1,169 research outputs found
Classical Optimizers for Noisy Intermediate-Scale Quantum Devices
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits
Bias-Reduction in Variational Regularization
The aim of this paper is to introduce and study a two-step debiasing method
for variational regularization. After solving the standard variational problem,
the key idea is to add a consecutive debiasing step minimizing the data
fidelity on an appropriate set, the so-called model manifold. The latter is
defined by Bregman distances or infimal convolutions thereof, using the
(uniquely defined) subgradient appearing in the optimality condition of the
variational method. For particular settings, such as anisotropic and
TV-type regularization, previously used debiasing techniques are shown to be
special cases. The proposed approach is however easily applicable to a wider
range of regularizations. The two-step debiasing is shown to be well-defined
and to optimally reduce bias in a certain setting.
In addition to visual and PSNR-based evaluations, different notions of bias
and variance decompositions are investigated in numerical studies. The
improvements offered by the proposed scheme are demonstrated and its
performance is shown to be comparable to optimal results obtained with Bregman
iterations.Comment: Accepted by JMI
Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory
We derive an exact mapping from the action of nonequilibrium dynamical
mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with
time-dependent parameters, which can be solved numerically by exact
diagonalization. The representability of the nonequilibrium DMFT action by a
SIAM is established as a rather general property of nonequilibrium Green
functions. We also obtain the nonequilibrium DMFT equations using the cavity
method alone. We show how to numerically obtain the SIAM parameters using
Cholesky or eigenvector matrix decompositions. As an application, we use a
Krylov-based time propagation method to investigate the Hubbard model in which
the hopping is switched on, starting from the atomic limit. Possible future
developments are discussed.Comment: 24 pages, 11 figure
Classical Optimizers for Noisy Intermediate-Scale Quantum Devices
We present a collection of optimizers tuned for usage on Noisy
Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of
applications in quantum computing, including the Variational Quantum
Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They
are also used for calibration tasks, hyperparameter tuning, in machine
learning, etc. We analyze the efficiency and effectiveness of different
optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical
minimizer step driving the next evaluation on the quantum processor. While most
results to date concentrated on tuning the quantum VQE circuit, we show that,
in the presence of quantum noise, the classical minimizer step needs to be
carefully chosen to obtain correct results. We explore state-of-the-art
gradient-free optimizers capable of handling noisy, black-box, cost functions
and stress-test them using a quantum circuit simulation environment with noise
injection capabilities on individual gates. Our results indicate that
specifically tuned optimizers are crucial to obtaining valid science results on
NISQ hardware, and will likely remain necessary even for future fault tolerant
circuits.Comment: 11 pages, 17 figure
Multiphoton Quantum Optics and Quantum State Engineering
We present a review of theoretical and experimental aspects of multiphoton
quantum optics. Multiphoton processes occur and are important for many aspects
of matter-radiation interactions that include the efficient ionization of atoms
and molecules, and, more generally, atomic transition mechanisms;
system-environment couplings and dissipative quantum dynamics; laser physics,
optical parametric processes, and interferometry. A single review cannot
account for all aspects of such an enormously vast subject. Here we choose to
concentrate our attention on parametric processes in nonlinear media, with
special emphasis on the engineering of nonclassical states of photons and
atoms. We present a detailed analysis of the methods and techniques for the
production of genuinely quantum multiphoton processes in nonlinear media, and
the corresponding models of multiphoton effective interactions. We review
existing proposals for the classification, engineering, and manipulation of
nonclassical states, including Fock states, macroscopic superposition states,
and multiphoton generalized coherent states. We introduce and discuss the
structure of canonical multiphoton quantum optics and the associated one- and
two-mode canonical multiphoton squeezed states. This framework provides a
consistent multiphoton generalization of two-photon quantum optics and a
consistent Hamiltonian description of multiphoton processes associated to
higher-order nonlinearities. Finally, we discuss very recent advances that by
combining linear and nonlinear optical devices allow to realize multiphoton
entangled states of the electromnagnetic field, that are relevant for
applications to efficient quantum computation, quantum teleportation, and
related problems in quantum communication and information.Comment: 198 pages, 36 eps figure
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