3,362 research outputs found
Efficient Toffoli Gates Using Qudits
The simplest decomposition of a Toffoli gate acting on three qubits requires
{\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or
controlled-NOT) gates this number climbs to six. We show that the number of
controlled-sign gates required to implement a Toffoli gate can be reduced to
just {\em three} if one of the three quantum systems has a third state that is
accessible during the computation, i.e. is actually a qutrit. Such a
requirement is not unreasonable or even atypical since we often artificially
enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic
polarization and spatial modes). We explore the implementation of these
techniques in optical quantum processing and show that linear optical circuits
could operate with much higher probabilities of success
Choice of Measurement Sets in Qubit Tomography
Optimal generalized measurements for state estimation are well understood.
However, practical quantum state tomography is typically performed using a
fixed set of projective measurements and the question of how to choose these
measurements has been largely unexplored in the literature. In this work we
develop theoretical asymptotic bounds for the average fidelity of pure qubit
tomography using measurement sets whose axes correspond to vertices of Platonic
solids. We also present complete simulations of maximum likelihood tomography
for mixed qubit states using the Platonic solid measurements. We show that
overcomplete measurement sets can be used to improve the accuracy of
tomographic reconstructions.Comment: 13 Pages, 6 figure
Time-reversal and super-resolving phase measurements
We demonstrate phase super-resolution in the absence of entangled states. The
key insight is to use the inherent time-reversal symmetry of quantum mechanics:
our theory shows that it is possible to \emph{measure}, as opposed to prepare,
entangled states. Our approach is robust, requiring only photons that exhibit
classical interference: we experimentally demonstrate high-visibility phase
super-resolution with three, four, and six photons using a standard laser and
photon counters. Our six-photon experiment demonstrates the best phase
super-resolution yet reported with high visibility and resolution.Comment: 4 pages, 3 figure
Manipulating biphotonic qutrits
Quantum information carriers with higher dimension than the canonical qubit
offer significant advantages. However, manipulating such systems is extremely
difficult. We show how measurement induced non-linearities can be employed to
dramatically extend the range of possible transforms on biphotonic qutrits; the
three level quantum systems formed by the polarisation of two photons in the
same spatio-temporal mode. We fully characterise the biphoton-photon
entanglement that underpins our technique, thereby realising the first instance
of qubit-qutrit entanglement. We discuss an extension of our technique to
generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of
quantum information.Comment: 4 pages, 4 figure
Distance measures to compare real and ideal quantum processes
With growing success in experimental implementations it is critical to
identify a "gold standard" for quantum information processing, a single measure
of distance that can be used to compare and contrast different experiments. We
enumerate a set of criteria such a distance measure must satisfy to be both
experimentally and theoretically meaningful. We then assess a wide range of
possible measures against these criteria, before making a recommendation as to
the best measures to use in characterizing quantum information processing.Comment: 15 pages; this version in line with published versio
Demonstration of a simple entangling optical gate and its use in Bell-state analysis
We demonstrate a new architecture for an optical entangling gate that is
significantly simpler than previous realisations, using partially-polarising
beamsplitters so that only a single optical mode-matching condition is
required. We demonstrate operation of a controlled-Z gate in both
continuous-wave and pulsed regimes of operation, fully characterising it in
each case using quantum process tomography. We also demonstrate a
fully-resolving, nondeterministic optical Bell-state analyser based on this
controlled-Z gate. This new architecture is ideally suited to guided optics
implementations of optical gates.Comment: 4 pages, 3 figures. v2: additional author, improved data and figures
(low res), some other minor changes. Accepted for publication in PR
Quantum process tomography of a controlled-NOT gate
We demonstrate complete characterization of a two-qubit entangling process -
a linear optics controlled-NOT gate operating with coincident detection - by
quantum process tomography. We use maximum-likelihood estimation to convert the
experimental data into a physical process matrix. The process matrix allows
accurate prediction of the operation of the gate for arbitrary input states,
and calculation of gate performance measures such as the average gate fidelity,
average purity and entangling capability of our gate, which are 0.90, 0.83 and
0.73, respectively.Comment: 4 pages, 2 figures. v2 contains new data corresponding to improved
gate operation. Figure quality slightly reduced for arXi
Experimental demonstration of Shor's algorithm with quantum entanglement
Shor's powerful quantum algorithm for factoring represents a major challenge
in quantum computation and its full realization will have a large impact on
modern cryptography. Here we implement a compiled version of Shor's algorithm
in a photonic system using single photons and employing the non-linearity
induced by measurement. For the first time we demonstrate the core processes,
coherent control, and resultant entangled states that are required in a
full-scale implementation of Shor's algorithm. Demonstration of these processes
is a necessary step on the path towards a full implementation of Shor's
algorithm and scalable quantum computing. Our results highlight that the
performance of a quantum algorithm is not the same as performance of the
underlying quantum circuit, and stress the importance of developing techniques
for characterising quantum algorithms.Comment: 4 pages, 5 figures + half-page additional online materia
Information flow in one-dimensional non-unitary quantum cellular automata
The information flow in a quantum system is a fundamental feature of its
dynamics. An important class of dynamics are quantum cellular automata (QCA),
systems with discrete updates invariant in time and space, for which an index
theory has been proposed for the quantification of the net flow of quantum
information across a boundary. While the index is rigid in the sense of begin
invariant under finite-depth local circuits, it is not defined when the system
is coupled to an environment, i.e. for non-unitary time evolution of open
quantum systems. We propose a new measure of information flow for non-unitary
QCA denoted the information current which is not rigid, but can be computed
locally based on the matrix-product operator representation of the map.Comment: 21 pages, 23 figure
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