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PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1278 (4 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.
Quantum Zeno dynamics: mathematical and physical aspects
, 903
"... Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, ..."
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Cited by 17 (1 self)
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Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hardwall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Zeno dynamics and constraints
, 2004
"... Abstract. We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Ze ..."
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Cited by 4 (0 self)
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Abstract. We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hardwall (Dirichlet) boundary conditions. By using a new approach to this problem, this result is found to be valid in an arbitrary Ndimensional compact domain. We then propose some preliminary ideas concerning the algebra of observables in the projected region and finally look at the case of a projection onto a lower dimensional space: in such a situation the Zeno ansatz turns out to be a procedure to impose constraints. § To whom correspondence should be addressed (paolo.facchi@ba.infn.it) Zeno dynamics and constraints 2 1.
IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
, 2007
"... Optimal control of quantum gates and suppression of decoherence in a system of interacting twolevel particles ..."
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Optimal control of quantum gates and suppression of decoherence in a system of interacting twolevel particles
Unitary Perturbation Theory Approach to RealTime Evolution Problems
, 809
"... Abstract. We discuss a new analytical approach to realtime evolution in quantum manybody systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to il ..."
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Abstract. We discuss a new analytical approach to realtime evolution in quantum manybody systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to illustrate the accuracy of this approach by studying dissipative quantum systems on all time scales. In particular, we obtain results for nonequilibrium correlation functions for general initial conditions. We illustrate our ideas for the exactly solvable dissipative oscillator, and, as a nontrivial model, for the dissipative twostate system. Unitary Perturbation Theory Approach to RealTime Evolution Problems 2 1.
unknown title
, 2007
"... Optimal control of quantum gates and suppression of decoherence in a system of interacting twolevel particles ..."
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Optimal control of quantum gates and suppression of decoherence in a system of interacting twolevel particles