7,619 research outputs found
Direct Application of the Phase Estimation Algorithm to Find the Eigenvalues of the Hamiltonians
The eigenvalue of a Hamiltonian, , can be estimated through the
phase estimation algorithm given the matrix exponential of the Hamiltonian,
. The difficulty of this exponentiation impedes the
applications of the phase estimation algorithm particularly when
is composed of non-commuting terms. In this paper, we present a method to use
the Hamiltonian matrix directly in the phase estimation algorithm by using an
ancilla based framework: In this framework, we also show how to find the power
of the Hamiltonian matrix-which is necessary in the phase estimation
algorithm-through the successive applications. This may eliminate the necessity
of matrix exponential for the phase estimation algorithm and therefore provide
an efficient way to estimate the eigenvalues of particular Hamiltonians. The
classical and quantum algorithmic complexities of the framework are analyzed
for the Hamiltonians which can be written as a sum of simple unitary matrices
and shown that a Hamiltonian of order written as a sum of number of
simple terms can be used in the phase estimation algorithm with
number of qubits and number of quantum operations, where is the
number of iterations in the phase estimation. In addition, we use the
Hamiltonian of the hydrogen molecule as an example system and present the
simulation results for finding its ground state energy.Comment: 10 pages, 3 figure
Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
Quantum phase estimation is a fundamental subroutine in many quantum
algorithms, including Shor's factorization algorithm and quantum simulation.
However, so far results have cast doubt on its practicability for near-term,
non-fault tolerant, quantum devices. Here we report experimental results
demonstrating that this intuition need not be true. We implement a recently
proposed adaptive Bayesian approach to quantum phase estimation and use it to
simulate molecular energies on a Silicon quantum photonic device. The approach
is verified to be well suited for pre-threshold quantum processors by
investigating its superior robustness to noise and decoherence compared to the
iterative phase estimation algorithm. This shows a promising route to unlock
the power of quantum phase estimation much sooner than previously believed
Quantum Enhanced Multiple Phase Estimation
We study the simultaneous estimation of multiple phases as a discretised
model for the imaging of a phase object. We identify quantum probe states that
provide an enhancement compared to the best quantum scheme for the estimation
of each individual phase separately, as well as improvements over classical
strategies. Our strategy provides an advantage in the variance of the
estimation over individual quantum estimation schemes that scales as O(d) where
d is the number of phases. Finally, we study the attainability of this limit
using realistic probes and photon-number-resolving detectors. This is a problem
in which an intrinsic advantage is derived from the estimation of multiple
parameters simultaneously.Comment: Accepted by Physical Review Letter
Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control
Optical phase estimation is a vital measurement primitive that is used to
perform accurate measurements of various physical quantities like length,
velocity and displacements. The precision of such measurements can be largely
enhanced by the use of entangled or squeezed states of light as demonstrated in
a variety of different optical systems. Most of these accounts however deal
with the measurement of a very small shift of an already known phase, which is
in stark contrast to ab-initio phase estimation where the initial phase is
unknown. Here we report on the realization of a quantum enhanced and fully
deterministic phase estimation protocol based on real-time feedback control.
Using robust squeezed states of light combined with a real-time Bayesian
estimation feedback algorithm, we demonstrate deterministic phase estimation
with a precision beyond the quantum shot noise limit. The demonstrated protocol
opens up new opportunities for quantum microscopy, quantum metrology and
quantum information processing.Comment: 5 figure
Adaptive phase estimation is more accurate than non-adaptive phase estimation for continuous beams of light
We consider the task of estimating the randomly fluctuating phase of a
continuous-wave beam of light. Using the theory of quantum parameter
estimation, we show that this can be done more accurately when feedback is used
(adaptive phase estimation) than by any scheme not involving feedback
(non-adaptive phase estimation) in which the beam is measured as it arrives at
the detector. Such schemes not involving feedback include all those based on
heterodyne detection or instantaneous canonical phase measurements. We also
demonstrate that the superior accuracy adaptive phase estimation is present in
a regime conducive to observing it experimentally.Comment: 15 pages, 9 figures, submitted to PR
- …