Related papers: Solving approximate hidden subgroup problems: quan…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric…
Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in…
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics, has been recently rediscovered as a new physical resource with potential commercial applications such as, for example,…
With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to…
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for…
Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation…
Fault Trees represent an essential tool in the reliability and risk assessment of engineering systems. By decomposing the structure of the system into Boolean function, Fault Trees allow the quantitative and qualitative analysis of the…
Quantum entanglement detection and characterization are crucial for various quantum information processes. Most existing methods for entanglement detection rely heavily on a complete description of the quantum state, which requires numerous…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
Entanglement is a key property of quantum states that acts as a resource for a wide range of tasks in quantum computing. Entanglement detection is a key conceptual and practical challenge. Without adaptive or joint measurements,…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
We present a new technique to reduce the expected number of measurements to declare an unknown quantum state as entangled. Our method is based on the geometric criterion and so requires only local Pauli measurements. Using concentration of…
It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the…
Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements implementable with local operations and…