arXiv subjects

K. Birgitta Whaley

Publications and source records attributed to K. Birgitta Whaley.

At least 145 records · Page 8Linked to original sources

arXiv2008

Adaptive homodyne phase discrimination and qubit measurement

Fast and accurate measurement is a highly desirable, if not vital, feature of quantum computing architectures. In this work we investigate the usefulness of adaptive measurements in improving the speed and accuracy of qubit measurement. We examine a particular class of quantum computing architectures, ones based on qubits coupled to well controlled harmonic oscillator modes (reminiscent of cavity-QED), where adaptive schemes for measurement are particularly appropriate. In such architectures, qubit measurement is equivalent to phase discrimination for a mode of the electromagnetic field, and we examine adaptive techniques for doing this. In the final section we present a concrete example of applying adaptive measurement to the particularly well-developed circuit-QED architecture.

quant-ph↗

arXiv2008

Scalability of quantum computation with addressable optical lattices

We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size of quantum computations, arising in 3D optical lattices from current limitations on the ability to perform single qubit gates in parallel and in 2D lattices from constraints on laser power. Our results suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e., $\sim 10^6$ qubits) may be achievable, provided two-qubit gates can be performed with sufficiently high precision and degree of parallelizability. Parallelizability of long range interaction-based two-qubit gates is qualitatively compared to that of collisional gates. Different methods of performing single qubit gates are compared, and a lower bound of $1 \times 10^{-5}$ is determined on the error rate for the error mechanisms affecting $^{133}$Cs in a blue-detuned lattice with Raman transition-based single qubit gates, given reasonable limits on experimental parameters.

quant-ph↗

arXiv2007

Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences

We present a detailed analysis of decoherence free subspaces and develop a rigorous theory that provides necessary and sufficient conditions for dynamically stable decoherence free subspaces. This allows us to identify a special class of decoherence free states which rely on incoherent generation of coherences. We provide examples of physical systems that support such states. Our approach employs Markovian master equations and applies primarily to finite-dimensional quantum systems.

quant-ph↗

arXiv2007

A measurement-based measure of the size of macroscopic quantum superpositions

Recent experiments claiming formation of quantum superposition states in near macroscopic sys- tems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analy- sis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.

quant-ph↗

arXiv2007

Suppression of 1/f noise in one-qubit systems

We investigate the generation of quantum operations for one-qubit systems under classical noise with 1/f^αpower spectrum, where 2>α> 0. We present an efficient way to approximate the noise with a discrete multi-state Markovian fluctuator. With this method, the average temporal evolution of the qubit density matrix under 1/f^αnoise can be feasibly determined from recently derived deterministic master equations. We obtain qubit operations such as quantum memory and the NOT}gate to high fidelity by a gradient based optimization algorithm. For the NOT gate, the computed fidelities are qualitatively similar to those obtained earlier for random telegraph noise. In the case of quantum memory however, we observe a nonmonotonic dependency of the fidelity on the operation time, yielding a natural access rate of the memory.

quant-ph↗

arXiv2007

Multi-particle decoherence free subspaces in extended systems

We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multi-particle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multi-particle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.

quant-ph↗

arXiv2005

Ohmic and step noise from a single trapping center hybridized with a Fermi sea

We show that single electron tunneling devices such as the Cooper-pair box or double quantum dot can be sensitive to the zero-point fluctuation of a single trapping center hybridized with a Fermi sea. If the trap energy level is close to the Fermi sea and has line-width γ> k_B T, its noise spectrum has an Ohmic Johnson-Nyquist form, whereas for γ< k_B T the noise has a Lorentzian form expected from the semiclassical limit. Trap levels above the Fermi level are shown to lead to steps in the noise spectrum that can be used to probe their energetics, allowing the identification of individual trapping centers coupled to the device.

cond-mat.mes-hall↗

arXiv2005

Quantum Error Correction of a Qubit Loss in an Addressable Atomic System

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum non-demolition and projective measurements are implemented using a cavity QED system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

quant-ph↗

arXiv2005

High fidelity one-qubit operations under random telegraph noise

We address the problem of implementing high fidelity one-qubit operations subject to time dependent noise in the qubit energy splitting. We show with explicit numerical results that high fidelity bit flips and one-qubit NOT gates may be generated by imposing bounded control fields. For noise correlation times shorter than the time for a pi-pulse, the time optimal pi-pulse yields the highest fidelity. For very long correlation times, fidelity loss is approximately due to systematic error, which is efficiently tackled by compensation for off-resonance with a pulse sequence (CORPSE). For intermediate ranges of the noise correlation time we find that short CORPSE, which is less accurate than CORPSE in correcting systematic errors, yields higher fidelities. Numerical optimization of the pulse sequences using gradient ascent pulse engineering results in noticeable improvement of the fidelities for the bit flip and marginal improvement for the NOT gate.

quant-ph↗

arXiv2005

Non-Perturbative Bounds on Hyperfine-Induced Electron Spin Coherence Times

We address the decoherence of a localized electron spin in an external magnetic field due to the hyperfine interaction with a lattice of nuclear spins. Using a completely non-perturbative method, rigorous bounds on the T_1 and T_2 coherence times for the electron spin are provided. It is shown that for magnetic fields B greater than some critical field B_c (B_c ~ .001 - 2 Tesla for the systems studied here), the z-polarization of the electron spin cannot relax, and hence T_1 is infinite. However, even at high fields dephasing can still occur. We provide a lower bound on the T_2 coherence time that explicitly takes into account the effects of a spin echo pulse sequence.

cond-mat.mes-hall↗

arXiv2005

Universal Scaling of Hyperfine-Induced Electron Spin Echo Decay

The decoherence of a localized electron spin in a lattice of nuclear spins is an important problem for potential solid-state implementations of a quantum computer. We demonstrate that even at high fields, virtual electron spin-flip processes due solely to the hyperfine interaction can lead to complex nuclear spin dynamics. These dynamics, in turn, can lead to single electron spin phase fluctuation and decoherence. We show here that remarkably, a spin echo pulse sequence can almost completely reverse these nuclear dynamics except for a small visibility loss, thereby suppressing contribution of the hyperfine interaction to T_2 processes. For small systems, we present numerical evidence which demonstrates a universal scaling of the magnitude of visibility loss that depends only on the inhomogeneous line width of the system and the magnetic field.

cond-mat.mes-hall↗

arXiv2005

Qubit coherence control in a nuclear spin bath

Coherent dynamics of localized spins in semiconductors is limited by spectral diffusion arising from dipolar fluctuation of lattice nuclear spins. Here we extend the semiclassical theory of spectral diffusion for nuclear spins I=1/2 to the high nuclear spins relevant to the III-V materials and show that applying successive qubit pi-rotations at a rate approximately proportional to the nuclear spin quantum number squared (I^2) provides an efficient method for coherence enhancement. Hence robust coherent manipulation in the large spin environments characteristic of the III-V compounds is possible without resorting to nuclear spin polarization, provided that the pi-pulses can be generated at intervals scaling as I^{-2}.

cond-mat.mes-hall↗

arXiv2005

Optimal generation of single-qubit operation from an always-on interaction by algebraic decoupling

We present a direct algebraic decoupling approach to generate arbitrary single-qubit operations in the presence of a constant interaction by applying local control signals. To overcome the difficulty of undesirable entanglement generated by the untunable interaction, we derive local control fields that are designed to both drive the qubit systems back to unentangled states at the end of the time interval over which the desired single-qubit operation is completed. This approach is seen to be particularly relevant for the physical implementation of solid-state quantum computation and for the design of low-power pulses in NMR.

quant-ph↗

arXiv2005

Atomistic Theory of Coherent Spin Transfer between Molecularly Bridged Quantum Dots

Time-resolved Faradary rotation experiments have demonstrated coherent transfer of electron spin between CdSe colloidal quantum dots coupled by conjugated molecules. We employ here a Green's function approach, using semi-empirical tight-binding to treat the nanocrystal Hamiltonian and Extended Huckel theory to treat the linking molecule Hamiltonian, to obtain the coherent transfer probabilities from atomistic calculations, without the introduction of any new parameters. Calculations on 1,4-dithiolbenzene and 1,4-dithiolcyclohexane linked nanocrystals agree qualitatively with experiment and provide support for a previous transfer Hamiltonian model. We find a striking dependence on the transfer probabilities as a function of nanocrystal surface site attachment and linking molecule conformation. Additionally, we predict quantum interference effects in the coherent transfer probabilities for 2,7-dithiolnaphthalene and 2,6-dithiolnaphthalene linking molecules. We suggest possible experiments based on these results that would test the coherent, through-molecule transfer mechanism.

cond-mat.other↗

arXiv2004

Generation of quantum logic operations from physical Hamiltonians

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of one-qubit operations can be transformed into a steering problem on the Bloch sphere, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes.

quant-ph↗

arXiv2004

Thomas-Fermi Theory of the Hyperfine Constants of Endohedral Fullerene Atoms

We present a modified Thomas-Fermi theory that describes the increase of the hyperfine coupling constants of endohedrally enclosed atoms. We use the March boundary conditions corresponding to a positively charged spherical shell surrounding the nuclear potential to represent the effect of the fullerene shell. We obtain quantitative agreement with experimental data for N@C$_{60}$ and N@C$_{70}$, and find that fullerene radius dominates over the fullerene charge in its effect on the hyperfine coupling constants. We also present predictions for the hyperfine coupling constants of the endohedral nitrogen fullerenes between C$_{60}$ and C$_{500}$, and discuss the implications for proposed quantum computing schemes.

cond-mat.dis-nn↗

arXiv2004

Electronic transport, structure, and energetics of endohedral Gd@C82 metallofullerenes

Electronic structure and transport properties of the fullerene C$_{82}$ and the metallofullerene Gd@C$_{82}$ are investigated with density functional theory and the Landauer-Buttiker formalism. The ground state structure of Gd@C$_{82}$ is found to have the Gd atom below the C-C bond on the C$_2$ molecular axis of C$_{82}$. Insertion of Gd into C$_{82}$ deforms the carbon chain in the vicinity of the Gd atoms. Significant overlap of the electron distribution is found between Gd and the C$_{82}$ cage, with the transferred Gd electron density localized mainly on the nearest carbon atoms. This charge localization reduces some of the conducting channels for the transport, causing a reduction in the conductivity of the Gd@C$_{82}$ species relative to the empty C$_{82}$ molecule. The electron transport across the metallofullerene is found to be insensitive to the spin state of the Gd atom.

cond-mat.other↗

arXiv2004

Minimum construction of two-qubit quantum operations

Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. We also demonstrate that for the highly scalable Josephson junction charge qubits, the B gate is also more easily and quickly generated than the CNOT gate for physically feasible parameters.

quant-ph↗