728 research outputs found
Programming Quantum Computers Using Design Automation
Recent developments in quantum hardware indicate that systems featuring more
than 50 physical qubits are within reach. At this scale, classical simulation
will no longer be feasible and there is a possibility that such quantum devices
may outperform even classical supercomputers at certain tasks. With the rapid
growth of qubit numbers and coherence times comes the increasingly difficult
challenge of quantum program compilation. This entails the translation of a
high-level description of a quantum algorithm to hardware-specific low-level
operations which can be carried out by the quantum device. Some parts of the
calculation may still be performed manually due to the lack of efficient
methods. This, in turn, may lead to a design gap, which will prevent the
programming of a quantum computer. In this paper, we discuss the challenges in
fully-automatic quantum compilation. We motivate directions for future research
to tackle these challenges. Yet, with the algorithms and approaches that exist
today, we demonstrate how to automatically perform the quantum programming flow
from algorithm to a physical quantum computer for a simple algorithmic
benchmark, namely the hidden shift problem. We present and use two tool flows
which invoke RevKit. One which is based on ProjectQ and which targets the IBM
Quantum Experience or a local simulator, and one which is based on Microsoft's
quantum programming language Q.Comment: 10 pages, 10 figures. To appear in: Proceedings of Design, Automation
and Test in Europe (DATE 2018
A Quantum Time-Space Lower Bound for the Counting Hierarchy
We obtain the first nontrivial time-space lower bound for quantum algorithms
solving problems related to satisfiability. Our bound applies to MajSAT and
MajMajSAT, which are complete problems for the first and second levels of the
counting hierarchy, respectively. We prove that for every real d and every
positive real epsilon there exists a real c>1 such that either: MajMajSAT does
not have a quantum algorithm with bounded two-sided error that runs in time
n^c, or MajSAT does not have a quantum algorithm with bounded two-sided error
that runs in time n^d and space n^{1-\epsilon}. In particular, MajMajSAT cannot
be solved by a quantum algorithm with bounded two-sided error running in time
n^{1+o(1)} and space n^{1-\epsilon} for any epsilon>0. The key technical
novelty is a time- and space-efficient simulation of quantum computations with
intermediate measurements by probabilistic machines with unbounded error. We
also develop a model that is particularly suitable for the study of general
quantum computations with simultaneous time and space bounds. However, our
arguments hold for any reasonable uniform model of quantum computation.Comment: 25 page
Tensor Network States: Optimizations and Applications in Quantum Many-Body Physics and Machine Learning
Tensor network states are ubiquitous in the investigation of quantum many-body (QMB) physics. Their advantage over other state representations is evident from their reduction in the computational complexity required to obtain various quantities of interest, namely observables. Additionally, they provide a natural platform for investigating entanglement properties within a system. In this dissertation, we develop various novel algorithms and optimizations to tensor networks for the investigation of QMB systems, including classical and quantum circuits. Specifically, we study optimizations for the two-dimensional Ising model in a transverse field, we create an algorithm for the -SAT problem, and we study the entanglement properties of random unitary circuits. In addition to these applications, we reinterpret renormalization group principles from QMB physics in the context of machine learning to develop a novel algorithm for the tasks of classification and regression, and then utilize machine learning architectures for the time evolution of operators in QMB systems
Quantum Computation
In the last few years, theoretical study of quantum systems serving as
computational devices has achieved tremendous progress. We now have strong
theoretical evidence that quantum computers, if built, might be used as a
dramatically powerful computational tool. This review is about to tell the
story of theoretical quantum computation. I left out the developing topic of
experimental realizations of the model, and neglected other closely related
topics which are quantum information and quantum communication. As a result of
narrowing the scope of this paper, I hope it has gained the benefit of being an
almost self contained introduction to the exciting field of quantum
computation.
The review begins with background on theoretical computer science, Turing
machines and Boolean circuits. In light of these models, I define quantum
computers, and discuss the issue of universal quantum gates. Quantum
algorithms, including Shor's factorization algorithm and Grover's algorithm for
searching databases, are explained. I will devote much attention to
understanding what the origins of the quantum computational power are, and what
the limits of this power are. Finally, I describe the recent theoretical
results which show that quantum computers maintain their complexity power even
in the presence of noise, inaccuracies and finite precision. I tried to put all
results in their context, asking what the implications to other issues in
computer science and physics are. In the end of this review I make these
connections explicit, discussing the possible implications of quantum
computation on fundamental physical questions, such as the transition from
quantum to classical physics.Comment: 77 pages, figures included in the ps file. To appear in: Annual
Reviews of Computational Physics, ed. Dietrich Stauffer, World Scientific,
vol VI, 1998. The paper can be down loaded also from
http://www.math.ias.edu/~doria
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