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The purpose of quantum computing focuses on building an information theory with the features of quantum mechanics: instead of encoding a binary unit of information (), which can be switched to 1 or 0, a quantum binary unit of information (qubit) can simultaneously turn to be 0 and 1 at the same time, thanks to the phenomenon called superposition.
There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit. However, whereas the state of a bit can only be binary (either 0 or 1), the general state of a qubit according to quantum mechanics can arbitrarily be a coherent superposition of all computable states simultaneously. [2]
[1] [2] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit [3] subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates). [1] [4] [5]
1 ebit + 2 bits 1 qubit (i.e. quantum teleportation), where ⩾ {\displaystyle \geqslant } indicates "can do the job of". These principles were formulated around 1993 by Charles H. Bennett .
[3] The number of dimensions of the Hilbert spaces depends on what kind of quantum systems the register is composed of. Qubits are 2-dimensional complex spaces ( C 2 {\displaystyle \mathbb {C} ^{2}} ), while qutrits are 3-dimensional complex spaces ( C 3 {\displaystyle \mathbb {C} ^{3}} ), etc.
Example: The Hadamard transform on a 3-qubit register | . Here the amplitude for each measurable state is 1 ⁄ 2. The probability to observe any state is the square of the absolute value of the measurable states amplitude, which in the above example means that there is one in four that we observe any one of the individual four cases.
Time-bin encoding is done by having a single-photon go through a Mach–Zehnder interferometer (MZ), shown in black here. The photon coming from the left is guided through one of two paths (shown in blue and red); the guiding can be made by optical fiber or simply in free space using mirrors and polarising cubes.
It is known that DQC1 offers composability in the sense that the "one" clean qubit can be upgraded to "two" clean qubits, or even () many clean qubits, without modifying the class [3] Computation with Unitaries and One Pure Qubit. D. J. Shepherd.