arXiv subjects

Paolo Zanardi

Publications and source records attributed to Paolo Zanardi.

134 records · Page 8Linked to original sources

arXiv1999

Holonomic Quantum Computation

We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a $n$-fold degenerate eigenspace of a family of Hamiltonians parametrized by a manifold $\cal M$. The point of $\cal M$ represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops in the control $\cal M$ induce non trivial unitary transformations on the computational space. For a generic system it is shown that this mechanism allows for universal quantum computation by composing a generic pair of loops in $\cal M.$

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arXiv1999

Non-Abelian Berry connections for quantum computation

In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible, for a specific model, to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multi-partite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.

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arXiv1999

Symmetrizing Evolutions

We introduce quantum procedures for making $\cal G$-invariant the dynamics of an arbitrary quantum system S, where $\cal G$ is a finite group acting on the space state of S. Several applications of this idea are discussed. In particular when S is a N-qubit quantum computer interacting with its environment and $\cal G$ the symmetric group of qubit permutations, the resulting effective dynamics admits noiseless subspaces. Moreover it is shown that the recently introduced iterated-pulses schemes for reducing decoherence in quantum computers fit in this general framework. The noise-inducing component of the Hamiltonian is filtered out by the symmetrization procedure just due to its transformation properties.

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arXiv1999

Computation on a Noiseless Quantum Code and Symmetrization

Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.

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arXiv1998

Quantum Cloning in $d$ dimensions

The quantum state space $\cal S$ over a $d$-dimensional Hilbert space is represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset {\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then associated with the affine transformations of ${\bf{R}}^D,$ and $N\mapsto M$ {\it cloners} induce polynomial mappings. In this geometrical setting it is shown that an optimal cloner can be chosen covariant and induces a map between reduced density matrices given by a simple contraction of the associated $D$-dimensional Bloch vectors.

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arXiv1998

Quantum Information in Semiconductors: Noiseless Encoding in a Quantum-Dot Array

A potential implementation of quantum-computation schemes in semiconductor-based structures is proposed. In particular, an array of quantum dots is shown to be an ideal quantum register for a noiseless information encoding. In addition to the suppression of phase-breaking processes in quantum dots due to the well-known phonon bottleneck, we show that a proper quantum encoding allows to realise a decoherence-free evolution on a time-scale long compared to the femtosecond scale of modern ultrafast laser technology. This result might open the way to the realization of semiconductor-based quantum processors.

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arXiv1998

Subdecoherent Information Encoding in a Quantum-Dot Array

A potential implementation of quantum-information schemes in semiconductor nanostructures is studied. To this end, the formal theory of quantum encoding for avoiding errors is recalled and the existence of noiseless states for model systems is discussed. Based on this theoretical framework, we analyze the possibility of designing noiseless quantum codes in realistic semiconductor structures. In the specific implementation considered, information is encoded in the lowest energy sector of charge excitations of a linear array of quantum dots. The decoherence channel considered is electron-phonon coupling We show that besides the well-known phonon bottleneck, reducing single-qubit decoherence, suitable many-qubit initial preparation as well as register design may enhance the decoherence time by several orders of magnitude. This behaviour stems from the effective one-dimensional character of the phononic environment in the relevant region of physical parameters.

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arXiv1998

Dissipation and Decoherence in a Quantum Register

A model for a quantum register $\cal R$ made of $N$ replicas of a $d$-dimensional quantum system (cell) coupled with the environment, is studied by means of a Born-Markov Master Equation (ME). Dissipation and decoherence are discussed in various cases in which a sub-decoherent enconding can be rigorously found. For the qubit case ($d=2$) we have solved, for small $N,$ the ME by numerical direct integration and studied, as a function of the coherence length $ξ_c$ of the bath, fidelity and decoherence rates of states of the register. For large enough $ξ_c$ the singlet states of the global $su(2)$ pseudo-spin algebra of the register (noiseless at $ξ_c=\infty$) are shown to have a much smaller decoherence rates than the rest of the Hilbert space.

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