![]() We also say that an operator is real if all the entries of its matrix representation with respect to the computational basis are real numbers. We say that is a real state if all its amplitudes are real numbers. For example, the first orbit contains the state and corresponds to the unentangled Clifford states. More exactly, where the orbit is made up of states with entanglement entropy. We prove that has 8640 states and if we define two states and in to be equivalent if, with a local transformation in, then the resulting quotient space has five orbits. This paper studies the set of all three-qubit Clifford states. We will refer to states in as Clifford states. Let us denote by the Clifford group (the circuit or operations generated by Hadamard, phase and the controlled-NOT gates) and by the set of qubit states that can be prepared by circuits from the Clifford group. The deep reinforcement learning based compiling method allows for fast computation times, which could in principle be exploited for real-time quantum compiling. Deep reinforcement learning allows creating single-qubit operations in real time, after an arbitrary long training period during which a strategy for creating sequences to approximate unitary operators is built. We exploit the deep reinforcement learning method as an alternative strategy, which has a significantly different trade-off between search time and exploitation time. Therefore, traditional approaches are time-consuming tasks, unsuitable to be employed during quantum computation. Since a unitary transformation may require significantly different gate sequences, depending on the base considered, such a problem is of great complexity and does not admit an efficient approximating algorithm. The existence of an approximating sequence of one qubit quantum gates is guaranteed by the Solovay-Kitaev theorem, which implies sub-optimal algorithms to establish it explicitly. The general problem of quantum compiling is to approximate any unitary transformation that describes the quantum computation, as a sequence of elements selected from a finite base of universal quantum gates. The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The aim of this contribution is to show that our comprehensive results on symmetries of the Pauli gradings of quantum operator algebras - covering any single as well as composite finite quantum systems - directly correspond to Clifford groups defined as quotients with respect to U(1). Then the corresponding Clifford group is defined as the group of unitary operators leaving the Weyl-Heisenberg group invariant. In the general case of a single or composite quantum system with finite-dimensional Hilbert space the finite Weyl-Heisenberg group of unitary operators defines the quantum kinematics and the states of the quantum register. However, this fact does not diminish the importance of the Clifford model, since it may serve as a suitable starting point for a full-fledged quantum computation. Because of this restriction the Clifford model of quantum computation can be efficiently simulated on a classical computer (the Gottesmann-Knill theorem). The simplest Clifford group in multiqubit quantum computation is generated by a restricted set of unitary Clifford gates - the Hadamard, π/4-phase and controlled-X gates. Gottesmann in his investigation of quantum error-correcting codes. The term Clifford group was introduced in 1998 by D.
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