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All n-qubit registers are complex linear combinations of these computational basis states. Quantum logic gates, in contrast to classical logic gates, are always reversible. One requires a special kind of reversible function, namely a unitary mapping, that is, a linear transformation of a complex inner product space that preserves the Hermitian ...
Names # qubits Operator symbol Matrix Circuit diagram Some properties Refs Pauli X, NOT, bit flip 1 ,, []or. Hermitian; Pauli group; Traceless; Involutory [1] [6]Pauli Y: 1
Quantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment.
The Schrödinger equation describes how quantum systems that are not observed evolve over time, and is | = ^ | . When the system is in a stable environment, so it has a constant Hamiltonian, the solution to this equation is () = ^ /. [1]: 24–25 If the time is always the same it may be omitted for simplicity, and the way quantum states evolve can be described as | = | , just as in the above ...
The approach of topological qubits, which takes advantage of topological effects in quantum mechanics, has been proposed as needing many fewer or even a single physical qubit per logical qubit. [10]
The discrete logarithm algorithm and the factoring algorithm are instances of the period-finding algorithm, and all three are instances of the hidden subgroup problem. On a quantum computer, to factor an integer N {\displaystyle N} , Shor's algorithm runs in polynomial time , meaning the time taken is polynomial in log N {\displaystyle \log ...
Molecule of alanine used in NMR implementation of quantum computing. Qubits are implemented by spin states of the black carbon atoms. Nuclear magnetic resonance quantum computing (NMRQC) [1] is one of the several proposed approaches for constructing a quantum computer, that uses the spin states of nuclei within molecules as qubits.
by the Taylor series expansion. [6] This says that during the evolution of a quantum state, the Hamiltonian is applied over and over again to the system with a various number of repetitions. The first term is the identity matrix so the system doesn't change when it is applied, but in the second term the Hami