Related papers: Constant-Depth and Subcubic-Size Threshold Circuit…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
The paper discusses the gate complexity and the depth of reversible circuits consisting of NOT, CNOT and 2-CNOT gates in the case, when the number of additional inputs is limited. We study Shannon's gate complexity function $L(n, q)$ and…
We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for…
Circuit representation learning has shown promising results in advancing the field of Electronic Design Automation (EDA). Existing models, such as DeepGate Family, primarily utilize Graph Neural Networks (GNNs) to encode circuit netlists…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…
Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set…
Any monotone Boolean circuit computing the $n$-dimensional Boolean convolution requires at least $n^2$ and-gates. This precisely matches the obvious upper bound.
As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence…
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…
We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…
Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally…
In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two and three layers, a regime that has been surprisingly intractable to analyze. We prove the first super-linear…
We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds…
We show that lower bounds on the border rank of matrix multiplication can be used to non-trivially derandomize polynomial identity testing for small algebraic circuits. Letting $\underline{R}(n)$ denote the border rank of $n \times n \times…
The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…