41 research outputs found
Qudit-Basis Universal Quantum Computation using Interactions
We prove that universal quantum computation can be realized---using only
linear optics and (three-wave mixing) interactions---in any
-dimensional qudit basis of the -pump-photon subspace. First, we
exhibit a strictly universal gate set for the qubit basis in the
one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by
proving that Hamiltonians and photon-number operators generate the
full Lie algebra in the two-pump-photon subspace, and showing
how the qutrit controlled- gate can be implemented with only linear optics
and interactions. We then use proof by induction to obtain our
general qudit result. Our induction proof relies on coherent photon
injection/subtraction, a technique enabled by interaction between
the encoding modes and ancillary modes. Finally, we show that coherent photon
injection is more than a conceptual tool in that it offers a route to preparing
high-photon-number Fock states from single-photon Fock states.Comment: 9 pages, 3 figure
Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing
Leveraging quantum effects in metrology such as entanglement and coherence
allows one to measure parameters with enhanced sensitivity. However,
time-dependent noise can disrupt such Heisenberg-limited amplification. We
propose a quantum-metrology method based on the quantum-signal-processing
framework to overcome these realistic noise-induced limitations in practical
quantum metrology. Our algorithm separates the gate parameter
~(single-qubit Z phase) that is susceptible to time-dependent error
from the target gate parameter ~(swap-angle between |10> and |01>
states) that is largely free of time-dependent error. Our method achieves an
accuracy of radians in standard deviation for learning in
superconducting-qubit experiments, outperforming existing alternative schemes
by two orders of magnitude. We also demonstrate the increased robustness in
learning time-dependent gate parameters through fast Fourier transformation and
sequential phase difference. We show both theoretically and numerically that
there is an interesting transition of the optimal metrology variance scaling as
a function of circuit depth from the pre-asymptotic regime
to Heisenberg limit . Remarkably, in the pre-asymptotic regime
our method's estimation variance on time-sensitive parameter scales
faster than the asymptotic Heisenberg limit as a function of depth,
. Our work is the first
quantum-signal-processing algorithm that demonstrates practical application in
laboratory quantum computers
Finite-key analysis for time-energy high-dimensional quantum key distribution
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.United States. Office of Naval Research (Grant N00014- 13-1-0774)United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052)Natural Sciences and Engineering Research Council of Canada (Postdoctoral Fellowship