantum information is encoded in donor electron spins.

cond-mat.mtrl-sci↗