71 research outputs found
Coreset Clustering on Small Quantum Computers
Many quantum algorithms for machine learning require access to classical data
in superposition. However, for many natural data sets and algorithms, the
overhead required to load the data set in superposition can erase any potential
quantum speedup over classical algorithms. Recent work by Harrow introduces a
new paradigm in hybrid quantum-classical computing to address this issue,
relying on coresets to minimize the data loading overhead of quantum
algorithms. We investigate using this paradigm to perform -means clustering
on near-term quantum computers, by casting it as a QAOA optimization instance
over a small coreset. We compare the performance of this approach to classical
-means clustering both numerically and experimentally on IBM Q hardware. We
are able to find data sets where coresets work well relative to random sampling
and where QAOA could potentially outperform standard -means on a coreset.
However, finding data sets where both coresets and QAOA work well--which is
necessary for a quantum advantage over -means on the entire data
set--appears to be challenging
Product states optimize quantum -spin models for large
We consider the problem of estimating the maximal energy of quantum -local
spin glass random Hamiltonians, the quantum analogues of widely studied
classical spin glass models. Denoting by the (appropriately
normalized) maximal energy in the limit of a large number of qubits , we
show that approaches as increases. This value is
interpreted as the maximal energy of a much simpler so-called Random Energy
Model, widely studied in the setting of classical spin glasses.
Our most notable and (arguably) surprising result proves the existence of
near-maximal energy states which are product states, and thus not entangled.
Specifically, we prove that with high probability as , for any
there exists a product state with energy at sufficiently
large constant . Even more surprisingly, this remains true even when
restricting to tensor products of Pauli eigenstates. Our approximations go
beyond what is known from monogamy-of-entanglement style arguments -- the best
of which, in this normalization, achieve approximation error growing with .
Our results not only challenge prevailing beliefs in physics that extremely
low-temperature states of random local Hamiltonians should exhibit
non-negligible entanglement, but they also imply that classical algorithms can
be just as effective as quantum algorithms in optimizing Hamiltonians with
large locality -- though performing such optimization is still likely a hard
problem.
Our results are robust with respect to the choice of the randomness
(disorder) and apply to the case of sparse random Hamiltonian using Lindeberg's
interpolation method. The proof of the main result is obtained by estimating
the expected trace of the associated partition function, and then matching its
asymptotics with the extremal energy of product states using the second moment
method.Comment: Added a disclaimer about error in current draf
Efficient classical algorithms for simulating symmetric quantum systems
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements
Cold Matter Assembled Atom-by-Atom
The realization of large-scale fully controllable quantum systems is an
exciting frontier in modern physical science. We use atom-by-atom assembly to
implement a novel platform for the deterministic preparation of regular arrays
of individually controlled cold atoms. In our approach, a measurement and
feedback procedure eliminates the entropy associated with probabilistic trap
occupation and results in defect-free arrays of over 50 atoms in less than 400
ms. The technique is based on fast, real-time control of 100 optical tweezers,
which we use to arrange atoms in desired geometric patterns and to maintain
these configurations by replacing lost atoms with surplus atoms from a
reservoir. This bottom-up approach enables controlled engineering of scalable
many-body systems for quantum information processing, quantum simulations, and
precision measurements.Comment: 12 pages, 9 figures, 3 movies as ancillary file
A Meta-Analysis on Presynaptic Changes in Alzheimer's Disease
This work was funded by TauRx Therapeutics Ltd.,SingaporePeer reviewedPublisher PD
Efficient classical algorithms for simulating symmetric quantum systems
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements
Around a problem of Nicole BrillouĂ«tâBelluot
We determine nontrivial intervals I â (0,+â), numbers α â R and continuous
bijections f : I â I such that f(x)fâ1(x) = xα for every x â I
- âŠ