One of the key tasks in quantum computation is the correct and efficient manipulation of **qubits (quantum bits), the basic unit of information.** This operation is not easy due to the fact that an excellent control poses a challenge to prepare quantum systems. As well, the right sequence of operations must be applied. In addition, the measurement of qubits has to be done, but **they must be isolated from the environment to prevent decoherence.** Numerous publications have proposed a number of systems for quantum states transfer. **Does a quantum computer already exist?** What are the best qubits out there?

**Richard Feynman** proposed the idea that certain calculations could be computed much more efficiently with quantum mechanical rather than with classical computers; however, creating a quantum computer is not an easy task. In fact, it is extremely challenging. Then, why do we wish to have a quantum computer? It must be clear that it is unlikely that a quantum computer will run email or Web browser in the future, but, on the other hand, a classical computer has limitations on the tasks to be performed. A quantum computer provides a speed-up over some classical algorithms, as well as for some complex calculations (e.g. Shor’s algorithm [1]). Other tasks can be realized only using a quantum computer, that is the case for complicated simulations, such as many-body systems or biological processes.

On the atomic scale, the laws of quantum mechanics rule over the classical ones. Thus, quoting Moore’s Law: “The number of transistors per square inch on integrated circuits has doubled every year”, will carry the shrink of transistors where quantum effects will dominate over classical devices.

## What is a qubit?

A bit is the basic unit of information in classical computing. Analogously, the qubit is the basic unit in quantum computing. A qubit is a two-state quantum-mechanical system, in fact, an abstract entity that can be physically realized in different ways. The main differences between a bit and a qubit is that whereas in a classical computer a bit of information will encode either a 0 or a 1, the nature of the principle of superposition in quantum mechanics allows the qubit to be in a superposition of both states at the same time (as it is illustrated in Fig. 2). This means that a quantum computer could perform many calculations at the same time: a system with N qubits could execute 2^{N} calculations in parallel.

## Bit, qubit, qudit

Qubits are able to store quantum information during a certain period of time denominated **coherence time.** When the system is connected with the environment due to non desired interactions and out of control, there is a tendency of the quantum system to lose its quantumness [2], through a process called **decoherence.**

Another important feature is that multiple qubits can exhibit quantum entanglement, allowing **a set of qubits to express higher correlation than in classical systems**. In the entangled state, a system cannot be described by meanings of a local state.

**A qubit is a 2-dimensional system**; likewise a qudit is a d-dimensional system. Unfortunately, some difficulties are generated when we try to operate mathematically with them [3]. Nevertheless, there are several options under study that could shed some light to this problem, and facilitate the use of qudits in practical applications. Long-term, qudits could simplify some simulations of quantum mechanical systems and improve quantum cryptography.

**Araceli Venegas Gómez**

### References

[1] VanMeter and C. Horsman, Communications of the ACM **56**, 10 (2013).

[2] E. Northup and R. Blatt, Nature Photonics **8**, 356-363 (2014).

[3] Reich, G. Gualdi, and C.P. Koch, J. Phys. A: Math. Theor **47**, 385305 (2014).

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