# circuits Published articles for circuits. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Two's Complement and Group Theory DevFeed: [Two's Complement and Group Theory]() Original publisher: [Read original article]() Published: 2023-07-10T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [math](), [Mathematics](), [Computer science](), [Programming]() Tags: [abelian-groups](), [arithmetic](), [bits](), [boolean](), [circuits](), [computer-science](), [group-actions](), [groups](), [math](), [mathematics](), [programming](), [quotients](), [symmetry](), [twos-complement]() ### AI overview The article explains two's-complement signed integer arithmetic using group theory. It presents signed and unsigned n-bit integers as representations of the quotient group of integers modulo 2^n, clarifying why the same arithmetic circuits can operate on both. ### Source excerpt Before I discovered math, I was a first year undergrad computer science student taking Electrical Engineering 101. The first topic I learned was what bits and boolean gates are, and the second was the two's complement representation of a negative n-bit integer. At the time two's complement seemed to me like a bizarre quirk of computer programming, with minutiae you just had to memorize. If the leading bit is 1, it's negative, and otherwise it's positive. ## Concrete Examples of Quantum Gates DevFeed: [Concrete Examples of Quantum Gates]() Original publisher: [Read original article]() Published: 2016-01-11T14:05:22Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [circuit]() Tags: [circuit](), [circuits](), [linear-maps](), [mathematics](), [matrices](), [python](), [quantum](), [quantum-computing]() ### AI overview A quantum-computing tutorial explains how local quantum gates affect the full state vector of a multi-qubit register, using a three-qubit swap-gate example. ### Source excerpt So far in this series we've seen a lot of motivation and defined basic ideas of what a quantum circuit is. But on rereading my posts, I think we would all benefit from some concreteness. "Local" operations So by now we've understood that quantum circuits consist of a sequence of gates $ A_1, \dots, A_k$, where each $ A_i$ is an 8-by-8 matrix that operates "locally" on some choice of three (or fewer) qubits. ## Multiple Qubits and the Quantum Circuit DevFeed: [Multiple Qubits and the Quantum Circuit]() Original publisher: [Read original article]() Published: 2015-01-26T09:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [circuit]() Tags: [2](), [bits](), [circuits](), [entanglement](), [linear-algebra](), [multiple](), [physics](), [quantum](), [quantum-computing](), [tensor-product](), [tensors]() ### AI overview This article explains why the tensor product is the natural mathematical representation of the joint state of multiple qubits. It also introduces basic quantum gates and the definition of a quantum circuit. ### Source excerpt Last time we left off with the tantalizing question: how do you do a quantum "AND" operation on two qubits? In this post we'll see why the tensor product is the natural mathematical way to represent the joint state of multiple qubits. Then we'll define some basic quantum gates, and present the definition of a quantum circuit. Working with Multiple Qubits In a classical system, if you have two bits with values $ b_1, b_2$, then the "joint state" of the two bits is given by the concatenated string $ b_1b_2$. ## The Quantum Bit DevFeed: [The Quantum Bit]() Original publisher: [Read original article]() Published: 2014-12-15T10:00:52Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Quantum Computing](), [Computing](), [circuit]() Tags: [bits](), [circuit](), [circuits](), [complex-numbers](), [computing](), [linear-algebra](), [mathematics](), [measurement](), [quantum](), [quantum-computing](), [quantum-mechanics](), [qubit](), [unitary-matrices]() ### AI overview An introduction to quantum computing that extends classical circuit concepts to qubits. It defines a qubit as a unit vector in the complex plane of two dimensions and explains why extracting information from qubits differs from reading classical bits. ### Source excerpt The best place to start our journey through quantum computing is to recall how classical computing works and try to extend it. Since our final quantum computing model will be a circuit model, we should informally discuss circuits first. A circuit has three parts: the "inputs," which are bits (either zero or one); the "gates," which represent the lowest-level computations we perform on bits; and the "wires," which connect the outputs of gates to the inputs of other gates.