Related papers: Majorization and the time complexity of linear opt…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
Boson sampling, a computational task believed to be classically hard to simulate, is expected to hold promise for demonstrating quantum computational advantage using near-term quantum devices. However, noise in experimental implementations…
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
Recently, Motes, Gilchrist, Dowling & Rohde [Phys. Rev. Lett. 113, 120501 (2014)] presented a scheme for photonic boson-sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full,…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
An emerging generative artificial intelligence (AI) based on neural networks starts to grow in popularity with a revolutionizing capability of creating new and original content. As giant generative models with millions to billions of…
Regularized quantum information metrics are calculated for the scattering process $e^-e^+ \rightarrow \gamma,Z\rightarrow \mu^-\mu^+$ that has a witness photon entangled with the initial electron-positron state. Unitarity implies the…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To…
Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…
We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the…
Multiphoton interference is at the very heart of quantum foundations and applications in quantum sensing and information processing. In particular, boson sampling experiments have the potential to demonstrate quantum computational supremacy…
We introduce a novel approach for the characterization of the quality of a laser beam that is not based on particular criteria for beam width definition. The Lorenz curve of a light beam is a sophisticated version of the so-called…
Quantization is a widely used compression method that effectively reduces redundancies in over-parameterized neural networks. However, existing quantization techniques for deep neural networks often lack a comprehensive error analysis due…
Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and…
Boson sampling is the problem of generating a quantum bit stream whose average is the permanent of a $n\times n$ matrix. The bitstream is created as the output of a prototype quantum computing device with $n$ input photons. It is a…
We introduce the technique of generic chaining and majorizing measures for controlling sequential Rademacher complexity. We relate majorizing measures to the notion of fractional covering numbers, which we show to be dominated in terms of…