This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.Quantum computers are expected to allow us to perform high-speed computations over classical computations for problems in a wide range of scientific and technological fields. Environments in which quantum algorithms can be executed by real quantum devices are currently being provided [1][2][3]. Real quantum devices with several tens of qubits will soon be realized in near future, although those are the socalled noisy intermediate-scale quantum (NISQ) devices that impose several practical limitations on their Y. Suzuki, S. Uno: Equally contributing authors.

Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow. Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |psi_1> from s_1 to t_1 and |psi_2> from s_2 to t_2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |psi_1> and |psi_2> is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |psi_1> and |psi_2> are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.Comment: 27pages, 11figures. The 12page version will appear in 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007

Serotonin (5-HT) is a potent mitogen in many cells types, an action which is frequently mediated through pertussis toxin-sensitive G proteins. In the current study, we used pharmacological inhibitors and dominant negative signaling constructs to delineate elements which participate in the activation of MAPK, a growth-associated mitogen-activated protein kinase, by human G protein-coupled 5-HT1A receptor transfected into CHO-K1 cells in a stable manner. The activation pathway does not directly involve phorbol ester-sensitive protein kinase C types, but does require (i) pertussis toxin-sensitive G protein beta gamma-subunits, (ii) a staurosporine- and genistein-sensitive protein kinase, (iii) phosphoinositide-3'-kinase activity, (iv) activation of Sos in a multimolecular complex that contains p46Shc, and p52Shc, and Grb2, (v) the GTPase p21Ras, and (vi) the protein kinase p74Raf-1. These data demonstrate that the 5-HT1A receptor mediates MAPK activity by convergence upon a common activation pathway that is shared with receptor tyrosine kinases.