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Start Towards the Quantum Computer: Qubits and Qudits
12 December 2016

Towards the Quantum Computer: Qubits and Qudits

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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.

Richard Feynman / Image: Caltech
Richard Feynman / Image: Caltech

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 2N calculations in parallel.

Difference between a classical bit and a qubit
Difference between a classical bit and a qubit

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

@sciencefreak_

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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