Leonard Wossnig - Stealth | LinkedIn
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Leonard Wossnig is an entrepreneur and executive. He is Co-Founder of a new stealth…
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Publications
arXiv June 1, 2018
Adversarial learning is one of the most successful approaches to modelling high-dimensional probability
distributions from data. The quantum computing community has recently begun to generalize
this idea and to look for potential applications. In this work, we derive an adversarial algorithm
for the problem of approximating an unknown quantum pure state. Although this could be done
on error-corrected quantum computers, the adversarial formulation enables us to execute the…
Adversarial learning is one of the most successful approaches to modelling high-dimensional probability
distributions from data. The quantum computing community has recently begun to generalize
this idea and to look for potential applications. In this work, we derive an adversarial algorithm
for the problem of approximating an unknown quantum pure state. Although this could be done
on error-corrected quantum computers, the adversarial formulation enables us to execute the algorithm
on near-term quantum computers. Two ansatz circuits are optimized in tandem: One tries to
approximate the target state, the other tries to distinguish between target and approximated state.
Supported by numerical simulations, we show that resilient backpropagation algorithms perform
remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design
an efficient heuristic for the stopping criteria. Our approach may find application in quantum state
tomography.
arXiv November 1, 2017
Optimization problems in disciplines such as machine learning are commonly solved with
iterative methods. Gradient descent algorithms find local minima by moving along the
direction of steepest descent while Newton's method takes into account curvature
information and thereby often improves convergence. Here, we develop quantum versions
of these iterative optimization algorithms and apply them to polynomial optimization with a
unit norm constraint. In each step, multiple…
Optimization problems in disciplines such as machine learning are commonly solved with
iterative methods. Gradient descent algorithms find local minima by moving along the
direction of steepest descent while Newton's method takes into account curvature
information and thereby often improves convergence. Here, we develop quantum versions
of these iterative optimization algorithms and apply them to polynomial optimization with a
unit norm constraint. In each step, multiple copies of the current candidate are used to
improve the candidate using quantum phase estimation, an adapted quantum principal
component analysis scheme, as well as quantum matrix multiplications and inversions. The
required operations perform polylogarithmically in the dimension of the solution vector and
exponentially in the number of iterations. Therefore, the quantum algorithm can be …
arXiv
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not
necessarily sparse. Our algorithm is based on the assumption that the entries of the
Hamiltonian are stored in a data structure that allows for the efficient preparation of states
that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to
achieve a poly-logarithmic dependence on the precision. The time complexity measured in
terms of circuit depth of our…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not
necessarily sparse. Our algorithm is based on the assumption that the entries of the
Hamiltonian are stored in a data structure that allows for the efficient preparation of states
that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to
achieve a poly-logarithmic dependence on the precision. The time complexity measured in
terms of circuit depth of our algorithm is $ O (t\sqrt {N}\lVert H\rVert\text {polylog}(N, t\lVert
H\rVert, 1/\epsilon)) $, where $ t $ is the evolution time, $ N $ is the dimension of the system,
and $\epsilon $ is the error in the final state, which we call precision. Our algorithm can
directly be applied as a subroutine for unitary Hamiltonians and solving linear systems,
achieving a $\widetilde {O}(\sqrt {N}) $ dependence for both applications. Subjects …
arXiv
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to
be one of the foremost applications of quantum computers. We consider the approximation
of Hamiltonian dynamics using subsampling methods from randomized numerical linear
algebra. We propose conditions for the efficient approximation of state vectors evolving
under a given Hamiltonian. As an immediate application, we show that sample based
quantum simulation, a type of evolution where the…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to
be one of the foremost applications of quantum computers. We consider the approximation
of Hamiltonian dynamics using subsampling methods from randomized numerical linear
algebra. We propose conditions for the efficient approximation of state vectors evolving
under a given Hamiltonian. As an immediate application, we show that sample based
quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be
efficiently classically simulated under specific structural conditions. Our main technical
contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The
proof leverages the Nystr\" om method to obtain low-rank approximations of the Hamiltonian.
We envisage that techniques from randomized linear algebra will bring further insights …
Physical review letters
Solving linear systems of equations is a frequently encountered problem in machine
learning and optimization. Given a matrix A and a vector b the task is to find the vector x such
that A x= b. We describe a quantum algorithm that achieves a sparsity-independent runtime
scaling of O (κ 2 n polylog (n)/ε) for an n× n dimensional A with bounded spectral norm,
where κ denotes the condition number of A, and ε is the desired precision parameter. This
amounts to a polynomial…
Solving linear systems of equations is a frequently encountered problem in machine
learning and optimization. Given a matrix A and a vector b the task is to find the vector x such
that A x= b. We describe a quantum algorithm that achieves a sparsity-independent runtime
scaling of O (κ 2 n polylog (n)/ε) for an n× n dimensional A with bounded spectral norm,
where κ denotes the condition number of A, and ε is the desired precision parameter. This
amounts to a polynomial improvement over known quantum linear system algorithms when
applied to dense matrices, and poses a new state of the art for solving dense linear systems
on a quantum computer. Furthermore, an exponential improvement is achievable if the rank
of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value
estimation subroutine, which makes use of a memory architecture that allows for efficient …
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The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution
of a linear system provides an exponential speed-up over its classical counterpart. The
problem of solving a system of linear equations has a wide scope of applications, and thus
HHL constitutes an important algorithmic primitive. In these notes, we present the HHL
algorithm and its improved versions in detail, including explanations of the constituent subroutines.
More specifically, we discuss…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution
of a linear system provides an exponential speed-up over its classical counterpart. The
problem of solving a system of linear equations has a wide scope of applications, and thus
HHL constitutes an important algorithmic primitive. In these notes, we present the HHL
algorithm and its improved versions in detail, including explanations of the constituent subroutines.
More specifically, we discuss various quantum subroutines such as quantum phase
estimation and amplitude amplification, as well as the important question of loading data
into a quantum computer, via quantum RAM. The improvements to the original algorithm
exploit variable-time amplitude amplification as well as a method for implementing linear
combinations of unitary operations (LCUs) based on a decomposition of the operators using
Fourier and Chebyshev series. Finally, we discuss a linear solver based on the quantum
singular value estimation (QSVE) subroutine.
Proc. R. Soc. A
Recently, increased computational power and data availability, as well as algorithmic
advances, have led machine learning (ML) techniques to impressive results in regression,
classification, data generation and reinforcement learning tasks. Despite these successes,
the proximity to the physical limits of chip fabrication alongside the increasing size of
datasets is motivating a growing number of researchers to explore the possibility of
harnessing the power of quantum…
Recently, increased computational power and data availability, as well as algorithmic
advances, have led machine learning (ML) techniques to impressive results in regression,
classification, data generation and reinforcement learning tasks. Despite these successes,
the proximity to the physical limits of chip fabrication alongside the increasing size of
datasets is motivating a growing number of researchers to explore the possibility of
harnessing the power of quantum computation to speed up classical ML algorithms. Here
we review the literature in quantum ML and discuss perspectives for a mixed readership of
classical ML and quantum computation experts. Particular emphasis will be placed on
clarifying the limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for …
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We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the
training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due
to a recent formulation of semi-supervised learning as an optimization problem, the algorithm can further be
used to find the optimal model parameters for deep generative models. In particular, we present a truncated
saddle-free Newton’s method based on recent…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the
training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due
to a recent formulation of semi-supervised learning as an optimization problem, the algorithm can further be
used to find the optimal model parameters for deep generative models. In particular, we present a truncated
saddle-free Newton’s method based on recent insight from optimization, analysis of deep neural networks and
random matrix theory. By combining these with the specific quantum subroutines we are able to exhaust quantum
computing in order to arrive at a new quantum-classical hybrid algorithm design. Our algorithm is expected
to perform at least as well as existing classical algorithms while achieving a polynomial speedup. The speedup
is limited by the required classical read-out. Omitting this requirement can in theory lead to an exponential
speedup.
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Quantum mechanics fundamentally forbids deterministic discrimination of quantum
states and processes. However, the ability to optimally distinguish various
classes of quantum data is an important primitive in quantum information science.
In this work, we train near-term quantum circuits to classify data represented by
non-orthogonal quantum probability distributions using the Adam stochastic optimization
algorithm. This is achieved by iterative interactions of a classical…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum
states and processes. However, the ability to optimally distinguish various
classes of quantum data is an important primitive in quantum information science.
In this work, we train near-term quantum circuits to classify data represented by
non-orthogonal quantum probability distributions using the Adam stochastic optimization
algorithm. This is achieved by iterative interactions of a classical device
with a quantum processor to discover the parameters of an unknown non-unitary
quantum circuit. This circuit learns to simulates the unknown structure of a generalized
quantum measurement, or Positive-Operator-Value-Measure (POVM), that
is required to optimally distinguish possible distributions of quantum inputs. Notably
we use universal circuit topologies, with a theoretically motivated circuit design,
which guarantees that our circuits can in principle learn to perform arbitrary
input-output mappings. Our numerical simulations show that shallow quantum
circuits could be trained to discriminate among various pure and mixed quantum
states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes
with comparable performance to theoretically optimal POVMs. We train
the circuit on different classes of quantum data and evaluate the generalization
error on unseen mixed quantum states. This generalization power hence distinguishes
our work from standard circuit optimization and provides an example of
quantum machine learning for a task that has inherently no classical analogue.
Honors & Awards
Google PhD Fellowship
Apr 2019
Google PhD Fellowship in Quantum Computing
Royal Society PhD Fellowship with Simone Severini
Royal Society
Sep 2017
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