Exact solutions of holonomic quantum computation
نویسندگان
چکیده
منابع مشابه
Exact Solutions of Holonomic Quantum Computation
Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard, CNOT and 2-qubit discrete Fourier transformation gates are explicitly constructed.
متن کاملExact solutions for universal holonomic quantum gates
We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one and two qubits gates. Our method is analytical and is not based on numerical search in the space of all loops. email:[email protected] email:[email protected]...
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The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a k-dimensional unitary gate which operat...
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We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a n-fold degenerate eigenspace of a family of Hamiltonians parametrized by a manifold M. The point of M represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops...
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A considerable understanding of the formal description of quantum mechanics has been achieved after Berry’s discovery [2] of a geometric feature related to the motion of a quantum system. He showed that the wave function of a quantum object retains a memory of its evolution in its complex phase argument, which, apart from the usual dynamical contribution, only depends on the “geometry” of the p...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2004
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2004.03.057