170 research outputs found
A study of heuristic guesses for adiabatic quantum computation
Adiabatic quantum computation (AQC) is a universal model for quantum
computation which seeks to transform the initial ground state of a quantum
system into a final ground state encoding the answer to a computational
problem. AQC initial Hamiltonians conventionally have a uniform superposition
as ground state. We diverge from this practice by introducing a simple form of
heuristics: the ability to start the quantum evolution with a state which is a
guess to the solution of the problem. With this goal in mind, we explain the
viability of this approach and the needed modifications to the conventional AQC
(CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7
bit random instances of the satisfiability problem (3-SAT), we show how this
heuristic approach is possible and we identify that the performance of the
particular algorithm proposed is largely determined by the Hamming distance of
the chosen initial guess state with respect to the solution. Besides the
possibility of introducing educated guesses as initial states, the new strategy
allows for the possibility of restarting a failed adiabatic process from the
measured excited state as opposed to restarting from the full superposition of
states as in CAQC. The outcome of the measurement can be used as a more refined
guess state to restart the adiabatic evolution. This concatenated restart
process is another heuristic that the CAQC strategy cannot capture.Comment: 13 pages, 5 figures. Quantum Information Processing. In Pres
Recommended from our members
A Study of Heuristic Guesses for Adiabatic Quantum Computation
Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.Chemistry and Chemical Biolog
Quantum Algorithms
This article surveys the state of the art in quantum computer algorithms,
including both black-box and non-black-box results. It is infeasible to detail
all the known quantum algorithms, so a representative sample is given. This
includes a summary of the early quantum algorithms, a description of the
Abelian Hidden Subgroup algorithms (including Shor's factoring and discrete
logarithm algorithms), quantum searching and amplitude amplification, quantum
algorithms for simulating quantum mechanical systems, several non-trivial
generalizations of the Abelian Hidden Subgroup Problem (and related
techniques), the quantum walk paradigm for quantum algorithms, the paradigm of
adiabatic algorithms, a family of ``topological'' algorithms, and algorithms
for quantum tasks which cannot be done by a classical computer, followed by a
discussion.Comment: 71 pages, 1 figure, to appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Building an iterative heuristic solver for a quantum annealer
A quantum annealer heuristically minimizes quadratic unconstrained binary
optimization (QUBO) problems, but is limited by the physical hardware in the
size and density of the problems it can handle. We have developed a
meta-heuristic solver that utilizes D-Wave Systems' quantum annealer (or any
other QUBO problem optimizer) to solve larger or denser problems, by
iteratively solving subproblems, while keeping the rest of the variables fixed.
We present our algorithm, several variants, and the results for the
optimization of standard QUBO problem instances from OR-Library of sizes 500
and 2500 as well as the Palubeckis instances of sizes 3000 to 7000. For
practical use of the solver, we show the dependence of the time to best
solution on the desired gap to the best known solution. In addition, we study
the dependence of the gap and the time to best solution on the size of the
problems solved by the underlying optimizer.Comment: 21 pages, 4 figures; minor edit
Recommended from our members
Designing and Probing Open Quantum Systems: Quantum Annealing, Excitonic Energy Transfer, and Nonlinear Fluorescence Spectroscopy
The 20th century saw the first revolution of quantum mechanics, setting the rules for our understanding of light, matter, and their interaction. The 21st century is focused on using these quantum mechanical laws to develop technologies which allows us to solve challenging practical problems. One of the directions is the use quantum devices which promise to surpass the best computers and best known classical algorithms for solving certain tasks. Crucial to the design of realistic devices and technologies is to account for the open nature of quantum systems and to cope with their interactions with the environment. In the first part of this dissertation, we show how to tackle classical optimization problems of interest in the physical sciences within one of these quantum computing paradigms, known as quantum annealing (QA). We present the largest implementation of QA on a biophysical problem (six different experiments with up to 81 superconducting quantum bits). Although the cases presented here can be solved on a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This is the first step towards studying optimization problems in biophysics and statistical mechanics using quantum devices. In the second part of this dissertation, we focus on the problem of excitonic energy transfer. We provide an intuitive platform for engineering exciton transfer dynamics and we show that careful consideration of the properties of the environment leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dy- namics. Finally, we develop the theory for a two-dimensional electronic spectroscopic technique based on fluorescence (2DFS) and challenge previous theoretical results claiming its equivalence to the two-dimensional photon echo (2DPE) technique which is based on polarization. Experimental realization of this technique confirms our the- oretical predictions. The new technique is more sensitive than 2DPE as a tool for conformational determination of excitonically coupled chromophores and o↵ers the possibility of applying two-dimensional electronic spectroscopy to single-molecules
Data-Driven Quantum Approximate Optimization Algorithm for Cyber-Physical Power Systems
Quantum technology provides a ground-breaking methodology to tackle
challenging computational issues in power systems, especially for Distributed
Energy Resources (DERs) dominant cyber-physical systems that have been widely
developed to promote energy sustainability. The systems' maximum power or data
sections are essential for monitoring, operation, and control, while high
computational effort is required. Quantum Approximate Optimization Algorithm
(QAOA) provides a promising means to search for these sections by leveraging
quantum resources. However, its performance highly relies on the critical
parameters, especially for weighted graphs. We present a data-driven QAOA,
which transfers quasi-optimal parameters between weighted graphs based on the
normalized graph density, and verify the strategy with 39,774 instances.
Without parameter optimization, our data-driven QAOA is comparable with the
Goemans-Williamson algorithm. This work advances QAOA and pilots the practical
application of quantum technique to power systems in noisy intermediate-scale
quantum devices, heralding its next-generation computation in the quantum era
Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid
quantum-classical variational algorithm designed to tackle combinatorial
optimization problems. Despite its promise for near-term quantum applications,
not much is currently understood about QAOA's performance beyond its
lowest-depth variant. An essential but missing ingredient for understanding and
deploying QAOA is a constructive approach to carry out the outer-loop classical
optimization. We provide an in-depth study of the performance of QAOA on MaxCut
problems by developing an efficient parameter-optimization procedure and
revealing its ability to exploit non-adiabatic operations. Building on observed
patterns in optimal parameters, we propose heuristic strategies for
initializing optimizations to find quasi-optimal -level QAOA parameters in
time, whereas the standard strategy of random
initialization requires optimization runs to achieve similar
performance. We then benchmark QAOA and compare it with quantum annealing,
especially on difficult instances where adiabatic quantum annealing fails due
to small spectral gaps. The comparison reveals that QAOA can learn via
optimization to utilize non-adiabatic mechanisms to circumvent the challenges
associated with vanishing spectral gaps. Finally, we provide a realistic
resource analysis on the experimental implementation of QAOA. When quantum
fluctuations in measurements are accounted for, we illustrate that optimization
will be important only for problem sizes beyond numerical simulations, but
accessible on near-term devices. We propose a feasible implementation of large
MaxCut problems with a few hundred vertices in a system of 2D neutral atoms,
reaching the regime to challenge the best classical algorithms.Comment: 13+10 pages, 15 figure
Readiness of Quantum Optimization Machines for Industrial Applications
There have been multiple attempts to demonstrate that quantum annealing and,
in particular, quantum annealing on quantum annealing machines, has the
potential to outperform current classical optimization algorithms implemented
on CMOS technologies. The benchmarking of these devices has been controversial.
Initially, random spin-glass problems were used, however, these were quickly
shown to be not well suited to detect any quantum speedup. Subsequently,
benchmarking shifted to carefully crafted synthetic problems designed to
highlight the quantum nature of the hardware while (often) ensuring that
classical optimization techniques do not perform well on them. Even worse, to
date a true sign of improved scaling with the number of problem variables
remains elusive when compared to classical optimization techniques. Here, we
analyze the readiness of quantum annealing machines for real-world application
problems. These are typically not random and have an underlying structure that
is hard to capture in synthetic benchmarks, thus posing unexpected challenges
for optimization techniques, both classical and quantum alike. We present a
comprehensive computational scaling analysis of fault diagnosis in digital
circuits, considering architectures beyond D-wave quantum annealers. We find
that the instances generated from real data in multiplier circuits are harder
than other representative random spin-glass benchmarks with a comparable number
of variables. Although our results show that transverse-field quantum annealing
is outperformed by state-of-the-art classical optimization algorithms, these
benchmark instances are hard and small in the size of the input, therefore
representing the first industrial application ideally suited for testing
near-term quantum annealers and other quantum algorithmic strategies for
optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied
versio
Recommender systems inspired by the structure of quantum theory
Physicists use quantum models to describe the behavior of physical systems.
Quantum models owe their success to their interpretability, to their relation
to probabilistic models (quantization of classical models) and to their high
predictive power. Beyond physics, these properties are valuable in general data
science. This motivates the use of quantum models to analyze general
nonphysical datasets. Here we provide both empirical and theoretical insights
into the application of quantum models in data science. In the theoretical part
of this paper, we firstly show that quantum models can be exponentially more
efficient than probabilistic models because there exist datasets that admit
low-dimensional quantum models and only exponentially high-dimensional
probabilistic models. Secondly, we explain in what sense quantum models realize
a useful relaxation of compressed probabilistic models. Thirdly, we show that
sparse datasets admit low-dimensional quantum models and finally, we introduce
a method to compute hierarchical orderings of properties of users (e.g.,
personality traits) and items (e.g., genres of movies). In the empirical part
of the paper, we evaluate quantum models in item recommendation and observe
that the predictive power of quantum-inspired recommender systems can compete
with state-of-the-art recommender systems like SVD++ and PureSVD. Furthermore,
we make use of the interpretability of quantum models by computing hierarchical
orderings of properties of users and items. This work establishes a connection
between data science (item recommendation), information theory (communication
complexity), mathematical programming (positive semidefinite factorizations)
and physics (quantum models)
Multistart Methods for Quantum Approximate Optimization
Hybrid quantum-classical algorithms such as the quantum approximate
optimization algorithm (QAOA) are considered one of the most promising
approaches for leveraging near-term quantum computers for practical
applications. Such algorithms are often implemented in a variational form,
combining classical optimization methods with a quantum machine to find
parameters to maximize performance. The quality of the QAOA solution depends
heavily on quality of the parameters produced by the classical optimizer.
Moreover, the presence of multiple local optima in the space of parameters
makes it harder for the classical optimizer. In this paper we study the use of
a multistart optimization approach within a QAOA framework to improve the
performance of quantum machines on important graph clustering problems. We also
demonstrate that reusing the optimal parameters from similar problems can
improve the performance of classical optimization methods, expanding on similar
results for MAXCUT
- …