Circuit Model of Quantum Computation

Abstract Quantum circuits are an abstract framework to represent quantum dynamics. They are used to formally describe and reason about processes within quantum information technology. They are primarily used in quantum computation, quantum communication, and quantum cryptography—for which they provide a machine code–level description of quantum algorithms and protocols. The quantum circuit model is an abstract representation of these technologies based on the use of quantum circuits, with which algorithms and protocols can be concretely developed and studied. Quantum circuits are typically based on the concept of qubits: two-level quantum systems that serve as a fundamental unit of quantum hardware. In their simplest form, circuits take a set of qubits initialized in a simple known state, apply a set of discrete single- and two-qubit evolutions known as “gates,” and then finally measure all qubits. Any quantum computation can be expressed in this form through a suitable choice of gates, in a quantum analogy of the Boolean circuit model of conventional digital computation. More complex versions of quantum circuits can include features such as qudits, which are higher level quantum systems, as well as the ability to reset and measure qubits or qudits throughout the circuit. However, even the simplest form of the model can be used to emulate such behavior, making it fully sufficient to describe quantum information technology. It is possible to use the quantum circuit model to emulate other models of quantum computing, such as the adiabatic and measurement-based models, which formalize quantum algorithms in a very different way. As well as being a theoretical model to reason about quantum information technology, quantum circuits can also provide a blueprint for quantum hardware development. Corresponding hardware is based on the concept of building physical systems that can be controlled in the way required for qubits or qudits, including applying gates on them in sequence and performing measurements.