Related papers: Some Notes on the Sample Complexity of Approximate…
The exponential server timing channel is known to be the simplest, and in some sense canonical, queuing timing channel. The capacity of this infinite-memory channel is known. Here, we discuss practical finite-length restrictions on the…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number ($R_{\lambda}$), well-resolved DNS are…
Translating a general quantum circuit on a specific hardware topology with a reduced set of available gates, also known as transpilation, comes with a substantial increase in the length of the equivalent circuit. Due to decoherence, the…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the…
The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von…
Sparse superposition codes, or sparse regression codes (SPARCs), are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a…
The data broadcast problem is to find a schedule for broadcasting a given set of messages over multiple channels. The goal is to minimize the cost of the broadcast plus the expected response time to clients who periodically and…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
In 2010, Silva, Kschischang and K\"otter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper we consider a generalisation of…
This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…
Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…