26 research outputs found
Faster quantum mixing for slowly evolving sequences of Markov chains
Markov chain methods are remarkably successful in computational physics,
machine learning, and combinatorial optimization. The cost of such methods
often reduces to the mixing time, i.e., the time required to reach the steady
state of the Markov chain, which scales as , the inverse of the
spectral gap. It has long been conjectured that quantum computers offer nearly
generic quadratic improvements for mixing problems. However, except in special
cases, quantum algorithms achieve a run-time of , which introduces a costly dependence on the Markov chain size
not present in the classical case. Here, we re-address the problem of mixing of
Markov chains when these form a slowly evolving sequence. This setting is akin
to the simulated annealing setting and is commonly encountered in physics,
material sciences and machine learning. We provide a quantum memory-efficient
algorithm with a run-time of ,
neglecting logarithmic terms, which is an important improvement for large state
spaces. Moreover, our algorithms output quantum encodings of distributions,
which has advantages over classical outputs. Finally, we discuss the run-time
bounds of mixing algorithms and show that, under certain assumptions, our
algorithms are optimal.Comment: 20 pages, 2 figure
Flexible resources for quantum metrology
Quantum metrology offers a quadratic advantage over classical approaches to
parameter estimation problems by utilizing entanglement and nonclassicality.
However, the hurdle of actually implementing the necessary quantum probe states
and measurements, which vary drastically for different metrological scenarios,
is usually not taken into account. We show that for a wide range of tasks in
metrology, 2D cluster states (a particular family of states useful for
measurement-based quantum computation) can serve as flexible resources that
allow one to efficiently prepare any required state for sensing, and perform
appropriate (entangled) measurements using only single qubit operations.
Crucially, the overhead in the number of qubits is less than quadratic, thus
preserving the quantum scaling advantage. This is ensured by using a
compression to a logarithmically sized space that contains all relevant
information for sensing. We specifically demonstrate how our method can be used
to obtain optimal scaling for phase and frequency estimation in local
estimation problems, as well as for the Bayesian equivalents with Gaussian
priors of varying widths. Furthermore, we show that in the paradigmatic case of
local phase estimation 1D cluster states are sufficient for optimal state
preparation and measurement.Comment: 9+18 pages, many figure
SelenIRIS: a Moon-Earth Optical Communication Terminal for CubeSats
Satellite miniaturization and sinking costs of manu-facturing and launches are bringing Moon missions in the focus of many space companies and agencies. However, achieving the desired data rates on CubeSats over long ranges is proving increasingly challenging with traditional radio-frequency communication systems. Free-space optical (FSO) communications offer a compact, light, and low-power alternative with higher data throughput and fewer limitations (e.g., fewer governmental regulations, channel interference, eavesdropping...). Based on its long heritage of laser communications and new-space technology, the German Aerospace Center (DLR) is investigating SelenIRIS-a miniaturized terminal for Moon-Earth optical data transmissions-for its OSIRIS program. This paper will analyze the necessary adaptations that are required to transfer the technology from the flight-proven low Earth orbit terminals like OSIRIS4CubeSat (O4C) to a concept mission in Lunar orbit
Hamiltonian purification
The problem of Hamiltonian purification introduced by Burgarth et al. [D. K.
Burgarth et al., Nat. Commun. 5, 5173 (2014)] is formalized and discussed.
Specifically, given a set of non-commuting Hamiltonians {h1, . . ., hm}
operating on a d-dimensional quantum system Hd, the problem consists in
identifying a set of commuting Hamiltonians {H1,...,Hm} operating on a larger
dE-dimensional system H_{dE} which embeds H_d as a proper subspace, such that
hj = PHjP with P being the projection which allows one to recover Hd from HdE .
The notions of spanning-set purification and generator purification of an
algebra are also introduced and optimal solutions for u(d) are provided.Comment: 13 pages, 3 figure
International time transfer between precise timing facilities secured with a quantum key distribution network
Global Navigation Satellite Systems (GNSSs), such as GPS and Galileo, provide
precise time and space coordinates globally and constitute part of the critical
infrastructure of modern society. To reliably operate GNSS, a highly accurate
and stable system time is required, such as the one provided by several
independent clocks hosted in Precise Timing Facilities (PTFs) around the world.
Periodically, the relative clock offset between PTFs is measured to have a
fallback system to synchronize the GNSS satellite clocks. The security and
integrity of the communication between PTFs is of paramount importance: if
compromised, it could lead to disruptions to the GNSS service. Therefore, it is
a compelling use-case for protection via Quantum Key Distribution (QKD), since
this technology provides information-theoretic security. We have performed a
field trial demonstration of such use-case by sharing encrypted time
synchronization information between two PTFs, one located in Oberpfaffenhofen
(Germany) and one in Matera (Italy) - more than 900km apart as the crow flies.
To bridge this large distance, a satellite-QKD system is required, plus a
"last-mile" terrestrial link to connect the optical ground station (OGS) to the
actual location of the PTF. In our demonstration we have deployed two full QKD
systems to protect the last-mile connection at both the locations and have
shown via simulation that upcoming QKD satellites will be able to distribute
keys between Oberpfaffenhofen and Matera exploiting already existing OGSs
On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number
Quantum algorithms for solving the Quantum Linear System (QLS) problem are
among the most investigated quantum algorithms of recent times, with potential
applications including the solution of computationally intractable differential
equations and speed-ups in machine learning. A fundamental parameter governing
the efficiency of QLS solvers is , the condition number of the
coefficient matrix , as it has been known since the inception of the QLS
problem that for worst-case instances the runtime scales at least linearly in
[Harrow, Hassidim and Lloyd, PRL 103, 150502 (2009)]. However, for the
case of positive-definite matrices classical algorithms can solve linear
systems with a runtime scaling as , a quadratic improvement
compared to the the indefinite case. It is then natural to ask whether QLS
solvers may hold an analogous improvement. In this work we answer the question
in the negative, showing that solving a QLS entails a runtime linear in
also when is positive definite. We then identify broad classes of
positive-definite QLS where this lower bound can be circumvented and present
two new quantum algorithms featuring a quadratic speed-up in : the
first is based on efficiently implementing a matrix-block-encoding of ,
the second constructs a decomposition of the form to
precondition the system. These methods are widely applicable and both allow to
efficiently solve BQP-complete problems.Comment: 49 pages, 3 figures, section on Variable-Time Amplitude Amplification
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Quantum Computation, Control and Privacy
Nella prima parte della tesi si studiano comparativamente quattro implementazioni di Blind Quantum Computation. In seguito si analizzano funzioni crittografiche primitive, indagando quali di queste sono implementabili in modo incondizionatamente sicuro e quali relazioni è possibile stabilire tra di esse. Come contributo originale in particolare si dimostra l'impossibilità di realizzare QPQ (Quantum Private Queries) sotto ipotesi standard della crittografia quantistica. Infine nel contesto della Teoria del Controllo vengono presentati risultati originali su come ottenere Purificazione di Hamiltoniane in modo efficiente