147 research outputs found
An Arbitrary Two-qubit Computation In 23 Elementary Gates
Quantum circuits currently constitute a dominant model for quantum
computation. Our work addresses the problem of constructing quantum circuits to
implement an arbitrary given quantum computation, in the special case of two
qubits. We pursue circuits without ancilla qubits and as small a number of
elementary quantum gates as possible. Our lower bound for worst-case optimal
two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2
CNOTs. To this end, we constructively prove a worst-case upper bound of 23
elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions.
Our analysis shows that synthesis algorithms suggested in previous work,
although more general, entail much larger quantum circuits than ours in the
special case of two qubits. One such algorithm has a worst case of 61 gates of
which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie
theory as well as the polar and spectral (symmetric Shur) matrix decompositions
from numerical analysis and operator theory. They are related to the canonical
decomposition of a two-qubit gate with respect to the ``magic basis'' of
phase-shifted Bell states, published previously. We further extend this
decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC
"quantum compiler". Version 3 adds justification for our choice of elementary
gates and adds a comparison with classical library-less logic synthesis. It
adds acknowledgements and a new reference, adds full details about the 8-gate
decomposition of topC-V and stealthily fixes several minor inaccuracies.
NOTE: Using a new technique, we recently improved the lower bound to 18 gates
and (tada!) found a circuit decomposition that requires 18 gates or less.
This work will appear as a separate manuscrip
Synthesis of Quantum Circuits for Linear Nearest Neighbor Architectures
While a couple of impressive quantum technologies have been proposed, they
have several intrinsic limitations which must be considered by circuit
designers to produce realizable circuits. Limited interaction distance between
gate qubits is one of the most common limitations. In this paper, we suggest
extensions of the existing synthesis flow aimed to realize circuits for quantum
architectures with linear nearest neighbor (LNN) interaction. To this end, a
template matching optimization, an exact synthesis approach, and two reordering
strategies are introduced. The proposed methods are combined as an integrated
synthesis flow. Experiments show that by using the suggested flow, quantum cost
can be improved by more than 50% on average.Comment: 14 pages, 11 figures, 3 table
Anomaly in the K^0_S Sigma^+ photoproduction cross section off the proton at the K* threshold
The photoproduction reaction is
investigated in the energy region from threshold to \,MeV. The
differential cross section exhibits increasing forward-peaking with energy, but
only up to the threshold. Beyond, it suddenly returns to a flat
distribution with the forward cross section dropping by a factor of four. In
the total cross section a pronounced structure is observed between the
and thresholds. It is speculated whether this signals
the turnover of the reaction mechanism from t-channel exchange below the
production threshold to an s-channel mechanism associated with the formation of
a dynamically generated -hyperon intermediate state.Comment: 14 pages, 7 figure
Linearly polarised photon beams at ELSA and measurement of the beam asymmetry in pi^0-photoproduction off the proton
At the electron accelerator ELSA a linearly polarised tagged photon beam is
produced by coherent bremsstrahlung off a diamond crystal. Orientation and
energy range of the linear polarisation can be deliberately chosen by accurate
positioning of the crystal with a goniometer. The degree of polarisation is
determined by the form of the scattered electron spectrum. Good agreement
between experiment and expectations on basis of the experimental conditions is
obtained. Polarisation degrees of P = 40% are typically achieved at half of the
primary electron energy. The determination of P is confirmed by measuring the
beam asymmetry, \Sigma, in pi^0 photoproduction and a comparison of the results
to independent measurements using laser backscattering.Comment: 9 pages, 10 figures, submitted to EPJ
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