Quantum circuits are collections of quantum gates interconnected by quantum wires. The actual structure of a quantum circuit, the number and the types of gates, as well as the interconnection scheme are dictated by the unitary transformation, U, carried out by the circuit. Though in our description of quantum circuits [1] we use the concepts input and output registers of qubits, we should be aware that physically, the input and the output of a quantum circuit are not separated as their classical counterparts are; this convention allows us to describe the effect of unitary transformation carried out by the circuit in a more coherent fashion.

Quantum algorithms are most commonly described by a quantum circuit, of which a simple example is shown in the figure below. A quantum circuit is a model for quantum computation, where the steps to solve the problem are quantum gates performed on one or more qubits. A quantum gate is an operation applied [2] to a qubit that changes the quantum state of the qubit. Quantum gates can be divided into single-qubit gates and two-qubit gates, depending on the number of qubits on which they are applied at the same time. Three-qubit gates and other multi-qubit gates can also be defined. A quantum circuit is concluded with a measurement on one or more qubits figure 1 shown below.

Figure1: Quantum Circuit

Simulation techniques

The present quantum circuit simulator consists of three mutually independent sub-programs, referred to as three working modes of the simulator, i.e., full amplitude, partial amplitude and single amplitude mode. The fundamental [3] methodologies for the three modes are completely different. They are, respectively, direct evolution of quantum state, circuit partition by decomposing controlled-Z gate10, and the complex undirected graphical model9. In addition, noisy one- and two-qubit gates are defined to emulate the effect of noise. A description of the instruction set of our simulator and an illustrative example of the input and output are given in the supplementary material.

Cryptography

The most common area people associate quantum computing with is advanced cryptography. The ordinary computers we use today make it infeasible to break encryption that uses very large prime number factorization with quantum computers, this decryption could become trivial, leading to much stronger [4] protection of our digital lives and assets. Of course, we’ll also be able to break traditional encryption much faster.

Aviation

Quantum technology could enable much more complex computer modelling like aeronautical scenarios. Aiding in the routing and scheduling of aircrafts has enormous commercial benefits for time and costs. Large companies like Airbus and Lockheed Martin are actively researching and investing in the space to take advantage of the computing power and the optimization potential of the technology.

Pattern Matching

Finding patterns in data and using these to predict future patterns is highly valuable. Volkswagen is currently looking into how they can use quantum computing to inform drivers of traffic conditions 45 minutes in advance. Matching traffic patterns and predicting the behavior of a system as complex as modern-day traffic is so far not possible for today’s computers, but this is going to change with quantum computers.

References:

1. https://qiskit.org/textbook/ch-algorithms/defining-quantum-circuits.html
2. https://www.sciencedirect.com/topics/computer-science/quantum-circuit
3. www.nature.com/articles/s41598-020-79777-y
4. https://www.pluralsight.com/resource-center/guides/quantum-computing

Cite this article:

S. Nandhinidwaraka (2021) Process Involved in Quantum Circuits, AnaTechmaz, pp.5