Quantum Computers and Dissipation

We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.Comment: 20 pages, Latex, 7 Postscript figure

Quantum Algorithms: Entanglement Enhanced Information Processing

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc. (Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum Computation: Theory and Experiment'', held in November 199

Geometric phases for mixed states in interferometry

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection-form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.Comment: Two column, 4 pages, Latex file, No figures, Few change

Reply to `Singularities of the mixed state phase'

The only difference between Bhandari's viewpoint [quant-ph/0108058] and ours [Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo $2\pi$, whereas Bhandari argues that two phases that differ by $2\pi n$, $n$ integer, may be distinguished experimentally in a history-dependent manner.Comment: 2 page

Experimental Demonstration of Quantum State Multi-meter and One-qubit Fingerprinting in a Single Quantum Device

We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Using the same device, we also demonstrate one-qubit quantum fingerprinting

Surface Acoustic Wave Single-Electron Interferometry

We propose an experiment to observe interference of a single electron as it is transported along two parallel quasi-one-dimensional channels trapped in a single minimum of a travelling periodic electric field. The experimental device is a modification of the surface acoustic wave (SAW) based quantum processor. Interference is achieved by creating a superposition of spatial wavefunctions between the two channels and inducing a relative phase shift via either a transverse electric field or a magnetic field. The interference can be used to estimate the decoherence time of an electron in this type of solid-state device

Optimal universal quantum cloning and state estimation

We derive a tight upper bound for the fidelity of a universal N to M qubit cloner, valid for any M \geq N, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalise the operation of a quantum cloner to mixed and/or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind.Comment: 4 pages (RevTeX

Tomographic Quantum Cryptography: Equivalence of Quantum and Classical Key Distillation

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.Comment: 4 pages, 1 figur

A universal quantum estimator

Almost all computational tasks in the modem computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly discuss how these gates can be used in quantum networks