Quantum information is the physics of knowledge. To be more specific, the field of quantum information studies the implications that quantum mechanics has on the fundamental nature of information. By studying this relationship between quantum theory and information, it is possible to design a new type of computer—a quantum computer. A largescale, working quantum computer—the kind of quantum computer some scientists think we might see in 50 years—would be capable of performing some tasks impossibly quickly.
To date, the two most promising uses for such a device are quantum search and quantum factoring. To understand the power of a quantum search, consider classically searching a phonebook for the name which matches a particular phone number. If the phonebook has 10,000 entries, on average you'll need to look through about half of them—5,000 entries—before you get lucky. A quantum search algorithm only needs to guess 100 times. With 5,000 guesses a quantum computer could search through a phonebook with 25 million names.
Although quantum search is impressive, quantum factoring algorithms pose a legitimate, considerable threat to security. This is because the most common form of Internet security, public key cryptography, relies on certain math problems (like factoring numbers that are hundreds of digits long) being effectively impossible to solve. Quantum algorithms can perform this task exponentially faster than the best known classical strategies, rendering some forms of modern cryptography powerless to stop a quantum codebreaker.
Quantum computers are fundamentally different from classical computers because the physics of quantum information is also the physics of possibility. Classical computer memories are constrained to exist at any given time as a simple list of zeros and ones. In contrast, in a single quantum memory many such combinations—even all possible lists of zeros and ones—can all exist simultaneously. During a quantum algorithm, this symphony of possibilities split and merge, eventually coalescing around a single solution. The complexity of these large quantum states made of multiple possibilities make a complete description of quantum search or factoring a daunting task.
Rather than focusing on these large systems, therefore, the goal of this article is to describe the most fundamental, the most intriguing, and the most disturbing consequences of quantum information through an in-depth description of the smallest quantum systems. By learning how to think about the smallest quantum computers, it becomes possible to get a feeling for how and why larger quantum computers are so powerful. To that end, this article is divided into three parts:
Single qubits. The quantum bit, or qubit, is the simplest unit of quantum information. We look at how single qubits are described, how they are measured, how they change, and the classical assumptions about reality that they force us to abandon.
Pairs of qubits. The second section deals with two-qubit systems, and more importantly, describes what two-qubit systems make possible: entanglement. The crown jewel of quantum mechanics, the phenomenon of entanglement is inextricably bound to the power of quantum computers.
Quantum physics 101. The first two sections will focus on the question of how qubits work, avoiding the related question of why they work they way they do. Here we take a crash course in qualitative quantum theory, doing our best to get a look at the man behind the curtain. The only prerequisites for this course are a little courage and a healthy willingness to ignore common sense...
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