41,642 research outputs found
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
The efficient calculation of Hamiltonian spectra, a problem often intractable
on classical machines, can find application in many fields, from physics to
chemistry. Here, we introduce the concept of an "eigenstate witness" and
through it provide a new quantum approach which combines variational methods
and phase estimation to approximate eigenvalues for both ground and excited
states. This protocol is experimentally verified on a programmable silicon
quantum photonic chip, a mass-manufacturable platform, which embeds entangled
state generation, arbitrary controlled-unitary operations, and projective
measurements. Both ground and excited states are experimentally found with
fidelities >99%, and their eigenvalues are estimated with 32-bits of precision.
We also investigate and discuss the scalability of the approach and study its
performance through numerical simulations of more complex Hamiltonians. This
result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with
minor typos corrected.
The Short Path Algorithm Applied to a Toy Model
We numerically investigate the performance of the short path optimization
algorithm on a toy problem, with the potential chosen to depend only on the
total Hamming weight to allow simulation of larger systems. We consider classes
of potentials with multiple minima which cause the adiabatic algorithm to
experience difficulties with small gaps. The numerical investigation allows us
to consider a broader range of parameters than was studied in previous rigorous
work on the short path algorithm, and to show that the algorithm can continue
to lead to speedups for more general objective functions than those considered
before. We find in many cases a polynomial speedup over Grover search. We
present a heuristic analytic treatment of choices of these parameters and of
scaling of phase transitions in this model.Comment: 11 pages, 9 figures; v2 final version published in Quantu
Introduction to topological quantum computation with non-Abelian anyons
Topological quantum computers promise a fault tolerant means to perform
quantum computation. Topological quantum computers use particles with exotic
exchange statistics called non-Abelian anyons, and the simplest anyon model
which allows for universal quantum computation by particle exchange or braiding
alone is the Fibonacci anyon model. One classically hard problem that can be
solved efficiently using quantum computation is finding the value of the Jones
polynomial of knots at roots of unity. We aim to provide a pedagogical,
self-contained, review of topological quantum computation with Fibonacci
anyons, from the braiding statistics and matrices to the layout of such a
computer and the compiling of braids to perform specific operations. Then we
use a simulation of a topological quantum computer to explicitly demonstrate a
quantum computation using Fibonacci anyons, evaluating the Jones polynomial of
a selection of simple knots. In addition to simulating a modular circuit-style
quantum algorithm, we also show how the magnitude of the Jones polynomial at
specific points could be obtained exactly using Fibonacci or Ising anyons. Such
an exact algorithm seems ideally suited for a proof of concept demonstration of
a topological quantum computer.Comment: 51 pages, 51 figure
Coherent control using adaptive learning algorithms
We have constructed an automated learning apparatus to control quantum
systems. By directing intense shaped ultrafast laser pulses into a variety of
samples and using a measurement of the system as a feedback signal, we are able
to reshape the laser pulses to direct the system into a desired state. The
feedback signal is the input to an adaptive learning algorithm. This algorithm
programs a computer-controlled, acousto-optic modulator pulse shaper. The
learning algorithm generates new shaped laser pulses based on the success of
previous pulses in achieving a predetermined goal.Comment: 19 pages (including 14 figures), REVTeX 3.1, updated conten
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
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