Related papers: Two Slightly-Entangled NP-Complete Problems
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
The problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the 2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly to the…
In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory -- its…
We consider pure quantum states of $N\gg 1$ spins or qubits and study the average entanglement that can be \emph{localized} between two separated spins by performing local measurements on the other individual spins. We show that all…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of identifying entanglement has still not reached a general solution for systems larger than…
In this work, we experimentally created and characterized a class of qubit-ququart PPT (positive under partial transpose) entangled states using three nuclear spins on an nuclear magnetic resonance (NMR) quantum information processor.…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
Two quantum algorithms are presented, which tackle well--known problems in the context of numerical semigroups: the numerical semigroup membership problem (NSMP) and the Sylvester denumerant problem (SDP).
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where…
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…
Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as Separable Neural Network Quantum States (SNNS), employs…
We consider a quantum many-body system made of $N$ interacting $S{=}1/2$ spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to…
Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends…
Analytical expressions for the entanglement measures concurrence, i-concurrence and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
Entanglement is considered to be one of the most profound features of quantum mechanics. An entangled state of a system consisting of two subsystems cannot be described as a product of the quantum states of the two subsystems. In this sense…
We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running…