arXiv subjects

D. A. Lidar

Publications and source records attributed to D. A. Lidar.

66 records · Page 4Linked to original sources

arXiv2002

Efficient Universal Leakage Elimination for Physical and Encoded Qubits

Decoherence-induced leakage errors can couple a physical or encoded qubit to other levels, thus potentially damaging the qubit. They can therefore be very detrimental in quantum computation and require special attention. Here we present a general method for removing such errors by using simple decoupling and recoupling pulse sequences. The proposed gates are experimentally accessible in a variety of promising quantum computing proposals.

quant-ph↗

arXiv2001

Reducing Constraints on Quantum Computer Design by Encoded Selective Recoupling

The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for single-qubit operations in a large subset of quantum computer proposals: those governed by isotropic and XXZ,XY-type anisotropic exchange interactions. Our method employs an encoding of one logical qubit into two physical qubits, while logic operations are performed using an analogue of the NMR selective recoupling method.

quant-ph↗

arXiv2001

Power of Anisotropic Exchange Interactions: Universality and Efficient Codes for Quantum Computing

We study the quantum computational power of a generic class of anisotropic solid state Hamiltonians. A universal set of encoded logic operations are found which do away with difficult-to-implement single-qubit gates in a number of quantum computer proposals, e.g., quantum dots and donor atom spins with anisotropic exchange coupling, quantum Hall systems, and electrons floating on helium.We show how to make the corresponding Hamiltonians universal by encoding one qubit into two physical qubits, and by controlling nearest neighbor interactions.

quant-ph↗

arXiv2001

Quantum Computing with Quantum Dots on Linear Supports

Motivated by the recently demonstrated ability to attach quantum dots to polymers at well defined locations, we propose a condensed phase analog of the ion trap quantum computer: a scheme for quantum computation using chemically assembled semiconductor nanocrystals attached to a linear support. The linear support is either a molecular string (e.g., DNA) or a nanoscale rod. The phonon modes of the linear support are used as a quantum information bus between the dots. Our scheme offers greater flexibiliy in optimizing material parameters than the ion trap method but has additional complications. We discuss the relevant physical parameters, provide a detailed feasibility study, and suggest materials for which quantum computation may be possible with this approach. We find that Si is a potentially promising quantum dot material, already allowing 5-10 qubits quantum computer to operate with an error threshold of 10^-3.

quant-ph↗

arXiv2001

Encoded Universality in Physical Implementations of a Quantum Computer

We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally available interactions. A key element of this approach is the realization that the fungible nature of quantum information allows for universal manipulations using quantum information encoded in a subspace of the full system Hilbert space, as an alternative to using physical qubits directly. Starting with the interactions intrinsic to the physical system, we show how to determine the possible universality resulting from these interactions over an encoded subspace. We outline a general Lie-algebraic framework which can be used to find the encoding for universality and give several examples relevant to solid-state quantum computing.

quant-ph↗

arXiv2001

The manipulation of massive ro-vibronic superpositions using time-frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in Time-Frequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 1000 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated frequency-resolved CARS, while the third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing - all single qubit operations and the two-qubit controlled-NOT (CNOT) gate - are available in time resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally "wired" for carrying out all single qubit operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit.

physics.chem-ph↗

arXiv1999

Robustness of Decoherence-Free Subspaces for Quantum Computation

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.

quant-ph↗

arXiv1999

Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes

An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFSs are the class of quantum error correcting codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate.

quant-ph↗

arXiv1998

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent γ, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.

cond-mat.soft↗

arXiv1998

Decoherence Free Subspaces for Quantum Computation

Decoherence in quantum computers is formulated within the Semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for error-less quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators. It is shown that these subspaces are stable to perturbations and moreover, that universal quantum computation is possible within them.

quant-ph↗

arXiv1998

Structure Determination of Disordered Metallic Sub-Monolayers by Helium Scattering: A Theoretical and Experimental Study

An approach based on He scattering is used to develop an atomic-level structural model for an epitaxially grown disordered sub-monolayer of Ag on Pt(111) at 38K. Quantum scattering calculations are used to fit structural models to the measured angular intensity distribution of He atoms scattered from this system. The structure obtained corresponds to narrowly size-dispersed compact clusters with modest translational disorder, and not to fractals which might be expected due to the low surface temperature. The clusters have up to two layers in height, the lower one having few defects only. The relations between specific features of the angular scattering distribution, and properties such as the cluster sizes and shapes, the inter-cluster distance distribution etc., are discussed. The results demonstrate the usefulness of He scattering as a tool for unraveling new complex surface phases.

cond-mat.mtrl-sci↗

arXiv1997

Randomness and Apparent Fractality

We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically relevant cutoffs. This range, spanning between one and two decades for densities of 0.1 and lower, is in good agreement with the typical range observed in experiments. The dimensions are not universal and depend on density. Our observations are applicable to spatial, temporal and spectral random structures, all with non-zero measure. Fat fractal analysis does not seem to add information over routine fractal analysis procedures. Most significantly, we find that this apparent fractal behavior is robust even to the presence of moderate correlations. We thus propose that apparent fractal behavior observed experimentally over a limited range in some systems, may often have its origin in underlying randomness.

cond-mat↗