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Tuesday, May 14th 2019

1:00 pm:

The state of a classical computer at a given moment is described by a sequence (↑↓↑↑↓...), where ↑ and ↓ represent bits of information – realized as the on and off states of individual transistors. The computation process consists in switching some transistors between their ↑ and ↓ states according to a prescribed program.

In quantum computing one replaces the classical two-state element by a quantum element with two basic states, called the quantum bit, or qubit. The simplest object of this kind is the electron spin, which can have only two possible projections on any axis: +ћ/2 or −ћ/2. For some chosen axis, we can again denote the two basic quantum states of the spin as ↑ and ↓.

However an arbitrary spin state is described by the wave function ψ = a↑ + b↓, where a and b are complex numbers, satisfying the condition |a|2 + |b|2 = 1. In contrast to the classical bit that can be only in one of the two states, ↑ or ↓, the qubit can be in a continuum of states defined by the quantum amplitudes a and b. The qubit is a continuous object.

With N qubits, there are 2N basic states of the type (↑↓↓↑↑↓↑↓...). Accordingly, the general state of a system with N qubits is described by 2N complex parameters restricted by the normalization condition only. So, while the state of the classical computer with N bits at any given moment coincides with one of its 2N possible discreet states, the state of a quantum computer with N qubits is defined by the values of 2N continuous variables, that we should be able to control.

Thus, basic quantum mechanics tells us that the hypothetical quantum computer is an analog machine whose state at any given moment is described by a very large number of continuous parameters. Note that for a toy quantum computer with only 300 qubits this number greatly exceeds the number of particles in the observable Universe!

An important issue is related to the energies of the ↑ and ↓ states. While the notion of energy is of primordial importance in all domains of physics, both classical and quantum, it is not in the vocabulary of QC theorists. They implicitly assume that the energies of all 2N states of an ensemble of qubits are exactly equal. Otherwise, the existence of an energy difference ∆E leads to oscillations of the quantum amplitudes with a frequency Ω = ∆E/ ћ, where ћ is the Planck constant, and this again is a basic fact of Quantum Mechanics. (For example, one of the popular candidates for a qubit, the electron spin, will make a precession around the direction of the Earth's magnetic field with a frequency ~ 1 MHz).

On the basis of these elementary facts, the obvious answer to the question in title is - NO!

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