Related papers: Computational complexity of the quantum separabili…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a…
For a given density matrix $\rho$ of a bipartite quantum system an asymptotical separability criterion is suggested. Using the continuous ensemble method, a sequence of separable density matrices is built which converges to $\rho$ if and…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Heisenberg's uncertainty principle states that it is not possible to compute both the position and momentum of an electron with absolute certainty. However, this computational limitation, which is central to quantum mechanics, has no…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any…
A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble…
We present the variational separability verifier (VSV), which is a novel variational quantum algorithm (VQA) that determines the closest separable state (CSS) of an arbitrary quantum state with respect to the Hilbert-Schmidt distance (HSD).…
Quantum Inverse Problem (QIP) is the problem of estimating an unknown quantum system $\rho$ from a set of measurements, whereas the classical counterpart is the Inverse Problem of estimating a distribution from a set of observations. In…
We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
Recently, a lot of attention has been devoted to finding physically realisable operations that realise as closely as possible certain desired transformations between quantum states, e.g. quantum cloning, teleportation, quantum gates, etc.…
The number of qubits of current quantum computers is one of the most dominating restrictions for applications. So it is naturally conceived to use two or more small capacity quantum computers to form a larger capacity quantum computing…