945 research outputs found
Efficient learning of -doped stabilizer states with single-copy measurements
One of the primary objectives in the field of quantum state learning is to
develop algorithms that are time-efficient for learning states generated from
quantum circuits. Earlier investigations have demonstrated time-efficient
algorithms for states generated from Clifford circuits with at most
non-Clifford gates. However, these algorithms necessitate multi-copy
measurements, posing implementation challenges in the near term due to the
requisite quantum memory. On the contrary, using solely single-qubit
measurements in the computational basis is insufficient in learning even the
output distribution of a Clifford circuit with one additional gate under
reasonable post-quantum cryptographic assumptions. In this work, we introduce
an efficient quantum algorithm that employs only nonadaptive single-copy
measurement to learn states produced by Clifford circuits with a maximum of
non-Clifford gates, filling a gap between the previous positive and
negative results.Comment: 6 page
Poly[bisÂ(Îź2-4,4â˛-bipyridine)bisÂ(3-nitroÂbenzoato)cobalt(II)]
The hydroÂthermal reaction of cobalt nitrate with 4,4â˛-bipyridine and 3-nitroÂbenzoic acid lead to the formation of the title complex, [Co(C7H4NO4)2(C10H8N2)2]n. In the crystal structure, the CoII atoms are coordinated by two terminal carboxylÂate anions and four 4,4â˛-bipyridine ligands within slightly distorted octaÂhedra. The CoII atom and one of the two independent 4,4â˛-bipyridine ligands are located on a twofold rotation axis, while the second independent 4,4â˛-bipyridine molÂecule is located on a centre of inversion. One of the two rings of one 4,4â˛-bipyridine ligand is disordered over two orientations and was refined using a split model [occupancy ratio 0.68â
(2):0.32â
(2)]. The CoII atoms are connected by the 4,4â˛-bipyridine ligands into layers, which are located parallel to the ab plane
Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming
Semidefinite programming (SDP) is a central topic in mathematical
optimization with extensive studies on its efficient solvers. In this paper, we
present a proof-of-principle sublinear-time algorithm for solving SDPs with
low-rank constraints; specifically, given an SDP with constraint matrices,
each of dimension and rank , our algorithm can compute any entry and
efficient descriptions of the spectral decomposition of the solution matrix.
The algorithm runs in time
given access to a sampling-based low-overhead data structure for the constraint
matrices, where is the precision of the solution. In addition, we
apply our algorithm to a quantum state learning task as an application.
Technically, our approach aligns with 1) SDP solvers based on the matrix
multiplicative weight (MMW) framework by Arora and Kale [TOC '12]; 2)
sampling-based dequantizing framework pioneered by Tang [STOC '19]. In order to
compute the matrix exponential required in the MMW framework, we introduce two
new techniques that may be of independent interest:
Weighted sampling: assuming sampling access to each individual
constraint matrix , we propose a procedure that gives a
good approximation of .
Symmetric approximation: we propose a sampling procedure that gives
the \emph{spectral decomposition} of a low-rank Hermitian matrix . To the
best of our knowledge, this is the first sampling-based algorithm for spectral
decomposition, as previous works only give singular values and vectors.Comment: 37 pages, 1 figure. To appear in the Proceedings of the 45th
International Symposium on Mathematical Foundations of Computer Science (MFCS
2020
Neoadjuvant bevacizumab and chemoradiotherapy in locally advanced rectal cancer: early outcome and technical impact on toxicity
Type I interferon inhibits varicella-zoster virus replication by interfering with the dynamic interaction between mediator and IE62 within replication compartments
Quantum-Inspired Algorithms for Solving Low-Rank Linear Equation Systems with Logarithmic Dependence on the Dimension
We present two efficient classical analogues of the quantum matrix inversion algorithm [16] for low-rank matrices. Inspired by recent work of Tang [27], assuming length-square sampling access to input data, we implement the pseudoinverse of a low-rank matrix allowing us to sample from the solution to the problem Ax = b using fast sampling techniques. We construct implicit descriptions of the pseudo-inverse by finding approximate singular value decomposition of A via subsampling, then inverting the singular values. In principle, our approaches can also be used to apply any desired âsmoothâ function to the singular values. Since many quantum algorithms can be expressed as a singular value transformation problem [15], our results indicate that more low-rank quantum algorithms can be effectively âdequantisedâ into classical length-square sampling algorithms
On the Quantum Complexity of Closest Pair and Related Problems
The closest pair problem is a fundamental problem of computational geometry:
given a set of points in a -dimensional space, find a pair with the
smallest distance. A classical algorithm taught in introductory courses solves
this problem in time in constant dimensions (i.e., when ).
This paper asks and answers the question of the problem's quantum time
complexity. Specifically, we give an algorithm in constant
dimensions, which is optimal up to a polylogarithmic factor by the lower bound
on the quantum query complexity of element distinctness. The key to our
algorithm is an efficient history-independent data structure that supports
quantum interference.
In dimensions, no known quantum algorithms perform
better than brute force search, with a quadratic speedup provided by Grover's
algorithm. To give evidence that the quadratic speedup is nearly optimal, we
initiate the study of quantum fine-grained complexity and introduce the Quantum
Strong Exponential Time Hypothesis (QSETH), which is based on the assumption
that Grover's algorithm is optimal for CNF-SAT when the clause width is large.
We show that the na\"{i}ve Grover approach to closest pair in higher dimensions
is optimal up to an factor unless QSETH is false. We also study the
bichromatic closest pair problem and the orthogonal vectors problem, with
broadly similar results.Comment: 46 pages, 3 figures, presentation improve
THREE HAMP GENES OF NILE TILAPIA WERE DIFFERENTIALLY ACTIVATED IN SPLEEN TO DEFEND AGAINST STREPTOCOCCUS INIAE INFECTION
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